Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations

Grotjahn, Robin; Furche, Filipp; Kaupp, Martin

doi:10.1063/5.0113083

Title: Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations

Journal Article · Fri Sep 16 00:00:00 UTC 2022 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/5.0113083 · OSTI ID:2282592

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Technische Universität Berlin (Germany); University of California, Irvine, CA (United States); University of California, Irvine
University of California, Irvine, CA (United States)
Technische Universität Berlin (Germany)

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange–correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π→π$$^{*}_{⊥}$$ excitations are heavily gauge-dependent with average changes of –0.17 and –0.28 eV, respectively, while π→π$$^{*}_{∥}$$ excitations are marginally affected (–0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. Here, the results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.

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Research Organization:: University of California, Irvine, CA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0018352

OSTI ID:: 2282592

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 11 Vol. 157; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Title: Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations

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