CONTRIBUTION TO FORCE FIELD MODELING & ENERGY MINIMIZATION OF NANOSTRUCTURES - Chatzieleftheriou, Stavros (Σχολή Πολιτικών Μηχανικών, 2018)
The potential energy of molecules and nanostructures is commonly calculated in the molecular mechanics formalism by superimposing bonded and nonbonded atomic energy terms. In this work a new, generalized numerical simulation is presented for studying the mechanical behaviour of three-dimensional nanostructures at the atomic scale. The energy gradient and Hessian matrix of such assemblies are usually computed numerically; a potential energy finite element model is proposed herein where these two components are expressed analytically. The global tangent stiffness matrix for any nanostructure is formed as an assembly of the generalized finite elements and is directly equivalent to the Hessian matrix of the potential energy. The advantages of the proposed model are identified both in terms of accuracy and computational efficiency. In the case of popular force fields (e.g. CHARMM) the computation of the Hessian matrix by implementing the proposed method is of the same order to that of the energy computation. Furthermore a new energy minimization strategy is presented, that achieves excellent convergence and is suitable for dealing with large-scale molecular systems. The basis of the proposed minimization strategy (SimNano) is a trust region algorithm based on exact second order derivative information. In order to present the efficiency of the proposed energy minimization strategy several test examples are examined and the results achieved are compared with those obtained by one of the most popular molecular simulations software, i.e. the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The results indicate that the proposed minimization strategy depict superior convergence properties compared to those of the algorithms that are generally employed in the field (i.e. the non-linear conjugate gradient, Broyden– Fletcher–Goldfarb–Shanno (BFGS) algorithms, etc.). Finally an application in computational material science (stress strain curve and computation of elastic moduli of atactic polystyrene based on the quasi-harmonic approximation) that benefits from fast and rigorous energy minimization is examined.