Local Enhancement of Dynamic Correlation in Excited States: Fresh Perspective on Ionicity and Development of Correlation Density Functional Approximation Based on the On-Top Pair Density.

Michał Hapka,Oleg V Gritsenko,Katarzyna Pernal

doi:10.1021/acs.jpclett.0c01616

Michał Hapka, Oleg V Gritsenko + Show 1 more

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https://doi.org/10.1021/acs.jpclett.0c01616

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Abstract

We discuss the interplay between the nondynamic and dynamic electron correlation in excited states from the perspective of the suppression of dynamic correlation (SDC) and enhancement of dynamic correlation (EDC) effects. We reveal that there exists a connection between the ionic character of a wave function and EDC. Following this finding we introduce a quantitative measure of ionicity based solely on local functions without referring to valence bond models. The ability to recognize both the SDC and EDC regions underlies the presented method, named CASΠDFT, combining complete active space (CAS) wave function and density functional theory (DFT) via the on-top pair density (Π) function. We extend this approach to excited states by devising an improved representation of the EDC effect in the correlation functional. The generalized CASΠDFT uses different DFT functionals for ground and excited states. Numerical demonstration for singlet π → π* excitations shows that CASΠDFT offers satisfactory accuracy at a fraction of the cost of the ab initio approaches.

Highlights

We discuss the interplay between the nondynamic and dynamic electron correlation in excited states from the perspective of the suppression of dynamic correlation (SDC) and enhancement of dynamic correlation (EDC) effects
Excited states of a singlet multiplicity pose a particular challenge to both ab initio and density functional theory (DFT) methods because of their multireference character and the related diverse electronic structure.[1−3] In π-conjugated systems it is customary to use the classification into states of a covalent and ionic character which originates from the valence bond theory (VB) description.[4]
The complete active space (CAS) excitation energy obtained as a difference between excited-state and ground-state self-consistent CAS (CASSCF) energies is impaired with the serious neglect of dynamic correlation

Summary

CAS molecule state

Where the indices 0 and i correspond to a ground state and an excited state of interest, respectively Note that setting both P[X] correction functions to 1 reduces eq 10 to evaluation of the excitation energy based on a simple addition of LYP correlation to the CASSCF energy, which we term the CAS +LYP method. Another achievement of this work is the introduction of the quantitative index of the wave function ionicity While both the EDC-derived measure of ionicity and its counterpart based on the VB theory agree, the former identifies states as “ionic” only from the relative importance of the fundamental effects of suppressed and enhanced dynamic correlation. Derivation of the XCAS(r) ratio; details on the effective projection on the CAS(4,4) wave function; additional results including ionicity index values obtained with LYP and PBE correlation functionals, as well as total CASSCF, CAS+LYP, and CASΠDFT electronic energies (PDF)

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