Anharmonic Rovibrational Partition Functions for Fluxional Species at High Temperatures via Monte Carlo Phase Space Integrals

Abstract

Monte Carlo phase space integration (MCPSI) is used to compute full dimensional and fully anharmonic, but classical, rovibrational partition functions for 22 small- and medium-sized molecules and radicals. Several of the species considered here feature multiple minima and low-frequency nonlocal motions, and efficiently sampling these systems is facilitated using curvilinear (stretch, bend, and torsion) coordinates. The curvilinear coordinate MCPSI method is demonstrated to be applicable to the treatment of fluxional species with complex rovibrational structures and as many as 21 fully coupled rovibrational degrees of freedom. Trends in the computed anharmonicity corrections are discussed. For many systems, rovibrational anharmonicities at elevated temperatures are shown to vary consistently with the number of degrees of freedom and with temperature once rovibrational coupling and torsional anharmonicity are accounted for. Larger corrections are found for systems with complex vibrational structures, such as systems with multiple large-amplitude modes and/or multiple minima.

Popular Integration Grids Can Result in Large Errors in DFT-Computed Free Energies

“…To this end, the quasi-harmonic and quasi-RRHO approximations [51][52] reduce, but do not eliminate, these grid errors. At the same time, despite continued advances in more rigorous treatments of the entropic contributions of low-frequency vibrational modes, [61][62] such approaches are still impractical for the organic and organometallic systems most often subject to DFT computations. Baik et al 11 recently warned of the unphysical contributions of low frequency vibrational modes to the free energies in organometallic systems, showing that rotations of a Cp ring in a Rh-complex can lead to variations of nearly 2 kcal mol -1 in the free energy.…”

Anharmonic kinetics of the cyclopentane reaction with hydroxyl radical

“…Although the quasiharmonic approximation is not expected to provide a good account of low-frequency anharmonicity at high temperatures, it is expected that some of the vibrational anharmonicity may cancel out in the rate constant calculation. Recently, Jasper et al 73 estimated a correction factor for anharmonicity by classical Monte Carlo phase space integrals. They estimated, based on these integrals, that when torsional effects are separately estimated (as was done in the present work), the cumulative effect of the remaining vibrational anharmonicity on the partition functions can be estimated as 1.03 n vib at 2500 K (and less at lower temperatures) where n vib is the number of vibrational modes.…”

“…Although the quasiharmonic approximation is not expected to provide a good account of lowfrequency anharmonicity at high temperatures, it is expected that some of the vibrational anharmonicity may cancel out in the rate constant calculation. Recently, Jasper et al 73 estimated a correction factor for anharmonicity by classical Monte Carlo phase space integrals. They estimated, based on these integrals, that Fig.…”

Popular Integration Grids Can Result in Large Errors in DFT-Computed Free Energies

“…To this end, the quasi-harmonic and quasi-RRHO approximations [49][50] reduce, but do not eliminate, these grid errors. At the same time, despite continued advances in more rigorous treatments of the entropic contributions of low-frequency vibrational modes, [61][62] such approaches are still impractical for the organic and organometallic systems most often subject to DFT computations. Baik et al 63 recently warned of the unphysical contributions of low frequency vibrational modes to the free energies in organometallic systems, showing that rotations of a Cp ring in a Rh-complex can lead to variations of nearly 2 kcal mol -1 in the free energy.…”