Trajectory Surface Hopping Approach to Nonadiabatic Molecular Collisions: The Reaction of H+ with D2

Abstract

An extension of the classical trajectory approach is proposed that may be useful in treating many types of nonadiabatic molecular collisions. Nuclei are assumed to move classically on a single potential energy surface until an avoided surface crossing or other region of large nonadiabatic coupling is reached. At such points the trajectory is split into two branches, each of which follows a different potential surface. The validity of this model as applied to the HD2+ system is assessed by numerical integration of the appropriate semiclassical equations. A 3d “trajectory surface hopping” treatment of the reaction of H+ with D2 at a collision energy of 4 eV is reported. The excellent agreement with experiment is an encouraging indication of the potential usefulness of this approach.

GPU-Accelerated State-Averaged Complete Active Space Self-Consistent Field Interfaced with Ab Initio Multiple Spawning Unravels the Photodynamics of Provitamin D3

“…Ab initio nonadiabatic molecular dynamics represents a compromise between efficiency and accuracy that includes surface crossing (nonadiabatic) effects while determining the required potential energy surfaces from simultaneous solution of the electronic Schrödinger equation. [12][13][14][15][16][17][18][19][20][21] Quantum mechanical effects related to surface crossing can be described either by a swarm of classical trajectories that can hop between electronic states -trajectory surface hopping (TSH) [22][23][24] -or by an expansion of the nuclear wavefunctions in terms of frozen Gaussians following classical trajectories called "trajectory basis functions" -Full Multiple Spawning (FMS) [12][13][25][26][27] and related methods. 19,[28][29][30] The propagation of trajectories substantially reduces the cost of the nuclear propagation compared to grid-based solution of the time-dependent Schrödinger equation.…”

Quantum modeling of ultrafast photoinduced charge separation

“…In this formulation, nonadiabatic transitions of classical trajectories are described in terms of a connection formula of the semiclassical Wentzel-Kramers-Brillouin [212,213] wavefunctions associated to two or more coupled electronic states. This intuitively appealing picture of trajectories hopping between coupled potential-energy surfaces gave rise to a number of mixed quantum-classical implementations of this idea [214]. Recently, a novel coupled-trajectory approach derived from the exact factorization theorem [215] was proposed.…”

Analog of Rabi oscillations in resonant electron-ion systems

“…10 The adiabatic many-body electronic states are obtained by diagonalizing H e after the quantum operatorsR have been substituted by classical parameters, R:…”

“…On the other hand, part of the electron-ion correlation is missed by ED, leading in some cases to qualitatively wrong predictions. 8,10,21 Nevertheless, ED remains computationally appealing because it does not require the explicit knowledge of the adiabatic PESs, i.e., a costly diagonalization of H e at each time-step is avoided. Therefore, in contrast with other schemes, ED can be employed to simulate large atomic systems, 19 including metals.…”

“…6 Including electronic transitions and-possibly classical-atomic motion in a consistent 7,8 and computationally effective molecular dynamics scheme has been the object of intense theoretical and computational investigations during the last decades. [9][10][11][12][13][14][15][16][17][18][19] In the surface hopping algorithm 10 -and similar approaches 12,14,18 that treat atomic evolution classicallyvertical electronic transitions are included in a stochastic way. By averaging over a large ensemble of such stochastic quantum-classical evolutions, one obtains a reliable approximation to the quantum electron-ion 20 dynamics.…”