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.