Abstract
Nuclear vibrational theories based upon the Watson Hamiltonian are ubiquitous in quantum chemistry, but are generally unable to model systems in which the wavefunction can delocalise over multiple energy minima, i.e. molecules that have low-energy torsion and inversion barriers. In a 2019 Chemical Reviews article, Puzzarini et al. note that a common workaround is to simply decouple these problematic modes from all other vibrations in the system during anharmonic frequency calculations. They also point out that this approximation can be "ill-suited", but do not quantify the errors introduced. In this work, we present the first systematic investigation into how separating out or constraining torsion and inversion vibrations within potential energy surface (PES) expansions affects the accuracy of computed fundamental wavenumbers for the remaining vibrational modes, using a test set of 19 tetratomic molecules for which high quality analytic potential energy surfaces and fully-coupled anharmonic reference fundamental frequencies are available. We find that the most effective and efficient strategy is to remove the mode in question from the PES expansion entirely. This introduces errors of up to +10 cm-1 in stretching fundamentals that would otherwise couple to the dropped mode, and ±5 cm-1 in all other fundamentals. These errors are approximately commensurate with, but not necessarily additional to, errors due to the choice of electronic structure model used in constructing spectroscopically accurate PES.
Highlights
Harmonic normal mode analysis and scaled harmonic frequencies continue to enjoy great popularity in assisting the assignment of vibrational infrared and Raman spectra,[1] but can fail to accurately model anharmonically coupled systems, e.g. the OH stretching spectrum of carboxylic acid dimers.[2]
Nuclear vibrational theories based upon the Watson Hamiltonian are ubiquitous in quantum chemistry, but are generally unable to model systems in which the wavefunction can delocalise over multiple energy minima, i.e. molecules that have low-energy torsion and inversion barriers
We present the first systematic investigation into how separating out or constraining torsion and inversion vibrations within potential energy surface (PES) expansions affects the accuracy of computed fundamental wavenumbers for the remaining vibrational modes, using a test set of 19 tetratomic molecules for which high quality analytic potential energy surfaces and fully-coupled anharmonic reference fundamental frequencies are available
Summary
Harmonic normal mode analysis and scaled harmonic frequencies continue to enjoy great popularity in assisting the assignment of vibrational infrared and Raman spectra,[1] but can fail to accurately model anharmonically coupled systems, e.g. the OH stretching spectrum of carboxylic acid dimers.[2]. If the large-amplitude vibration itself is of interest, one needs to account for its curvilinear nature using more sophisticated models.[7] In some special cases, the Watson Hamiltonian is still suitable if the potential energy surface (PES) and wavefunction can be expanded about a saddle point connecting two symmetric minima This approach has been used to compute tunnelling splittings for the inversion modes of H3O+ and NH3,8,9 but cannot be extended to other types of motions, such as torsions.[9]. Informed by the tetratomic benchmarking results, we will construct Watson Hamiltonian models in which the computational sources of error are carefully controlled, and assess their accuracy against high-resolution experimental data for a series of pentatomic and hexatomic molecules, including the textbook example methanol
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