A derivation of the frozen-orbital unrestricted open-shell and restricted closed-shell second-order perturbation theory analytic gradient expressions

. A detailed derivation of the frozen-orbital second-order perturbation theory (MP2) analytic gradient in the spin-orbital basis is presented. The summation ranges and modification of the MP2 gradient terms that result from the frozen-orbital approximation are clearly identified. The frozen-orbital analytic gradients for unrestricted MP2 and closed-shell MP2 are determined from the spin-orbital derivation. A discussion of useful implementation procedures is included. Timings from full and frozen-orbital MP2 gradient calculations on the molecule silicocene (the silicon analog of the sandwich compound ferrocene) are also presented.