Relativistic Four-Component DFT Calculations of Vibrational Frequencies.

Katarzyna Jakubowska,Magdalena Pecul,Kenneth Ruud

doi:10.1021/acs.jpca.1c07398

Katarzyna Jakubowska, Magdalena Pecul + Show 1 more

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https://doi.org/10.1021/acs.jpca.1c07398

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Abstract

We investigate the effect of relativity on harmonic vibrational frequencies. Density functional theory (DFT) calculations using the four-component Dirac–Coulomb Hamiltonian have been performed for 15 hydrides (H2X, X = O, S, Se, Te, Po; XH3, X = N, P, As, Sb, Bi; and XH4, X = C, Si, Ge, Sn, Pb) as well as for HC≡CPbH3. The vibrational frequencies have been calculated using finite differences of the molecular energy with respect to geometrical distortions of the nuclei. The influences of the choice of basis set, exchange–correlation functional, and step length for the numerical differentiation on the calculated harmonic vibrational frequencies have been tested, and the method has been found to be numerically robust. Relativistic effects are noticeable for the heavier congeners H2Te and H2Po, SbH3 and BiH3, and SnH4 and PbH4 and are much more pronounced for the vibrational modes with higher frequencies. Spin–orbit effects constitute a very small fraction of the total relativistic effects, except for H2Te and H2Po. For HC≡CPbH3 we find that only the frequencies of the modes with large contributions from Pb displacements are significantly affected by relativity.

Highlights

IntroductionRelativistic effects are commonly separated into scalar relativistic effects, which are due to (among other contributions) the mass−velocity and Darwin corrections, and the effects due to the spin−orbit interaction
For molecules containing heavy atoms, relativistic effects play a crucial role in their electronic structure and chemical bonding.[1]Relativistic effects are commonly separated into scalar relativistic effects, which are due to the mass−velocity and Darwin corrections, and the effects due to the spin−orbit interaction
In most cases where potential energy surfaces are concerned, it is sufficient to account for scalar relativistic effects using for example effective core potentials,[2] but for systems where strong spin−orbit effects may be expected, it is important to have an apparatus to calculate total relativistic effects using the four-component Dirac−Coulomb

Summary

Introduction

Relativistic effects are commonly separated into scalar relativistic effects, which are due to (among other contributions) the mass−velocity and Darwin corrections, and the effects due to the spin−orbit interaction The former lead for instance to contraction of the inner-shell orbitals (the energies of core levels are lower than those for the nonrelativistic case), and the latter result in the spin−orbit splitting of molecular orbital energy levels. The contraction of the inner-shell orbitals in turn increases the screening of the nuclear charge for the outer-shell electrons, giving rise to an indirect effect that results in expansion of the valence orbitals. These relativistic effects affect the valence orbitals involved with chemical bonding and the potential energy surfaces.[1]. In most cases where potential energy surfaces are concerned, it is sufficient to account for scalar relativistic effects using for example effective core potentials,[2] but for systems where strong spin−orbit effects may be expected, it is important to have an apparatus to calculate total relativistic effects using the four-component Dirac−Coulomb (or Dirac−Coulomb−Breit)

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