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

Abstract

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 () is developed and released to interface with the Gaussian 16 quantum chemistry software package to perform this calculation.

Electrocatalytic water oxidation of coral-like porous Zn-CoP nanohybrids synergistically inspired by photothermal and photoelectronic effects

“…65 The unrestricted spin is set in all calculations because the Co atom is an open-shell element. 66 The core electrons of the metal atoms were treated using the effective core potentials (ECP), [67][68][69] and the orbital cutoff was 4.5 Å for all atoms. For the geometry optimization, the convergences of the energy, maximum force, and maximum displacement were set as 1 × 10 −5 Ha, 2 × 10 −3 Ha Å −1 , and 5 × 10 −3 Å, and the SCF convergence for each electronic energy was set as 1.0 × 10 −6 Ha.…”

Unravelling the 6sp ← 6s absorption spectra of Bi(iii) complexes

“…The limitations of TDDFT-SOC calculations for the calculation of excited states of heavy atoms have also been recently pointed out, as the perturbative SOC coupling treatment is not appropriate if its magnitude is comparable to the excited state energy gap. 22 In this work, we sought to investigate the absorption spectra of a series of small Bi(III) complexes (Scheme 1), using both TDDFT calculations and wave function approaches. Thus, we investigated the octahedral [BiCl 6 ] 3− complex as a model system, and compared its absorption spectrum with that of the square pyramidal [BiCl 5 ] 2− complex.…”

“…The limitations of TDDFT-SOC calculations for the calculation of excited states of heavy atoms have also been recently pointed out, as the perturbative SOC coupling treatment is not appropriate if its magnitude is comparable to the excited state energy gap. 22…”

Comparison of Variational and Perturbative Spin–Orbit Coupling within Two-Component CASSCF

“…Perturbation theory is the most popular approach to address SOC. − This method starts by variationally obtaining a set of zeroth-order states in the absence of SOC and subsequently introducing SOC via first-order perturbation theory. This is also known as a state interaction.…”