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

[Image: see text] 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 Au(25)(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.