  A resolution of identity approach to explicitly correlated congruent
transformed Hamiltonian (CTH) is presented. One of the principle challenges
associated with the congruent transformation of the many-electron Hamiltonian
is the generation of three, four, five, and six particle operators. Successful
application of the congruent transformation requires efficient implementation
of the many-particle operators. In this work, we present the resolution of
identity congruent transformed Hamiltonian (RI-CTH) method to handle
many-particle operators. The resolution of identity was used to project the
explicitly correlated operator in a N-particle finite basis to avoid explicit
computation of the many-particle operators. Single-particle states were
obtained by performing Hartee-Fock calculations, which were then used for
construction of many-particle states. The limitation of the finite nature of
the resolution of identity was addressed by developing partial infinite order
(PIOS) diagrammatic summation technique. In the PIOS method, the matrix
elements of the projected congruent transformed Hamiltonian was expressed in
terms of diagrammatic notation and a subset of diagrams were summed up to
infinite order. The RI-CTH and RI-CTH-PIOS methods were applied to
isoelectronic series of 10-electron systems (Ne,HF,H2O,NH3,CH4) and results
were compared with CISD and CCSD(T) calculations. One of the key results from
this work is that for identical basis set, the RI-CTH-PIOS energies are lower
than CISD and CCSD(T) values.
