SimNano: A Trust Region Strategy for Large-Scale Molecular Systems Energy Minimization Based on Exact Second-Order Derivative Information

In this work, a new energy minimization strategy is presented that achieves better convergence properties than the standard algorithms employed in the field (fewer steps and usually a lower minimum) and is also computationally efficient; therefore, it becomes suitable for dealing with large-scale molecular systems. The proposed strategy is integrated into the SimNano energy minimization platform that is also described herein. SimNano relies on the analytical calculation of the molecular systems’ gradient vectors and Hessian matrices using the computational modeling framework proposed by the authors (Chatzieleftheriou, S.; Adendorff, M. R.; Lagaros, N. D. Generalized Potential Energy Finite Elements for Modeling Molecular Nanostructures. J. Chem. Inf. Model. 2016, 56 (10), 1963−1978). The basis of the proposed minimization strategy is a trust region algorithm based on exact second-order derivative information. Taking advantage of the Hessian matrices’ sparsity, a specialized treatment of the data structure is implemented. The latter is beneficial and often rather necessary, especially in the case of large-scale molecular systems, improving the speed and reducing the memory requirements. In order to demonstrate 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 simulation software packages, i.e., the Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The results indicate that the proposed minimization strategy exhibits superior convergence properties compared with the typical algorithms (i.e., nonlinear conjugate gradient algorithm, limited-memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) algorithm, etc.). The SimNano energy minimization platform can be downloaded from the site http://users.ntua.gr/nlagaros/simnano.html, enabling researchers in the field to build molecular systems and perform energy minimization runs using input files in LAMMPS format.