A benchmark of Gutzwiller conjugate gradient minimization method in ground state energy calculations of dimers

Abstract

We present numerical results of ground-state energies of 9 molecules in the wellestablished G2 molecule set given by the Gutzwiller conjugate gradient minimization (GCGM) method. The method, beyond the commonly used Gutzwiller approximation, was recently developed based on Gutzwiller variational wave functions. We find that compared to benchmark data given by full configuration interaction, GCGM total energies are reasonably well reproduced with the minimum basis set. To include the dynamical correlation beyond the minimal basis calculations, we adopt the local density approximation for the dynamical correlation energy c E . By comparing the results with benchmark data given by experiments and large-basis configuration interaction, the GCGM total energies with c E are in general better reproduced, but discrepancies are still observed for some dimers.

Ground-state properties of the Hubbard model in one and two dimensions from the Gutzwiller conjugate gradient minimization theory

“…In our previous studies, we have developed the GCGM method for correlated electron systems and benchmarked it with molecules [3,4,7] and bulk systems, in particular, the Hubbard model [5,6]. As our previous study only focused on the single-band Hubbard model, in this work we continue our investigation and validate the GCGM method with a 2-band/orbital Hubbard model with demonstrated accuracy.…”

“…We have been developing such a many-body approach, namely, the Gutzwiller conjugate gradient minimization (GCGM) method [1][2][3][4][5][6][7]. The GCGM method is based on the Gutzwiller wave function (GWF) that was proposed by Gutzwiller in the 1960s [8][9][10].…”

“…In the GCGM theory, we use the GWF without using the GA and evaluate the expectation value of an observable in a more rigorous way. Our previous work has demonstrated the improved accuracy of the GCGM method with benchmark tests of molecules, such as energy calculations of both the ground and the excited states of dimers [2][3][4]. The benchmark tests on periodic bulk systems have focused mainly on the Hubbard model, both oneand two-dimensional, but with only one band [5].…”

The Gutzwiller conjugate gradient minimization method for correlated electron systems

“…To directly compare with experiments, we need to go beyond the minimal basis set, i.e., include the dynamical correlation in energy calculations. In reference [12], we used the local density approximation (LDA) for the dynamical correlation energy and evaluated it with the PySCF package [30], but only with limited success. With the rotationally invariant scheme later introduced in this review, we greatly improve the efficiency of GCGM and can afford to perform large-basis calculations.…”

“…Moving toward this goal, we have been developing an ab initio many-body approach, the Gutzwiller conjugate gradient minimization (GCGM) method [10][11][12][13][14], based on the Gutzwiller variational wave function (GWF) that were proposed by Gutzwiller in the 1960s [15][16][17]. The GWF introduces correlations into a trial wave function via an on-site correlation factor.…”