Prefactor phase differences ϕ(t) = phase[C t (p(0), q(0))] at different levels K of the CFD-PSB approximation for the ground state energy. The left panel is for a CO2 trajectory and the right for a H2O trajectory.
Prefactor modulus relative error at different levels K of the CFD-PSB approximation for the ground state energy. The left panel is for a CO2 trajectory and the right for a H2O trajectory.
Water molecule vibrational dynamics. (Left panel) Normalized trajectory distribution versus the total initial trajectory energy for different Gaussian a, b sampling standard deviations; the bin width for the histogram distributions is 200 cm−1. (Right panel) The resulting power spectrum.
Dependence of the distribution of rejected sampled trajectories with respect to the value of K for the CFD interpolated Hessian. Orange line is for the total number of sampled trajectories and other color lines are for the rejected trajectories. The sampling width is nσ = (na, nb) where n is an integer.
Water power spectra, given by the colored lines, calculated with different levels of approximation of the CFD-Bofill Hessian update scheme. A total of 3200 trajectories are sampled according to the Husimi distribution with the a,b parameters set to σ. The black line is the spectrum without the Hessian approximation.
Energy distributions for sampled and rejected trajectories for multiple coherent states sampling of the water molecule with eight Gaussian sampling centers (see text). The orange line is the distribution for the total trajectories and the other lines are for the rejected trajectories at different levels of the CFD approximation.
Water power spectra for MC-SC-IVR simulations with different sampling parameters. For each set of parameters the K = 8 CFD approximated spectrum (red line) is compared with the MC-SC-IVR spectrum without the CFD approximation (black line). The σ = ∞ is the 8-trajectory simulation.
Direct dynamics power spectra for carbon dioxide calculated at different levels of the CFD-Bofill Hessian update scheme. The simulations were performed with the MC-SC-IVR method using 8 trajectories. The black line is the spectrum without the Hessian CFD approximation and the colored lines are for different levels of the CFD Hessian approximation.
Water vibrational energy levels. a
Water vibrational eigenvalues with the CFD approximation included with the MC-SC-IVR method. a
MC-SC-IVR vibrational spectra for CO2 obtained with direct dynamics and the CFD Hessian approximation. a
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