A method is proposed for carrying out molecular dynamics simulations of processes that involve electronic transitions. The time dependent electronic Schrödinger equation is solved self-consistently with the classical mechanical equations of motion of the atoms. At each integration time step a decision is made whether to switch electronic states, according to probabilistic ‘‘fewest switches’’ algorithm. If a switch occurs, the component of velocity in the direction of the nonadiabatic coupling vector is adjusted to conserve energy. The procedure allows electronic transitions to occur anywhere among any number of coupled states, governed by the quantum mechanical probabilities. The method is tested against accurate quantal calculations for three one-dimensional, two-state models, two of which have been specifically designed to challenge any such mixed classical–quantal dynamical theory. Although there are some discrepancies, initial indications are encouraging. The model should be applicable to a wide variety of gas-phase and condensed-phase phenomena occurring even down to thermal energies.

We apply "molecular dynamics with quantum transitions" (MDQT), a surface-hopping method previously used only for electronic transitions, to proton transfer in solution, where the quantum particle is an atom. We use full classical mechanical molecular dynamics for the heavy atom degrees of freedom. including the solvent molecules, and treat the hydrogen motion quantum mechanically. We identify new obstacles that arise in this application of MDQT and present methods for overcoming them. We implement these new methods to demonstrate that application of MDQT to proton transfer in solution is computationally feasible and appears capable of accurately incorporating quantum mechanical phenomena such as tunneling and isotope effects. As an initial application of the method, we employ a model used previously by Azzouz and Borgis to represent the proton transfer reaction AH-B-.=.A --H+B in liquid methyl chloride, where the AH-B complex corresponds to a typical phenol-amine complex. We have chosen this model, in part, because it exhibits both adiabatic and diabatic behavior, thereby offering a stringent test of the theory. MDQT proves capable of treating both limits, as well as the intermediate regime. Up to four quantum states were included in this simulation, and the method can easily be extended to include additional excited states, so it can be applied to a wide range of processes, such as photoassisted tunneling. In addition, this method is not perturbative, so trajectories can be continued after the barrier is crossed to follow the subsequent dynamics.

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.

No abstract

Nonadiabatic dynamics-nuclear motion evolving on multiple potential energy surfaces-has captivated the interest of chemists for decades. Exciting advances in experimentation and theory have combined to greatly enhance our understanding of the rates and pathways of nonadiabatic chemical transformations. Nevertheless, there is a growing urgency for further development of theories that are practical and yet capable of reliable predictions, driven by fields such as solar energy, interstellar and atmospheric chemistry, photochemistry, vision, single molecule electronics, radiation damage, and many more. This Perspective examines the most significant theoretical and computational obstacles to achieving this goal, and suggests some possible strategies that may prove fruitful.

We present an analysis of the equilibrium limits of the two most widely used approaches for simulating the dynamics of molecular systems that combine both quantum and classical degrees of freedom. For a two-level quantum system connected to an infinite number of classical particles, we derive a simple analytical expression for the equilibrium mean energy attained by the self-consistent-field (Ehrenfest) method and show that it deviates substantially from Boltzmann. By contrast, "fewest switches" surface hopping achieves Boltzmann quantum state populations. We verify these analytical results with simulations.

A generalization of classical adiabatic molecular dynamics, which we term molecular dynamics with electronic frictions, is described for nuclear motion on a continuum of potential-energy surfaces, such as for adsorbate dynamics at a metal surface. In this situation, the Born–Oppenheimer approximation fails, since for any molecular motion—such as vibrations, rotations, or translations—there are resonant electronic excitations of the metal. However, such excitations are often highly delocalized, so that the continuum of electronic potential-energy surfaces on which nuclear motion occurs are all of similar shape, and can be replaced by a single, effective potential. Nonadiabatic energy exchange between nuclear and electronic degrees of freedom is then represented by frictional and fluctuating forces on the nuclei, and no explicit electronic dynamics are required. The friction in general involves memory, although it is shown that the Markov limit in which memory vanishes is likely to be quite broadly applicable. Expressions for the electronic friction in the Markov limit are obtained in terms of the electronic structure of the gas-surface system, which opens the way for direct calculation of these quantities. There is exact agreement between the frictions and previous time-dependent perturbation theory results for the lifetime of excited adsorbate vibrations at metal surfaces.

We present an ab initio direct Ehrenfest dynamics scheme using a three time-step integrator. The three different time steps are implemented with nuclear velocity Verlet, nuclear-position-coupled midpoint Fock integrator, and time-dependent Hartree-Fock with a modified midpoint and unitary transformation algorithm. The computational cost of the ab initio direct Ehrenfest dynamics presented here is found to be only a factor of 2-4 larger than that of Born-Oppenheimer (BO) dynamics. As an example, we compute the vibration of the NaCl molecule and the intramolecular torsional motion of H2C=NH2+ by Ehrenfest dynamics compared with BO dynamics. For the vibration of NaCl with an initial kinetic energy of 1.16 eV, Ehrenfest dynamics converges to BO dynamics with the same vibrational frequency. The intramolecular rotation of H2C=NH2+ produces significant electronic excitation in the Ehrenfest trajectory. The amount of nonadiabaticity, suggested by the amplitude of the coherent progression of the excited and ground electronic states, is observed to be directly related to the strength of the electron-nuclear coupling. Such nonadiabaticity is seen to have a significant effect on the dynamics compared with the adiabatic approximation.