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Abstract: We recently developed a correlation matrix renormalization (CMR) theory to treat the electronic correlation effects in ground state total energy calculations of molecular and condensed systems using Gutzwiller variational wavefunction (GWF). The CMR method goes beyond the conventional Gutzwiller approximation and incorporates Coulomb interactions between two localized electrons on different atomic sites. By adopting several approximations, the computational workload of the CMR can be reduced to a level similar to Hartree-Fock calculations. In order to minimize the error originating from some of these approximations, we introduce a novel sum-rule correction scheme to obtain accurate descriptions of the inter-site electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method. Using linear hydrogen chain as a benchmark periodic system, we show that the results from the CMR method compare very well with those obtained recently by accurate auxiliary field quantum Monte Carlo (AFQMC) calculations. We also study the equation of states of three-dimensional crystalline phases of atomic hydrogen. The work was done in collaboration with K. M. Ho, Y. X. Yao, J. Lu, X. Zhao, and Z. Ye. |