Semiclassical initial value representation treatment of a hydrogen bonded complex of rigid water molecules from a single trajectory in Cartesian coordinates

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.

“…In Johnson's multichannel Wentzel-Kramers-Brillouin approximation, 48,[77][78][79] one assumes that the matrix α t varies slowly, i.e.,α t ≈ 0, which yields…”

Section: Appendix A: Single-hessian Approximations Of the Herman-klukmentioning

confidence: 99%

Single-Hessian thawed Gaussian approximation

Begušić

Cordova

Vaníček

2019

“…In the last decade many developments in the SC-IVR method have been undertaken. [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] Among them have been prescriptions for the calculation of vibrational states, 24,29,[32][33][34][35][36] vibronic absorption spectra, 26 reactive processes, 21 and quantum coherence. 27 Recently, two research groups have been involved in investigating ab initio SC-IVR, where the trajectories are calculated on the fly.…”

Section: Introductionmentioning

confidence: 99%

“…Kaledin and Miller 24,36 have obtained the vibrational states of H 2 ,H 2 O, NH 3 ,C H 4 ,C H 2 D 2 and H 2 CO with SC-IVR as well as time-averaged SC-IVR. 24 Roy and coworkers 23,[32][33][34][35] developed a reduced-dimensionality approach through Cartesian geometric constraints [applying it to Ar 3 and (H 2 O) 2 ], which is amenable for the computation of larger systems.…”

Section: Introductionmentioning

confidence: 99%

Determination of molecular vibrational state energies using the ab initio semiclassical initial value representation: Application to formaldehyde

Wong

Benoit

Lewerenz

et al. 2011

Self Cite

We have demonstrated the use of ab initio molecular dynamics (AIMD) trajectories to compute the vibrational energy levels of molecular systems in the context of the semiclassical initial value representation (SC-IVR). A relatively low level of electronic structure theory (HF/3-21G) was used in this proof-of-principle study. Formaldehyde was used as a test case for the determination of accurate excited vibrational states. The AIMD-SC-IVR vibrational energies have been compared to those from curvilinear and rectilinear vibrational self-consistent field/vibrational configuration interaction with perturbation selected interactions-second-order perturbation theory (VSCF/VCIPSI-PT2) and correlation-corrected vibrational self-consistent field (cc-VSCF) methods. The survival amplitudes were obtained from selecting different reference wavefunctions using only a single set of molecular dynamics trajectories. We conclude that our approach is a further step in making the SC-IVR method a practical tool for first-principles quantum dynamics simulations.

“…60 The Cartesian coordinates allow them to properly include kinetic cross terms. [61][62][63][64] In their first principles simulations, 20 000 trajectories of 244 fs simulation time each were employed. Even if a certain percentage of these trajectories is discarded according to the spectra energy window of interest, this is clearly an intensive calculation because the Hessian must be evaluated at each time-step.…”

Section: First Principles Semiclassical Molecular Dynamics Of Formmentioning

confidence: 99%

Fighting the curse of dimensionality in first-principles semiclassical calculations: Non-local reference states for large number of dimensions

Ceotto

Tantardini

Aspuru‐Guzik

2011

Semiclassical methods face numerical challenges as the dimensionality of the system increases. In the general context of the theory of differential equations, this is known as the “curse of dimensionality.” In the present manuscript, we apply the recently-introduced multi-coherent states semiclassical initial value representation (MC-SC-IVR) approach to extend the applicability of first-principles semiclassical calculations. The proposed strategy involves the use of non-local coherent states with the goal of increasing accuracy in the Fourier transforms, and on the other hand, allows for the selection of peaks of different frequencies. The ability to filter desired peaks is important for analyzing the power spectra of complex systems. The MC-SC-IVR approach allows us to solve a 19-dimensional test system and to resolve on-the-fly the power spectra of the formaldehyde molecule with very few classical trajectories.