Analytical gradient of the linear combination of Gaussian-type orbitals—local spin density energy

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Abstract
An expression has been derived for the analytical evaluation of the energy gradient within the linear combination of Gaussian-type orbitals—local spin density method. This expression is valid for any exchange-correlation energy functional which can be represented in a density gradient expansion. In practice, because the exchange-correlation terms are fitted with auxiliary functions, one has to introduce an approximation. Results are reported of tests on diatomics that show that it is possible to attain a typical accuracy of ±0.01 a.u. on equilibrium distances, relative to the energy minimum. The formulas for molecular integral derivatives that we implemented are based on the highly efficient recurrence formulas of Obara and Saika. We report here an additional formula for angular momentum transfer which is very useful for efficient programming of the gradient. In all cases studied, the time required to compute the gradient is a fraction of the time spent to solve the self-consistent-field Kohn–Sham equations.