High-order geometric integrators for the local cubic variational Gaussian wavepacket dynamics
arXiv:2310.05633 · doi:10.1063/5.0180070
Abstract
Gaussian wavepacket dynamics has proven to be a useful semiclassical approximation for quantum simulations of high-dimensional systems with low anharmonicity. Compared to Heller's original local harmonic method, the variational Gaussian wavepacket dynamics is more accurate, but much more difficult to apply in practice because it requires evaluating the expectation values of the potential energy, gradient, and Hessian. If the variational approach is applied to the local cubic approximation of the potential, these expectation values can be evaluated analytically, but still require the costly third derivative of the potential. To reduce the cost of the resulting local cubic variational Gaussian wavepacket dynamics, we describe efficient high-order geometric integrators, which are symplectic, time-reversible, and norm-conserving. For small time steps, they also conserve the effective energy. We demonstrate the efficiency and geometric properties of these integrators numerically on a multi-dimensional, nonseparable coupled Morse potential.
References in corpus (20)
- Gaussian Wavepacket Dynamics: semiquantal and semiclassical phase space formalism
- Computing quantum dynamics in the semiclassical regime
- Semiclassical "Divide-and-Conquer" Method for Spectroscopic Calculations of High Dimensional Molecular Systems
- On-the-fly ab initio semiclassical dynamics: Identifying degrees of freedom essential for emission spectra of oligothiophenes
- Semiquantal dynamics of fluctuations: Ostensible quantum chaos
- Single-Hessian thawed Gaussian approximation: The missing rung on the ladder
- Semiclassical Approach to Photophysics Beyond Kasha's Rule and Vibronic Spectroscopy Beyond the Condon Approximation. The Case of Azulene
- On-the-fly ab initio semiclassical evaluation of electronic coherences in polyatomic molecules reveals a simple mechanism of decoherence
- Relation of exact Gaussian basis methods to the dephasing representation: Theory and application to time-resolved electronic spectra
- On-the-fly ab initio semiclassical evaluation of third-order response functions for two-dimensional electronic spectroscopy
- Vibrational Investigation of Nucleobases by Means of Divide and Conquer Semiclassical Dynamics
- Symplectic Semiclassical Wave Packet Dynamics
- Efficient geometric integrators for nonadiabatic quantum dynamics. II. The diabatic representation
- Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation
- Family of Gaussian wavepacket dynamics methods from the perspective of a nonlinear Schrödinger equation
- The Siegel Upper Half Space is a Marsden-Weinstein Quotient: Symplectic Reduction and Gaussian Wave Packets
- Geometry and Dynamics of Gaussian Wave Packets and their Wigner Transforms
- Symmetry and Conservation Laws in Semiclassical Wave Packet Dynamics
- High-order geometric integrators for the variational Gaussian approximation
- Isotope effects in the electronic spectra of ammonia from ab initio semiclassical dynamics