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Effective harmonic oscillator description of anharmonic molecular vibrations
The validity of an effective harmonic oscillator approximation for anharmonic molecular vibrations is tested and compared with vibrational self consistent field and vibrational configurational interaction results. The effective harmonic oscillator is constructed variationally, by taking the trial wave function as a harmonic oscillator eigenfunction with the centroid and width parameter as variational paraeters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar to the vibrational self consistent field results. Coriolis coupling is also included in these studies.
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A comparative study of independent particle model based approaches for thermal averages
A comparative study is done on thermal average calculation by using the state specific vibrational self-consistent field method (ss-VSCF), the virtual vibrational self-consistent field (v-VSCF) method and the thermal self-consistent field (t-SCF) method. The different thermodynamic properties and expectation values are calculated using these three methods and the results are compared with full configuration interaction method (FVCI). We find that among these three independent particle model based methods, the ss-VSCF method provides most accurate results in the thermal averages followed by t-SCF and the v-VSCF is the least accurate. However, the ss-VSCF is found to be computationally very expensive for the large molecules. The t-SCF gives better accuracy compared to the v-VSCF counterpart especially at higher temperatures.
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In this work, we present a systematic study on the effect of non-local Hartree-Fock (HF) exchange term of density functional methods on the vibrational description of polyatomic molecules. Working with three different functionals PBE0, B3LYP, and B2PLYP, we find that the standard deviations of errors with different amounts of HF exchange term in the functionals are well fitted with cubic polynomials. Sensitivity of the accuracy of vibrational frequencies with the HF exchange differs for different types of vibrations (e.g., high energy hydrogen stretching modes, stretching modes, bending modes, etc.). The wavenumbers decrease systematically with the increasing HF exchange in the functional as a result of the decrease in the geometric parameters at the equilibrium structures. The changes in harmonic wavenumbers are significant, and the anharmonic corrections are much less affected. The magnitudes of minimum errors with optimum values of the HF exchange terms differ from the default formulation.
The effect of non-local Hartree-Fock exchange term of DFT functionals on the vibrational description is assessed for PBE0, B3LYP, and B2PLYP. The sensitivity of the accuracy of harmonic and anharmonic vibrational frequencies with the HF exchange differs for different types of vibrations. The wavenumbers decrease systematically with the increasing HF exchange in the functional. The magnitudes of minimum errors with optimum values of the HF exchange terms differ from the default formulation.
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Journal of Chemical Sciences
Volume 135, 2023
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