Abstract
One of the important points in molecular conformation problems is the evaluation of the gradient and Hessian of potential energy functions. These functions consist of a set of energy contributions, called the force field, for approximating the interactions between atoms of a molecule. Our discussion will focus on potential energy functions that have most common terms in general force fields. We can describe potential energy functions using Cartesian coordinates or internal coordinates (bond lengths, bond angles, and torsion angles). Analytic evaluation of the gradient with respect to the internal coordinates requires O(N 4) steps, where N is the number of atoms involved. We prove that the gradient and Hessian with respect to the Cartesian coordinates are evaluated in O(N 2)and O(N 3)steps, respectively.
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Lavor, C., Maculan, N. (2004). Reducing the Cost of Evaluation of the Gradient and Hessian of Molecular Potential Energy Functions. In: Floudas, C.A., Pardalos, P. (eds) Frontiers in Global Optimization. Nonconvex Optimization and Its Applications, vol 74. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0251-3_15
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DOI: https://doi.org/10.1007/978-1-4613-0251-3_15
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