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Notes: A free energy perturbation technique is described in which configurations from a classical simulation (molecular dynamics or Monte Carlo) with empirical solute–solvent interactions are used to calculate free energies with quantum mechanically derived solute–solvent interactions. This approach is much less costly than simulations with forces derived from quantum mechanics at each time step, since it only requires quantum energies to be calculated at classically determined configurations. The method is not limited to free energies of solvation, and can potentially be applied to calculations of activation energies and other condensed phase chemical transformations. As a test, this method was used to calculate the free energy of hydration of water at ambient conditions. With a good classical model the method gives accurate results with only 50 quantum calculations. The method is self-correcting in the sense that it can be used to recognize a bad classical model, and improved classical models can be derived by a least-squares fitting to the quantum energies. As a result, this method also provides novel information about the comparative strengths and weaknesses of classical solute models. © 1999 American Institute of Physics.

Notes: Surface diffusion rates have been simulated using classical molecular dynamics in a model of CO adsorbed on Ni(111). This paper describes the energy distribution among adsorbate modes at the transition state, energy relaxation after crossing the transition state, and correlations among adsorbate modes near the transition state. The adsorbate bending (frustrated rotation) mode is strongly coupled to lateral translational motion. This molecular mode provides an important source of energy for reaching the transition state to diffusion, and an important frictional force that dissipates excess lateral translational energy. In this model, the molecular bending mode is a more important source (and sink) of lateral translational energy than the surface at short times. This result is interpreted as a consequence of directional bonding to the surface, and it should be generally important in surface diffusion of chemisorbed molecules.

Notes: We have developed theoretical models of precursor-mediated (nondissociative) molecular chemisorption and used the stochastic classical trajectory method to simulate experiments capable of determining whether a precursor is present. The simulations employ empirical many-dimensional potentials and include the full effects of surface vibrations, coupling among molecular degrees of freedom, and coupling between the molecule and surface. We find that coupling between molecular rotational and translational modes strongly affects the experimentally observable quantities. As a result, reasoning based on the usual one-dimensional picture of a precursor is unreliable. The most notable effect of a precursor is the strong rotational polarization it induces in desorbing molecules. We discuss the origins of rotational polarization and conclude that with no precursor, polarization will be weak and opposite in sign to that of the precursor case. The sticking probability as a function of incident energy and surface temperature can also distinguish whether precursor mediation is important but, again, inferences from one-dimensional models can be misleading. We also find that equilibrium diffusion rates for precursor molecules are faster than for chemisorbed molecules. However, the equilibrium process is relatively slow and until it is complete, chemisorbed molecules may well move farther across the surface than precursors.

Notes: Neural networks provide an efficient, general interpolation method for nonlinear functions of several variables. This paper describes the use of feed-forward neural networks to model global properties of potential energy surfaces from information available at a limited number of configurations. As an initial demonstration of the method, several fits are made to data derived from an empirical potential model of CO adsorbed on Ni(111). The data are error-free and geometries are selected from uniform grids of two and three dimensions. The neural network model predicts the potential to within a few hundredths of a kcal/mole at arbitrary geometries. The accuracy and efficiency of the neural network in practical calculations are demonstrated in quantum transition state theory rate calculations for surface diffusion of CO/Ni(111) using a Monte Carlo/path integral method. The network model is much faster to evaluate than the original potential from which it is derived. As a more complex test of the method, the interaction potential of H2 with the Si(100)-2×1 surface is determined as a function of 12 degrees of freedom from energies calculated with the local density functional method at 750 geometries. The training examples are not uniformly spaced and they depend weakly on variables not included in the fit. The neural net model predicts the potential at geometries outside the training set with a mean absolute deviation of 2.1 kcal/mole. © 1995 American Institute of Physics.

Notes: The ab initio/classical free energy perturbation (ABC-FEP) method proposed previously by Wood et al. [J. Chem. Phys. 110, 1329 (1999)] uses classical simulations to calculate solvation free energies within an empirical potential model, then applies free energy perturbation theory to determine the effect of changing the empirical solute–solvent interactions to corresponding interactions calculated from ab initio methods. This approach allows accurate calculation of solvation free energies using an atomistic description of the solvent and solute, with interactions calculated from first principles. Results can be obtained at a feasible computational cost without making use of approximations such as a continuum solvent or an empirical cavity formation energy. As such, the method can be used far from ambient conditions, where the empirical parameters needed for approximate theories of solvation may not be available. The sources of error in the ABC-FEP method are the approximations in the ab initio method, the finite sample of configurations, and the classical solvent model. This article explores the accuracy of various approximations used in the ABC-FEP method by comparing to the experimentally well-known free energy of hydration of water at two state points (ambient conditions, and 973.15 K and 600 kg/m3). The TIP4P-FQ model [J. Chem. Phys. 101, 6141 (1994)] is found to be a reliable solvent model for use with this method, even at supercritical conditions. Results depend strongly on the ab initio method used: a gradient-corrected density functional theory is not adequate, but a localized MP2 method yields excellent agreement with experiment. Computational costs are reduced by using a cluster approximation, in which ab initio pair interaction energies are calculated between the solute and up to 60 solvent molecules, while multi-body interactions are calculated with only a small cluster (5 to 12 solvent molecules). Sampling errors for the ab initio contribution to solvation free energies are ±2 kJ/mol or less when 50–200 configurations are used. Using the largest clusters and most accurate ab initio methods, ABC-FEP predicts hydration free energies of water at both state points that agree with equations of state, within the sampling error. These results are the first calculation of a free energy of solvation at extreme conditions from a fully atomistic model with ab initio methods. © 2000 American Institute of Physics.