How to VPT2: Accurate and Intuitive Simulations of CH Stretching Infrared Spectra Using VPT2+K with Large Effective Hamiltonian Resonance Treatments

Abstract

This article primarily discusses the utility of vibrational perturbation theory for the prediction of X–H stretching vibrations with particular focus on the specific variant, second-order vibrational perturbation theory with resonances (VPT2+K). It is written as a tutorial, reprinting most important formulas and providing numerous simple examples. It discusses the philosophy and practical considerations behind vibrational simulations with VPT2+K, including but not limited to computational method selection, cost-saving approximations, approaches to evaluating intensity, resonance identification, and effective Hamiltonian structure. Particular attention is given to resonance treatments, beginning with simple Fermi dyads and gradually progressing to arbitrarily large polyads that describe both Fermi and Darling–Dennison resonances. VPT2+K combined with large effective Hamiltonians is shown to be a reliable framework for modeling the complicated CH stretching spectra of alkenes. An error is also corrected in the published analytic formula for the VPT2 transition moment between the vibrational ground state and triply excited states.

Transfer learned potential energy surfaces: accurate anharmonic vibrational dynamics and dissociation energies for the formic acid monomer and dimer

“…It should be noted 25 that VPT2 calculations are known to have limitations for proton bound dimers. 98 This is also consistent with the present finding that the ZPEs of FAD from DMC simulations and VPT2 calculations using PES TL differ by 0.14 kcal/mol (50 cm −1 ) whereas that for FAM is virtually identical.…”

“…Paper PCCP 98 This is also consistent with the present finding that the ZPEs of FAD from DMC simulations and VPT2 calculations using PES TL differ by 0.14 kcal mol À1 (50 cm À1 ) whereas that for FAM is virtually identical. The shifts from finite-T MD simulations still suffer from the limitation that the anharmonicity of the OH stretch is not sufficiently sampled, irrespective of the level of theory at which the PES was determined.…”

CC-stretched formic acid: isomerisation, dimerisation, and carboxylic acid complexation

“…† If not further specified, symmetry and very tight optimisation thresholds are used, and in case of DFT calculations the integration grid is set to superfine. To enhance the quality and remove some deficiencies of the harmonic MP2 force field, 73 the Hessian is replaced by the corresponding harmonic CCSD(T)-F12a 74 force field which has been computed using Molpro version 2018.1. 75,76 For the DFT and MP2 calculations, Dunning's correlation consistent aug-cc-pVXZ (aVXZ) 77 and for CCSD(T)-F12a, explicitly correlated VXZ-F12 basis sets by Peterson et al 78 are used.…”

Accuracy and Reliability in the Simulation of Vibrational Spectra: A Comprehensive Benchmark of Energies and Intensities Issuing From Generalized Vibrational Perturbation Theory to Second Order (GVPT2)

“…More details on the derivations of the equations can be found in References. (Nielsen, 1951;Plíva, 1990;Willets et al, 1990;Vázquez and Stanton, 2006;Franke et al, 2021). For a similar reason, reference equations are recalled, but most of the concepts, especially regarding the problem of resonances, are introduced in a descriptive way, focusing on the physical concepts and implications.…”