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A resolution of identity approach to explicitly correlated congruenttransformed Hamiltonian (CTH) is presented. One of the principle challengesassociated with the congruent transformation of the many-electron Hamiltonianis the generation of three, four, five, and six particle operators. Successfulapplication of the congruent transformation requires efficient implementationof the many-particle operators. In this work, we present the resolution ofidentity congruent transformed Hamiltonian (RI-CTH) method to handlemany-particle operators. The resolution of identity was used to project theexplicitly correlated operator in a N-particle finite basis to avoid explicitcomputation of the many-particle operators. Single-particle states wereobtained by performing Hartee-Fock calculations, which were then used forconstruction of many-particle states. The limitation of the finite nature ofthe resolution of identity was addressed by developing partial infinite order(PIOS) diagrammatic summation technique. In the PIOS method, the matrixelements of the projected congruent transformed Hamiltonian was expressed interms of diagrammatic notation and a subset of diagrams were summed up toinfinite order. The RI-CTH and RI-CTH-PIOS methods were applied toisoelectronic series of 10-electron systems (Ne,HF,H2O,NH3,CH4) and resultswere compared with CISD and CCSD(T) calculations. One of the key results fromthis work is that for identical basis set, the RI-CTH-PIOS energies are lowerthan CISD and CCSD(T) values.

Infinite-order diagrammatic summation approach to explicitly correlated congruent transformed Hamiltonian