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.
Highlights
Simulation of vibrationally resolved electronic spectra of large polyatomic molecules is a challenge for computational chemistry
We focus our attention on the thawed Gaussian approximation (TGA),20,21 which, as several other semiclassical22–27 and quantum28–30 dynamics methods, has been implemented in an on-the-fly fashion and combined with an ab initio evaluation of the potential
To reduce the cost of ab initio Hessian calculations, the on-thefly ab initio thawed Gaussian approximation is readily combined with an interpolation scheme, where the Hessians are computed only every few steps and the intermediate Hessians are obtained from a second-order polynomial interpolation
Summary
Simulation of vibrationally resolved electronic spectra of large polyatomic molecules is a challenge for computational chemistry. A popular method for computing vibronic spectra constructs global harmonic models of the two potential energy surfaces.. Time-dependent approaches, based on computing the dipole time correlation function, have been developed at different levels of accuracy, ranging from global harmonic models to exact quantum dynamics methods on anharmonic potential energy surfaces. We propose a new approach, which still uses a fully anharmonic classical trajectory to guide the Gaussian wavepacket but only a single Hessian to propagate the width This “single-Hessian thawed Gaussian approximation” further reduces the cost of spectra calculations to that of a single classical trajectory. We explore the relation between this single-Hessian approach and similar well-known approximations to the prefactor in the semiclassical Herman–Kluk initial value representation
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