Combining spin-adapted open-shell TD-DFT with spin–orbit coupling

Abstract

The recently proposed spin-adapted time-dependent density functional theory (S-TD-DFT) is extended to the relativistic domain for fine-structure splittings of excited states of open-shell systems. Scalar-relativistic effects are treated to infinite order via the spin-free (sf) part of the exact two-component (X2C) Hamiltonian, whereas the spin–orbit couplings (SOC) between the scalar-excited states are treated perturbatively via an effective one-electron spin–orbit operator derived from the same X2C Hamiltonian. The calculated results for prototypical open-shell systems containing heavy elements reveal that the composite approach sf-X2C-S-TD-DFT-SOC is very promising. The fine-structure splitting of a spatially degenerate ground state can also be described properly by taking a non-degenerate excited state as the reference.

Keywords:

• spin-adapted TD-DFT
• spin-free X2C
• spin–orbit coupling
• fine structure
• open-shell systems

Acknowledgements

The research of this work was supported by grants from the National Natural Science Foundation of China (Project Nos. 21033001, 21273011, 21290190 and 21173006).

Notes

^aA set of diffuse spd Slater functions was further augmented to the basis sets used in [9].

^bRef. [9].

^cRef. [13].

^dRef. [46].

^aRef. [47].

^bRef. [46].

^a Ref. [47].

^b Ref. [48].

^c Ref. [46].

^a SOC-EOMEA-CCSD [48].

^b SOC-EOMIP-CCSD [47].

^c Ref. [49].

^d Ref. [46].

^a Ref. [48].

^b Ref. [51]. 13eT: triple corrections for the 13 valence electrons.

^c Ref. [52].

^d Ref. [50].

^a Ref. [48].

^b Ref. [53].

^a Ref. [47].

^b Ref. [52].

^c Ref. [52]. The Gaunt contribution was estimated at the mean-field level.

^d Ref. [54].