Second derivatives of the local-density-functional total energy when the local potential is fitted

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Abstract
Second derivatives of the total energy with respect to nuclear coordinates and self-consistent-field parameters within the linear-combination-of-atomic-orbitals approach to local-density-functional theory are discussed. We explicitly include the effects of the fitting procedures for both the electrostatic and the exchange-correlation energies of the electrons in the evaluation of derivative expressions by solving for the fitting coefficients in the appropriate Lagrangian before any differentiation. The advantages and disadvantages of fitting vis–à–vis accurate three-dimensional numerical integration are discussed.

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