Supporting Information: Site-Selected Dynamics of Azidolysozyme
Seyedeh Maryam Salehi
Markus Meuwly
Seyedeh Maryam Salehi
Markus Meuwly
The spectroscopic response of and structural dynamics around all azido-modified alanine residues (AlaN$_3$) in Lysozyme is characterized. It is found that AlaN$_3$ is a positionally sensitive probe for the local dynamics, covering a frequency range of $\sim 15$ cm$^{-1$ for the center frequency of the line shape. This is consistent with findings from selective replacements of amino acids in PDZ2 which reported a frequency span of $\sim 10$ cm$^{-1$ for replacements of Val, Ala, or Glu by azidohomoalanine (AHA). For the frequency fluctuation correlation functions (FFCFs) the long-time decay constants $\tau_2$ range from $\sim 1$ to $\sim 10$ ps which compares with experimentally measured correlation times of 3 ps. Attaching azide to alanine residues can yield dynamics that decays to zero on the few ps time scale (i.e. static component $\Delta_0 \sim 0$ ps$^{-1$) or to a remaining, static contribution of $\sim 0.5$ ps$^{-1$ (corresponding to 2.5 cm$^{-1$), depending on the local environment on the 10 ps time scale. The magnitude of the static component correlates qualitatively with the degree of hydration of the spectroscopic probe. Although attaching azide to alanine residues is found to be structurally minimally invasive with respect to the overall protein structure, analysis of the local hydrophobicity indicates that the hydration around the modification site differs for modified and unmodified alanine residues, respectively.
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\author{Seyedeh Maryam Salehi} \affiliation[University of
  Basel]{Department of Chemistry, University of Basel,
  Klingelbergstrasse 80 , CH-4056 Basel, Switzerland.}
\author{Markus Meuwly} \affiliation[University of Basel]{Department of
  Chemistry, University of Basel, Klingelbergstrasse 80 , CH-4056
  Basel, Switzerland.}  \email{m.meuwly@unibas.ch}


\title {Site-Selective Dynamics of Azidolysozyme}

\begin{document}

\begin{abstract}
The spectroscopic response of and structural dynamics around all
azido-modified alanine residues (AlaN$_3$) in Lysozyme is
characterized. It is found that AlaN$_3$ is a positionally sensitive
probe for the local dynamics, covering a frequency range of $\sim 15$
cm$^{-1}$ for the center frequency of the line shape. This is
consistent with findings from selective replacements of amino acids in
PDZ2 which reported a frequency span of $\sim 10$ cm$^{-1}$ for
replacements of Val, Ala, or Glu by azidohomoalanine (AHA). For the
frequency fluctuation correlation functions (FFCFs) the long-time
decay constants $\tau_2$ range from $\sim 1$ to $\sim 10$ ps which
compares with experimentally measured correlation times of 3
ps. Attaching azide to alanine residues can yield dynamics that decays
to zero on the few ps time scale (i.e. static component $\Delta_0 \sim
0$ ps$^{-1}$) or to a remaining, static contribution of $\sim 0.5$
ps$^{-1}$ (corresponding to 2.5 cm$^{-1}$), depending on the local
environment on the 10 ps time scale. The magnitude of the static
component correlates qualitatively with the degree of hydration of the
spectroscopic probe. Although attaching azide to alanine residues is
found to be structurally minimally invasive with respect to the
overall protein structure, analysis of the local hydrophobicity
indicates that the hydration around the modification site differs for
modified and unmodified alanine residues, respectively.
\end{abstract}


\section{Introduction}
Understanding the structural and functional dynamics of proteins in
the condensed phase is a prerequisite for characterizing cellular
processes at a molecular level.\cite{schuler:2017} As an example,
knowledge of the mechanisms and physical principles underlying
protein-ligand recognition facilitates rational drug design for
treatment of diseases.\cite{zhou:2016,zhang:2019} One possibility to
directly and quantitatively probe the structure and dynamics of
proteins and protein-ligand complexes is vibrational, in particular
2-dimensional infrared (2D-IR) spectroscopy.\cite{2DIRbook-Hamm-2011}
\\

\noindent
Given the spectroscopic response of proteins in solution that cover
the range up to $\sim 1700$ cm$^{-1}$ and frequencies above $\sim
2800$ cm$^{-1}$, suitable vibrational labels should absorb in the
window between $\sim 1700$ and $\sim 2800$
cm$^{-1}$.\cite{gai:2011,hamm.rev:2015} A range of such probes has
been proposed and considered in the past, including
cyanophenylalanine\cite{thielges:2015}, nitrile-derivatized amino
acids,\cite{gai:2003} the sulfhydryl band of
cysteines,\cite{hamm:2008} deuterated carbons,\cite{romesberg:2011}
non-natural labels consisting of metal-tricarbonyl modified with a
-(CH$_2$)$_{\rm n}$- linker,\cite{zanni:2013} nitrile
labels,\cite{fayer.ribo:2012} cyano\cite{romesberg.cn:2011} and
SCN\cite{bredenbeck:2014} groups, or cyanamide.\cite{cho:2018} Another
promising and sensitive label that was recently used is
azidohomoalanine (AHA)\cite{hamm:2012} for which it has been
demonstrated that it can be used to characterize the recognition site
between the PDZ2 domain and its binding partner to provide
site-specific insight into the underlying mechanisms of how signaling
proteins function.\cite{stock:2018}\\

\noindent
The noncanonical amino acid AHA absorbs around $\sim 2100$ cm$^{-1}$
with a comparatively large extinction coefficient of up to 400
M$^{-1}$cm$^{-1}$.\cite{hamm:2012} From a preparative perspective
attachment of N$_3^{-}$ to alanine (to give AlaN$_3$) and AHA and
incorporation at almost any position of a protein through known
expression techniques has been demonstrated.\cite{bertozzi:2002}
Furthermore, attachment of an N$_3^-$ probe is a spatially small
modification and the chemical perturbations induced are expected to be
small. This makes AlaN$_3$ and AHA worthwhile modifications to probe
local protein dynamics.\\

\noindent
Optical spectroscopy, and especially two-dimensional infrared (2D-IR)
spectroscopy, quantitatively provides information about the structure
and dynamics of the solvent environment surrounding a probe
molecule.\cite{hamm:2015} Such techniques can also be used to measure
the subpicosecond to picosecond dynamics in condensed-phase
systems. With that, the coupling between inter- and intramolecular
degrees of freedom such as the hydrogen bonding network in solution,
or structural features of biological macromolecules can be
investigated by monitoring the fluctuation of fundamental vibrational
frequencies of a probe molecule or ligand attached to a complex or a
biological macromolecule. The possibility to use infrared spectroscopy
for characterizing protein-ligand complexes has already been proposed
for the nitrile containing inhibitor IDD743 complexed with WT and
mutant human aldose reductase\cite{Suydam.halr.sci.2006} and
explicitly demonstrated for cyano-benzene in the active site of WT and
mutant lysozyme.\cite{MM.lys:2017} \\

\noindent
The AHA label was previously used in 2D-IR spectroscopy studies of
ligand binding to the PDZ2 domain.\cite{hamm:2012} The spectral
changes observed for various modified pepdidic binders were consistent
with the known X-ray structure of the wild-type peptide bound to the
protein. This suggests that AHA is suitable as a specific IR reporter
and to highlight subtle changes of the electrostatic environment on
the protein surface.\cite{stock:2018} In the present work, attaching
N$_3^-$ to all alanine residues in Lysozyme in succession is used to
characterize the local dynamics around such modification site.\\

\noindent
Recent investigations have demonstrated that the vibrational dynamics
of N$_3^{-}$ in the gas phase and in solution can be captured
quantitatively.\cite{Salehi:N3-JPCB2019} Based on high-level
electronic structure calculations at the multi-reference configuration
interaction (MRCI) level of theory and representing the 3-dimensional
potential energy surface (PES) as a reproducing kernel Hilbert space
(RKHS),\cite{RKHS-Rabitz-1996,MM.rkhs:2017} the infrared spectroscopy
in the gas and condensed phase was correctly described. Also, the
frequency correlation function exhibited time scales consistent with
experiment which suggests that the coupling between solvent and solute
was correctly described.\\

\noindent
The present work explores the local dynamics of all alanine residues
in lysozyme as a typical model system by attaching N$_3^{-}$ as a
spectroscopic reporter. First, the computational methods are
summarized. Then, the structural dynamics and spectroscopy for all 14
AlaN$_3$ labels is discussed and the local dynamics and hydration are
explored. Finally, conclusions are drawn.\\


\section{Methods}

\subsection{Molecular Dynamics Simulations} 
For the Molecular Dynamics (MD) simulations of WT and modified
Lysozyme in solution, CHARMM\cite{Charmm-Brooks-2009} together with
the CHARMM\cite{charmmFF22} force field was used. A suitably modified
version of CHARMM was employed for the simulations with the
3-dimensional RKHS PESs (see below).\cite{Salehi:N3-JPCB2019} The
initial lysozyme structure was the X-ray structure
(3FE0\cite{pdblyso-2009}). Simulations of Lysozyme in TIP3P
water\cite{TIP3P-Jorgensen-1983} were carried out in a cubic box of
size $(62.1)^3$ \AA\/$^3$. Figure \ref{fig:lys} shows the structure of
the system for the present work in which N$_3^-$ is attached
individually to each of the 14 Ala residues, replacing one hydrogen
atom of the terminal CH$_3$ group. This yields Azidoalanine-modified
Lysozyme.\cite{bertozzi:2002} Compared with protein structures in
which AHA is introduced, the two modifications differ by one
CH$_2$-group.\cite{bertozzi:2002}.\\

\noindent
The systems were minimized, heated for 25 ps and equilibrated for 100
ps in the $NVT$ ensemble. Production runs, 2 ns in length, were
carried out in the $NVT$ ensemble, with coordinates saved every 5 fs
for subsequent analysis. All nonbonded interactions were treated with
a 14 \AA\/ cutoff switched at 10 \AA\/,\cite{Steinbach1994} and bonds
involving hydrogen atoms are constrained using
SHAKE\cite{SHAKE-Gunsteren-1997}.\\

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.8\textwidth]{figs/lyso.pdf}
\caption{Structure of Lysozyme with positions of Alanine residues
  indicated. The Alanine residues are at positions 9, 26, 32, 42, 47,
  73, 76, 83, 90, 92, 94, 96, 108, 111. Ala residues are displayed as
  CPK spheres and the rest of the protein structure is shown as
  NewRibbons. As an example, AlaN$_3$ is shown at residue 47.}
\label{fig:lys}
\end{center}
\end{figure}


\subsection{Energy Function for the Spectroscopic Probe}
For representing the 3-dimensional energy function of the N$_3^{-}$
label two strategies were pursued. First, the existing 3-dimensional
PES for N$_3^{-}$, computed at the MRCI+Q level of theory in the gas
phase, was used to describe the stretching and bending distortions of
the label attached to the CH$_2$ group of alanine.\\

\noindent
Because the N$_3^{-}$ moiety and the rest of the Ala residue are not
fully electronically decoupled, a second approach was pursued. For
this, the structure of AHA was optimized at the MP2/aug-cc-pVTZ level
of theory. Next, the structure of AHA was frozen except for the
coordinates involving the spectroscopic label. Then, a new
3-dimensional PES was computed at the pair natural orbital based
coupled cluster level
(PNO-LCCSD(T)-F12)\cite{lccsd-schwilk-2017,lccsdf12-schwilk-2017}
together with the aug-cc-pVTZ basis set\cite{DUN:JCP89} using the
MOLPRO suite of codes.\cite{molpro2} As for the gas phase
PES,\cite{Salehi:N3-JPCB2019} the \textit{ab initio} energies were
calculated in Jacobi coordinates $(R, r, \theta)$, see Figure
\ref{fig:pes}B, where $r$ is the distance between the nitrogen atoms
N1 and N2, $R$ is the distance between their center of mass and the
atom N3, and $\theta$ is the angle between $\vec{r}$ and
$\vec{R}$. The angular grid ($\theta$) used here contains 5
Gauss-Legendre quadrature points between $156^\circ$ and
$180^\circ$. The radial grids include 16 points along $r$ ranging from
0.90 to 1.51 \AA\/ and 16 points along $R$ between 1.45 and 2.12 \AA.
The PNO-LCCSD(T)-F12 level of theory was chosen as it combines
accuracy with feasibility for the present problem because recomputing
the MRCI PES for AHA is computationally intractable.\\

\noindent
For both PESs the parameters for the C-N3 stretch, the C-C-N3 and the
C-N3-N2 bend are those from Swissparam.\cite{swissparam-Zoete-2011}
All remaining parameters for the alanine residues were those of the
CHARMM force field and were not readjusted after attaching N$_3^-$ to
guarantee compatibility with the CHARMM22 force field.\\

\noindent
To carry out MD simulations for labelled Lysozyme, a continuous and
differentiable representation of the {\it ab initio} energies is
required. For this, a reproducing kernel Hilbert space-based
representation\cite{RKHS-Rabitz-1996,MM.rkhs:2017} is used. A RKHS
representation provides approximate values for a function $f(x)$ at
positions $x$, away from the grid points $x_i$. For this, the linear
problem $f(x_i) = \sum_{j} \alpha_{j} k(x_i,x_j)$ for the
1-dimensional kernels is solved which yields the coefficients
$\alpha_{j}$. There are many possible choices for the kernel functions
$k(\cdot,\cdot)$ but inverse powers of the distance have been found to
perform well for intermolecular
interactions.\cite{RKHS-Rabitz-1996,MM.heh2.1998,hutson:2000} For
multidimensional problems, tensor products of 1-dimensional kernels
can be used.\cite{hollebeek1999constructing,MM.rkhs:2017}\\

\noindent
For the present work, the 3-dimensional kernel $K$ is
\begin{equation}
K(X,X')=k^{(n,m)}(R,R')k^{(n,m)}(r,r')k^{(2)}(z,z').
\end{equation}
where $X$ stands for all dimensions involved, $r$, and $R$ are as
defined above (see also Figure \ref{fig:pes}), and
$z=\dfrac{1-\cos(\theta)}{2}$ maps the angle $\theta$ onto the
interval $[0,1]$. Reciprocal power decay kernels ($k^{(n,m)}$) with
smoothness $n=2$ and asymptotic decay $m=6$
\begin{equation}
 k^{(2,6)}(x,x') = \frac{1}{14}\frac{1}{x^7_{>}} - \frac{1}{18}\frac{x_<}{x^8_>},
\end{equation}
are used for $r$ and $R$ whereby $x_>$ and $x_<$ are the larger and
smaller values of $x$ and $x'$, respectively. For the angular degree
of freedom, a Taylor spline kernel
\begin{equation}
 k^{(2)}(z,z') = 1 + z_<z_> + 2z^2_<z_> - \frac{2}{3}z^3_<
\end{equation}
is used.\\

\noindent
Charges were calculated for the optimized structure of AlaN$_3$ at the
MP2/aug-cc-pVTZ level of theory from an NBO\cite{NBO-Foster-1980}
analysis using Gaussian\cite{g09}and scaled to maintain overall
neutrality. This yields a charge of $-0.2460e$ for the nitrogen atom
N1 attached to CH$_2$ group, $0.1607e$ for the central N2 and
$-0.0464e$ for the terminal nitrogen N3.\\


\subsection{Frequency Fluctuation Correlation Function and Lineshape}
From each production simulation, $4\times10^5$ snapshots are taken as
a time-ordered series for computing the frequency fluctuation
correlation function (FFCF) $\langle \delta \omega(0) \delta \omega(t)
\rangle$ and line shapes. Here, $\delta \omega(t) = \omega(t) -
\langle \omega(t) \rangle$ and $\langle \omega(t) \rangle$ is the
ensemble average of the transition frequency. The FFCF was determined
from instantaneous harmonic vibrational frequencies based on a normal
mode analysis.\cite{MM.insulin:2020} Normal modes were determined for
each snapshot after minimizing the structure of the N$_3$ label and
keeping the surrounding solvent frozen. Thus, frequency trajectories
$\omega_i(t)$ for label $i$ were obtained for the asymmetric stretch
vibration of N$_3$ attached to Ala. From the FFCF the line shape
function
\begin{equation}
\label{eq:gt}
g(t) = \int_{0}^{t} \int_{0}^{\tau^{'}} \langle \delta
\omega(\tau^{''}) \delta \omega(0) \rangle d\tau^{''} d\tau^{'}.
\end{equation}
is determined within the cumulant approximation. To compute $g(t)$,
the FFCF is numerically integrated using the trapezoidal rule and the
1D-IR spectra is then calculated as\cite{n3exph20-Maekawa-2004}
\begin{equation}
I(\omega) = 2 \Re \int^\infty_0
e^{i(\omega-\langle\omega\rangle)t} e^{-g(t)} e^{-\frac{t}{2T_1}}
e^{-2D_{\rm OR}t} dt,
\end{equation}
where $\langle\omega\rangle$ is the average transition frequency
obtained from the distribution, $T_1$ ($0.8 \pm 0.1$ ps) is the
vibrational relaxation time and $D_{\rm OR} = 1/6T_R$ with $T_R = 1.3
\pm 0.3$ ps is the rotational diffusion coefficient which accounts for
lifetime broadening.\cite{timedecay-Owrutsky-2003}\\

\noindent
From the FFCF, the decay time can be determined by fitting the FFCF to
a general expression\cite{hynes:2004}
\begin{equation}
  \langle \delta \omega(t) \delta \omega(0) \rangle =
  a_{1} \cos(\gamma t) e^{-t/\tau_{1}} + \sum_{i=2}^{n} a_{i}
  e^{-t/\tau_{i}} + \Delta_0
\label{eq:ffcffit}
\end{equation}
where $a_{i}$, $\tau_{i}$, $\gamma$ and $\Delta_0$ are fitting
parameters. The decay times $\tau_i$ of the frequency fluctuation
correlation function reflect the characteristic time-scales of the
solvent fluctuations to which the solute degrees of freedom are
coupled. In all cases the FFCFs were fitted to an expression
containing two decay times (i.e. $n_{\rm max} = 2$) using an automated
curve fitting tool from the SciPy library.\cite{2020SciPy-NMeth}\\


\section{Results}

\subsection{The Potential Energy Surface for the N$_3^{-}$ Label}
Two PESs for the energetics of the N$_3^{-}$ are considered in the
present work. One is based on earlier MRCI+Q calculations with the
aug-cc-pVTZ basis set for N$_3^{-}$ in the gas
phase\cite{Salehi:N3-JPCB2019} which was used without change for the
simulation of the AlaN$_3$ unit. The second one was the LCCSD(T) PES
for AHA which included coupling between the
N$_3^{-}$ probe and the amino acid framework. The RKHS representations
of the two PESs are reported in Figures \ref{fig:pes}A and B and the
scans within CHARMM are shown in panels C and D.\\

\noindent  
The RKHS representation of the PES for AHA was constructed from 1280
{\it ab initio} LCCSD(T)-F12 energies. An additional 230 {\it ab
  initio} energies are calculated at off-grid geometries to assess the
quality of the RKHS representation. Figure S1 shows
the correlation between the reference energies and the RKHS with a
correlation coefficient of $R^{2} = 0.9999$ and the root mean squared
error is 0.38 kcal/mol. This confirms the high quality of the RKHS
PES.\\



\noindent
Figure \ref{fig:pes}A and B report the RKHS interpolation of the {\it
  ab initio} calculated energies whereas Figures \ref{fig:pes}C and D
are from scanning the $r$ and $R$ coordinates for AHA in the gas phase
in CHARMM. Comparing the PNO-LCCSD(T)-F12 PES (Figure \ref{fig:pes}A)
with that at the MRCI+Q level of theory (Figure \ref{fig:pes}B) shows
that the minima for the two are slightly displaced ($r = 1.19$ \AA\/
vs. $r = 1.24$ \AA\/ and $R = 1.77$ \AA\/ vs. $R = 1.76$
\AA\/). Furthermore, the LCCSD(T) PES is steeper along both, the $r$
and $R$ coordinates, which pushes the respective vibrations up
compared with the MRCI+Q PES, see Figure S2. Differences
between the two PESs are due to both, the methods (MRCI+Q
vs. PNO-LCCSD(T)-F12) and the model system (N$_3^-$ vs. AHA)
considered. Comparing the isolated, gas-phase PESs (panels A and B)
with those for AlaN$_3$ (panels C and D) indicates that the PESs are
close but not identical due to coupling between the spectroscopic
probe and the alanine residue.\\


\begin{figure}[H]
\begin{center}
\includegraphics[width=0.8\textwidth]{figs/multi_pes.pdf}
\caption{Contour diagrams of the RKHS representations for AHA (panel
  A, PNO-LCCSD(T)-F12) and N$_3^-$ (panel B, MRCI+Q/aug-cc-pVQZ) PESs
  based on {\it ab initio} points calculated in Jacobi coordinates
  $(R, r, \theta)$ for $\theta=180^\circ$, see inset in panel
  B. Panels C and D report the corresponding CHARMM energies for
  AHA. All energies are in kcal/mol and relative to the zero of energy
  which is the minimum energy structure.}
\label{fig:pes}
\end{center}
\end{figure}

\noindent
In the following, all MD simulations were carried out with the
PNO-LCCSD(T)-F12 PES as it yields harmonic frequencies for AlaN$_3$
around 2110 cm$^{-1}$ cm$^{-1}$ (see Table \ref{tab:ffcffit}) which is
consistent with those experimentally observed for the replacement of
AHA\cite{stock:2018} in PDZ2 domain at 2114 cm$^{-1}$ and for
AlaN3\cite{alan3-jcp-2015} in H$_2$O at 2116 cm$^{-1}$,
respectively. Moreover, the influence of the covalent bonding to the
Alanine residue is included in the construction of the potential
energy surface. Additional refinements of the PES would, in principle,
be possible through morphing\cite{JMB91morphing,MM.morph:1999} but
were not deemed necessary for the present work which is mainly
concerned with the differential dynamics, i.e. the relative positional
sensitivity, and spectroscopy for the same label at different
positions along the polypeptide chain.\\


\subsection{Structural Dynamics}
For the structural dynamics first the root mean squared deviation
(RMSD) of unmodified and modified Lysozyme in solution compared with
the starting X-ray structure as the reference is analyzed. For this,
the RMSD of all C$_{\alpha}$ atoms was considered. Figure
\ref{fig:rmsd_lys} shows the RMSD for all C$_{\alpha}$ atoms (blue)
and those for the 14 Alanine residues (red) specifically from the 2 ns
simulation of the modified protein at position Ala47. For the WT
protein similar RMSD values are reported in Figure S3. The RMSD values fluctuate below or around 1
\AA\/ which is indicative of a stable simulation. This suggests that
attaching a N$_3^-$ label to Ala has an insignificant effect on the
structural dynamics of Lysozyme, consistent with earlier findings for
the PDZ domain for which also a minimally invasive effect was
reported.\cite{stock:2018}\\

\begin{figure}[H]
\centering
\includegraphics[width=0.4\textwidth,angle=-90]{figs/lyso_rmsd_wazo.pdf}
\caption{The structural RMSD for the C$_{\alpha}$ atoms from all
  residues (blue) and for the 14 Ala residues (red) specifically for
  Ala76N$_3$.}
\label{fig:rmsd_lys}
\end{figure}



\subsection{Vibrational Spectra and Frequency Correlation Functions}
First, the power spectra and frequency trajectories for the asymmetric
stretch of the azide label attached to all 14 alanine residues are
presented. The power spectra as determined from the Fourier transform
of the N2-N3 distance correlation function are shown in Figure
\ref{fig:avgps}A for all AlaN$_3$ from 2 ns production runs. The peak
maxima $\omega_{\rm max}$ cover a range of $\sim 20$ cm$^{-1}$
(between 2160 and 2180 cm$^{-1}$) and the full widths at half maximum
(fwhm) of the spectra are around 20 cm$^{-1}$. Hence, although the
same energy function was used for all modified AlaN$_3$ moieties,
their power spectra differ depending on the position of the modified
Ala residue along the polypeptide chain.\\

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.38\textwidth,angle=-90]{figs/avgps_lyso.pdf}
\caption{Power spectrum based on the N$2$--N$3$ separation for all
  modified AlaN$_3$ residues. The position of the frequency maxima
  differ for most of the AlaN$_3$ labels and cover a range between
  2160 and 2180 cm$^{-1}$.}
\label{fig:avgps}
\end{center}
\end{figure}


\noindent
The power spectra reported in Figure \ref{fig:avgps} are also
representative of the infrared spectrum as shown in Figure
S4. The top panel of Figure S4
reports the power spectrum and peak positions of all three modes for
Ala47N$_3$ with the asymmetric stretch centered around 2170 cm$^{-1}$,
the symmetric stretch at 1333 cm$^{-1}$ and the bending mode at 610
cm$^{-1}$. The bottom panel of Figure S4
demonstrates that the infrared spectrum (IR) determined from the
dipole autocorrelation function supports the peak positions found from
the power spectrum to within 2 cm$^{-1}$.\\

\noindent
Next, the frequency trajectories $\omega_i(t)$ for each of the
spectroscopic probes $i$ from $4 \times 10^5$ snapshots were
determined from instantaneous normal mode calculations. From the
frequency time series the frequency fluctuation correlation functions
(FFCFs) are obtained. They contain valuable information about the
environmental dynamics around each site $i$, i.e. the azide probes of
the various Ala residues considered.\\

\noindent
The FFCFs, shown in Figure \ref{fig:ffcffit}, are fitted to
Eq. \ref{eq:ffcffit} with a parametrization motivated by the overall
shape of the FFCF.\cite{hynes:2004} This functional form has also been
used in previous work.\cite{hynes:2004,skinner:2006,MM.cn:2013} It is
an extension of the typical multiexponential decay, which is
traditionally employed\cite{hamm:1998} to capture an anticorrelation
at short times ($t < 1$ ps). Figure \ref{fig:ffcffit} provides a
comparison between the raw data (black) and the fits (red) and Table
\ref{tab:ffcffit} reports the corresponding fitting parameters.\\

\begin{figure}[H]
\centering
\includegraphics[width=0.9\textwidth]{figs/ffcf_log.pdf}
\caption{FFCFs from correlating the instantaneous harmonic frequencies
  for all 14 AlaN$_3$ in Lysozyme. The labels in each panel refer to
  the alanine residue which carries the azide label. Black traces are
  the raw data and red dashed lines the fits to
  Eq. \ref{eq:ffcffit}. The $y-$axis is logarithmic.}
\label{fig:ffcffit}
\end{figure}

\noindent
The shape of the FFCFs can differ appreciably. Some of them display a
pronounced minimum at short correlation times ($t \sim 0.1$ ps)
whereas others do not. This feature has also been found in previous
simulations\cite{skinner:2006} and has been related to the strength of
the interaction between the infrared probe and its
environment.\cite{hynes:2004,MM.cn:2013,NMA2dir-MM-2014} Several of
the FFCFs show one (Ala9, Ala32, Ala42, Ala76, Ala94, Ala96, Ala108,
Ala111) or even two (Ala92) recurrences at short correlation
times. For the remaining Alanine residues this feature is less
pronounced (Ala47, Ala73, Ala83, Ala90) or entirely absent
(Ala26). Similarly, some of the FFCFs exhibit clear static components
$\Delta_0 \simeq 0.5$ ps$^{-2}$ (Ala26, Ala73, Ala96) whereas the
remaining ones decay to zero on the $\sim 10$ ps time scale. With
respect to the correlation times, the fast correlation is generally
$\tau_1 \sim 0.1$ ps whereas the long time scale ranges from $\tau_2 =
1.1$ ps to $\tau_2 < 13$ ps, see Table \ref{tab:ffcffit}. Typically,
the amplitude of the fast decay is one order of magnitude larger than
that of the slow contribution (Table \ref{tab:ffcffit}). Hence, the
characteristics of the FFCFs vary considerably depending on the
position at which the Alanine residue is located along the
polypeptide chain. This suggests that AlaN$_3$ is a positionally
sensitive probe to provide quantitative information about the local
dynamics of a protein.\\

\begin{table}[H]
\footnotesize
%\scriptsize
\centering
\caption{Parameters obtained from fitting the FFCF to
  Eq. \ref{eq:ffcffit} for INM frequencies for all different AlaN$_3$
  residues in lysozyme. Average frequency $\langle\omega\rangle$ of
  the asymmetric stretch in cm$^{-1}$, the amplitudes $a_1$ to $a_3$
  in ps$^{-2}$, the decay times $\tau_1$ to $\tau_3$ in ps, the
  parameter $\gamma$ in ps$^{-1}$, the offset $\Delta_0$ in ps$^{-2}$,
  and the conformationally averaged local hydrophobicity (LH).}
\centering
\begin{tabular}{r|c|crc|cc|c||c}
\hline\hline
Res& $\langle\omega\rangle$ & $a_{1}$ & $\gamma$ &$\tau_{1}$ &$a_{2}$ &$\tau_{2}$ & $\Delta_0$& LH\\
\hline
\textbf{9} &2103.7& 1.17 & 13.16 &  0.129 & 0.07 &  7.62 &   0.02 & 0.33\\
\hline
\textbf{26} &2107.9& 1.82 & 8.69 & 0.079 &   0.24 &   1.73 &   0.41 &1.91 \\
\hline
\textbf{32} &2112.8&  3.60 & 13.39 &  0.164 &   0.13 &  13.05  &   0.19&0.11 \\
\hline
\textbf{42} &2111.4&  3.57 & 14.08 & 0.104 &   0.32 &  2.15 &   0.04&0.95\\
\hline
\textbf{47}&2107.5&  1.54 & 9.99 &  0.081 &  0.21 &   1.17 &  0.01&1.21 \\
\hline
\textbf{73}&2114.6&  3.18 & 15.07 &   0.080 &   0.24 &   3.61 &    0.81&1.34 \\
\hline
\textbf{76} & 2107.1&  1.94 & 11.94&   0.084 &   0.15 &   2.77 &    0.02&0.40\\
\hline
\textbf{83} &2109.2&  2.75 & 11.48 &  0.069 &  0.17 &   2.11 &     0.18 &1.59\\
\hline
\textbf{90} &2107.5&  1.57 & 11.71 &   0.056 &  0.22 &   1.42 &    0.30 &1.13\\
\hline
\textbf{92} &2110.4&  4.08 & 14.02 &   0.184 &   0.10 &  1.33 & 0.10 &0.58\\
\hline
\textbf{94} &2104.8&  1.05 & 9.36  &  0.100 &   0.08 &   5.89 &   0.09 &1.17\\
\hline
\textbf{96}& 2116.3&  3.74 & 13.33 &  0.077&   0.43 &   2.19 &   0.48 &0.44\\
\hline
\textbf{108} &2108.4& 1.83 & 10.77 &  0.084 &   0.35 &   2.43 &    0.04 &0.54\\
\hline
\textbf{111} &2110.6& 2.22 & 13.13 &  0.090 &   0.41 &    2.27 &   0.12&1.50\\
\hline\hline
\end{tabular}
\label{tab:ffcffit}
\end{table}

\noindent
Numerical integration of $g(t)$ and using Eq. \ref{eq:ffcffit} yields
the 1-dimensional IR spectra for each label based on instantaneous
normal modes, see Figure \ref{fig:ir}. Similar to the power spectra,
the center frequencies cover a range of $\sim 15$ cm$^{-1}$, with
center frequencies of 2104 cm$^{-1}$ for Ala9N$_3$ and 2116 cm$^{-1}$
for Ala96N$_3$, and the fwhm ranges from 13 to 21 cm$^{-1}$. Also, the
$\omega_{\rm max}$ for Ala9N$_3$ (blue solid line in Figures
\ref{fig:avgps} and \ref{fig:ir}) is lowest in frequency and those for
Ala96N$_3$ (dashed red) and Ala73N$_3$ (solid green) are highest from
the power spectra and the INM lineshapes, respectively. The blue shift
of the power spectra compared with those from INM for the symmetric
and asymmetric stretch modes was already found for N$_3^-$ in
solution.\cite{Salehi:N3-JPCB2019} The magnitude of this shift is
larger in the present case probably due to coupling between the
spectroscopy probe and the amino acid it is attached to.\\

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.38\textwidth,angle=-90]{figs/spec_lyso.pdf}
\caption{1D IR spectra for all 14 AlaN$_3$ residues in Lysozyme. For
  the IR lineshape the raw FFCF from the INM analysis was numerically
  integrated to give $g(t)$ from which the 1D lineshape is obtained.}
\label{fig:ir}
\end{center}
\end{figure}

\noindent
An alternative to instantaneous normal modes is to obtain
instantaneous frequencies from solving the 1- or 3-dimensional nuclear
Schr\"odinger equation. For this, the corresponding 1- or 3-d PES is
scanned for a given snapshot with frozen
environment\cite{MM.cn:2013,MM.insulin:2020,MM.rev.jcp:2020} and
represented as a RKHS. This is a computationally much more demanding
approach, in particular in 3 spatial
dimensions.\cite{Salehi:N3-JPCB2019} Here, the 1-dimensional PES along
the asymmetric stretch motion was mapped out for $4 \times 10^5$
snapshots and the nuclear Schr\"odinger equation was solved. Then, the
FFCF was again determined and fit to Eq. \ref{eq:ffcffit}, see Figure S5. From this, the
1-dimensional IR lineshape was determined, see solid lines in Figure
S6. This was done for Ala90N$_3$ and Ala94N$_3$. As was
found for the 1-d lineshapes from INM, the frequency maximum for
Ala90N$_3$ is shifted to the blue relative to Ala94N$_3$ but the shift
is smaller (1 cm$^{-1}$ vs. 3 cm$^{-1}$).\\

\noindent
Recently, the ``INM'', ``scan'' and ``map'' approaches have been
compared for insulin monomer and dimer.\cite{MM.insulin:2020} It was
found that the ``INM'' and ``scan'' approaches yield comparable 1-d
infrared spectra for the amide-I bands and conclusions drawn from the
spectra concerning monomeric and dimeric insulin are
consistent. Nevertheless, the two approaches can differ in the
absolute frequencies as is also found in the present case.\\

\noindent
Typically, spectroscopic work has used AHA as an infrared label
instead of azidoalanine as used here. To quantify the difference
between AlaN$_3$ and AHA, residue Ala47 has also been replaced by AHA
through inserting an additional CH$_2$ group before the N$_3^{-}$
label. The parametrization of the CH$_2$ group is identical to that
already used for alanine. Then, a 2 ns simulation for AHA in water was
carried out and the IR spectrum was determined from an INM analysis,
see Figure S7. It is found that the position of the
frequency maximum for the asymmetric stretch of the azide label
differs by less than 1 cm$^{-1}$ from that with AlaN$_3$ which
confirms that for IR spectroscopy, the two systems are very similar.\\

\section{Solvent Structure and Dynamics}
Next, the solvent structuring around the modification sites is
characterized. This also provides the information for an attempt to
relate the spectral signatures (position of the frequency maximum,
characteristics of the FFCFs) for the azide labels at different
positions along the polypeptide chain with structural features and
environmental properties. For this, the solvent structure around each
of the 14 AlaN$_3$ probes was analyzed. First, the radial distribution
functions $g(r)$ were computed along all production simulations for
the 14 modified proteins, see Figure \ref{fig:grnr}. The distance
analyzed was the separation between the water-oxygen atom (O$_{\rm
  W}$) and the middle nitrogen (N2) of the N$_3$ probe in
AlaN$_3$. The corresponding running coordination number $N(r)$ is
\begin{equation*}
N(r)= 4\pi \int^r_0   r^2 g(r) \rho dr 
\end{equation*}
where $\rho$ is the pure water density (Figure \ref{fig:grnr}B). As is
shown in Figure \ref{fig:grnr}, the $g(r)$ and $N(r)$ differ for the
14 modification sites.\\

\noindent
For some of the residues (Ala26, Ala42, Ala47, Ala73, Ala76, Ala108,
Ala111; Set1) the $g(r)$ exhibits a pronounced first maximum at $3.5
\leq r_{\rm max1} \leq 4$ \AA\/ whereas for the remaining labels
(Ala9, Ala32, Ala83, Ala90, Ala92, Ala94, Ala96; Set2) such a first
maximum is largely absent. This suggests that the residues in Set1 are
solvent exposed whereas those in Set2 are not. The total number $N(r)$
of water molecules within a distance $r$ supports this, see Figure
\ref{fig:grnr}B. Up to a distance of 5 \AA\/, which is typically the
extent of the first hydration shell, residues in Set1 contain 10 or
more water molecules whereas those belonging to Set2 have not more
than 1 water molecule in their vicinity.\\

\begin{figure}[H]
  \centering
    \includegraphics[width=\textwidth]{figs/grnr_combine.pdf}
    \caption{The radial distribution function $g(r)$ (panel A) and the
      number of water oxygen atoms $N(r)$ (panel B) between O of water
      and N2 of AlaN$_3$ for all alanine residues from the 2 ns
      production simulations. The color code for the lines is given in
      panel B.}
    \label{fig:grnr}
\end{figure}

\noindent
A structural illustration for this observation is given in Figure
\ref{fig:solv_dist} which reports all water molecules within 7 \AA\/
of Ala47N$_3$ (belonging to Set1) and Ala96N$_3$ (belonging to
Set2). Consistent with Figure \ref{fig:grnr} only 3 water molecules
are within the cutoff radius of atom N2 of Ala96N$_3$ whereas the
hydration shell of Ala47N$_3$ is extensive.\\


\begin{figure}[H]
  \centering
    \includegraphics[width=\textwidth]{figs/solv_dist.pdf}
    \caption{Solvent distribution based on the water-oxygen atoms
      within 7 \AA\/ of any atom of residues Ala96N$_3$ (panel A) and
      Ala47N$_3$ (panel B). The small and large hydration spheres are
      consistent with the $g(r)$ and $N(r)$ reported in Figure
      \ref{fig:grnr}.}
    \label{fig:solv_dist}
\end{figure}

\noindent
Another measure to quantify the solvent exposure of amino acids is to
determine the time dependent quantity,
$\delta\lambda_{\textrm{phob}}^{(r)}(t)$, which is referred to as the
local hydrophobicity (LH) of residue $r$ at time
$t$.\cite{Willard-jctc-2018,Willard-jpcb-2018} This measure is based
on analyzing the occupation and orientational statistics of surface
water molecules at the protein/water interface, given by the three
dimensional vector $\vec{\kappa} = (a, \cos \theta_{\rm OH1}, \cos
\theta_{\rm OH2})$. Here, $a$ is the distance of the water oxygen atom
to the nearest atom of residue $r$\cite{MM.hb:2020}, and $\theta_{\rm
  OH1}$ and $\theta_{\rm OH2}$ are the angles between the water OH1
and OH2 bonds and the interface normal. More specifically, the local
hydrophobicity (LH) is $\delta \lambda_\mathrm{phob}^{(r)}(t) =
\lambda_\mathrm{phob}^{(r)}(t) - \langle \lambda_\mathrm{phob}
\rangle_0$, where
\begin{equation}
    \lambda_\textrm{phob}^{(r)}(t) = -\frac{1}{{\sum_{a=1}^{N_a(r)}
        N_w(t;a)}}\sum_{a=1}^{N_a(r)} \sum_{i=1}^{N_w(t;a)} \ln{\left[
        \frac{P(\vec{\kappa}^{(i)}(t)|\textrm{phob})}{P(\vec{\kappa}^{(i)}(t)|\textrm{bulk})}
        \right]}
\label{eq:lh}
\end{equation}
and $\langle \lambda_\mathrm{phob} \rangle_0$ is the ensemble average
sampled from the ideal hydrophobic reference system (see below). The
summation over $N_a(r)$ involves all atoms in residue $r$ and the
summation over $N_w(t;a)$ includes all water molecules within a
cut-off of 6\AA\/ of atom $a$ at time $t$.\cite{MM.hb:2020} The vector
$\vec{\kappa}^{(i)}(t)$ describes the orientation (see above) of the
$i$th water molecule in the sampled population.\\

\noindent
The distribution $P(\vec{\kappa}^{(i)}(t)|\textrm{phob})$ is
determined for a reference hydrophobic reference system ('phob'),
whereas $P(\vec{\kappa}^{(i)}(t)|\textrm{bulk})$ is determined from
the actual simulations ('bulk').\cite{Willard-jctc-2018} As the
quantity LH includes both, the distance $a$ of the water molecules
from the interface and the orientation of a specific water molecule
($\theta_{\rm OH1}, \theta_{\rm OH2}$), LH can be considered as a
generalization of the radial distribution function $g(r)$. The local
hydrophobicity is a measure of the statistical similarity of the
sampled configurations to that of an ideal hydrophobic reference
system. When sampled configurations
$P(\vec{\kappa}^{(i)}(t)|\textrm{bulk})$ are dissimilar to the
hydrophobic reference system, this indicates that the site $r$
considered is less hydrophobic, i.e. rather hydrophilic and vice
versa. In other words, $\delta \lambda_\mathrm{phob}^{(r)}(t) \approx
0$ for a hydrophobic environment around residue r, whereas $\delta
\lambda_\mathrm{phob}^{(r)}(t)$ significantly larger than zero, the
environment is
hydrophilic.\cite{Willard-jctc-2018,Willard-jpcb-2018,MM.hb:2020} In
previous work\cite{MM.hb:2020}, sustained values of $\delta
\lambda_\mathrm{phob}^{(r)} > 0.5$ were considered indicative of
hydrophilicity. The magnitude of such a cutoff may, however, be
somewhat system-dependent.\\


\begin{figure}[H]
\centering
\includegraphics[width=0.4\textwidth,angle=-90]{figs/lys_hydro.pdf}
\caption{Local hydrophobicity as a function of time for all alanine
  residues from the simulation of WT Lysozyme. The LH coefficient was
  determined from Eq. \ref{eq:lh}. Values of $\delta \lambda_{\rm
    phob} \approx 0$ indicate a hydrophobic environment of the site
  considered\cite{Willard-jpcb-2018,MM.hb:2020} whereas values around
  2 point towards a hydrophilic site.}
\label{fig:hyd5}
\end{figure}


\noindent
Figure S8 gives an overview of the average LH per residue
and the fluctuations around the average for WT Lysozyme. The Alanine
residues (in red) are found to include both, low and high values for
LH, representative of more hydrophobic and hydrophilic environments,
respectively. The change in LH as a function of simulation time (over
2 ns) for WT (blue) and N$_3^{-}$ labelled (red) Lysozyme for Ala76 is
reported in Figure S9. Without spectroscopic label the
Ala-residue is rather hydrophilic on average whereas with the label
attached it is more hydrophobic (less hydrophilic). On the other hand,
the LH can have a rather pronounced time-dependence, see Figure
\ref{fig:hyd5} (solid orange line for Ala76) from the 5 ns simulation
of WT Lysozyme. Thus, attaching the N$_3^{-}$ label to Ala may
modulate recruitment or displacement of solvent molecules.\\


\section{Discussion and Conclusion}
The present findings confirm that azide attached to alanine residues
in Lysozyme is a structurally minimally invasive, specific infrared
label to quantitatively probe the local dynamics around the
modification site. This has already been reported for the PDZ2
domain.\cite{stock:2018} Similar to the situation in insulin monomer
and dimer, for which the amide-I vibration was
found\cite{MM.insulin:2019,MM.insulin:2020} to cover a range of $\sim
20$ cm$^{-1}$, attaching azide to give AlaN$_3$ spans a comparable
frequency range but in a region of the infrared spectrum (around 2100
cm$^{-1}$) that is typically ``empty''. Together with their minimal
impact on the overall protein structure (see Figure
\ref{fig:rmsd_lys}), and the still favourable extinction
coefficient\cite{hamm:2012}, such modifications bear great potential
to resolve the structural dynamics of proteins and protein-ligand
complexes at a molecular level. Studies that provide structural and
spectroscopic information at the same time are of great interest for
characterizing potential ligand-binding sites and for functional
studies of protein allostery.\\


\begin{figure}[H]
\begin{center}
  \includegraphics[width=\textwidth]{figs/fmaxir_nr_offset.pdf}
  \caption{Correlation between the maximum of the 1-d lineshape from
    INM and he static offset $\Delta_0$ of the FFCF (panel A) and the
    maximum of the 1-d lineshape from INM and the number of water
    molecules in the first hydration shell (panel B) for the residues
    that has been considered to be rather ``water exposed''
    (Set1). Residues of Set1 are shown as blue squares and those of
    Set2 as green circles. The solid line is an empirical linear fit
    and suggests that, typically, for more blue shifted frequency
    maxima the static component increases while the number of water
    molecules in the first hydration shell decreases, i.e.  with
    increasing hydration, $\omega_{\rm max}$ shifts typically to the
    red for alanine residues in Set1.}
\label{fig:correl.ir}
\end{center}
\end{figure}

\noindent
It is of interest to delineate whether correlations can be found
between structural and spectroscopic characteristics analyzed in the
present work. As the dynamics is coupled and involves a potentially
complicated superposition of different structural substates, no
``simple'' or ``obvious'' correlations are expected. Rather and at
best, discovering trends can be expected from such an analysis. One
example is shown in Figure \ref{fig:correl.ir}B which reports the
relationship between the number of water molecules in the first
hydration shell (see also Figure \ref{fig:grnr}) and the position of
the frequency maximum $\omega_{\rm max}$ from the 1-d lineshape
determined from the instantaneous normal mode analysis. Typically,
with increasing hydration, the position of $\omega_{\rm max}$ shifts
to the red. Similarly, the magnitude of the static offset $\Delta_0$
of the FFCF is related to $\omega_{\rm max}$ in that larger values of
$\Delta_0$ are associated with a blue shift of the position of the
frequency maximum, see Figure \ref{fig:correl.ir}A.\\


\noindent
Spectroscopic probes to characterize the local environment of a
protein provide valuable information about local hydration. This is of
particular relevance given the findings that individual water
molecules can play decisive roles in protein function. For example, in
HIV-I protease\cite{erickson:1995,prashar:2009} a single catalytic
water molecule was located in the active site of the protein or for
insulin\cite{MM.insulin:2019,MM.insulin:2018} individual water
molecules were found to attack the dimerization interface to reduce
the thermodynamic stability of the dimer by a factor of
two. Similarly, water molecules have been reported to play essential
roles in protein folding,\cite{weik:2015} and for
function.\cite{pocker:2000,zewail:2004} Thus, probing and
characterizing the local solvent environment of particular regions of
a protein can provide important insights into functional aspects of
proteins.\\

\noindent
The utility of infrared spectroscopy to study the strength of
protein-ligand complexes has been proposed\cite{Suydam.halr.sci.2006}
and explicitly demonstrated from molecular dynamics simulations for
cyano-substituted benzene in lysozyme.\cite{MM.lys:2017} Using AHA as
a probe, it was reported that unbound and ligand-bound PDZ2 differ in
that the frequency correlation function for the two systems decay to
different levels at longer correlation times. Similarly, infrared
spectroscopy is also a sensitive probe - both, in terms of
spectroscopy and dynamics - to characterize protein-protein
interactions.\cite{MM.insulin:2020} Together with experimental
studies,\cite{tokmakoff:2016.2,tokmakoff:2020,dinner:2020} such
efforts pave the way for functional, in vivo studies of protein-ligand
and protein-protein association.\cite{smith:2013}\\




\noindent
In conclusion, the present work provides a comprehensive analysis of
the spectroscopy and dynamics of azide-labelled alanine in
Lysozyme. The results demonstrate that AlaN$_3$ is a positionally
sensitive probe for the local dynamics, covering a frequency range of
$\sim 15$ cm$^{-1}$. This is consistent with findings from selective
replacements of amino acids in PDZ2 which reported a frequency span of
$\sim 10$ cm$^{-1}$ for replacements of Val, Ala, or Glu by
AHA.\cite{hamm:2012} Furthermore, the long-time decay constants
$\tau_2$ range from $\sim 1$ to $\sim 10$ ps which compares with
experimentally measured correlation times of 3 ps.\cite{hamm:2012}
Attaching azide to alanine residues can yield dynamics that decays to
zero on the few ps time scale (i.e. $\Delta_0 \sim 0$ ps$^{-1}$) or to
a remaining inhomogeneous contribution of $\sim 0.5$ ps$^{-1}$
(corresponding to 2.5 cm$^{-1}$). One exciting prospect of this is to
determine how the spectroscopy and dynamics of the modification site
changes upon ligand binding to the active site for Lysozyme or other
proteins.\\

\section*{Acknowledgments}
The authors gratefully acknowledge financial support from the Swiss
National Science Foundation through grant 200021-117810 and to the
NCCR-MUST. The authors thank Prof. P. Hamm and Dr. D. Koner for
discussions on the experiments and some of the electronic structure
calculations. \\

\section*{Data Availability Statement}
The data that support the findings of this study are available from
the corresponding author upon reasonable request.

\newpage

\bibliography{lyso}

\end{document}

supplement.tex
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\author{Seyedeh Maryam Salehi} \affiliation[University of
  Basel]{Department of Chemistry, University of Basel,
  Klingelbergstrasse 80 , CH-4056 Basel, Switzerland.}  \author{Markus
  Meuwly} \affiliation[University of Basel]{Department of Chemistry,
  University of Basel, Klingelbergstrasse 80 , CH-4056 Basel,
  Switzerland.}  \email{m.meuwly@unibas.ch}

\title {Supporting Information: Site-Selected Dynamics of
  Azidolysozyme}

\begin{document}


\begin{figure}[H]
\begin{center}
\includegraphics[width=0.5\textwidth]{figs/offgrid.pdf}
\caption{Correlation between {\it ab initio} and RKHS interpolation
  for 230 randomly selected geometries. The $R^2 = 0.9999$ and the
  RMSD is 0.38 kcal/mol over a range of 180 kcal/mol.}
\label{sifig:offgrid}
\end{center}
\end{figure}



\begin{figure}[H]
\begin{center}
\includegraphics[width=0.7\textwidth]{figs/diffps_ahamrci_lccsdt.pdf}
\caption{Power spectrum based on the N1-N2 separation for AHA in the
  gas phase and from MRCI+Q and LCCSD(T)-F12 surface.}
\label{sifig:aha}
\end{center}
\end{figure}

\begin{figure}[H]
\centering
\includegraphics[width=0.4\textwidth,angle=-90]{figs/lyso_rmsd_noazo.pdf}
\caption{The structural RMSD for the C$_{\alpha}$ atoms from all
  residues (blue) and for the 14 Ala residues (red) for WT Lysozyme.}
\label{sifig:rmsd_lys}
\end{figure}



\begin{figure}[H]
\begin{center}
\includegraphics[width=0.65\textwidth]{figs/psir_lyso47.pdf}
\caption{Power (PS, top panel) and IR (bottom panel) spectrum for
  Ala47N$_3$. The power spectrum is based on N2-N3 bond
  displacement. The inset shows the bending mode of the Azide
  group. IR spectrum is calculated the Fourier transform of the
  molecular dipole moment autocorrelation function.}
\label{sifig:ps_irdip}
\end{center}
\end{figure}


\begin{figure}[H]
\begin{center}
  \includegraphics[width=0.5\textwidth,angle=-90]{figs/ffcf_vibscan.pdf}
\caption{The FFCF for Ala90 based on INM (red) and scan (blue)
  frequencies. The dashed lines show the corresponding fit to
  Eq. \ref{eq:ffcffit} with 3 time scales and the fitting parameters
  are as follows: INM: $a_{1}=0.29$, $\gamma=21.00$, $\tau_{1}=0.18$
  ps, $a_{2}=1.38$, $\tau_{2}=0.05$ ps, $a_{3}=0.22$, $\tau_{3}=2.70$
  ps, $\Delta_0=0.25$ and scan: $a_{1}=0.21$, $\gamma=17.50$,
  $\tau_{1}=0.11$ ps, $a_{2}=0.39$, $\tau_{2}=0.08$ ps, $a_{3}=0.09$,
  $\tau_{3}=1.62$ ps, $\Delta_0=0.07$. The comparison shows that the
  two different ways to determine the instantaneous frequency
  ($\omega(t)$ and $\nu(t)$, respectively) does not affect the overall
  appearance of the FFCF except for the magnitude of the asymptotic
  value $\Delta_0$.}
\label{sifig:fitscan}
\end{center}
\end{figure}


\begin{figure}[H]
\begin{center}
\includegraphics[width=0.38\textwidth,angle=-90]{figs/spec_scan.pdf}
\caption{1D IR spectra for Ala90N$_3$ and Ala94N$_3$ of lysozyme
  obtained from frequency calculations using ``scan'' (solid lines)
  and INM (dashed lines). Both analyses agree in that the frequency
  maximum for Ala90N$_3$ is to the blue of that for Ala94N$_3$ but the
  magnitude of the shift differs for the two approaches.}
\label{sifig:scan}
\end{center}
\end{figure}

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.4\textwidth,angle=-90]{figs/diffir_alaaha.pdf}
\caption{Comparison between the 1D-IR spectra of AlaN$_3$ and AHA at
  position Ala47 in Lysozyme. For AHA, an additional CH$_2$ group is
  inserted before the N$_3^-$ label. The lineshapes for azidoalanine
  and azidohomoalanine are very similar. The position of the frequency
  maximum for the asymmetric stretch of the azide label differs by
  less than 1 cm$^{-1}$.}
\label{sifig:aha_alan3}
\end{center}
\end{figure}


\begin{figure}[H]
\begin{center}
\includegraphics[width=0.75\textwidth]{figs/avg_res.pdf}
\caption{Average local hydrophobicity together with fluctuations for
  WT Lysozyme (no N$_3^{-}$ labels attached) for the 5 ns
  simulation. LH for all residues in black and for Ala in red.}
\label{sifig:lh}
\end{center}
\end{figure}


\begin{figure}[H]
\centering
\includegraphics[width=0.4\textwidth,angle=-90]{figs/diff_hydro76.pdf}
\caption{Local hydrophobicity for residue 76 with and without azide
  group attached to Ala for 2 ns. The effect of attaching azide on the
  LH, and hence the hydration itself, is clearly visible.}
\label{sifig:hyd76}
\end{figure}

\end{document}





ms.bbl
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\
@article{Salehi:N3-JPCB2019,
	title        = {{Vibrational Spectroscopy of N$_{3}^{-}$ in
                  the Gas and Condensed Phase}},
	author       = {Salehi, Seyedeh Maryam and Koner, Debasish and
                  Meuwly, Markus},
	year         = {{2019}},
	journal      = jpcb,
	volume       = {{123}},
	number       = {{15}},
	pages        = {{3282--3290}}
}
@article{MM.rev.jcp:2020,
	title        = {Non-conventional force fields for applications in spectroscopy and chemical reaction dynamics},
	author       = {Koner, Debasish and Salehi, Seyadeh Maryam and Mondal, Padmabati and Meuwly, Markus},
	year         = 2020,
	journal      = jcp,
	volume       = 153,
	pages        = {010901}
}
@article{stock:2018,
	title        = {{Azidohomoalanine: A Minimally Invasive, Versatile, and Sensitive Infrared Label in Proteins To Study Ligand Binding}},
	author       = {Zanobini, Claudio and Bozovic, Olga and Jankovic, Brankica and Koziol, Klemens L. and Johnson, Philip J. M. and Hamm, Peter and Gulzar, Adnan and Wolf, Steffen and Stock, Gerhard},
	year         = {{2018}},
	journal      = jpcb,
	volume       = {{122}},
	number       = {{44}},
	pages        = {{10118--10125}}
}
@article{AHA-Hamm-jpca-2017,
	title        = {{2D-IR Spectroscopy of an AHA Labeled Photoswitchable PDZ2 Domain}},
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	doi          = {{10.1002/jcc.21287}},
	issn         = {{0192-8651}},
	abstract     = {{CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems. the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983. (C) 2009 Wiley Periodicals, Inc. J Comput Chem 30: 1545-1614, 2009}},
	type         = {{Review}},
	language     = {{English}},
	affiliation  = {{Brooks, BR (Reprint Author), NHLBI, Lab Computat Biol, NIH, Bldg 10, Bethesda, MD 20892 USA. {[}Brooks, B. R.] NHLBI, Lab Computat Biol, NIH, Bethesda, MD 20892 USA. {[}Brooks, C. L., III] Univ Michigan, Dept Chem, Ann Arbor, MI 48109 USA. {[}Brooks, C. L., III] Univ Michigan, Dept Biophys, Ann Arbor, MI 48109 USA. {[}Mackerell, A. D., Jr.] Univ Maryland, Sch Pharm, Dept Pharmaceut Sci, Baltimore, MD 21201 USA. {[}Nilsson, L.] Karolinska Inst, Dept Biosci \& Nutr, SE-14157 Huddinge, Sweden. {[}Petrella, R. J.; Karplus, M.] Harvard Univ, Dept Chem \& Chem Biol, Cambridge, MA 02138 USA. {[}Petrella, R. J.] Harvard Univ, Sch Med, Dept Med, Boston, MA 02115 USA. {[}Roux, B.] Univ Chicago, Dept Biochem \& Mol Biol, Gordon Ctr Integrat Sci, Chicago, IL 60637 USA. {[}Won, Y.] Hanyang Univ, Dept Chem, Seoul 133792, South Korea. {[}Karplus, M.] Univ Strasbourg, ISIS, Lab Chim Biophys, F-67000 Strasbourg, France.}},
	keywords     = {{biomolecular simulation; CHARMM program; molecular mechanics; molecular dynamics; molecular modeling; biophysical computation; energy function}},
	keywords-plus = {{Molecular-dynamics Simulations; Free-energy Calculations; Implicit Solvent Models; Empirical Force-field; Monte-carlo Simulations; Binding Free-energies; Particle-mesh Ewald; Intermolecular Potential Function; Classical Drude Oscillator; Side-chain Conformations}},
	subject-category = {{Chemistry, Multidisciplinary}},
	author-email = {{brbrooks@helix.nih.gov brookscl@umich.edu alex@outerbanks.umaryland.edu Lennart.Nilsson@ki.se petrella@fas.harvard.edu roux@uchicago.edu won@hanyang.ac.kr marci@tammy.harvard.edu}},
	funding-acknowledgement = {{NIH {[}RR023920]; NSF ; DOE ; Accelrys ; CNRS ; NHLBI }},
	funding-text = {{In a multiauthor article. there is a leuitimate concern that the people involved receive the credit that they deserve. In Peneral, this is not possible Without listing the contributions of each individual, as some journals are now requiring. For ail article of this length and complexity, however, an), attempt at such specific attribution of credit is impractical. All the authors contributed to the writing and rewriting of significant portions of the text. The corresponding authors. designated by asterisks, were also involved in planning the manuscript and overseeing sections in the early stages of the writing. In both groups (starred and unstarred), the listing is alphabetical. One author, R.J. Petrella, needs to be mentioned individually because, in addition to writing a significant portion of the article. he was instrumental in transforming a large number of separate write-ups into what is very nearly a unified whole. The authors thank the referees for their helpful comments and David A. Case for serving as the editor of the paper. A number of people, other than those in the author list, have read and commented on the manuscript. They include Kwangho Nam, Arjan van der Vaart, loan Andricioaei, and Tom Darden. In addition to all of the authors of the paper, many other scientists have participated significantly in the development of CHARMM through the years. See Table 3; this list is included with all distributions of the program (in ``charmm\_main.src{''}). Support for the development of CHARMM, per se, and for researchers concerned with CHARMM development, have come from many sources. including NSF, NIH, DOE, Accelrys, and CNRS. It is not possible to list all of the grants individually, but NIH grant RR023920 is acknowledged for its direct support of the ongoing CHARMM conversion project. Part of the research in the B.R. Brooks group was supported by the Intramural Research Program of the NIH, NHLBI.}},
	number-of-cited-references = {{721}},
	times-cited  = {{7}},
	journal-iso  = {{J. Comput. Chem.}},
	doc-delivery-number = {{461lx}},
	unique-id    = {{Isi:000267269600001}}
}
@article{CHARMMFF-ALL36-Hatcher-2009,
	title        = {CHARMM Additive All-Atom Force Field for Acyclic Polyalcohols, Acyclic Carbohydrates, and Inositol},
	author       = {Elizabeth R. Hatcher and Olgun Guvench and Alexander D. MacKerell, Jr.},
	year         = 2009,
	journal      = Jctc,
	volume       = 5,
	number       = 5,
	pages        = {1315--1327},
	doi          = {10.1021/ct9000608},
	url          = {http://dx.doi.org/10.1021/ct9000608}
}
@article{CHARMMFF-ALL36-Guvench2011,
	title        = {{CHARMM Additive All-Atom Force Field for Carbohydrate Derivatives and Its Utility in Polysaccharide and Carbohydrate-Protein Modeling}},
	author       = {Guvench, Olgun and Mallajosyula, Sairam S. and Raman, E. Prabhu and Hatcher, Elizabeth and Vanommeslaeghe, Kenno and Foster, Theresa J. and Jamison, II, Francis W. and MacKerell, Jr., Alexander D.},
	year         = {{2011}},
	month        = {{Oct}},
	journal      = Jctc,
	volume       = {{7}},
	number       = {{10}},
	pages        = {{3162--3180}},
	doi          = {{10.1021/ct200328p}},
	issn         = {{1549-9618}},
	unique-id    = {{Isi:000295655000016}}
}
@book{QUANTUM-CORR-Chen-2015,
	title        = {Nanoscale Energy Transport and Harvesting - A Computational Study},
	author       = {Jie Chen and Gang Zhang and Baowen Li},
	year         = 2015,
	publisher    = {Pan Stanford},
	pages        = {1--57},
	doi          = {10.1201/b15658-2},
	isbn         = {978-981-4463-02-7},
	lccn         = 2002070896
}
@article{MMPT-AAC-Howard-2015,
	title        = {{Infrared and Near-Infrared Spectroscopy of Acetylacetone and Hexafluoroacetylacetone}},
	author       = {Howard, Daryl L. and Kjaergaard, Henrik G. and Huang, Jing and Meuwly, Markus},
	year         = {{2015}},
	month        = {{Jul 23}},
	journal      = Jpca,
	volume       = {{119}},
	number       = {{29}},
	pages        = {{7980--7990}},
	doi          = {{10.1021/acs.jpca.5b01863}},
	issn         = {{1089-5639}},
	researcherid-numbers = {{Kjaergaard, Henrik /H-4333-2014 Huang, Jing/G-5320-2011}},
	orcid-numbers = {{Kjaergaard, Henrik /0000-0002-7275-8297 Huang, Jing/0000-0001-9639-2907}},
	unique-id    = {{Isi:000358624200004}}
}
@article{MMPT-DPT-Lammers-2007,
	title        = {On the Relationship between Infrared Spectra of Shared Protons in Different Chemical Environments: A Comparison of Protonated Diglyme and Protonated Water Dimer},
	author       = {S. Lammers and M. Meuwly},
	year         = 2007,
	journal      = Jpca,
	volume       = 111,
	pages        = 1638,
	owner        = {morzech},
	timestamp    = {2009.10.16}
}
@article{MMPT-DPT-Lammers,
	title        = {Double proton transfer using dissociable force fields},
	author       = {S. Lammers and M. Meuwly},
	year         = 2004,
	journal      = {Aust. J. Chem.},
	volume       = 57,
	pages        = {1223--1228}
}
@article{MMPT-Lutz-2011,
	title        = {Water-assisted Proton Transfer in Ferredoxin I},
	author       = {Lutz, S. and Tubert-Brohman, I. and Yang, Y. and Meuwly, M.},
	year         = 2011,
	journal      = {J. Biol. Chem.},
	volume       = 286,
	number       = 27,
	pages        = {23679--23687}
}
@article{MM.morph:1999,
	title        = {Morphing ab Initio potentials: A systematic study of Ne--HF},
	author       = {Markus Meuwly and Jeremy M. Hutson},
	year         = 1999,
	journal      = {J. Chem. Phys.},
	volume       = 110,
	number       = 17,
	pages        = {8338--8347}
}
@article{MMPT-Lammers-2008,
	title        = {Reactive Force Fields for Proton Transfer Dynamics},
	author       = {Lammers, Sven and Lutz, Stephan and Meuwly, Markus},
	year         = 2008,
	journal      = {J. Comput. Chem},
	publisher    = {Wiley Subscription Services, Inc., A Wiley Company},
	volume       = 29,
	number       = 7,
	pages        = {1048--1063},
	doi          = {10.1002/jcc.20864},
	issn         = {1096-987x},
	url          = {http://dx.doi.org/10.1002/jcc.20864},
	keywords     = {molecular dynamics, chemical reactions, force fields, proton transfer, morphing potentials}
}
@article{MMPT-MA-Yang-2010,
	title        = "A Generalized Reactive Force Field for Nonlinear Hydrogen Bonds: Hydrogen Dynamics and Transfer in Malonaldehyde",
	author       = "Yang, Yonggang and Meuwly, Markus",
	year         = 2010,
	journal      = "J. Chem. Phys.",
	volume       = 133,
	number       = 6,
	pages        = "064503",
	doi          = "http://dx.doi.org/10.1063/1.3447701",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/133/6/10.1063/1.3447701"
}
@article{MMPT-Mackeprang-2016,
	title        = "Spectroscopy and Dynamics of Double Proton Transfer in Formic Acid Dimer",
	author       = "Mackeprang, Kasper and Xu, Zhen-Hao and Maroun, Zeina and Meuwly, Markus and Kjaergaard, Henrik G.",
	year         = 2016,
	journal      = "Phys. Chem. Chem. Phys.",
	publisher    = "The Royal Society of Chemistry",
	pages        = "24654--24662",
	doi          = "10.1039/c6cp03462d",
	url          = "http://dx.doi.org/10.1039/C6CP03462D"
}
@phdthesis{MMPT-Huang-Thesis,
	title        = {Proton transfer and hydrogen bonding in chemical and biological systems : a force field approach},
	author       = {Jing Huang},
	year         = 2011,
	url          = {http://edoc.unibas.ch/1377/},
	school       = {University\_of\_Basel},
	abstract     = {
		Proton transfer and hydrogen bonds are fundamental for the function, stability, structure and dynamics of chemically and biologically relevant systems. Hydrogen bonds can be regarded as incipient proton transfer reactions, so theoretically they can be described in unitary way. Here, a molecular mechanics force field approach is pursued. This is a computationally effecient method, so it can be used to study the strong hydrogen bonding and proton transfer processes in large and complex systems.

		After reviewing experimental and theoretical methods for proton transfer processes, especially currently available simulation techniques, our method ``MMPT'' will be presented in detail. The implementation of the code and its validation is discussed. MMPT has been applied to a variety of diverse systems including organic molecules, proteins, and transition metal complexes, and the results will be presented in Chapter 3 - 5. And finally an extension of MMPT to allow proton transport, together with future plans for MMPT development, will be discussed.
	}
}
@article{MMPT-PIMD-Huang-2014,
	title        = {{Kinetic isotope effect in malonaldehyde from path integral Monte Carlo simulations}},
	author       = {J. Huang and M. Buchowiecki and T. Nagy and J. Vanicek and M. Meuwly},
	year         = {{2014}},
	journal      = pccp,
	volume       = {{16}},
	pages        = {{204--211}}
}
@book{DFT-Parr1989,
	title        = {Density-Functional Theory of Atoms and Molecules},
	author       = "Parr, R.G. and Yang, Weitao",
	year         = 1989,
	publisher    = {Oxford University Press, USA},
	series       = {International Series of Monographs on Chemistry},
	isbn         = 9780195357738,
	url          = {https://books.google.ch/books?id=mGOpScSIwU4C}
}
@article{BLYP-Gill1992,
	title        = "The performance of the Becke—Lee—Yang—Parr (B—LYP) density functional theory with various basis sets",
	author       = "Peter M.W. Gill and Benny G. Johnson and John A. Pople and Michael J. Frisch",
	year         = 1992,
	journal      = Cpl,
	volume       = 197,
	number       = "4–5",
	pages        = "499--505",
	doi          = "http://dx.doi.org/10.1016/0009-2614(92)85807-M",
	issn         = "0009-2614",
	url          = "http://www.sciencedirect.com/science/article/pii/000926149285807M",
	note         = ""
}
@article{MP2-HEADGORDON1988,
	title        = "MP2 Energy Evaluation by Direct Methods",
	author       = "Martin Head-Gordon and John A. Pople and Michael J. Frisch",
	year         = 1988,
	journal      = Cpl,
	volume       = 153,
	number       = 6,
	pages        = "503--506",
	doi          = "http://dx.doi.org/10.1016/0009-2614(88)85250-3",
	issn         = "0009-2614",
	url          = "http://www.sciencedirect.com/science/article/pii/0009261488852503",
	note         = ""
}
@article{MP2-Frisch1990,
	title        = "Semi-direct Algorithms for the MP2 Energy and Gradient",
	author       = "Michael J. Frisch and Martin Head-Gordon and John A. Pople",
	year         = 1990,
	journal      = Cpl,
	volume       = 166,
	number       = 3,
	pages        = "281--289",
	doi          = "http://dx.doi.org/10.1016/0009-2614(90)80030-H",
	issn         = "0009-2614",
	url          = "http://www.sciencedirect.com/science/article/pii/000926149080030H",
	note         = ""
}
@article{MP2-HEADGORDON1994,
	title        = "Analytic MP2 Frequencies without Fifth-Order Storage. Theory and Application to Bifurcated Hydrogen Bonds in the Water Hexamer",
	author       = "Martin Head-Gordon and Teresa Head-Gordon",
	year         = 1994,
	journal      = Cpl,
	volume       = 220,
	number       = 1,
	pages        = "122--128",
	doi          = "http://dx.doi.org/10.1016/0009-2614(94)00116-2",
	issn         = "0009-2614",
	url          = "http://www.sciencedirect.com/science/article/pii/0009261494001162",
	note         = ""
}
@article{MP2-FRISCH1990b,
	title        = "A Direct MP2 Gradient Method",
	author       = "Michael J. Frisch and Martin Head-Gordon and John A. Pople",
	year         = 1990,
	journal      = Cpl,
	volume       = 166,
	number       = 3,
	pages        = "275--280",
	doi          = "http://dx.doi.org/10.1016/0009-2614(90)80029-D",
	issn         = "0009-2614",
	url          = "http://www.sciencedirect.com/science/article/pii/000926149080029D",
	note         = ""
}
@article{ADMP-Iyengar-2001,
	title        = "Ab Initio Molecular Dynamics: Propagating the Density Matrix with Gaussian Orbitals. II. Generalizations Based on Mass-weighting, Idempotency, Energy Conservation and Choice of Initial Conditions",
	author       = "Iyengar, Srinivasan S. and Schlegel, H. Bernhard and Millam, John M. and A. Voth, Gregory and Scuseria, Gustavo E. and Frisch, Michael J.",
	year         = 2001,
	journal      = Jcp,
	volume       = 115,
	number       = 22,
	pages        = "10291--10302",
	doi          = "http://dx.doi.org/10.1063/1.1416876",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/115/22/10.1063/1.1416876"
}
@article{ADMP-Iyengar-2002,
	title        = {Ab Initio Molecular Dynamics: Propagating the Density Matrix with Gaussian Orbitals. IV. Formal Analysis of the Deviations from Born-Oppenheimer Dynamics},
	author       = {Iyengar, Srinivasan S. and Schlegel, H. Bernhard and Voth, Gregory A. and Millam, John M. and Scuseria, Gustavo E. and Frisch, Michael J.},
	year         = 2002,
	journal      = {Isr. J. Chem.},
	publisher    = {WILEY-VCH Verlag},
	volume       = 42,
	number       = {2-3},
	pages        = {191--202},
	doi          = {10.1560/glw2-8nvq-4n6t-6c92},
	issn         = {1869-5868},
	url          = {http://dx.doi.org/10.1560/GLW2-8NVQ-4N6T-6C92},
	abstract     = {In the context of the recently developed Atom-centered Density Matrix Propagation (ADMP) approach to ab initio molecular dynamics, a formal analysis of the deviations from the Born—Oppenheimer surface is conducted. These deviations depend on the fictitious mass and on the magnitude of the commutator of the Fock and density matrices. These quantities are found to be closely interrelated and the choice of the fictitious mass provides a lower bound on the deviations from the Born—Oppenheimer surface. The relations are illustrated with an example calculation for the Cl−(H2O)25 cluster. We also show that there exists a direct one-to-one correspondence between approximate Born—Oppenheimer dynamics, where SCF convergence is restricted by a chosen threshold value for the commutator of the Fock and density matrices, and extended Lagrangian dynamics performed using a finite value for the fictitious mass. The analysis is extended to the nuclear forces used in the ADMP approximation. The forces are shown to be more general than those standardly used in Born—Oppenheimer dynamics, with the addition terms in the nuclear forces depending on the commutator mentioned above.}
}
@article{ADMP-Schlegel-2002,
	title        = "Ab Initio Molecular Dynamics: Propagating the Density Matrix with Gaussian Orbitals. III. Comparison with Born-Oppenheimer Dynamics",
	author       = "Schlegel, H. Bernhard and Iyengar, Srinivasan S. and Li, Xiaosong and Millam, John M. and Voth, Gregory A. and Scuseria, Gustavo E. and Frisch, Michael J.",
	year         = 2002,
	journal      = Jcp,
	volume       = 117,
	number       = 19,
	pages        = "8694--8704",
	doi          = "http://dx.doi.org/10.1063/1.1514582",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/117/19/10.1063/1.1514582"
}
@article{CHELPG-Breneman-1990,
	title        = {Determining Atom-centered Monopoles From Molecular Electrostatic Potentials. The Need for High Sampling Density in Formamide Conformational Analysis},
	author       = {Breneman, Curt M. and Wiberg, Kenneth B.},
	year         = 1990,
	journal      = Jcc,
	publisher    = {John Wiley & Sons, Inc.},
	volume       = 11,
	number       = 3,
	pages        = {361--373},
	doi          = {10.1002/jcc.540110311},
	issn         = {1096-987x},
	url          = {http://dx.doi.org/10.1002/jcc.540110311},
	abstract     = {An improved method for computing potential-derived charges is described which is based upon the CHELP program available from QCPE.1 This approach (CHELPG) is shown to be considerably less dependent upon molecular orientation than the original CHELP program. In the second part of this work, the CHELPG point selection algorithm was used to analyze the changes in the potential-derived charges in formamide during rotation about the CN bond. In order to achieve a level of rotational invariance less than 10% of the magnitude of the electronic effects studied, an equally-spaced array of points 0.3 Å apart was required. Points found to be greater than 2.8 Å from any nucleus were eliminated, along with all points contained within the defined VDW distances from each of the atoms. The results are compared to those obtained by using CHELP. Even when large numbers of points (ca. 3000) were sampled using the CHELP selection routine, the results did not indicate a satisfactory level of rotatational invariance. On the basis of these results, the original CHELP program was found to be inadequate for analyzing internal rotations.}
}
@article{NBO-Foster-1980,
	title        = {Natural Hybrid Orbitals},
	author       = {J. P. Foster and F. Weinhold},
	year         = 1980,
	journal      = Jacs,
	volume       = 102,
	pages        = {7211--18}
}
@article{NBO-Reed-1983,
	title        = "Natural Bond Orbital Analysis of Near‐hartree-fock Water Dimer",
	author       = "Reed, Alan E. and Weinhold, Frank",
	year         = 1983,
	journal      = Jcp,
	volume       = 78,
	number       = 6,
	pages        = {4066--4073},
	doi          = "http://dx.doi.org/10.1063/1.445134",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/78/6/10.1063/1.445134"
}
@article{NBO-Reed-1985,
	title        = "Natural Localized Molecular Orbitals",
	author       = "Reed, Alan E. and Weinhold, Frank",
	year         = 1985,
	journal      = Jcp,
	volume       = 83,
	number       = 4,
	pages        = {1736--1740},
	doi          = "http://dx.doi.org/10.1063/1.449360",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/83/4/10.1063/1.449360"
}
@article{NBO-Reed-1988,
	title        = {Intermolecular Interactions from a Natural Bond Orbital, Donor-Acceptor Viewpoint},
	author       = {Alan E. Reed and Larry A. Curtiss and Frank Weinhold},
	year         = 1988,
	journal      = {Chemical Reviews},
	volume       = 88,
	number       = 6,
	pages        = {899--926},
	doi          = {10.1021/cr00088a005},
	url          = {http://dx.doi.org/10.1021/cr00088a005},
	eprint       = {http://dx.doi.org/10.1021/cr00088a005}
}
@article{NBO-book,
	title        = {NBO Version 3.1},
	author       = {E. D. Glendening and A. E. Reed and J. E. Carpenter and F. Weinhold},
	journal      = {NBO Version 3.1}
}
@article{NBO6,
	title        = {{NBO 6.0: Natural bond orbital analysis program}},
	author       = {Glendening, Eric D. and Landis, Clark R. and Weinhold, Frank},
	year         = {{2013}},
	month        = {{Jun 15}},
	journal      = {{Journal Of Computational Chemistry}},
	volume       = {{34}},
	number       = {{16}},
	pages        = {{1429--1437}},
	doi          = {{10.1002/jcc.23266}},
	issn         = {{0192-8651}},
	researcherid-numbers = {{Weinhold, Frank/L-5880-2019}},
	orcid-numbers = {{Weinhold, Frank/0000-0002-9580-054X}},
	unique-id    = {{Isi:000318696800008}}
}
@article{REAXFF-Rahaman2011,
	title        = {{Development of a ReaxFF Reactive Force Field for Glycine and Application to Solvent Effect and Tautomerization}},
	author       = {Rahaman, Obaidur and van Duin, Adri C. T. and Goddard, III, William A. and Doren, Douglas J.},
	year         = {{2011}},
	month        = {{Jan 20}},
	journal      = Jpcb,
	volume       = {{115}},
	number       = {{2}},
	pages        = {{249--261}},
	doi          = {{10.1021/jp108642r}},
	issn         = {{1520-6106}},
	unique-id    = {{Isi:000286090200005}}
}
@article{EVB-Warshel1980,
	title        = {{An Empirical Valence Bond Approach For Comparing Reactions In Solutions And In Enzymes}},
	author       = {WARSHEL, A and WEISS, RM},
	year         = {{1980}},
	journal      = Jacs,
	volume       = {{102}},
	number       = {{20}},
	pages        = {{6218--6226}},
	doi          = {{10.1021/ja00540a008}},
	issn         = {{0002-7863}},
	unique-id    = {{Isi:a1980kj43600008}}
}
@article{MSEVB-VothSchmitt1998,
	title        = {{Multistate empirical valence bond model for proton transport in water}},
	author       = {Schmitt, UW and Voth, GA},
	year         = {{1998}},
	month        = {{Jul 16}},
	journal      = Jpcb,
	volume       = {{102}},
	number       = {{29}},
	pages        = {{5547--5551}},
	doi          = {{10.1021/jp9818131}},
	issn         = {{1089-5647}},
	researcherid-numbers = {{Schmitt, Udo/A-1008-2011}},
	unique-id    = {{Isi:000075151300001}}
}
@article{MSEVB-VothDay2002,
	title        = {{A second generation multistate empirical valence bond model for proton transport in aqueous systems}},
	author       = {Day, TJF and Soudackov, AV and Cuma, M and Schmitt, UW and Voth, GA},
	year         = {{2002}},
	month        = {{Sep 22}},
	journal      = Jcp,
	volume       = {{117}},
	number       = {{12}},
	pages        = {{5839--5849}},
	doi          = {{10.1063/1.1497157}},
	issn         = {{0021-9606}},
	researcherid-numbers = {{Soudackov, Alexander/A-1159-2010 Schmitt, Udo/A-1008-2011}},
	orcid-numbers = {{Soudackov, Alexander/0000-0001-9581-8494 }},
	unique-id    = {{Isi:000177825500036}}
}
@article{MSEVB-VothWu2008,
	title        = {{An improved multistate empirical valence bond model for aqueous proton solvation and transport}},
	author       = {Wu, Yujie and Chen, Hanning and Wang, Feng and Paesani, Francesco and Voth, Gregory A.},
	year         = {{2008}},
	month        = {{Jan 17}},
	journal      = Jpcb,
	volume       = {{112}},
	number       = {{2}},
	pages        = {{467--482}},
	doi          = {{10.1021/jp076658h}},
	issn         = {{1520-6106}},
	researcherid-numbers = {{Paesani, Francesco/B-1435-2009 Wang, Feng/J-8583-2014 Chen, Hanning/G-9487-2014}},
	orcid-numbers = {{Wang, Feng/0000-0002-2740-3534 }},
	unique-id    = {{Isi:000252287200033}}
}
@article{MSEVB-VothSwanson2007,
	title        = {{Proton solvation and transport in aqueous and biomolecular systems: Insights from computer simulations}},
	author       = {Swanson, Jessica M. J. and Maupin, C. Mark and Chen, Hanning and Petersen, Matt K. and Xu, Jiancong and Wu, Yujie and Voth, Gregory A.},
	year         = {{2007}},
	month        = {{May 3}},
	journal      = Jpcb,
	volume       = {{111}},
	number       = {{17}},
	pages        = {{4300--4314}},
	doi          = {{10.1021/jp070104x}},
	issn         = {{1520-6106}},
	researcherid-numbers = {{Chen, Hanning/G-9487-2014}},
	unique-id    = {{Isi:000245954800004}}
}
@article{PT-HYDYN-Wolf2014,
	title        = {Explicit proton transfer in classical molecular dynamics simulations},
	author       = "Wolf, Maarten G. and Groenhof, Gerrit",
	year         = 2014,
	journal      = Jcc,
	volume       = 35,
	number       = 8,
	pages        = {657--671},
	doi          = {10.1002/jcc.23536},
	issn         = {1096-987x},
	keywords     = {proton transfer, λ-dynamics, force field, molecular dynamics, MC, excess proton}
}
@article{RPMD-Craig-2004,
	title        = "Quantum statistics and classical mechanics: Real time correlation functions from ring polymer molecular dynamics",
	author       = "Craig, Ian R. and Manolopoulos, David E.",
	year         = 2004,
	journal      = Jcp,
	volume       = 121,
	number       = 8,
	pages        = "3368--3373",
	doi          = "http://dx.doi.org/10.1063/1.1777575",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/121/8/10.1063/1.1777575"
}
@article{RPMD-rate-Craig-2005,
	title        = "Chemical reaction rates from ring polymer molecular dynamics",
	author       = "Craig, Ian R. and Manolopoulos, David E.",
	year         = 2005,
	journal      = "The Journal of Chemical Physics",
	volume       = 122,
	number       = 8,
	pages        = "",
	doi          = "http://dx.doi.org/10.1063/1.1850093",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/122/8/10.1063/1.1850093",
	eid          = 84106
}
@article{RPMD-rate-Craig-2-2005,
	title        = "A refined ring polymer molecular dynamics theory of chemical reaction rates",
	author       = "Craig, Ian R. and Manolopoulos, David E.",
	year         = 2005,
	journal      = "The Journal of Chemical Physics",
	volume       = 123,
	number       = 3,
	pages        = "",
	doi          = "http://dx.doi.org/10.1063/1.1954769",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/123/3/10.1063/1.1954769",
	eid          = 34102
}
@article{RPMD-diffu-Miller-2005,
	title        = "Quantum diffusion in liquid water from ring polymer molecular dynamics",
	author       = "Miller, Thomas F. and Manolopoulos, David E.",
	year         = 2005,
	journal      = "The Journal of Chemical Physics",
	volume       = 123,
	number       = 15,
	pages        = "",
	doi          = "http://dx.doi.org/10.1063/1.2074967",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/123/15/10.1063/1.2074967",
	eid          = 154504
}
@article{RPMD-short-Braams-2006,
	title        = "On the short-time limit of ring polymer molecular dynamics",
	author       = "Braams, Bastiaan J. and Manolopoulos, David E.",
	year         = 2006,
	journal      = "The Journal of Chemical Physics",
	volume       = 125,
	number       = 12,
	pages        = "",
	doi          = "http://dx.doi.org/10.1063/1.2357599",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/125/12/10.1063/1.2357599",
	eid          = 124105
}
@article{RPMD-rate-Collepardo-Guevara-2008,
	title        = "Proton transfer in a polar solvent from ring polymer reaction rate theory",
	author       = "Collepardo-Guevara, Rosana and Craig, Ian R. and Manolopoulos, David E.",
	year         = 2008,
	journal      = "The Journal of Chemical Physics",
	volume       = 128,
	number       = 14,
	pages        = "",
	doi          = "http://dx.doi.org/10.1063/1.2883593",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/128/14/10.1063/1.2883593",
	eid          = 144502
}
@article{RPMD-dev-Markland-2008,
	title        = "An efficient ring polymer contraction scheme for imaginary time path integral simulations",
	author       = "Markland, Thomas E. and Manolopoulos, David E.",
	year         = 2008,
	journal      = "The Journal of Chemical Physics",
	volume       = 129,
	number       = 2,
	pages        = "",
	doi          = "http://dx.doi.org/10.1063/1.2953308",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/129/2/10.1063/1.2953308",
	eid          = 24105
}
@article{RPMD-rate-Markland2008256,
	title        = "A refined ring polymer contraction scheme for systems with electrostatic interactions",
	author       = "Thomas E. Markland and David E. Manolopoulos",
	year         = 2008,
	journal      = Cpl,
	volume       = 464,
	number       = "4–6",
	pages        = "256--261",
	doi          = "http://dx.doi.org/10.1016/j.cplett.2008.09.019",
	issn         = "0009-2614",
	url          = "http://www.sciencedirect.com/science/article/pii/S0009261408012542",
	note         = "",
	abstract     = "We have recently shown how path integral simulations can be streamlined by decomposing the potential into a sum of rapidly-varying short-range and slowly-varying long-range contributions. Here, we introduce an efficient way to perform this decomposition for systems with electrostatic interactions and illustrate the method with an application to a flexible water model. In the limit of large system size, where the calculation of long-range forces dominates, the present method enables path integral simulations of liquid water to be performed with less than twice the computational effort of classical molecular dynamics simulations."
}
@article{RPMD-rate-Collepardo-Guevara-2009,
	title        = "Bimolecular reaction rates from ring polymer molecular dynamics",
	author       = "Collepardo-Guevara, Rosana and Suleimanov, Yury V. and Manolopoulos, David E.",
	year         = 2009,
	journal      = "The Journal of Chemical Physics",
	volume       = 130,
	number       = 17,
	pages        = "",
	doi          = "http://dx.doi.org/10.1063/1.3127145",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/130/17/10.1063/1.3127145",
	eid          = 174713
}
@article{RPMD-KIE-Suleimanov-2013,
	title        = "A ring polymer molecular dynamics study of the isotopologues of the H + H2 reaction",
	author       = "Suleimanov, Yury V. and de Tudela, Ricardo Perez and Jambrina, Pablo G. and Castillo, Jesus F. and Saez-Rabanos, Vicente and Manolopoulos, David E. and Aoiz, F. Javier",
	year         = 2013,
	journal      = "Phys. Chem. Chem. Phys.",
	publisher    = "The Royal Society of Chemistry",
	volume       = 15,
	pages        = "3655--3665",
	doi          = "10.1039/c2cp44364c",
	url          = "http://dx.doi.org/10.1039/C2CP44364C",
	issue        = 10,
	abstract     = "The inclusion of Quantum Mechanical (QM) effects such as zero point energy (ZPE) and tunneling in simulations of chemical reactions{,} especially in the case of light atom transfer{,} is an important problem in computational chemistry. In this respect{,} the hydrogen exchange reaction and its isotopic variants constitute an excellent benchmark for the assessment of approximate QM methods. In particular{,} the recently developed ring polymer molecular dynamics (RPMD) technique has been demonstrated to give very good results for bimolecular chemical reactions in the gas phase. In this work{,} we have performed a detailed RPMD study of the H + H2 reaction and its isotopologues Mu + H2{,} D + H2 and He[small mu ] + H2{,} at temperatures ranging from 200 to 1000 K. Thermal rate coefficients and kinetic isotope effects have been computed and compared with exact QM calculations as well as with quasiclassical trajectories and experiment. The agreement with the QM results is good for the heaviest isotopologues{,} with errors ranging from 15% to 45%{,} and excellent for Mu + H2{,} with errors below 15%. We have seen that RPMD is able to capture the ZPE effect very accurately{,} a desirable feature of any method based on molecular dynamics. We have also verified Richardson and Althorpe{'}s prediction [J. O. Richardson and S. C. Althorpe{,} J. Chem. Phys.{,} 2009{,} 131{,} 214106] that RPMD will overestimate thermal rates for asymmetric reactions and underestimate them for symmetric reactions in the deep tunneling regime. The ZPE effect along the reaction coordinate must be taken into account when assigning the reaction symmetry in the multidimensional case."
}
@article{RPMD-rate-PdT-2012,
	title        = {Chemical Reaction Rates from Ring Polymer Molecular Dynamics: Zero Point Energy Conservation in Mu + H2 → MuH + H},
	author       = {Ricardo Pérez de Tudela and F. J. Aoiz and Yury V. Suleimanov and David E. Manolopoulos},
	year         = 2012,
	journal      = {The Journal of Physical Chemistry Letters},
	volume       = 3,
	number       = 4,
	pages        = {493--497},
	doi          = {10.1021/jz201702q},
	url          = {http://dx.doi.org/10.1021/jz201702q},
	note         = {Pmid: 26286053},
	eprint       = {http://dx.doi.org/10.1021/jz201702q}
}
@article{RPMD-abini-Shiga2008175,
	title        = "Ab Initio Path Integral Ring Polymer Molecular Dynamics: Vibrational Spectra of Molecules",
	author       = "Motoyuki Shiga and Akira Nakayama",
	year         = 2008,
	journal      = Cpc,
	volume       = 451,
	number       = "4–6",
	pages        = "175--181",
	doi          = "http://dx.doi.org/10.1016/j.cplett.2007.11.091",
	issn         = "0009-2614",
	url          = "http://www.sciencedirect.com/science/article/pii/S0009261407015709",
	note         = "",
	abstract     = "The path integral ring polymer molecular dynamics method is combined with ‘on-the-fly’ ab initio electronic structure calculations and applied to vibrational spectra of small molecules, LiH and H2O, at the room temperature. The results are compared with those of the numerically exact solution and ab initio path integral centroid molecular dynamics calculation. The peak positions in the calculated spectra are found to be reasonable, showing the red-shift due to potential anharmonicity. This unification enables the investigation of real-time quantum dynamics of chemically complex molecular systems on the ab initio Born-Oppenheimer potential energy surface."
}
@article{RPMD-ipi-Ceriotti20141019,
	title        = "I-Pi: A Python Interface for ab Initio Path Integral Molecular Dynamics Simulations",
	author       = "Michele Ceriotti and Joshua More and David E. Manolopoulos",
	year         = 2014,
	journal      = Cpc,
	volume       = 185,
	number       = 3,
	pages        = "1019--1026",
	doi          = "http://dx.doi.org/10.1016/j.cpc.2013.10.027",
	issn         = "0010-4655",
	url          = "http://www.sciencedirect.com/science/article/pii/S001046551300372X",
	note         = "",
	keywords     = "Path integral"
}
@article{RPMD-Rossi-2014,
	title        = "How to Remove the Spurious Resonances From Ring Polymer Molecular Dynamics",
	author       = "Rossi, Mariana and Ceriotti, Michele and Manolopoulos, David E.",
	year         = 2014,
	journal      = Jcp,
	volume       = 140,
	number       = 23,
	pages        = 234116,
	doi          = "http://dx.doi.org/10.1063/1.4883861",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/140/23/10.1063/1.4883861"
}
@article{RPMD-review-Habershon-2013,
	title        = {Ring-polymer Molecular Dynamics: Quantum Effects in Chemical Dynamics from Classical Trajectories in an Extended Phase Space},
	author       = {Scott Habershon and David E. Manolopoulos and Thomas E. Markland and Thomas F. Miller-III},
	year         = 2013,
	journal      = {Annu. Rev. Phys. Chem.},
	volume       = 64,
	number       = 1,
	pages        = {387--413},
	doi          = {10.1146/annurev-physchem-040412-110122},
	url          = {http://dx.doi.org/10.1146/annurev-physchem-040412-110122}
}
@article{RPMD-IR-DMS-LiuBowman2015,
	title        = {{Quantum Calculations of the IR Spectrum of Liquid Water Using ab Initio and Model Potential and Dipole Moment Surfaces and Comparison with Experiment}},
	author       = {Liu, Hanchao and Wang, Yimin and Bowman, Joel M.},
	year         = {{2015}},
	month        = {{May 21}},
	journal      = Jcp,
	volume       = {{142}},
	number       = {{19}},
	pages        = 194502,
	doi          = {{10.1063/1.4921045}},
	issn         = {{0021-9606}},
	eissn        = {{1089-7690}},
	unique-id    = {{Isi:000355006200027}}
}
@article{RPMD-IR-HuangBowman2008,
	title        = "Comparison of quantum, classical, and ring-polymer molecular dynamics infra-red spectra of Cl−(H2O) and H+(H2O)2",
	author       = "Xinchuan Huang and Scott Habershon and Joel M. Bowman",
	year         = 2008,
	journal      = Cpl,
	volume       = 450,
	number       = "4–6",
	pages        = "253--257",
	doi          = "http://dx.doi.org/10.1016/j.cplett.2007.11.048",
	issn         = "0009-2614",
	url          = "http://www.sciencedirect.com/science/article/pii/S0009261407015783",
	note         = "",
	abstract     = "We present a comparison of the infra-red spectra of Cl−(H2O) and H+(H2O)2 obtained with classical and ring-polymer molecular dynamics with previous quantum calculations. Full-dimensional ab initio-based potential and dipole-moment surfaces are used in these calculations."
}
@article{RPMD-IR-TIP4P-HabershonManolopoulos2009,
	title        = "Competing quantum effects in the dynamics of a flexible water model",
	author       = "Habershon, Scott and Markland, Thomas E. and Manolopoulos, David E.",
	year         = 2009,
	journal      = Jcp,
	volume       = 131,
	number       = 2,
	pages        = "024501",
	doi          = "http://dx.doi.org/10.1063/1.3167790",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/131/2/10.1063/1.3167790"
}
@article{RPMD-IR-HabershonManolopoulos2008,
	title        = "Comparison of Path Integral Molecular Dynamics Methods for the Infrared Absorption Spectrum of Liquid Water",
	author       = "Habershon, Scott and Fanourgakis, George S. and Manolopoulos, David E.",
	year         = 2008,
	journal      = Jcp,
	volume       = 129,
	number       = 7,
	pages        = "074501",
	doi          = "http://dx.doi.org/10.1063/1.2968555",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/129/7/10.1063/1.2968555;jsessionid=6BqkXqN50agciBo0gOk_yKLd.x-aip-live-03",
	eid          = 74501
}
@article{RPMD-IR-LiuCase2009,
	title        = "Quantum dynamical effects in liquid water: A semiclassical study on the diffusion and the infrared absorption spectrum",
	author       = "Liu, Jian and Miller, William H. and Paesani, Francesco and Zhang, Wei and Case, David A.",
	year         = 2009,
	journal      = Jcp,
	volume       = 131,
	number       = 16,
	pages        = 164509,
	doi          = "http://dx.doi.org/10.1063/1.3254372",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/131/16/10.1063/1.3254372"
}
@article{DFTB-Pu2004,
	title        = {Combining Self-consistent-charge Density-functional Tight-binding (SCC-DFTB) with Molecular Mechanics by the Generalized Hybrid Orbital (GHO) Method},
	author       = {Jingzhi Pu and Jiali Gao and Donald G. Truhlar},
	year         = 2004,
	journal      = {J. Phys. Chem. A},
	volume       = 108,
	pages        = {5454--5463}
}
@article{DFTB-Elstner1998,
	title        = {Self-consistent-charge Density-functional Tight-binding Method for Simulations of Complex Materials Properties},
	author       = {Elstner, M. and Porezag, D. and Jungnickel, G. and Elsner, J. and Haugk, M. and Frauenheim, Th. and Suhai, S. and Seifert, G.},
	year         = 1998,
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	publisher    = {American Physical Society},
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	doi          = {10.1103/PhysRevB.58.7260},
	url          = {http://link.aps.org/doi/10.1103/PhysRevB.58.7260},
	issue        = 11,
	numpages     = {0}
}
@article{DFTB-Elstner2000,
	title        = {A Self-consistent Charge Density-functional Based Tight-binding Scheme for Large Biomolecules},
	author       = {Elstner, M. and Frauenheim, Th. and Kaxiras, E. and Seifert, G. and Suhai, S.},
	year         = 2000,
	journal      = {Phys. Stat. Sol. B},
	publisher    = {WILEY-VCH Verlag Berlin GmbH},
	volume       = 217,
	number       = 1,
	pages        = {357--376},
	doi          = {10.1002/(sici)1521-3951(200001)217:1<357::aid-pssb357>3.0.co;2-j},
	issn         = {1521-3951},
	url          = {http://dx.doi.org/10.1002/(SICI)1521-3951(200001)217:1<357::AID-PSSB357>3.0.CO;2-J}
}
@article{DFTB-Frauenheim2002,
	title        = {Atomistic Simulations of Complex Materials: Ground-State and Excited-State Properties},
	author       = {Thomas Frauenheim and Gotthard Seifert and Marcus Elstner and Thomas Niehaus and Christof K\"{o}hler and Marc Amkreutz and Michael Sternberg and Zolt\'{a}n Hajnal and Aldo Di Carlo and S\'{a}ndor Suhai},
	year         = 2002,
	journal      = {J. Phys.-Condens. Mat.},
	volume       = 14,
	number       = 11,
	pages        = {3015--3047},
	url          = {http://stacks.iop.org/0953-8984/14/i=11/a=313}
}
@article{DFTB-Walewski2004,
	title        = "Fast QM/MM method and its application to molecular systems",
	author       = "\L{}. Walewski and P. Ba\l{}a and M. Elstner and Th. Frauenheim and B. Lesyng",
	year         = 2004,
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	volume       = 397,
	number       = "4-6",
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	doi          = "http://dx.doi.org/10.1016/j.cplett.2004.09.012",
	issn         = "0009-2614",
	url          = "http://www.sciencedirect.com/science/article/pii/S0009261404013764",
	note         = ""
}
@article{DFTB-meuwly-jcp-02,
	title        = {Simulation of Proton Transfer Along Ammonia Wires: An ab Initio and Semiempirical Density Functional Comparison of Potentials and Classical Molecular Dynamics},
	author       = {M. Meuwly and M. Karplus},
	year         = 2002,
	journal      = jcp,
	volume       = 116,
	pages        = {2572--2585}
}
@article{DFTB-Cui2001,
	title        = {{A QM/MM Implementation of the Self-Consistent Charge Density Functional Tight Binding (SCC-DFTB) Method}},
	author       = {Cui, Q and Elstner, M and Kaxiras, E and Frauenheim, T and Karplus, M},
	year         = {{2001}},
	month        = {{Jan 18}},
	journal      = Jpcb,
	volume       = {{105}},
	number       = {{2}},
	pages        = {{569--585}},
	doi          = {{10.1021/jp0029109}},
	issn         = {{1089-5647}},
	researcherid-numbers = {{Elstner, Marcus/H-3463-2013 Frauenheim, Thomas/C-5653-2015}},
	orcid-numbers = {{Frauenheim, Thomas/0000-0002-3073-0616}},
	unique-id    = {{Isi:000166490900029}}
}
@article{DFTB-Riccardi2006,
	title        = {{Development of Effective Quantum Mechanical/Molecular Mechanical (QM/MM) Methods for Complex Biological Processes}},
	author       = {Riccardi, D and Schaefer, P and Yang, Y and Yu, HB and Ghosh, N and Prat-Resina, X and Konig, P and Li, GH and Xu, DG and Guo, H and Elstner, M and Cui, Q},
	year         = {{2006}},
	journal      = Jpcb,
	volume       = {{110}},
	number       = {{13}},
	pages        = {{6458--6469}}
}
@article{Perrin2009,
	title        = "High-resolution Fourier transform study of the $\nu_{\text{3}}$ fundamental band of \textit{trans}-formic acid",
	author       = "A. Perrin and J. Vander Auwera and Z. Zelinger",
	year         = 2009,
	journal      = "J. Quant. Spectrosc. Ra.",
	volume       = 110,
	number       = "9-10",
	pages        = "743--755",
	doi          = "http://dx.doi.org/10.1016/j.jqsrt.2008.09.006",
	issn         = "0022-4073",
	url          = "http://www.sciencedirect.com/science/article/pii/S0022407308001908"
}
@article{Birer2009,
	title        = {High-Resolution Infrared Spectroscopy of the Formic Acid Dimer},
	author       = {Birer, O. and Havenith, M.},
	year         = 2009,
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	volume       = 60,
	pages        = {263–275}
}
@article{Freytes2002,
	title        = {Overtone Spectroscopy of Formic Acid},
	author       = {Freytes, M. and Hurtmans, D. and Kassi, S. and Li\'{e}vin, J. and Auwera, J. V. and Campargue, A. and Herman, M.},
	year         = 2002,
	journal      = {Chem. Phys.},
	volume       = 283,
	pages        = {47–61}
}
@article{Hurtmans2000,
	title        = {Spectroscopic and ab Initio Investigation of the $\nu_{\text{OH}}$ Overtone Excitation in \textit{trans}-Formic Acid},
	author       = {Hurtmans, D. and Herregodts, F. and Herman, M. and Li\'{e}vin, J. and Campargue, A. and Garnache, A. and Kachanov, A. A.},
	year         = 2000,
	journal      = {J. Chem. Phys.},
	volume       = 113,
	pages        = {1535–1545}
}
@article{Bonner1938,
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	title        = {Vibrational action spectroscopy of the C-H and C-D stretches in partially deuterated formic acid dimer},
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	journal      = {Phys. Rev.},
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@article{Vener2001,
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@article{Durlak2009,
	title        = {Car-Parrinello molecular dynamics and density functional theory simulations of infrared spectra of acetic acid monomers and cyclic dimers},
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@article{Heger2014,
	title        = "Communication: Towards the binding energy and vibrational red shift of the simplest organic hydrogen bond: Harmonic constraints for methanol dimer",
	author       = "Heger, Matthias and Suhm, Martin A. and Mata, Ricardo A.",
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	volume       = 141,
	number       = 10,
	pages        = 101105,
	doi          = "http://dx.doi.org/10.1063/1.4895728",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/141/10/10.1063/1.4895728"
}
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@article{walbran_tsevb_2001,
	title        = {Proton transport in polarizable water},
	author       = {Walbran, S. and Kornyshev, A. A.},
	volume       = 114,
	number       = 22,
	pages        = {10039--10048},
	doi          = {10.1063/1.1370393},
	issn         = {0021-9606, 1089-7690},
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	abstract     = {Protonmobility in water determines the conductive properties of water-based protonconductors. We address the problem of protonmobility in pure water using a new, simple, Newtonian molecular dynamicswater model which is applicable to proton-rich environments (e.g., polymer electrolyte membranes). This model has degrees of freedom that are “inertial” and “inertialess” relative to the proton. The solvated proton is treated using a local empirical valence bond Hamiltonian, which allows for the efficient simulation of full charge, energy-conserving dynamics in single and multiple-proton systems. The solvated proton displays the Grotthus-type proton transfer mechanism, giving significantly enhanced transport in comparison with the classical diffusion of an H 3 O + ion. The model yields an activation energy of 0.11 {eV}, in excellent agreement with experiment. The results are consistent with the observation that nonpolarizable water models, conditioned to reproduce correct values of the static dielectric constant, are predestined to give too large activation energies of protonmobility due to the overweighted spectrum of the slower nuclear modes.},
	journaltitle = Jcp,
	date         = {2001-06-08},
	keywords     = {Activation energies, Carrier mobility, Classical transport, Conductors, Protons}
}
@article{voth_schmitt_multistate_1998,
	title        = {Multistate Empirical Valence Bond Model for Proton Transport in Water},
	author       = {Schmitt, Udo W. and Voth, Gregory A.},
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	number       = 29,
	pages        = {5547--5551},
	doi          = {10.1021/jp9818131},
	issn         = {1520-6106},
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	abstract     = {A multistate empirical valence bond ({MS}-{EVB}) model for describing proton transport in aqueous systems is presented. In this approach the electrostatic interaction of the solvent water molecules with an exchange charge distribution is explicitly included in the off-diagonal elements of the {EVB} Hamiltonian. The {MS}-{EVB} model is parametrized to reproduce geometrical and energetic quantities of selected H3O+·(H2O)N clusters. The obtained geometries, formation energies, and energy barriers are in excellent agreement with results from high-level ab initio calculations. It is furthermore applied in a classical molecular dynamics simulation of condensed-phase water with an excess proton in order to estimate the proton-transfer rate.},
	journaltitle = {The Journal of Physical Chemistry B},
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}
@article{voth_lefohn_multistate_2001,
	title        = {A Multistate Empirical Valence Bond Approach to a Polarizable and Flexible Water Model†},
	author       = {Lefohn, Aaron E. and Ovchinnikov, M. and Voth, Gregory A.},
	volume       = 105,
	number       = 28,
	pages        = {6628--6637},
	doi          = {10.1021/jp010103j},
	issn         = {1520-6106},
	url          = {http://dx.doi.org/10.1021/jp010103j},
	urldate      = {2015-09-06},
	abstract     = {A new polarizable and flexible water potential has been developed based on the multistate empirical valence bond ({MS}-{EVB}) method. The model adds a charge-determination step to the simple point charge/flexible ({SPC}/F) potential. Two models have been developed:? one that is polarizable only along the principal axis, and another that is polarizable in both directions within the molecular plane. The two models give nearly identical radial distribution functions ({RDF}) for the three site?site {RDFs} in water:? oxygen?oxygen, oxygen?hydrogen, and hydrogen?hydrogen. The new model exhibits a liquid structure that is more ordered than {SPC}/F but is still well matched to experiment. The gas-phase monomer and dimer properties of the polarizable models are much closer to the experimental result than is {SPC}/F. Experimental condensed phase properties, such as the bond angle, bond length, molecular dipole moment, and total energy, are also reasonably well reproduced. The static dielectric constant and self-diffusion constant of the model with two directions of polarizability are also reasonably accurate. The {MS}-{EVB} method is shown to provide a simple approach to including both polarizability and bond flexibility into a water potential.},
	journaltitle = {The Journal of Physical Chemistry B},
	shortjournal = {J. Phys. Chem. B},
	date         = {2001-07-01}
}
@article{voth_day_multistate_second_2002,
	title        = {A second generation multistate empirical valence bond model for proton transport in aqueous systems},
	author       = {Day, Tyler J. F. and Soudackov, Alexander V. and Čuma, Martin and Schmitt, Udo W. and Voth, Gregory A.},
	volume       = 117,
	number       = 12,
	pages        = {5839--5849},
	doi          = {10.1063/1.1497157},
	issn         = {0021-9606, 1089-7690},
	url          = {http://scitation.aip.org/content/aip/journal/jcp/117/12/10.1063/1.1497157},
	urldate      = {2015-09-06},
	abstract     = {Building on the previously developed multistate empirical valence bond model [U. W. Schmitt and G. A. Voth, J. Chem. Phys 111, 9361 (1999)] for the dynamics and energetics of an excess proton in bulk phase water, a second generation model is described. This model is shown to produce similar dynamic and structural properties to the previous model, while allowing for the use of the full hydronium charge. This characteristic of the model is required for its implementation in a host of realistic applications beyond bulk water. An improved state selection algorithm is also presented, resulting in a significantly reduced energy drift during microcanonical molecular dynamics simulations. The unusually high self diffusion constant of an excess proton in water due to the proton hopping (Grotthuss) process is observed in the simulation data and is found to be quantitatively in the same range as the experimental value if a quantum correction is taken into consideration. Importantly, a more complete analysis of protontransport process is also presented.},
	journaltitle = {The Journal of Chemical Physics},
	date         = {2002-09-22},
	keywords     = {molecular dynamics, Protons, Self diffusion, State selected dynamics, Transport processes}
}
@article{voth_wu_multistate_improved_2008,
	title        = {An Improved Multistate Empirical Valence Bond Model for Aqueous Proton Solvation and Transport†},
	author       = {Wu, Yujie and Chen, Hanning and Wang, Feng and Paesani, Francesco and Voth, Gregory A.},
	volume       = 112,
	number       = 2,
	pages        = {467--482},
	doi          = {10.1021/jp076658h},
	issn         = {1520-6106},
	url          = {http://dx.doi.org/10.1021/jp076658h},
	urldate      = {2015-09-06},
	abstract     = {A new multistate empirical valence bond model ({MS}-{EVB}3) is developed for proton solvation and transport in aqueous solutions. The new model and its quantum version ({qMS}-{EVB}3) are based on the {MS}-{EVB}2 model [Day et al., J. Chem. Phys. 2002, 117, 5839] and recently developed flexible water modelsthe {SPC}/Fw model [Wu et al. J. Chem. Phys. 2006, 124, 24503] and the {qSPC}/Fw model [Paesani et al. J. Chem. Phys. 2006, 125, 184507]for classical and quantum simulations, respectively. Using ab initio data as benchmarks, the binding energies and optimized geometries calculated with the new model for protonated water clusters, as well as the potential energy surface for proton shuttling between water molecules in a cluster environment, are improved in comparison to the {MS}-{EVB}2 model. For aqueous solutions, classical and quantum molecular dynamics simulations with the {MS}-{EVB}3 model yield a more accurate description of the solvation structure and diffusive dynamics of the excess proton. New insight is also provided into the proton solvation and hopping dynamics in water, as well as the ?amphiphilic? nature of the hydrated proton that has been predicted to give rise to its enhanced concentration at aqueous interfaces and an effectively lower {pH} of the air?water interface [Petersen et al. J. Phys. Chem. B 2004, 108, 14804].},
	journaltitle = {The Journal of Physical Chemistry B},
	shortjournal = {J. Phys. Chem. B},
	date         = {2008-01-01}
}
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	url          = {http://dx.doi.org/10.1021/acs.jpca.5b08358},
	eprint       = {http://dx.doi.org/10.1021/acs.jpca.5b08358}
}
@article{Florio2003,
	title        = "Theoretical modeling of the OH stretch infrared spectrum of carboxylic acid dimers based on first-principles anharmonic couplings",
	author       = "Florio, Gina M. and Zwier, Timothy S. and Myshakin, Evgeniy M. and Jordan, Kenneth D. and Sibert, Edwin L.",
	year         = 2003,
	journal      = "J. Chem. Phys.",
	volume       = 118,
	number       = 4,
	pages        = "1735--1746",
	doi          = "http://dx.doi.org/10.1063/1.1530573",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/118/4/10.1063/1.1530573"
}
@book{bookAtmoschem,
	title        = {Atmospheric Chemistry and Physics: From Air Polution to Climate Change},
	author       = {John H. Seinfeld and Spyros N. Pandis},
	year         = 2006,
	publisher    = {John Wiley & Sons, Inc., Hoboken, New Jersey},
	edition      = {2nd}
}
@article{Andreae1988,
	title        = {Formic and acetic acid over the central Amazon region, Brazil: 1. Dry season},
	author       = {Andreae, M. O. and Talbot, R. W. and Andreae, T. W. and Harriss, R. C.},
	year         = 1988,
	journal      = {J. Geophys. Res.-Atmos.},
	volume       = 93,
	number       = {D2},
	pages        = {1616--1624},
	doi          = {10.1029/JD093iD02p01616},
	issn         = {2156-2202},
	url          = {http://dx.doi.org/10.1029/JD093iD02p01616},
	keywords     = {Troposphere: composition and chemistry, Biosphere/atmosphere interactions, Cloud physics and chemistry}
}
@article{Dawson1980,
	title        = {Formic and acetic acids in the atmosphere of the southwest U.S.A.},
	author       = {Dawson, G. A. and Farmer, J. Carl and Moyers, Jarvis L.},
	year         = 1980,
	journal      = {Geophys. Res. Lett.},
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	number       = 9,
	pages        = {725--728},
	doi          = {10.1029/GL007i009p00725},
	issn         = {1944-8007},
	url          = {http://dx.doi.org/10.1029/GL007i009p00725},
	keywords     = {Geochemistry: Chemistry of the atmosphere, Meteorology: Chemical composition and chemical interactions}
}
@article{Talbot1988,
	title        = {Atmospheric geochemistry of formic and acetic acids at a mid-latitude temperate site},
	author       = {Talbot, R. W. and Beecher, K. M. and Harriss, R. C. and Cofer, W. R.},
	year         = 1988,
	journal      = {J. Geophys. Res.-Atmos.},
	volume       = 93,
	number       = {D2},
	pages        = {1638--1652},
	doi          = {10.1029/JD093iD02p01638},
	issn         = {2156-2202},
	url          = {http://dx.doi.org/10.1029/JD093iD02p01638},
	keywords     = {Geochemical cycles, Biosphere/atmosphere interactions, Troposphere: composition and chemistry, Diurnal, seasonal, and annual cycles}
}
@article{Hanst1982,
	title        = "A long-path infra-red study of Los Angeles smog",
	author       = "Philip L. Hanst and Ngai Woon Wong and Joseph Bragin",
	year         = 1982,
	journal      = "Atmos. Environ.",
	volume       = 16,
	number       = 5,
	pages        = "969--981",
	doi          = "http://dx.doi.org/10.1016/0004-6981(82)90183-4",
	issn         = "0004-6981",
	url          = "http://www.sciencedirect.com/science/article/pii/0004698182901834",
	note         = ""
}
@article{Farmer1982,
	title        = {Condensation sampling of soluble atmospheric trace gases},
	author       = {Farmer, J. C. and Dawson, G. A.},
	year         = 1982,
	journal      = {J. Geophys. Res.-Oceans},
	volume       = 87,
	number       = {C11},
	pages        = {8931--8942},
	doi          = {10.1029/JC087iC11p08931},
	issn         = {2156-2202},
	url          = {http://dx.doi.org/10.1029/JC087iC11p08931},
	keywords     = {Geochemistry: Chemistry of the atmosphere, Instruments and techniques, Meteorology: Air quality}
}
@article{Lawrence1994,
	title        = {Measurement of Atmospheric Formic and Acetic Acids: Methods Evaluation and Results from Field Studies},
	author       = {Joy E. Lawrence and Petros. Koutrakis},
	year         = 1994,
	journal      = {Environ. Sci. Technol.},
	volume       = 28,
	number       = 5,
	pages        = {957--964},
	doi          = {10.1021/es00054a031},
	url          = {http://dx.doi.org/10.1021/es00054a031},
	eprint       = {http://dx.doi.org/10.1021/es00054a031}
}
@article{Ito2008,
	title        = "Infrared spectra of (HCOOH)$_2$ and (DCOOH)$_2$ in rare gas matrices: A comparative study with gas phase spectra",
	author       = "Ito, Fumiyuki",
	year         = 2008,
	journal      = "J. Chem. Phys.",
	volume       = 128,
	number       = 11,
	pages        = 114310,
	doi          = "http://dx.doi.org/10.1063/1.2841078",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/128/11/10.1063/1.2841078",
	eid          = 114310
}
@article{Michielsen2012,
	title        = "C-X (X = S, P) hydrogen bonding: The complexes of halothane with dimethyl sulfide and trimethylphosphine",
	author       = "B. Michielsen and C. Verlackt and B.J. van der Veken and W.A. Herrebout",
	year         = 2012,
	journal      = "J. Mol. Struc.",
	volume       = 1023,
	number       = "",
	pages        = "90--95",
	doi          = "http://dx.doi.org/10.1016/j.molstruc.2012.02.063",
	issn         = "0022-2860",
	url          = "http://www.sciencedirect.com/science/article/pii/S0022286012001901",
	keywords     = "Cryospectroscopy"
}
@article{Michielsen2010,
	title        = "The complexes of halothane with benzene: the temperature dependent direction of the complexation shift of the aliphatic C-H stretching",
	author       = "Michielsen, Bart and Dom, Johan J. J. and Veken, Benjamin J. van der and Hesse, Susanne and Xue, Zhifeng and Suhm, Martin A. and Herrebout, Wouter A.",
	year         = 2010,
	journal      = "Phys. Chem. Chem. Phys.",
	publisher    = "The Royal Society of Chemistry",
	volume       = 12,
	pages        = "14034--14044",
	doi          = "10.1039/c0cp00771d",
	url          = "http://dx.doi.org/10.1039/C0CP00771D",
	issue        = 42,
	abstract     = "The formation of C-H[three dots{,} centered][small pi] bonded complexes of halothane with benzene(-d6) has been studied using infrared and Raman spectroscopy of solutions in liquid krypton{,} in supersonic jet expansions and in room temperature vapour phase. The formation of complexes with 1 [ratio] 1 and 2 [ratio] 1 stoichiometry was observed. The complexation enthalpy in liquid krypton for the 1 [ratio] 1 complex was determined to be -9.8(2) kJ mol-1 and the enthalpy for the addition of a second halothane molecule to the 1 [ratio] 1 complex was determined at -7.0(3) kJ mol-1. The stretching mode of the halothane C-H bond involved in the formation of the complex in the jets was observed to blue shift by 7.7(10) cm-1. In contrast{,} for the solutions of liquid krypton and the room temperature measurements a small red shift was observed. Supported by ab initio calculations and Monte Carlo simulations{,} this shift was explained by the differences in thermal populations of the van der Waals vibrations of the complex in the different experiments."
}
@article{Hippler2010,
	title        = "Quantum-chemical study and FTIR jet spectroscopy of CHCl$_3$-NH$_3$ association in the gas phase",
	author       = "Hippler, Michael and Hesse, Susanne and Suhm, Martin A.",
	year         = 2010,
	journal      = "Phys. Chem. Chem. Phys.",
	publisher    = "The Royal Society of Chemistry",
	volume       = 12,
	pages        = "13555--13565",
	doi          = "10.1039/c0cp00530d",
	url          = "http://dx.doi.org/10.1039/C0CP00530D",
	issue        = 41,
	abstract     = "High level ab initio quantum chemical calculations have been performed on the association of chloroform with ammonia in the gas phase (counterpoise corrected MP2 and coupled-cluster CCSD(T) calculations with 6-311++G(d{,}p) basis functions). Minimum energy equilibrium structures have been found for CHCl3-NH3 dimer{,} CHCl3-(NH3)2 trimer and CHCl3-(NH3)3 tetramer. Association is characterised by a CH[three dots{,} centered]N hydrogen bond between a chloroform and an ammonia molecule{,} with further ammonia units attached by hydrogen bonds to ammonia and by an electrostatic NH[three dots{,} centered]Cl interaction to chloroform. Cooperative effects provide additional stabilisation. The complexes exhibit characteristic shifts of vibrational bands and change of IR intensity; in particular there is a pronounced progressive shift of the CH-stretching vibration towards lower wavenumber with each unit of ammonia attached in the complex. The shift is accompanied by an up to 600 fold increase in IR intensity. The experimental FTIR jet spectra have provided firm evidence of CHCl3-NH3 association{,} with the clearest effects seen in the region of the CH-stretching vibration. First tentative assignments have been made based on the dependence of relative intensities of cluster features on the concentration of monomers{,} and assignments have been corroborated by the quantum chemical calculations. The present combined ab initio and FTIR spectroscopy study reveals the structure and energetics of cluster formation and intermolecular bonding in CHCl3-NH3 association."
}
@article{Heger2015,
	title        = "Soft hydrogen bonds to alkenes: the methanol-ethene prototype under experimental and theoretical scrutiny",
	author       = "Heger, Matthias and Mata, Ricardo A. and Suhm, Martin A.",
	year         = 2015,
	journal      = "Chem. Sci.",
	publisher    = "The Royal Society of Chemistry",
	volume       = 6,
	pages        = "3738--3745",
	doi          = "10.1039/c5sc01002k",
	url          = "http://dx.doi.org/10.1039/C5SC01002K",
	issue        = 7,
	abstract     = "An FTIR spectroscopic study of the elusive hydrogen-bonded methanol-ethene complex{,} the most elementary example for weak intermolecular alcohol hydrogen bonding to a [small pi] cloud{,} is presented. By isolating the complex in a supersonic jet{,} the rigorous comparability to high-level quantum chemical calculations is ensured. In stark contrast to classical hydrogen bonds{,} experimental overtone analysis reveals the harmonic oscillator approximation for the OH red shift to be accurate. Harmonic calculations up to explicitly correlated local coupled-cluster level are thus found to agree very well with experiment. The experimental OH values for the red shift (45 cm-1){,} the small change in diagonal anharmonicity (-3 cm-1) and the overtone intensity attenuation (2 [times] 102-fold) together with theoretical predictions for the preferred structural arrangement and the zero-point-corrected dissociation energy (8 kJ mol-1) may thus be regarded as definitive reference values for related systems and for more approximate computational methods. In particular{,} MP2 calculations are shown to fail for this kind of weak intermolecular interaction."
}
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	journal      = jcp,
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@article{johnson:2013,
	title        = {{Hiding in Plain Sight: Unmasking the Diffuse Spectral Signatures of the Protonated N-terminus in Isolated Dipeptides Cooled in a Cryogenic Ion Trap}},
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	year         = {{2013}},
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	number       = {{20}},
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	author       = {Johnson, Christopher J. and Dzugan, Laura C. and Wolk, Arron B. and Leavitt, Christopher M. and Fournier, Joseph A. and McCoy, Anne B. and Johnson, Mark A.},
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	author       = "Timo Graen and Helmut Grubmüller",
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	volume       = 198,
	number       = "",
	pages        = "169--178",
	doi          = "https://doi.org/10.1016/j.cpc.2015.08.023",
	issn         = "0010-4655",
	url          = "http://www.sciencedirect.com/science/article/pii/S0010465515003203",
	note         = ""
}
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	title        = {{Simultaneous Fitting of a Potential-energy Surface and its Corresponding Force Fields Using Feedforward Neural Networks}},
	author       = {Pukrittayakamee, A. and Malshe, M. and Hagan, M. and Raff, L. M. and Narulkar, R. and Bukkapatnum, S. and Komanduri, R.},
	year         = {{2009}},
	journal      = jcp,
	volume       = {{130}},
	number       = {{13}}
}
@article{behler.2011,
	title        = {{Neural Network Potential-energy Surfaces in Chemistry: A Tool for Large-scale Simulations}},
	author       = {Behler, Joerg},
	year         = {{2011}},
	journal      = pccp,
	volume       = {{13}},
	number       = {{40}},
	pages        = {{17930--17955}}
}
@article{parrinello.prl.2007,
	title        = {{Generalized Neural-network Representation of High-dimensional Potential-energy Surfaces}},
	author       = {Behler, Joerg and Parrinello, Michele},
	year         = {{2007}},
	journal      = prl,
	volume       = {{98}},
	number       = {{14}}
}
@article{hollebeek1999constructing,
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	publisher    = {Annual Reviews 4139 El Camino Way, PO Box 10139, Palo Alto, CA 94303-0139, USA},
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@article{castro2014computational,
	title        = {Computational Study of Collisions between O (3P) and NO (2$\Pi$) at Temperatures Relevant to the Hypersonic Flight Regime},
	author       = {Castro-Palacio, Juan Carlos and Nagy, Tibor and Bemish, Raymond J and Meuwly, Markus},
	year         = 2014,
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@article{unke2016collision,
	title        = {Collision-induced Rotational Excitation in N2+ (2$\Sigma$g+, v= 0)--Ar: Comparison of Computations and Experiment},
	author       = {Unke, Oliver T and Castro-Palacio, Juan Carlos and Bemish, Raymond J and Meuwly, Markus},
	year         = 2016,
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	publisher    = {AIP Publishing},
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	number       = 22,
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@article{meuwly.2016.mbno,
	title        = {
		{Structural Interpretation of Metastable States in Myoglobin-NO

		}
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	author       = {Soloviov, Maksym and Das, Akshaya K. and Meuwly, Markus},
	year         = {{2016}},
	month        = {{Aug 16}},
	journal      = Aci,
	volume       = {{55}},
	number       = {{34}},
	pages        = {{10126--10130}},
	doi          = {{10.1002/anie.201604552}},
	issn         = {{1433-7851}},
	eissn        = {{1521-3773}},
	unique-id    = {{Isi:000383373000060}}
}
@article{MM15.mbno,
	title        = {{Reproducing Kernel Potential Energy Surfaces in Biomolecular Simulations: Nitric Oxide Binding to Myoglobin}},
	author       = {Soloviov, Maksym and Meuwly, Markus},
	year         = {{2015}},
	journal      = jcp,
	volume       = {{143}},
	number       = {{10}},
	article-number = {{105103}}
}
@article{MM.heh2.1998,
	title        = {{The Potential Energy Surface and Near-dissociation States of He-H$_2^+$}},
	author       = {Meuwly, M and Hutson, JM},
	year         = {{1999}},
	journal      = jcp,
	volume       = {{110}},
	number       = {{7}},
	pages        = {{3418--3427}}
}
@article{SplitOperator,
	title        = "{Solution of the Sch\"{o}dinger Equation by a Spectral Method}",
	author       = "M. D. Feit and J. A. Fleck,Jr. and A Steiger",
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	pages        = "412--433"
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@article{TDWP:JCP16,
	title        = "{Scattering Study of the Ne + NeH$^+$(v$_0$ = 0, j$_0$ = 0) $\rightarrow$ NeH$^+$ + Ne Reaction on an ab Initio Based Analytical Potential Energy Surface}",
	author       = "Koner, Debasish and Barrios, Lizandra and Gonz\'{a}lez-Lezana, Tom\'{a}s and Panda, Aditya N.",
	year         = 2016,
	journal      = jcp,
	volume       = 144,
	pages        = "034303",
	doi          = "http://dx.doi.org/10.1063/1.4939952",
	url          = "http://scitation.aip.org/content/aip/journal/jcp/144/3/10.1063/1.4939952"
}
@article{hamm:2015,
	title        = {{Fast Infrared Spectroscopy of Protein Dynamics: Advancing Sensitivity and Selectivity}},
	author       = {Koziol, Klemens L. and Johnson, Philip J. M. and Stucki-Buchli, Brigitte and Waldauer, Steven A. and Hamm, Peter},
	year         = {{2015}},
	journal      = cosb,
	volume       = {{34}},
	pages        = {{1--6}}
}
@article{hamm:2017,
	title        = {{2D-IR Spectroscopy of an AHA Labeled Photoswitchable PDZ2 Domain}},
	author       = {Stucki-Buchli, Brigitte and Johnson, Philip J. M. and Bozovic, Olga and Zanobini, Claudio and Koziol, Klemens L. and Hamm, Peter and Gulzar, Adnan and Wolf, Steffen and Buchenberg, Sebastian and Stock, Gerhard},
	year         = {{2017}},
	journal      = jpca,
	volume       = {{121}},
	number       = {{49}},
	pages        = {{9435--9445}}
}
@article{hamm:2012,
	title        = {{Ligand Binding Studied by 2D IR Spectroscopy Using the Azidohomoalanine Label}},
	author       = {Bloem, Robbert and Koziol, Klemens and Waldauer, Steven A. and Buchli, Brigitte and Walser, Reto and Samatanga, Brighton and Jelesarov, Ilian and Hamm, Peter},
	year         = {{2012}},
	journal      = jpcb,
	volume       = {{116}},
	number       = {{46}},
	pages        = {{13705--13712}}
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@article{MM.rev:2017,
	title        = {{Implications of Short Time Scale Dynamics on Long Time Processes}},
	author       = {El Hage, Krystel and Brickel, Sebastian and Hermelin, Sylvain and Gaulier, Geoffrey and Schmidt, Cedric and Bonacina, Luigi and van Keulen, Siri C. and Bhattacharyya, Swarnendu and Chergui, Majed and Hamm, Peter and Rothlisberger, Ursula and Wolf, Jean-Pierre and Meuwly, Markus},
	year         = {{2017}},
	journal      = sd,
	volume       = {{4}},
	pages        = {{061507}}
}
@article{MM.lys:2017,
	title        = "Vibrational Stark Spectroscopy for Assessing Ligand-Binding Strengths in a Protein",
	author       = "Mondal, Padmabati and Meuwly, Markus",
	year         = 2017,
	journal      = pccp,
	volume       = 19,
	pages        = "16131--16143",
	issue        = 24
}
@article{NMA:JPCB2014,
	title        = {Computational Two-Dimensional Infrared Spectroscopy without Maps: N-Methylacetamide in Water},
	author       = {Cazade, Pierre-André and Bereau, Tristan and Meuwly, Markus},
	year         = 2014,
	journal      = jpcb,
	volume       = 118,
	number       = 28,
	pages        = {8135--8147}
}
@article{Suydam.halr.sci.2006,
	title        = {Electric Fields at the Active Site of an Enzyme : Direct Comparison of Experiment with Theory.},
	author       = {Suydam, I. T. and Snow, C. D. and Pande, V. S. and Boxer, S. G.},
	year         = 2006,
	journal      = sci,
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@article{cho:2011,
	title        = {{Azido Homoalanine is a Useful Infrared Probe for Monitoring Local Electrostatistics and Side-Chain Solvation in Proteins}},
	author       = {Choi, Jun-Ho and Raleigh, Daniel and Cho, Minhaeng},
	year         = {{2011}},
	journal      = jpcl,
	volume       = {{2}},
	number       = {{17}},
	pages        = {{2158--2162}}
}
@article{hynes:2004,
	title        = {{Hydrogen Bond Dynamics in Water and Ultrafast Infrared Spectroscopy: A Theoretical Study}},
	author       = {Moller, KB and Rey, R and Hynes, JT},
	year         = {{2004}},
	journal      = jpca,
	volume       = {{108}},
	number       = {{7}},
	pages        = {{1275--1289}}
}
@article{Hynes1998,
	title        = {{Vibrational Phase and Energy Relaxation of CN$^-$ in water}},
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	year         = 1998,
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	pages        = {142--153}
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@article{zanni2001,
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	year         = 2001,
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﻿
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