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.

The insulating ground state of 5d transition metal oxide CaIrO 3 has been classified as a Mott-type insulator. Based on a systematic density functional theory (DFT) study with local, semilocal, and hybrid exchangecorrelation functionals, we reveal that the Ir t 2g states exhibit large splittings and one-dimensional electronic states along the c axis due to a tetragonal crystal field. Our hybrid DFT calculation adequately describes the antiferromagnetic (AFM) order along the c direction via a superexchange interaction between Ir 4+ spins. Furthermore, the spin-orbit coupling (SOC) hybridizes the t 2g states to open an insulating gap. These results indicate that CaIrO 3 can be represented as a spin-orbit Slater insulator, driven by the interplay between a longrange AFM order and the SOC. Such a Slater mechanism for the gap formation is also demonstrated by the DFT + dynamical mean field theory calculation, where the metal-insulator transition and the paramagnetic to AFM phase transition are concomitant with each other. PACS numbers: 71.20.Be, 71.70.Ej, 75.10.Lp, 71.15.Mb One of the most important phenomena in condensed matter physics is the Mott transition driven by electron-electron correlations [1,2]. In 3d transition-metal oxides (TMOs), the localized 3d orbitals are responsible for the strong on-site Coulomb repulsion (U), leading to a Mott-Hubbard insulator where U splits a half-filled band into lower and upper Hubbard bands. Surprisingly, despite weaker U in 5d TMOs due to the very delocalized 5d orbitals, a series of Ir oxides such as Sr 2 IrO 4 [3][4][5][6][7], Na 2 IrO 3 [8][9][10], and CaIrO 3 [11][12][13][14][15] including Ir 4+ ions with five valence electrons exhibit an insulating ground state. For this unusual insulating behavior of the 5d iridates, it was proposed that spin-orbit coupling (SOC) splits the Ir t 2g states into completely filled j eff = 3/2 bands and a narrow half-filled j eff = 1/2 band at the Fermi level (E F ), and the latter band is further split into two Hubbard subbands by moderate Coulomb repulsion [3][4][5]. Such a j eff = 1/2 Mott-Hubbard scenario has, however, been challenged by an alternative scenario of Slater mechanism [16] based on the single-particle band picture, where the opening of insulating gap in 5d TMOs is driven by a long-range magnetic ordering [6,7,17,18].Here we focus on the post-perovskite CaIrO 3 with a highly anisotropic geometry where IrO 6 octahedra share corners along the c axis and have common edges along the a axis (see Fig. 1). Recently, the nature of the ground state in CaIrO 3 has been an object of hot debate [11][12][13][14][15]. On the basis of resonant x-ray magnetic scattering (RMXS) experiment, Ohgushi et al. [12] claimed the robustness of the j eff = 1/2 ground state against structural distortions. However, a resonant inelastic x-ray scattering (RIXS) experiment of Sala et al. [13] concluded that CaIrO 3 is not a j eff = 1/2 iridate by showing that the j eff = 1/2 state is severely altered by a large tetragonal crystal field splitting, ther...

We present an efficient method for calculating the electronic structure and total energy of strongly correlated electron systems. The method extends the traditional Gutzwiller approximation for one-particle operators to the evaluation of the expectation values of two particle operators in the many-electron Hamiltonian. The method is free of adjustable Coulomb parameters, and has no double counting issues in the calculation of total energy, and has the correct atomic limit. We demonstrate that the method describes well the bonding and dissociation behaviors of the hydrogen and nitrogen clusters, as well as the ammonia composed of hydrogen and nitrogen atoms. We also show that the method can satisfactorily tackle great challenging problems faced by the density functional theory recently discussed in the literature. The computational workload of our method is similar to the Hartree-Fock approach while the results are comparable to high-level quantum chemistry calculations.