title: Communication: Certifying the potential energy landscape.
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 certification. Here, we apply Smale's α-theory to stationary points, providing a certification serving as a mathematical proof 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(N) atomic clusters for N = 7, ..., 14.
authors: Department of Physics, Syracuse University, Syracuse, New York 13244, USA. dbmehta@syr.edu
authors: Dhagash
authors: D
authors: Mehta
authors: Jonathan D
authors: JD
authors: Hauenstein
authors: David J
authors: DJ
authors: Wales