The treatment of classically forbidden electronic transitions in semiclassical trajectory surface hopping calculations

Abstract

A family of four weakly coupled electronically nonadiabatic bimolecular model photochemical systems is presented. Fully converged quantum mechanical calculations with up to 25 269 basis functions were performed for full-dimensional atom-diatom collisions to determine the accurate scattering dynamics for each of the four systems. The quantum mechanical probabilities for electronically nonadiabatic reaction and for nonreactive electronic deexcitation vary from 10 Ϫ1 to 10 Ϫ5 . Tully's fewest-switches ͑TFS͒ semiclassical trajectory surface-hopping method ͑also called molecular dynamics with quantum transitions or MDQT͒ is tested against the accurate quantal results. The nonadiabatic reaction and nonreactive deexcitation events are found to be highly classically forbidden for these systems, which were specifically designed to model classically forbidden electronic transitions ͑also called frustrated hops͒. The TFS method is shown to systematically overestimate the nonadiabatic transition probabilities due to the high occurrence of frustrated hops. In order to better understand this problem and learn how to best minimize the errors, we test several variants of the TFS method on the four new weakly coupled systems and also on a set of three more strongly coupled model systems that have been presented previously. The methods tested here differ from one another in their treatment of the classical trajectory during and after a frustrated hopping event. During the hopping event we find that using a rotated hopping vector results in the best agreement of semiclassical and quantal results for the nonadiabatic transition probabilities. After the hopping event, we find that ignoring frustrated hops instead of reversing the momentum along the nonadiabatic coupling vector results in the best agreement with the accurate quantum results for the final vibrational and rotational moments. We also test the use of symmetrized probabilities in the equations for the TFS hopping probabilities. These methods systematically lead to increased error for systems with weakly coupled electronic states unless the hopping probabilities are symmetrized according to the electronic state populations.

Introductory lecture: Nonadiabatic effects in chemical dynamics

“…Using the þ, À, and cV and prescriptions, the trajectory does not change electronic states at a frustrated hop, which violates the self-consistency argument originally 107 used to justify the TFS hopping probability, and numerical studies 75,128 have shown that using these prescriptions leads to inaccurate electronic-state trajectory distributions. The fewest-switches with time-uncertainty (FSTU) method 128 has been developed to correct this deficiency.…”

“…75 The TFS algorithm may predict a nonzero hopping probability to a higher-energy electronic state in regions where the nuclear momentum is insufficient to allow for an energy adjustment that will conserve total energy. For example, due to tunneling, quantum mechanical particles have some probability density in regions of phase space that are classically forbidden.…”

“…68 OWVP calculations have been performed more recently on a variety of model systems, including three qualitatively different types of chemical systems: (1) systems with conical intersections, [69][70][71][72][73] (2) systems with diabatic surfaces that cross and adiabatic surfaces that do not intersect, 74 and (3) systems with wide regions of weak coupling where neither the diabatic nor the adiabatic surfaces cross. 75,76 This set of calculations includes reactive 69,72,[74][75][76] and nonreactive 71,72 scattering collisions as well as unimolecular excited-state decay processes. 70,73 The availability of accurate quantum mechanical results for realistic full-dimensional non-BO systems allows for the systematic study of the accuracy of more approximate methods, and we have identified a subset of the calculations discussed above to serve as benchmark test cases.…”

“…OWVP calculations with 20659 basis functions were carried out 74 for all three MXH PEMs at total energies from 1.07 to 1.13 eV. The second family of PEMs included in the set of benchmark cases is the YRH family, 75 which contains two Rosen-Zener-Demkov-type PEMs, [80][81][82] featuring wide regions of weakly coupled and nearly parallel surfaces where neither the diabatic surfaces nor the adiabatic surfaces cross. The two YRH PEMs differ from one another in the strength of their coupling and describe the reaction…”

“…1(b). OWVP calculations with 25269 basis functions were carried out 75 for both YRH PEMs at total energies from 0.99 to 1.13 eV. The various PEMs are distinguished by the strtength of coupling of the diabats, as measured by a parameter U max 12 .…”