Effects of Surface Crossing in Chemical Reactions: The H3+ System

Abstract

Approximate potential-energy surfaces for the two lowest singlet states of H3+ are calculated using the diatomics-in-molecules approach. The nonadiabatic terms which couple these surfaces can be directly computed in this approximation. From the magnitudes of these coupling terms it is apparent that, for excitation energies below about 10 eV, nonadiabatic transitions must be confined almost entirely to a region localized at the avoided crossing of the two surfaces. This fact suggests the following simplified picture of the dynamics of the H++H2 reaction: As the H+ and H2 approach, they remain on the lower potential surface (there is no initial electron jump). They continue to follow adiabatically the lower surface in the close-collision region, so the probability of a nonadiabatic transition does not appear to be related to the lifetime of the collision complex. It is while the products are receding that electronic transitions become important. Consequences of this model on the threshold for formation of H2+ and on the partition of vibrational energy in the products are discussed, and a comparison with recent experiments of Krenos and Wolfgang is included.

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

“…We defer consideration of this aspect to Sec. III.͒ Tully 15,22 proposed two schemes for sampling P a→b (t n ) along the classical trajectory, which he called the ants and the anteater algorithms.…”

“…In the ants algorithm 15 each trajectory in the ensemble begins the simulation on a particular potential energy surface and is integrated to the first decision point t 1 , at which it splits into two branches. One branch continues to follow the initial potential energy surface and is called the nonhopping branch, whereas the other branch hops to follow the unoccupied potential surface and is called the hopping branch.…”

Potential energy surface and wave packet calculations on the Li+HF→LiF+H reaction

“…13,22,23 However, all of these GPES are unsatisfactory for several reasons: the diatomics-in-molecules ͑DIM͒ surface of Preston and Tully, 22 which is the most widely used in trajectory calculations, is qualitatively correct; it was the first study of the avoided crossing due to the presence of two dissociation channels, H 2 ( 1 ⌺ g ϩ )ϩH ϩ and H 2 ϩ ( 2 ⌺ u ϩ )ϩH, but it is not accurate even at low energies; the Schinke et al GPES 13 is based on their ab initio calculations but the functional form used has discontinuous derivatives and contains unphysically deep minima for certain regions, probably due to the small number of ab initio points. The most recent GPES of Prosmiti et al 23 is a combination of two potential forms using the energy switching approach of Varandas 24 to connect them.…”

“…In fact, the most recent dynamical study of this system using a quantum-mechanical approach 25 is based on the very approximate DIM GPES. 22 Moreover, in a first attempt to obtain a calculated spectrum for near-dissociation H 3 ϩ , 21 Henderson and Tennyson have used the MBB LPES 9 that lacks any representation of the regions near dissociation. In this paper we also present a global analytical representation of the adiabatic ground-state 1 1 AЈ potential for the H 3 ϩ system.…”

Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics

“…5,11 The classical treatment has to be modified as well, for example, by incorporating surface hopping procedures. 12,13 For an extensive discussion of various mixed quantum/classical and also semi-classical methods see the review by Stock and Thoss. 14 In this work we pursue the question of how non-adiabatic coupling is visible in the quantum dynamics of wave-packets which depend on both, the electronic and nuclear degrees of freedom.…”