An index-resolved fixed-point homotopy and potential energy landscapes

Tianran Chen; Dhagash Mehta

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arXiv · 1504.06622

An index-resolved fixed-point homotopy and potential energy landscapes

Tianran Chen·Dhagash Mehta

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Abstract

Stationary points (SPs) of the potential energy landscapes can be classified by their Morse index, i.e., the number of negative eigenvalues of the Hessian evaluated at the SPs. In understanding chemical clusters through their potential energy landscapes, only SPs of a particular Morse index are needed. We propose a modification of the "fixed-point homotopy" method which can be used to directly target stationary points of a specified Morse index. We demonstrate the effectiveness of our approach by applying it to the Lennard-Jones clusters.

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cond-mat.soft cond-mat.mtrl-sci cs.NA math.DS math.NA math.OC

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Tianran Chen, Dhagash Mehta. 2015-04-24. An index-resolved fixed-point homotopy and potential energy landscapes. https://arxiv.org/abs/1504.06622

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