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

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