Gaussian Process Model for Collision Dynamics of Complex Molecules

We show that a Gaussian process model can be combined with a small number (of order 100) of scattering calculations to provide a multidimensional dependence of scattering observables on the experimentally controllable parameters (such as the collision energy or temperature) as well as the potential energy surface (PES) parameters. For the case of $\mathrm{Ar}\text{−}{\mathrm{C}}_6{\mathrm{H}}_6$ collisions, we show that 200 classical trajectory calculations are sufficient to provide a ten-dimensional hypersurface, giving the dependence of the collision lifetimes on the collision energy, internal temperature, and eight PES parameters. This can be used for solving the inverse scattering problem, for the efficient calculation of thermally averaged observables, for reducing the error of the molecular dynamics calculations by averaging over the PES variations, and for the analysis of the sensitivity of the observables to individual parameters determining the PES. Trained by a combination of classical and quantum calculations, the model provides an accurate description of the quantum scattering cross sections, even near scattering resonances.

Figure 1

(a),(b) The lifetime dependence on the rotational temperature and collision energy for ${\mathrm{C}}_6{\mathrm{H}}_6\text{−}\mathrm{Ar}$ collisions. (c) The surface produced by the GP model. The lines connect the values (circles) computed from the classical trajectories with the values predicted by the GP model. (d) The surface produced by the GP model for ${\mathrm{C}}_6{\mathrm{H}}_6\text{−}\mathrm{RG}$ collision lifetimes versus the atomic mass and the PES depth for $T_r=4\mathrm{K}$ and $E=4{\mathrm{cm}}^{-1}$. The surface (c) is produced with only 20 scattering calculations on input and has the normalized error ${ϵ}_S<8\%$. The surface (d) is produced with 40 scattering calculations and has the error ${ϵ}_S=5.09\%$.

Figure 2

Accuracy of the GP model with variable PES parameters for the prediction of the collision lifetimes. The scatter plot compares the predicted values with the computed values. The error of the GP model is the deviation of the points from the diagonal line. This GP model is trained by only 200 scattering calculations, enough to produce a ten-dimensional hypersurface with the error ${ϵ}_S=4\%$. Left inset: energy dependence of the collision lifetime for the $\mathrm{Ar}\text{−}{\mathrm{C}}_6{\mathrm{H}}_6$ system with the error interval obtained by varying all the individual PES parameters by $\pm 3\%$. Right inset: relative effect of the variation of $T_r$, $E$, and the PES parameters on the collision lifetimes. The filled area of the bars shows the uncorrelated contribution of the corresponding variable and the open area shows the effect that depends on one or more other variables.

Figure 3

GP models (curves) of quantum scattering cross sections (symbols) for ${\mathrm{C}}_6{\mathrm{H}}_6\text{−}\mathrm{He}$ collisions. The blue dashed line represents the results of the GP model (6) trained by the quantum calculations. The red solid line represents the predictions of the GP model (8) trained by a combination of classical and quantum results. The CT results stabilize the GP model predictions of the quantum calculations. The models are trained by the points represented by squares. The circles are used to illustrate the accuracy.