Exponential convergence of the local diabatic representation for nonadiabatic models

Abstract

The discrete variable local diabatic representation (LDR) provides a divergence-free framework for exact conical intersection dynamics simulation. In this work, we investigate the convergence with respect to the number of "nuclear" grid points and "electronic" states of LDR for the eigenvalue problems using coupled oscillator models. The performance of LDR is compared with traditional approaches based on the Born-Huang ansatz and on the crude adiabatic representation. Our results demonstrate that for weak vibronic couplings, LDR shows similar convergence rate as the exact Born-Huang representation including not only the first-order derivative couplings but also the diagonal Born-Oppenheimer corrections and second-order derivative couplings. Surprisingly, for strong vibronic couplings, LDR shows a significant faster convergence rate with respect to the number of grid points, hence the number of electronic structure computations, than the exact Born-Huang representation. The crude adiabatic representation in generally shows a much slower convergence rate for all cases. The diagonal Born-Oppenheimer corrections and second-order derivative couplings are found to be important in the Born-Huang framework.

References in corpus (6)

• Path Integral Molecular Dynamics for Exact Quantum Statistics of Multi-Electronic-State Systems
• Nonadiabatic Field: A Conceptually Novel Approach for Nonadiabatic Quantum Molecular Dynamics
• Local diabatic representation of conical intersection quantum dynamics
• The moving crude adiabatic alternative to the adiabatic representation in excited state dynamics
• Nonadiabatic conical intersection dynamics in the local diabatic representation with Strang splitting and Fourier basis
• Coarse-Grained Geometric Quantum Dynamics in the Tensor Network Representation