SURFXsim: Free-Energy Simulations of Spin-Forbidden Events with a Spin-Gap Collective Variable

Abstract

Spin-forbidden processes are central to catalysis, photochemistry, and transition-metal reactivity, yet their simulation remains challenging because the relevant transformations proceed between potential energy surfaces of different spin multiplicities and are frequently thermally activated rare events. Existing computational strategies typically provide either static descriptions of crossing regions, such as minimum-energy crossing point searches, or dynamically explicit but computationally demanding nonadiabatic simulations that are difficult to apply to medium- and large-sized systems. Here, we present SURFXsim, a computational framework for simulating spin-forbidden events by combining atomistic molecular dynamics, a configuration-dependent mixed Hamiltonian, and enhanced sampling along a spin-gap collective variable. The method should be understood as a finite-temperature sampling and interpolation strategy, rather than as a direct simulation of coherent spin–orbit-coupled electronic-state dynamics. It enables smooth propagation between end-state basins while using metadynamics to drive the exploration of crossing regions and reconstruct free-energy landscapes. SURFXsim is implemented in Python on top of ASE and interfaced with PLUMED, allowing the use of both machine-learning and conventional electronic-structure calculators. We illustrate the approach with distortion-driven and reactivity-driven spin-crossing examples using machine learning potentials and further demonstrate compatibility with a quantum-mechanical backend through the Gaussian package. Together, these results position SURFXsim as a practical and flexible route for studying spin-forbidden chemistry beyond the scale routinely accessible to fully nonadiabatic dynamics.