  The extent of contact and solvent shared ion pairs of phosphate groups with
Na$^+$, Ca$^{2+}$ and Mg$^{2+}$ ions in aqueous environment and their relevance
for the stability of polyanionic DNA and RNA structures is highly debated.
Employing the asymmetric phosphate stretching vibration of dimethyl phosphate
(DMP), a model system of the sugar-phosphate backbone of DNA and RNA, we
present linear infrared, femtosecond infrared pump-probe and absorptive 2D-IR
spectra that report on contact ion pair formation via the presence of blue
shifted spectral signatures. Compared to the linear infrared spectra, the
nonlinear spectra reveal contact ion pairs with increased sensitivity because
the spectra accentuate differences in peak frequency, transition dipole moment
strength, and excited state lifetime. The experimental results are corroborated
by long time scale MD simulations, benchmarked by density functional
simulations on phosphate-ion-water clusters. The microscopic interpretation
reveals subtle structural differences of ion pairs formed by the phosphate
group and the ions Na$^+$, Ca$^{2+}$ and Mg$^{2+}$. Intricate properties of the
solvation shell around the phosphate group and the ion are essential to explain
the experimental observations. The present work addresses a challenging to
probe topic with the help of a model system and establishes new experimental
data of contact ion pair formation, thereby underlining the potential of
nonlinear 2D-IR spectroscopy as an analytical probe of phosphate-ion
interactions in complex biological systems.
