Single-Hessian Gaussian wavepacket dynamics (GWD) significantly reduces the computational burden of Heller's local harmonic GWD, while maintaining comparable accuracy in approximating vibronic spectra. Here, we provide a new, symplectic derivation of the equations of motion of single-Hessian GWD and show that, unlike the local harmonic version, this method conserves the non-canonical symplectic structure on the manifold of Gaussian wavepackets and $-$ for bounded dynamics in smooth potentials $-$ avoids the drift of energy. Our numerical results suggest that, despite being much more efficient than the local harmonic variant, the single-Hessian GWD exhibits the same $\mathcal{O}(\hbar)$ asymptotic error in averages of observables. To further accelerate numerical simulations, we implement high-order time-stepping geometric integrators that are time-reversible and conserve the norm and symplectic structure exactly, regardless of the time step. In addition, we present explicit expressions for the exact evolution of the width of a single-Hessian Gaussian wavepacket in a general potential, as well as for the exact evolution of the whole wavepacket in a global harmonic potential. Using on-the-fly ab initio Gaussian wavepacket dynamics on the first excited-state surface of ammonia, we numerically confirm the conservation of geometric properties by these integrators and demonstrate that high-order integrators can enhance both accuracy and computational efficiency. We also compute the photoelectron spectrum of the difluorocarbene anion and the absorption spectrum of methylamine, and find that, in comparison with experiment, single-Hessian GWD outperforms global harmonic models and matches the accuracy of local harmonic GWD. Finally, we identify which spectral features are sensitive to the choice of reference Hessian.Single-Hessian Gaussian wavepacket dynamics (GWD) significantly reduces the computational burden of Heller's local harmonic GWD, while maintaining comparable accuracy in approximating vibronic spectra. Here, we provide a new, symplectic derivation of the equations of motion of single-Hessian GWD and show that, unlike the local harmonic version, this method conserves the non-canonical symplectic structure on the manifold of Gaussian wavepackets and$-$for bounded dynamics in smooth potentials$-$avoids the drift of energy. Our numerical results suggest that, despite being much more efficient than the local harmonic variant, the single-Hessian GWD exhibits the same $\mathcal{O}(\hbar)$ asymptotic error in averages of observables. To further accelerate numerical simulations, we implement high-order time-stepping geometric integrators that are time-reversible and conserve the norm and symplectic structure exactly, regardless of the time step. In addition, we present explicit expressions for the exact evolution of the width of a single-Hessian Gaussian wavepacket in a general potential, as well as for the exact evolution of the whole wavepacket in a global harmonic potential. Using on-the-fly ab initio Gaussian wavepacket dynamics on the first excited-state surface of ammonia, we numerically confirm the conservation of geometric properties by these integrators and demonstrate that high-order integrators can enhance both accuracy and computational efficiency. We also compute the photoelectron spectrum of the difluorocarbene anion and the absorption spectrum of methylamine, and find that, in comparison with experiment, single-Hessian GWD outperforms global harmonic models and matches the accuracy of local harmonic GWD. Finally, we identify which spectral features are sensitive to the choice of reference Hessian.

physics.chem-phCross-listedarXiv:2605.07440May 11, 2026

Wavepacket Dynamics on Dynamically Adapting Grids: Application of the Equidistribution Principle

Keith H. Hughes, Róbert E. Wyatt

A moving grid approach to wavepacket dynamics is described that enables grid points to be used efficiently in regions where high resolution of the wavepacket is required. The grid movement is based on the principle of equidistribution and by using a grid smoothing technique the grid points trace a path that continuously adapt to reflect the dynamics of the wavepacket. The technique is robust and allows accurate computations to be obtained for long wavepacket propagation times. Results are presented for two systems: tunnelling dynamics in a double well potential and scattering of a wavepacket from a repulsive Eckart barrier.A moving grid approach to wavepacket dynamics is described that enables grid points to be used efficiently in regions where high resolution of the wavepacket is required. The grid movement is based on the principle of equidistribution and by using a grid smoothing technique the grid points trace a path that continuously adapt to reflect the dynamics of the wavepacket. The technique is robust and allows accurate computations to be obtained for long wavepacket propagation times. Results are presented for two systems: tunnelling dynamics in a double well potential and scattering of a wavepacket from a repulsive Eckart barrier.

APSMar 1, 20030 citations

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for bounded dynamics in smooth potentials

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avoids the drift of energy. Our numerical results suggest that, despite being much more efficient than the local harmonic variant, the single-Hessian GWD exhibits the same

\mathcal{O}(\hbar)

asymptotic error in averages of observables. To further accelerate numerical simulations, we implement high-order time-stepping geometric integrators that are time-reversible and conserve the norm and symplectic structure exactly, regardless of the time step. In addition, we present explicit expressions for the exact evolution of the width of a single-Hessian Gaussian wavepacket in a general potential, as well as for the exact evolution of the whole wavepacket in a global harmonic potential. Using on-the-fly ab initio Gaussian wavepacket dynamics on the first excited-state surface of ammonia, we numerically confirm the conservation of geometric properties by these integrators and demonstrate that high-order integrators can enhance both accuracy and computational efficiency. We also compute the photoelectron spectrum of the difluorocarbene anion and the absorption spectrum of methylamine, and find that, in comparison with experiment, single-Hessian GWD outperforms global harmonic models and matches the accuracy of local harmonic GWD. Finally, we identify which spectral features are sensitive to the choice of reference Hessian.