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On-the-fly parameterization of internal coordinate force constants for quasi-Newton geometry optimization in atomistic calculations
A variant of quasi-Newton geometry optimization in Cartesian coordinates for atomistic calculations is proposed. Like other schemes, it starts from an approximate Hessian diagonal in redundant internal coordinates (bond lengthes, bond angles) which is improved by Broyden-Fletcher-Goldfarb-Shanno (BFGS) updates. The key idea is to parameterize the diagonal elements of the starting Hessian on the fly. By automatically classifying all interatomic bonds according to bond length and elements involved, and treating all similar bonds equal, one arrives at a very small number of parameters that can be determined from few displacements, often only one. The superior performance for supercell calculations compared to a standard Cartesian-coordinate optimizer is demonstrated.