Derivation of spin-orbit couplings in collinear linear-response TDDFT: A rigorous formulation

Abstract

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Using an approach based upon a set of auxiliary many-electron wavefunctions we present a rigorous derivation of spin-orbit coupling (SOC) within the framework of linear-response time-dependent density functional theory (LR-TDDFT). Our method is based on a perturbative correction of the nonrelativistic collinear TDDFT equations using a Breit-Pauli spin-orbit Hamiltonian. The derivation, which is performed within both the Casida and Sternheimer formulations of LR-TDDFT, is valid for any basis set. The requirement of spin noncollinearity for the treatment of spin-flip transitions is also discussed and a possible alternative solution for the description of these transitions in the collinear case is also proposed. Our results are validated by computing the SOC matrix elements between singlet and triplet states of two molecules, formaldehyde and acetone. In both cases, we find excellent agreement with benchmark calculations performed with a high level correlated wavefunction method.

A general method to describe intersystem crossing dynamics in trajectory surface hopping

“…Other promising electronic structure methods are, for example, the approximately size-consistent MRCI variant linear-response-theory multireference average-quadratic coupled-cluster (LRT-MRAQCC) [177] or density matrix normalization group (DMRG) approaches. [195] Furthermore, it will be possible to employ time-dependent density functional theory (TDDFT) in ISC dynamics studies with the help of recent developments, [161,162] although care has to be taken that the excited-state potential energy surfaces are described correctly in the case of strongly multiconfigurational state character.…”

“…[160] Surface-hopping using these states has been adopted in several cases, either assuming a constant value for the SOC matrix elements [100,101] or with geometry-dependent SOC. [107,109,161,162] Finally, the most advanced schemes to describe ISC employ a diagonalization of the electronic Hamiltonian including SOC, and basically conduct Tully's surface hopping using the obtained eigenstates. Because the full electronic Hamiltonian is diagonal in the basis of these states, here we label it the "diagonal" basis (also called "spin-adiabatic" elsewhere [160] ).…”

Surface Hopping Dynamics with DFT Excited States

“…In [85], H SO is approximated by the one-electron Breit-Pauli operator [86]. The computation of the two-electron operator is discussed by Chiodo and Russo in [87,88].…”

“…Recently, spin-orbit coupling elements [85] were also derived based on the Casida wavefunctions, opening the possibility of performing surface hopping between surfaces with different multiplicities within the TDDFT approach. The coupling between singlet and triplet states, for instance, is given by…”

Quantum modeling of ultrafast photoinduced charge separation

“…the derivation of spin-orbit couplings (SOC) within TDDFT and their combination with TSH dynamics for the investigation of inter-system crossing events [256,257].…”