  The present work shows that the free energy landscape associated with alanine
dipeptide isomerization can be effectively represented by specific interatomic
distances without explicit reference to dihedral angles. Conventionally, two
stable states of alanine dipeptide in vacuum, i.e., C$7_{\mathrm{eq}}$
($\beta$-sheet structure) and C$7_{\mathrm{ax}}$ (left handed $\alpha$-helix
structure), have been primarily characterized using the main chain dihedral
angles, $\varphi$ (C-N-C$_\alpha$-C) and $\psi$ (N-C$_\alpha$-C-N). However,
our recent deep learning combined with "Explainable AI" (XAI) framework has
shown that the transition state can be adequately captured by a free energy
landscape using $\varphi$ and $\theta$ (O-C-N-C$_\alpha$) [T. Kikutsuji, et al.
J. Chem. Phys. 156, 154108 (2022)]. In perspective of extending these insights
to other collective variables, a more detailed characterization of transition
state is required. In this work, we employ the interatomic distances and bond
angles as input variables for deep learning, rather than the conventional and
more elaborate dihedral angles. Our approach utilizes deep learning to
investigate whether changes in the main chain dihedral angle can be expressed
in terms of interatomic distances and bond angles. Furthermore, by
incorporating XAI into our predictive analysis, we quantified the importance of
each input variable and succeeded in clarifying the specific interatomic
distance that affects the transition state. The results indicate that
constructing a free energy landscape based on using the identified interatomic
distance can clearly distinguish between the two stable states and provide a
comprehensive explanation for the energy barrier crossing.
