# Theoretical Study of Vibrationally Averaged Dipole Moments for the Ground and Excited CO Stretching States of *trans*-Formic Acid

journal contribution

posted on 09.03.2010, 00:00 by Leif O. Paulson, Jakub Kaminský, David T. Anderson, Petr Bouř, Jan KubelkaRecent experimental studies of

*trans-*formic acid (FA) in solid para-hydrogen (pH_{2}) highlighted the importance of vibrationally averaged dipole moments for the interpretation of the high-resolution infrared (IR) spectra, in particular for the CO stretch (ν_{3}) mode. In this report, dipole moments for the ν_{3}ground (*v*= 0) and excited (*v*= 1, 2, 3, and 4) anharmonic vibrational states in*trans*-FA are investigated using two different approaches: a single mode approximation, where the vibrational states are obtained from the solution of the one-dimensional Schrödinger equation for the harmonic normal coordinate, and a limited vibrational configuration interaction (VCI) approximation. Density functional theory (B3LYP, BPW91) and correlated ab initio (MP2 and CCSD(T)) electronic methods were employed with a number of double- and triple-ζ and correlation consistent basis sets. Both single mode and VCI approaches show comparable agreement with experimental data, which is more dependent on the level of theory used. In particular, the BPW91/cc-pVDZ level appears to perform remarkably well. Effects of solvation of FA in solid state Ar and pH_{2}matrices were simulated at the BPW91/cc-pVDZ level using a conductor-like polarized continuum model (CPCM). The Ar and pH_{2}solid-state matrices cause quite a substantial increase in the FA dipole moments. Compared to gas-phase calculations, the CPCM model for pH_{2}better reproduces the experimental FA spectral shifts caused by interaction with traces of ortho-hydrogen (oH_{2}) species in solid pH_{2}. The validity of the single mode approach is tested against the multidimensional VCI results, suggesting that the isolated (noninteracting) mode approximation is valid up to the third vibrationally excited state (*v*= 3). Finally, the contribution of the ground anharmonic vibrational states of the remaining modes to the resulting ν_{3}single mode dipole moments is examined and discussed.