Coarse-Grained Geometric Quantum Dynamics in the Tensor Network Representation

Quantum geometrical molecular dynamics provides a quantum geometric picture for understanding reactive dynamics, especially excited-state conical intersection dynamics, and also a numerically exact method for strongly correlated electron-nuclear dynamics. However, there are substantial challenges in describing medium-sized molecules with tens of nuclear degrees of freedom. The main challenge is that it uses a discrete variable representation to discretize the molecular configuration space, and thus requires a tremendous number of quantum chemistry calculations to construct the electronic overlap matrix. Moreover, the expansion coefficients scale exponentially with molecular size for direct-product basis sets. We address these challenges by first introducing a coarse-grained local diabatic ansatz, followed by a tensor network representation of the expansion coefficients and the molecular time-evolution operator. With a full 24-dimensional demonstration using the pyrazine molecule, we show that such developments provide a highly accurate and computationally tractable method for high-dimensional, fully quantum, strongly coupled electron-nuclear dynamics from first principles.