Spin-vibronic dynamics in open-shell systems beyond the spin Hamiltonian formalism

TL;DR

This paper develops a numerical approach to simulate vibronic and spin-vibronic dynamics in open-shell molecular systems, surpassing traditional spin Hamiltonian models, and applies it to transition metal and lanthanide complexes.

Contribution

It introduces a new method combining multi-reference ab initio calculations with open quantum system dynamics to accurately model spin relaxation in complex molecules.

Findings

Validated approach on Co(II) and Dy(III) complexes

Revealed importance of electronic excited states in spin relaxation

Highlighted limitations of effective spin Hamiltonian models

Abstract

Vibronic coupling has a dramatic influence over a large number of molecular processes, ranging from photo-chemistry, to spin relaxation and electronic transport. The simulation of vibronic coupling with multi-reference wavefunction methods has been largely applied to organic compounds, and only early efforts are available for open-shell systems such as transition metal and lanthanide complexes. In this work, we derive a numerical strategy to differentiate the molecular electronic Hamiltonian in the context of multi-reference ab initio methods and inclusive of spin-orbit coupling effects. We then provide a formulation of open quantum system dynamics able to predict the time evolution of the electrons' density matrix under the influence of a Markovian phonon bath up to fourth-order perturbation theory. We apply our method to Co(II) and Dy(III) molecular complexes exhibiting long spin relaxation times and successfully validate our strategy against the use of an effective spin Hamiltonian. Our study shed light on the nature of vibronic coupling, the importance of electronic excited states in spin relaxation, and the need for high-level computational chemistry to quantify it.