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Methods for computing spin-orbit coupling properties (SPOCK and SPOILER)

Many light-induced molecular processes involve a change in spin state and are formally forbidden in non-relativistic quantum theory. Over the past years, efficient quantum chemical methods for studying spin-forbidden transitions and other spin-dependent properties of large molecules have been developed in our laboratory. (Marian-2012, Penfold-2018)

The Spin–Orbit Coupling Kit (SPOCK) computes electronic spin–orbit interaction matrix elements of multi-reference configuration interaction and first-order perturbed wave functions. (For a benchmark see here.) SPOCK generates spin–mixed multi-reference configuration interaction wave functions either by means of quasi-degenerate perturbation theory (QDPT) or variationally in a multi-reference spin–orbit configuration interaction (MRSOCI) procedure. It has been used extensively to determine coupling matrix elements for intersystem crossing (ISC), phosphorescence lifetimes, fine-structure splittings, g-tensors, and other spin-dependent properties of molecules ranging from small organic molecules to large transition metal complexes. For the efficient evaluation of spin-orbit mean-field integrals, the Atomic Mean-Field Integral (AMFI) code is employed. For heavy-element compounds that serve, for example, as phosphorescent dyes in organic light-emitting diodes (OLEDs) or as building blocks of spin crossover materials for information storage, spin–orbit integrals employing effective core potentials (ECPs) are available instead.

Interstate spin–orbit couplings from amplitudes of full linear response time-dependent density functional theory (TDDFT) and response calculations in Tamm−Dancoff approximation (TDA) can be evaluated with the newly developed the Spin−Orbit Interaction LinEar Response (SPOILER) program. It turns out that the TDDFT spin–orbit matrix elements are rather insensitive with regard to the choice of eigenvectors (left, right, or mixed) of Casida’s equations as long as the auxiliary many-electron wave functions are normalized.

Early-stage researchers who want to join our team on method development in the realm of relativistic quantum chemistry should contact Prof. Christel Marian or Dr. Martin Kleinschmidt.