# Gradients not needed: ML-driven propagation of nonadiabatic molecular dynamics without reference gradients

## TL;DR

This paper introduces a machine learning method that allows nonadiabatic molecular dynamics simulations without needing analytical energy gradients, enabling more accurate and efficient simulations of complex chemical reactions.

## Contribution

The novel contribution is enabling gradient-free nonadiabatic molecular dynamics using ML, eliminating the need for analytical gradients from electronic structure methods.

## Key findings

- Gradient-free ML potentials accurately reproduce NAMD populations and dynamics across multiple levels of theory.
- The method enables dynamics simulations at the QD-NEVPT2 level, where analytical gradients are unavailable.
- Fully dimensional simulations of trans-azobenzene photoisomerization are achieved at high-level excited-state methods.

## Abstract

The recent development of machine learning (ML) methods for quantum chemistry has tremendously boosted the efficiency of molecular calculations. In this work, we use ML to enable nonadiabatic molecular dynamics (NAMD) simulations without access to the analytical energy gradients from the underlying target electronic structure method. By fine-tuning our foundational model for excited states, OMNI-P2x, on energies alone and leveraging automatic differentiability to obtain forces, we eliminate the gradient computation bottleneck that restricts calculations, such as NAMD, to methods with available analytical derivatives. First, we validate the method on the benchmark system, fulvene, demonstrating that gradient-free ML potentials accurately reproduce NAMD populations and dynamics across multiple levels of theory: AIQM1/MRCI, CASSCF, and MRSF-TDDFT. This enables, for the first time, performing dynamics at the QD-NEVPT2 level, where analytical gradients remain unavailable. We further benchmark the protocol on cyclohexadiene photoinduced ring-opening, where gradient-free training on XMS-CASPT2 energies reproduces reference dynamics with high accuracy, and compare them to QD-NEVPT2 results. Finally, we apply the approach to trans-azobenzene, a prototypical molecular photoswitch, by performing fully dimensional simulations of its photoisomerization dynamics at the CASSCF and QD-NEVPT2 levels, establishing the highest-level excited-state simulations of this photoreaction to date.

ML enables nonadiabatic molecular dynamics simulations without access to the analytical energy gradients from the underlying target electronic structure method.