John C. Tully

Molecular dynamics with electronic transitions

A method is proposed for carrying out molecular dynamics simulations of processes that involve electronic transitions. The time dependent electronic Schrodinger 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.

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

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.

Effects of surface crossing in chemical reactions - The H3 system

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 H...

Dynamics of gas–surface interactions: 3D generalized Langevin model applied to fcc and bcc surfaces

A three dimensional generalized Langevin formalism is presented and applied to Ar and Xe interactions with Pt (111). Approximations for the random force and friction terms are proposed which permit realistic description of the motion and response of the surface atoms, including proper correlations among neighboring atoms. A ’’ghost atom’’ technique is developed which provides convenient numerical solution of the generalized Langevin equations in such a way that the fluctuation–dissipation theorem relating the random force and friction is satisfied rigorously. A simple prescription for determining parameters in the random force and friction is outlined. The prescription is applied to a four‐atom active zone to obtain explicit relationships for all parameters, depending only on the bulk and surface Debye frequencies, for fcc (100), (110), and (111), and bcc (100) and (110) surfaces. Calculations of energy accommodation, sticking probabilities, and thermal desorption rates are reported for Ar and Xe on Pt(11...

Dynamics of gas–surface interactions: Scattering and desorption of NO from Ag(111) and Pt(111)

Empirical potential energy surfaces have been constructed to describe the nondissociative interaction of NO with the (111) faces of Ag and Pt. Stochastic trajectory simulations employing these interaction potentials accurately reproduce experimental angular and velocity scattering distributions. Measured rotational energy distributions of scattered molecules, including the observed ‘‘rotational rainbow’’ features, are also reproduced quantitatively. Arrhenius prefactors for desorption are computed to be large (1016 s−1), and the translational and rotational ‘‘temperatures’’ of desorbed molecules are found to be lower than the surface temperature, in agreement with experiment. Sticking probabilities, desorption rates, and the rotational energy of desorbed and scattered molecules are all found to be strongly influenced by the dependence of the attractive region of the gas‐surface potential on molecular orientation.

Transition state theory for collision complexes: product translational energy distributions

Abstract An approximate formula is derived for the distribution of relative translational energy of products from decay of collision complexes formed by bimolecular combination in molecular beams. The treatment applies to the case of large collisional angular momentum (often encountered in practice), for which centrifugal motion strongly affects the shape of the energy distribution.

Perspective: Nonadiabatic dynamics theory

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.

Molecular dynamics of surface diffusion. I. The motion of adatoms and clusters

The motion of isolated adatoms and small clusters on a crystal surface is investigated by a novel and efficient simulation technique. The trajectory of each atom is calculated by molecular dynamics, but the exchange of kinetic energy with the crystal lattice is included through interactions with a ’’ghost’’ atom. This atom represents surface atoms of the lattice and is subjected to random and dissipative forces that are related by the fluctuation–dissipation theorem. The diffusion process is characterized by measurements of the velocity autocorrelation function, mean square displacement, directional correlations between hops, and the mean displacement per hop. In addition, the rate of evaporation of single adatoms and the rate of dissociation of clusters are discussed. The diffusion of an isolated adatom is found to be somewhat faster than that predicted by the classical rate theory for an activated process. This effect is a result of diffusion jumps of several atomic diameters that occur preferentially a...

Dynamics of gas-surface interactions: Thermal desorption of Ar and Xe from platinum

Abstract Three-dimensional stochastic classical trajectory studies have been carried out of the thermal desorption of isolated Ar and Xe atoms from the (111) face of platinum. Realistic interaction potentials that produce quantitative agreement with experimental sticking probabilities and angular and velocity scattering distributions were employed. Energy exchange with lattice phonons was included accurately via empirically chosen friction and fluctuating forces. Application of techniques for the simulation of “infrequent events” allowed studies to be extended to experimentally accessible lifetimes. Atoms were found to desorb preferentially to wide angles, with mean energy considerably lower than 2k times the surface temperature. Significant curvature of the Arrhenius plots was exhibited, and pre-exponential factors were found to be lower than characteristic frequencies. These effects were determined to be mainly dynamical in origin; i.e., they cannot be described by conventional transition-state-theory models.

Extraction of kinetic parameters in temperature programmed desorption: A comparison of methods

An investigation of the temperature programmed desorption (TPD) of CO and D2 from Ni(111) has been carried out. It has been shown that a differential method for the extraction of the kinetic parameters, threshold temperature programmed desorption (TTPD), can be applied with accuracy near the limit of zero coverage. In this limit, agreement is found between integral and differential methods for kinetic parameter evaluation. The factors which limit the applicability of TTPD are explored and a method to verify its proper application is presented.