Single-Hessian thawed Gaussian approximation: The missing rung on the ladder

Abstract

To alleviate the computational cost associated with on-the-fly ab initio semiclassical calculations of molecular spectra, we propose the single-Hessian thawed Gaussian approximation, in which the Hessian of the potential energy at all points along an anharmonic classical trajectory is approximated by a constant matrix. The spectra obtained with this approximation are compared with the exact quantum spectra of a one-dimensional Morse potential and with the experimental spectra of ammonia and quinquethiophene. In all cases, the single-Hessian version performs almost as well as the much more expensive on-the-fly ab initio thawed Gaussian approximation and significantly better than the global harmonic schemes. Remarkably, unlike the thawed Gaussian approximation, the proposed method conserves energy exactly, despite the time dependence of the corresponding effective Hamiltonian, and, in addition, can be mapped to a higher-dimensional time-independent classical Hamiltonian system. We also provide a detailed comparison with several related approximations used for accelerating prefactor calculations in semiclassical simulations.

v2: Added Section II.G and Appendix A on PQ method and Hamiltonian structure. Added Section II.H on comparison with single-Hessian approximations of the Herman-Kluk prefactor. v3: Changed notation for the A parameter of the Gaussian wavepacket and moved Section II.H of v2 to Appendix B. v4 (this version): Only added comments on v2, v3, v4. Manuscript in v4 is exactly the same as in v3

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