Geometric properties and integrators for ab initio single-Hessian Gaussian wavepacket dynamics

Single-Hessian Gaussian wavepacket dynamics (GWD) enables simulations of spectra of high-dimensional, slightly anharmonic systems at the cost of ab initio classical molecular dynamics^1,2. This semiclassical method significantly reduces the computational burden of Heller's local harmonic GWD, while maintaining comparable accuracy in approximating spectra. The unexpected but very useful behavior of this method has been hypothesized to stem from the superior geometric properties of the single-Hessian approach over the local harmonic version³. Indeed, here we prove that, similar to the optimal variational GWD, the single-Hessian GWD conserves the non-canonical symplectic structure on the manifold of Gaussian wavepackets, and we derive expressions suitable for numerical verification of symplecticity. To preserve the advantages of the method in numerical simulations, we implement high-order geometric integrators that are time-reversible and conserve the norm and symplectic structure exactly, regardless of the time step. Using on-the-fly ab initio Gaussian wavepacket dynamics on the first excited-state surface of ammonia, we numerically assess the conservation of geometric properties by these integrators, demonstrating that high-order integrators can enhance both accuracy and computational efficiency.

¹ T. Begušić, M. Cordova, and J. Vaníček, J. Chem. Phys. 150, 154117 (2019).

² T. Begušić, E. Tapavicza, and J. Vaníček, J. Chem. Theory Comput. 18, 3065 (2022).

³ J. J. L. Vaníček, J. Chem. Phys. 159, 014114 (2023).