Machine Learning Optimal Effective Hamiltonians for Excited State Molecular Systems*

Excited state molecular dynamics calculations require many expensive excited state calculations, severely limiting the length and time scales of examinable phenomena. Effective Hamiltonian models (such as tight-binding, the Hubbard, Hückel theory and semi-empirical methods), which retain the quantum complexity of the original problem albeit in a reduced parameter subspace, provide an opportunity to sidestep this bottleneck. These methods can be very accurate when properly tuned to the system at hand.

In recent years, Machine Learning algorithms have accurately reproduced both energies and properties derived from quantum chemistry without the need to solve the Schrödinger equation. Here, databases of optimized effective Hamiltonians for molecular systems are used to train a deep neural network, which can then produce optimized effective Hamiltonians for new systems on the fly. This methodology is applied to various semi-empirical forms, including Hückel and Modified Neglect of Diatomic Overlap (MNDO) type Hamiltonians. The accuracy of these optimized Hamiltonians is quantified by comparing orbital energies, excited state energies, and various molecular properties to higher level ab initio calculations.