Coarse-Grained Geometric Quantum Dynamics in the Tensor Network Representation

Abstract

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.

Figures (4)

• Figure 1: (a) The adiabatic potential energy surfaces of the $S_1$ and $S_2$ states of pyrazine. (b) Time evolution of the electronic population of two states. The result from the coarse-grained method ($\epsilon=10^{-6}$, $D_{\max}=100$, orange dashed line) is compared with the benchmark result from the direct product method (blue solid line) over the first 75fs.
• Figure 2: (a) The absolute value of the autocorrelation function, $|a(t)|$, obtained using the tensor train method compared with the benchmark result from the direct product method. (b) Comparison of the $S_2$ state absorption spectra calculated by the coarse-grained method and the direct product method.
• Figure 3: Nonadiabatic conical intersection dynamics for the full 24-mode pyrazine model. (a) Electronic populations of the initially state $S_2$, and the lower-lying state $S_1$. (b) Expectation values of the position for the coupling mode $q_{10a}$, and the tuning mode $q_{6a}$.
• Figure 4: Reduced probability densities for the 24-mode pyrazine model on the $S_2$ (bottom) and $S_1$ (top) surfaces. The densities are projected onto the branching plane spanned by the coupling mode $q_{10a}$ and the tuning mode $q_{6a}$. The position of the conical intersection is indicated by a star. The wavepacket is initially excited to the $S_2$ state. At 50fs, the density transferred to the $S_1$ surface exhibits a nodal line along $q_{10a}=0$, a signature of the geometric phase effect induced by the conical intersection.