Simulating Highly Activated Sticking of H2 on Al(110): Quantum versus Quasi-Classical Dynamics

Abstract

We evaluate the importance of quantum effects on the sticking of H₂ on Al(110) for conditions that are close to those of molecular beam experiments that have been done on this system. Calculations with the quasi-classical trajectory (QCT) method and with quantum dynamics (QD) are performed using a model in which only motion in the six molecular degrees of freedom is allowed. The potential energy surface used has a minimum barrier height close to the value recently obtained with the quantum Monte Carlo method. Monte Carlo averaging over the initial rovibrational states allowed the QD calculations to be done with an order of magnitude smaller computational expense. The sticking probability curve computed with QD is shifted to lower energies relative to the QCT curve by 0.21 to 0.05 kcal/mol, with the highest shift obtained for the lowest incidence energy. Quantum effects are therefore expected to play a small role in calculations that would evaluate the accuracy of electronic structure methods for determining the minimum barrier height to dissociative chemisorption for H₂ + Al(110) on the basis of the standard procedure for comparing results of theory with molecular beam experiments.

Figure 1

Top view (A) and side view (B) of the surface unit cell of Al(110), illustrating the six coordinates describing the geometry of the H₂-Al(110) system in the BOSS model, and (C) six barrier geometries BG1-BG6. In (A), the black, green, red, blue, and yellow solid circles denote the top, short-bridge, long-bridge, hollow, and C-site, respectively.

Figure 2

Elbow plots of the H₂-Al(110) PES as directly calculated with DFT (red solid lines) and fitted with the CRP (blue dashed lines). The blue numbers label the contour lines of the PES. Red (blue) circles indicate the minimum energy path from reactants to product as computed directly with DFT (obtained from the CRP fit). The red (blue) square indicates the position of the barrier in 2D as computed with DFT (interpolated with the CRP). Results are given for the six barrier geometries indicated in Figure 1C and investigated in ref (41).

Figure 3

Sticking probabilities computed with the QCT method using averaging over all 319 v = 0, 1, and 2 (v, j, m_j) states (“NMC”) and Monte Carlo averaging over only 35 such states (“PMC”).

Figure 4

(E_i) computed with QD (black line) and QCT (blue squares) dynamics are compared for three different initial rovibrational states, of which (A) one with v = 0, (B) one with v = 1, and (C) one with v = 2.

Figure 5

Sticking probabilities computed with QD (blue squares) and with QCT (red circles) dynamics using the PMC procedure are compared. The distances along the energy axis (in kcal/mol) between the QD sticking probabilities and the spline interpolated QCT sticking curve are also presented in blue.

Figure 6

Histogram of the percentage contributions to S₀ of H₂ in its v = 0 (blue bars on the left), v = 1 (green bars in the middle), and v = 2 (red bars on the right) vibrational states to the sticking at the six different average incidence energies shown.

Figure 7

Histogram of the percentage contributions of H₂ incident in four ranges of incidence energies to the reaction of H₂ in a particular initial vibrational state v, for v = 0 (red bars on the left), v = 1 (green bars in the middle), and v = 2 (blue bars on the right) in the sticking at three different nozzle temperatures.

Figure 8

Flux-weighted translational energy distributions corresponding to the velocity distribution expression of eq 6, as determined from ref (45) for the conditions corresponding to T_N = 1100, 1400, and 1700 K (⟨E_i⟩ =5.1, 7.9, and 9.4 kcal/mol). The distributions have been rescaled to make their maximum coincide with 1.0.

Figure 9

Initial state-selected reaction probability for the (v,j = 0) state of H₂ is shown as a function of E_i for v = 0, 1, and 2, indicating energy spacings between the curves (in kcal/mol) for values of the reaction probability of 0.1, 0.25, and 0.5.