Efficient geometric integrators for nonadiabatic quantum dynamics. II. The diabatic representation
arXiv:1903.04946 · doi:10.1063/1.5094046
Abstract
Exact nonadiabatic quantum evolution preserves many geometric properties of the molecular Hilbert space. In a companion paper [S. Choi and J. Van\'ıček, 2019], we presented numerical integrators of arbitrary-order of accuracy that preserve these geometric properties exactly even in the adiabatic representation, in which the molecular Hamiltonian is not separable into a kinetic and potential terms. Here, we focus on the separable Hamiltonian in diabatic representation, where the split-operator algorithm provides a popular alternative because it is explicit and easy to implement, while preserving most geometric invariants. Whereas the standard version has only second-order accuracy, we implemented, in an automated fashion, its recursive symmetric compositions, using the same schemes as in the companion paper, and obtained integrators of arbitrary even order that still preserve the geometric properties exactly. Because the automatically generated splitting coefficients are redundant, we reduce the computational cost by pruning these coefficients and lower memory requirements by identifying unique coefficients. The order of convergence and preservation of geometric properties are justified analytically and confirmed numerically on a one-dimensional two-surface model of NaI and a three-dimensional three-surface model of pyrazine. As for efficiency, we find that to reach a convergence error of 10, a 600-fold speedup in the case of NaI and a 900-fold speedup in the case of pyrazine are obtained with the higher-order compositions instead of the second-order split-operator algorithm. The pyrazine results suggest that the efficiency gain survives in higher dimensions.
Changed caption of Fig.1, updated Fig.2, changed text in Sec. II E, changed caption of Fig. 4,5 and 9, added analysis of integration error in Appendix B, updated Fig. 12
References in corpus (3)
Cited by in corpus (20)
- Grid-based methods for chemistry simulations on a quantum computer
- Finite-temperature, anharmonicity, and Duschinsky effects on the two-dimensional electronic spectra from ab initio thermo-field Gaussian wavepacket dynamics
- On-the-fly ab initio semiclassical evaluation of third-order response functions for two-dimensional electronic spectroscopy
- Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation
- Strong Error Bounds for Trotter & Strang-Splittings and Their Implications for Quantum Chemistry
- Family of Gaussian wavepacket dynamics methods from the perspective of a nonlinear Schrödinger equation
- How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?
- High-order geometric integrators for representation-free Ehrenfest dynamics
- Which form of the molecular Hamiltonian is the most suitable for simulating the nonadiabatic quantum dynamics at a conical intersection?
- High-order geometric integrators for the variational Gaussian approximation
- High-order geometric integrators for the local cubic variational Gaussian wavepacket dynamics
- Which Algorithm Best Propagates the Meyer-Miller-Stock-Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics?
- A time-reversible integrator for the time-dependent Schrödinger equation on an adaptive grid
- On Hagedorn wavepackets associated with different Gaussians
- Finite-temperature vibronic spectra from the split-operator coherence thermofield dynamics
- Ehrenfest dynamics accelerated with SPEED
- Applicability of the thawed Gaussian wavepacket dynamics to the calculation of vibronic spectra of molecules with double-well potential energy surfaces
- Time-reversible and norm-conserving high-order integrators for the nonlinear time-dependent Schrödinger equation: Application to local control theory
- On the single-Hessian Gaussian wavepacket dynamics
- An implicit split-operator algorithm for the nonlinear time-dependent Schrödinger equation