We derive and implement the analytic energy gradient for the symmetry Projected Hartree-Fock (PHF) method avoiding the solution of coupled-perturbed HF-like equations, as in the regular unprojected method. Our formalism therefore has mean-field computational scaling and cost, despite the elaborate multi-reference character of the PHF wave function. As benchmark examples, we here apply our gradient implementation to the ortho-, meta-, and para-benzyne biradicals, and discuss their equilibrium geometries and vibrational frequencies.
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