Comparing the accuracy of perturbative and variational calculations for predicting fundamental vibrational frequencies of dihalomethanes

Abstract

Three dihalogenated methane derivatives (CHF, CHFCl, and CHCl) were used as model systems to compare and assess the accuracy of two different approaches for predicting observed fundamental frequencies: canonical operator Van Vleck vibrational perturbation theory (CVPT) and vibrational configuration interaction (VCI). For convenience and consistency, both methods employ the Watson Hamiltonian in rectilinear normal coordinates, expanding the potential energy surface (PES) as a Taylor series about equilibrium and constructing the wavefunction from a harmonic oscillator product basis. At the highest levels of theory considered here, fourth-order CVPT and VCI in a harmonic oscillator basis with up to 10 quanta of vibrational excitation in conjunction with a 4-mode representation sextic force field (SFF-4MR) computed at MP2/cc-pVTZ with replacement CCSD(T)/aug-cc-pVQZ harmonic force constants, the agreement between computed fundamentals is closer to 0.3 cm on average, with a maximum difference of 1.7 cm. The major remaining accuracy-limiting factors are the accuracy of the underlying electronic structure model, followed by the incompleteness of the PES expansion. Nonetheless, computed and experimental fundamentals agree to within 5 cm, with an average difference of 2 cm, confirming the utility and accuracy of both theoretical models. One exception to this rule is the formally IR-inactive but weakly allowed through Coriolis-coupling H-C-H out-of-plane twisting mode of dichloromethane, whose spectrum we therefore revisit and reassign. We also investigate convergence with respect to order of CVPT, VCI excitation level, and order of PES expansion, concluding that premature truncation substantially decreases accuracy, although VCI(6)/SFF-4MR results are still of acceptable accuracy, and some error cancellation is observed with CVPT2 using a quartic force field.

Fundamental studies of vibrational resonance phenomena by multivalued resummation of the divergent Rayleigh–Schrödinger perturbation theory series: deciphering polyad structures of three H216O isotopologues

“…The CVPT2/VCI(4) calculations in the numerical–analytic form were performed using the ANCO program 61,127 using essentially the same techniques as in our previous studies. 128–130 The obtained values of fundamental frequencies demonstrated sufficiently good agreement with the observed vibration–rotation band centers of about 0.1% (see Table 1). The residual errors of the calculation are within non-accounted typical fine quantum-mechanical electronic effects.…”

Accuracy and Interpretability: The Devil and the Holy Grail. New Routes across Old Boundaries in Computational Spectroscopy

“…Here, we focus on second-order vibrational perturbation theory (VPT2), the popularity of which derives from the significant improvement it offers over the harmonic approximation at a reasonable overall computational cost. Higher orders have been investigated, ,− but the increased cost is not justified by the marginal accuracy gain. As it is well-known, the PT2 expressions areat least in one dimensionexact for a Morse oscillator, and therefore certainly not correct for the incomplete quartic polynomial development, which, as mentioned above, is the most practical representation of the PES for medium- to large-sized molecules.…”

Novel methodology for systematically constructing global effective models from ab initio-based surfaces: A new insight into high-resolution molecular spectra analysis

“…This matrix is diagonalized for each block (J, C) for some low-J values (see Section IV) and the corresponding variational eigenpairs are stored. As already mentioned in Introduction, a large number of theoretical developments and associated computer codes based on sophisticated algorithms [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] are now able to perform accurate variational calculations, even for molecules with more than 10 atoms.…”

“…Variational calculations. The variational approach (VA) based on the use of ab initio potential energy surfaces (PES) is now very common for computing a consistent set of eigenvalues and associated wavefunctions, even for high energies [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] . As stated by Carter and…”