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Analytic gradients for spin multiplets in natural orbital functional theory

Analytic energy gradients with respect to nuclear motion are derived for non-singlet compounds in the natural orbital functional theory. We exploit the formulation for multiplets in order to obtain a simple formula valid for any many-electron system in its ground mixed state with a total spin S and all possible spin projection Sz values. We demonstrate that the analytic gradients can be obtained without resorting to linear response theory or involving iterative procedures. It is required a single evaluation, so integral derivatives can be computed on-the-fly along the calculation and thus improve the effectiveness of screening by the Schwarz inequality. Results for small and medium size molecules with many spin multiplicities are shown. Our results are compared with experimental data and accurate theoretical equilibrium geometries.