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Communication: Certifying the potential energy landscape
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/content/aip/journal/jcp/138/17/10.1063/1.4803162
2013-05-03
2014-10-22

Abstract

It is highly desirable for numerical approximations to stationary points for a potential energy landscape to lie in the corresponding quadratic convergence basin. However, it is possible that an approximation may lie only in the linear convergence basin, or even in a chaotic region, and hence not converge to the actual stationary point when further optimization is attempted. Proving that a numerical approximation will quadratically converge to the associated stationary point is termed . Here, we apply Smale's α-theory to stationary points, providing a certification serving as a that the numerical approximation does indeed correspond to an actual stationary point, independent of the precision employed. As a practical example, employing recently developed certification algorithms, we show how the α-theory can be used to certify all the known minima and transition states of Lennard-Jones LJ atomic clusters for = 7, …, 14.

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Scitation: Communication: Certifying the potential energy landscape
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/17/10.1063/1.4803162
10.1063/1.4803162
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