Construction of explicitly correlated geminal-projected particle-hole creation operators for many-electron systems using the diagrammatic factorization approach

The computational cost of performing a configuration interaction (CI) calculation for treating electron-electron correlation is directly proportional to the number of terms in the CI expansion. In this work, we present a diagrammatic projection approach for a priori identification of noncontributing terms in a CI expansion. This method known as the geminal-projected configuration interaction (GP-CI) method is based on using a two-body R12 geminal operator for describing electron-electron correlation in a reference many-electron wave function. The diagrammatic projection procedure was performed by first deriving the Hugenholtz diagrams of the energy expression of the R12 reference wave function and then performing diagrammatic factorization of effective particle-hole creation operators. The projection operation, which is a functional of the geminal function, was defined and used for the construction of the geminal-projected particle-hole creation operators. The form of the two-body R12 geminal operator was derived analytically by imposing an approximate Kato cusp condition. A linear combination of the geminal-projected one-particle one-hole and two-particle two-hole operators were used for the construction of the GP-CI wave function. The applicability and implementation of the diagrammatic projection method was demonstrated by performing proof-of-concept calculations on an isoelectronic series of 10 electron systems: CH4,NH3,H2O,HF, and Ne. The results from the calculations show that compared to conventional CI calculations, the GP-CI method was able to substantially reduce the size of the CI space (by a factor of 6-9) while maintaining an accuracy of 10-5 Hartrees for the ground-state energies. These results demonstrate the ability of the diagrammatic projection procedure to identify noncontributing states using an analytical form of the R12 geminal correlator operator. The geminal-projection method was also applied to second-order Møller-Plesset perturbation theory (GP-MP2) giving similar results to the GP-CI method in terms of reduction of the double excitation space and accuracy to the ground-state energy. This work also extends the analytical derivation of the geminal-projected particle-hole creation operators that were used for the construction of the CI wave function to coupled-cluster theory (GP-CCSD). This general derivation can also be applied to other many-electron theories and multideterminant quantum Monte Carlo calculations.