We generalized the commonly used Gutzwiller approximation for calculating the electronic structure and total energy of strongly correlated electron systems. In our method, the evaluation of one-body and two-body density matrix elements of the Hamiltonian is simplified using a renormalization approximation to achieve better scaling of the computational effort as a function of system size. To achieve a clear presentation of the concept and methodology, we describe the detailed formalism for a finite hydrogen system with minimal basis set. We applied the correlation matrix renormalization approximation approach to a H
2 dimer and H
8 cubic fragment with minimal basis sets, as well as a H
2 molecule with a large basis set. The results compare favorably with sophisticated quantum chemical calculations. We believe our approach can serve as an alternative way to build up the exchange-correlation energy functional for an improved density functional theory description of systems with strong electron correlations.
We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.
Developing accurate and computationally efficient methods to calculate the electronic structure and total energy of correlated-electron materials has been a very challenging task in condensed matter physics and materials science. Recently, we have developed a correlation matrix renormalization (CMR) method which does not assume any empirical Coulomb interaction
U parameters and does not have double counting problems in the ground-state total energy calculation. The CMR method has been demonstrated to be accurate in describing both the bonding and bond breaking behaviors of molecules. In this study, we extend the CMR method to the treatment of electron correlations in periodic solid systems. Using a linear hydrogen chain as a benchmark system, we show that the results from the CMR method compare very well with those obtained recently by accurate quantum Monte Carlo (QMC) calculations. We also study the equation of states of three-dimensional crystalline phases of atomic hydrogen. We show that the results from the CMR method agree much better with the available QMC data in comparison with those from density functional theory and Hartree-Fock calculations.