We recently proposed a correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [1, 2] 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 a number of approximations, the computational effort 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 to obtain a more accurate description 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 [3].

[1] Y. X. Yao, J. Liu, C. Z. Wang, and K. M. Ho, Correlation matrix renormalization approximation for total-energy calculations of correlated electron systems, Phys. Rev. B 89, 045131 (2014).
[2] Y. X. Yao, J. Liu, C. Liu, W. C. Lu, C. Z. Wang, and K. M. Ho,  Efficient and accurate treatment of electron correction with Correlation Matrix Renormalization theory, Sci. Rep. 5, 13478 (2015).
[3] C. Liu,  J. Liu, Y. X. Yao, P. Wu, C. Z. Wang, and K. M. Ho, Correlation Matrix Renormalization Theory: Improving Accuracy with Two-Electron Density-Matrix Sum Rules, J.  Chem. Theory Comput. 12, 4806 (2016).

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