Development of interatomic potentials based on ab initio methods and neural networks for molecular dynamics simulations

Computer simulation techniques, such as Molecular Dynamics (MD) play an important role in the study of various chemical, physical, biological and mechanical processes at the atomistic level. Computer simulations can complement both theoretical and experimental approaches. In conjunction with the developments in computer technology, the use of simulations has greatly extended the range of problems that can be studied. In chemistry, simulations are performed to study reaction dynamics. In engineering, simulations are used to study the behavior of a material under varying conditions in various processes, such as machining, indentation, tribology and melting. Such simulations can provide a useful insight into important mechanisms such as phase transformation and dislocation dynamics, which otherwise is not easily understood using other techniques. The most important part of MD simulations is the development of potential energy surfaces, which describe the interactions between the atoms within a system. It should provide a realistic description of the interatomic interactions to match the experimental observations. The usual approach for the development of potentials is to determine a functional form motivated by physical intuition and then adjust the parameters either to ab initio data and/or some physical properties, to come up with an empirical potential. Although, such empirical potentials provide a simple and physically interpretable description for the interatomic interactions their applicability is limited to the type of data to which it was fitted to. Once fitted, there is no easy way to improve upon it, without refitting the data. A solution to this problem is to model the system using ab initio electronic structure calculation, by solving the Schrodinger's equation and compute the potential energy and forces from the first principles. Such a technique can provide very accurate description of the interatomic interactions, but are computationally very extensive and hence limited only to small systems involving only a few atoms. Genetic algorithms (GA) can be used to fit highly nonlinear multivariate functional forms. GA uses a stochastic global search method that mimics the process of natural biological evolution. The concept is based on genetics in which different genetic representations of a set of variables are combined to produce a better solution. The technique is stochastic in nature rather than conventional gradient based approaches and hence the dimensionality of the problem does not pose a serious limitation. In this study, the parameters for Tersoff potential function are found for silicon clusters using GA. In the second part of the investigation, the reaction dynamics of vibrationally excited vinyl bromide was investigated using neural network potential surface fitted to ab initio energies obtained from electronic structure calculations. Dissociation rate coefficients and branching ratios for open reaction channels were computed at an internal energy of 6.44 eV. The potential energy hyper-surface is developed by fitting the ab initio energies using a multi-layer neural network (NN). The use of NN for developing potential energy hyper-surfaces obviates the need to assume a fixed underlined functional form and thus provides a greater flexibility.;In the last part of the investigation, a general method for the development of potential-energy hyper-surfaces is presented. The Generalized Potential Energy Surface (GPES) combines a many-body expansion to represent the potential-energy surface with multi-layer NNs. Each of the M-body terms in the expansion is represented by using a NN. Under the GPES methodology, all the NNs are trained simultaneously, so that the coupled nature NN parameters is preserved using Levenberg-Marquardt algorithm.