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A previous article proposed an electronic structure-based polarizable potential, called the explicit polarization (X-POL) potential, to treat many-body polarization and charge delocalization effects in polypeptides. Here, we present a variational version of the X-POL potential, in which the wave function of the entire molecular system is variationally optimized to yield the minimum total electronic energy. This allows the calculation of analytic gradients, a necessity for efficient molecular dynamics simulations. In this paper, the detailed derivations of the Fock matrix and analytic force are presented and discussed. The calculations involve a double self-consistent-field procedure in which the wave function of each fragment is self-consistently optimized in the presence of other fragments, and in addition the polarization of the entire system is self-consistently optimized. The variational X-POL potential has been implemented in the Chemistry at Harvard Molecular Mechanics (CHARMM) package and tested successfully for small model compounds.

The variational explicit polarization potential and analytical first derivative of energy: Towards a next generation force field