Structural transformation in $$(\hbox {MgO})_{{{n}}}$$ clusters using a gradient-only strategy and its comparison with a full Hessian-based calculation

Abstract

In the work, we intend to compare performance of two different techniques for locating transition state and constructing reaction paths for structural transformations in $$(\hbox {MgO})_{{\textit{n}}}$$ cluster with n = 6, 8, 9, 10, 11, 12, 15 and 16. The work has been carried out using an empirical potential energy surface to describe major interactions and using the stochastic optimization technique of simulated annealing to search out the surface. The two different strategies taken up for investigation involve one in which a full evaluation of Hessian matrix and its subsequent diagonalization have been done. The other strategy is based on calculating first derivatives or gradient only and using the information of gradients to evaluate the sign of the first eigenvalue of Hessian. As the second strategy gets rid of the costly process of evaluating second derivatives, it is expected to be a computationally advantageous option. The entire work tries to establish this notion and presents quantitative results in support of the proposition.