Development, implementation and application of the analytical calculation of energy derivatives, especially nuclear gradients, of electron-correlation methods employing wavefunctions that depend explictly on the interelectronic coordinates

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The explicitly correlated approach in computational quantum chemistry comprises a family of methods using wavefunctions that depend explicitly on all electron-electron distances in the atom or molecule of interest. Today, functions of the interelectronic distances are utilized in various forms. They appear in linear or exponential (Gaussian) terms in the wavefunction, in similarity-transformed Hamiltonians and in the Jastrow functions of quantum Monte-Carlo calculations. All of these methods have the potential to compute the ground- and excited-state energies of a molecule with very high accuracy, without the need for an inacceptably large basis set of one electron orbitals. However, to the best of our knowledge, these accurate energies can only be computed in a prescribed and fixed nuclear configuration and none of the explicitly correlated methods can be used to compute analytically the first derivative of the energy with respect to nuclear displacements. It is the goal of the present project to develop and implement (for the first time) the analytical calculation of nuclear energy gradients at the level of second-order perturbation theory with terms linear in the interelectronic distances.