Executive Summary : | The study of reaction dynamics and calculating accurate rovibrational spectra for molecular systems using quantum dynamics is a crucial area in computational chemistry. The Schrödinger equation (SE) is the most accurate way to study these dynamics, but solving the SE for high-dimensional systems is a formidable task. Although several numerical algorithms have been developed to solve the time-independent and time-dependent Schrödinger equation (TDSE) for molecular system dynamics and reactive scatterings, they are computationally expensive. Machine learning (ML) can be an efficient tool to solve the SE in a time-dependent fashion, studying the evolution of a molecular system in spacetime. This research proposal proposes a step-by-step procedure for solving the TDSE for model quantum systems in lower dimensions and real molecular systems using machine learning. The project aims to solve the TDSE, an important class of partial differential equations for molecular systems. The training set for the ML work will be computed by solving the dynamics of molecular systems for various atom-diatom type reactive collisions and small molecules using numerical integrators such as split-operator and Chebyshev real wave packet methods. Descriptors for the wavepacket/input-matrices will be optimized using an autoencoder, and the time evolution of the wavepacket will be trained using ML models like convolutional neural network (CNN), recurrent neural network (RNN), LSTM, and deep residual neural network. The ML model will be modified to be scalable for large systems and include potential energy and angular momentum as inputs, resulting in the action of the time evolution operator on a wavepacket for any system at a given time. |