State Interaction Linear Response Time-Dependent Density Functional Theory with Perturbative Spin–Orbit Coupling: Benchmark and Perspectives

Spin–orbit coupling (SOC) is an important driving
force
in photochemistry. In this work, we develop a perturbative spin–orbit
coupling method within the linear response time-dependent density
function theory framework (TDDFT-SO). A full state interaction scheme,
including singlet–triplet and triplet–triplet coupling,
is introduced to describe not only the coupling between the ground
and excited states, but also between excited states with all couplings
between spin microstates. In addition, expressions to compute spectral
oscillator strengths are presented. Scalar relativity is included
variationally using the second-order Douglas-Kroll-Hess Hamiltonian,
and the TDDFT-SO method is validated against variational SOC relativistic
methods for atomic, diatomic, and transition metal complexes to determine
the range of applicability and potential limitations. To demonstrate
the robustness of TDDFT-SO for large-scale chemical systems, the UV–Vis
spectrum of Au25(SR)18– is computed and compared to experiment.
Perspectives on the limitation, accuracy, and capability of perturbative
TDDFT-SO are presented via analyses of benchmark calculations. Additionally,
an open-source Python software package (PyTDDFT-SO) is developed and released to interface with the Gaussian 16 quantum
chemistry software package to perform this calculation.