Spin-orbit couplings within spin-conserving and spin-flipping time-dependent density functional theory: Implementation and benchmark calculations

We present a new implementation for computing spin-orbit couplings (SOCs) within a time-dependent density-functional theory (TD-DFT) framework in the standard spin-conserving formulation as well in the spin-flip variant (SF-TD-DFT). This approach employs the Breit-Pauli Hamiltonian and Wigner-Eckart's theorem applied to the reduced one-particle transition density matrices, together with the spin-orbit mean-field treatment of the two-electron contributions. We use a state-interaction procedure and compute the SOC matrix elements using zero-order non-relativistic states. Benchmark calculations using several closed-shell organic molecules, diradicals, and a single-molecule magnet illustrate the efficiency of the SOC protocol. The results for organic molecules (described by standard TD-DFT) show that SOCs are insensitive to the choice of the functional or basis sets, as long as the states of the same characters are compared. In contrast, the SF-TD-DFT results for small diradicals (CH2, NH2+, SiH2, and PH2+) show strong functional dependence. The spin-reversal energy barrier in a Fe(III) single-molecule magnet computed using non-collinear SF-TD-DFT (PBE0, omega PBEh/cc-pVDZ) agrees well with the experimental estimate.

Automated summary

In this study, we propose a new method for computing spin-orbit couplings (SOCs) within a time-dependent density-functional theory (TD-DFT) framework. We use the Breit-Pauli Hamiltonian and Wigner-Eckart's theorem to calculate the SOC matrix elements. Benchmark calculations on organic molecules, diradicals, and a single-molecule magnet demonstrate the efficiency of our approach. Furthermore, the results indicate that the SOC is insensitive to the choice of functional or basis sets for organic molecules with states of the same characters, while it shows strong functional dependence for specific small diradical systems.