Machine Learning-Assisted Excited State Molecular Dynamics with the State-Interaction State-Averaged Spin-Restricted Ensemble-Referenced Kohn–Sham Approach

We present a machine learning-assisted
excited state molecular
dynamics (ML-ESMD) based on the ensemble density functional theory
framework. Since we represent a diabatic Hamiltonian in terms of generalized
valence bond ansatz within the state-interaction state-averaged spin-restricted
ensemble-referenced Kohn–Sham (SI-SA-REKS) method, we can avoid
singularities near conical intersections, which are crucial in excited
state molecular dynamics simulations. We train the diabatic Hamiltonian
elements and their analytical gradients with the SchNet architecture
to construct machine learning models, while the phase freedom of off-diagonal
elements of the Hamiltonian is cured by introducing the phase-less
loss function. Our machine learning models show reasonable accuracy
with mean absolute errors of ∼0.1 kcal/mol and ∼0.5
kcal/mol/Å for the diabatic Hamiltonian elements and their gradients,
respectively, for penta-2,4-dieniminium cation. Moreover, by exploiting
the diabatic representation, our models can predict correct conical
intersection structures and their topologies. In addition, our ML-ESMD
simulations give almost identical result with a direct dynamics at
the same level of theory.