Benchmark of correlation matrix renormalization method in molecule calculations

Abstract

We report benchmark calculations of the correlation matrix renormalization (CMR) approach for 23 molecules in the well-established G2 molecule set. This subset represents molecules with spin-singlet ground state in a variety of chemical bonding and coordination environments. The QUAsi-atomic minimal basis-set orbitals (QUAMBOs) are used as local orbitals in both CMR and full configuration interaction (FCI) calculations for comparison. The results obtained from the calculations are also compared with available experimental data. It is shown that the CMR method produces binding and dissociation energy curves in good agreement with the QUAMBO-FCI calculations as well as experimental results. The CMR benchmark calculations yield a standard deviation of 0.09 Å for the equilibrium bond length and 0.018 Hartree/atom for the formation energy, with a gain of great computational efficiency which scales like Hartree-Fock method.

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

“…∑' indicates that the pure on-site terms are excluded from the summation. The sum-rule correction [21,22,24] is then used to efficiently reduce the HF-type factorization error by shifting the non-local inter-site terms to local onsite terms, which can be evaluated more accurately. After 1PDM and 2PCM are evaluated using Eq.…”

“…Recently, we developed methods based on Gutzwiller variational wave function (GWF), namely, the correlation matrix renormalization (CMR) method, [20][21][22][23] and the Gutzwiller conjugate gradient minimization (GCGM) method. [24,25] The GWF GWF Ψ is constructed by applying a correlation operator on a trial noninteracting wavefunction 0 Ψ so that each onsite valence electronic configuration is assigned an appropriate amplitude and phase factor.…”

Correlation matrix renormalization theory in multi-band lattice systems

“…The extra terms subtracted in the last two lines are to make up for the additional terms in constructing ρCMR (k) in equation (52)…”

“…While our previous publications [1][2] [52] on CMR provided proof of principle and benchmark test on the accuracy of the CMR for molecules and lattice systems with single correlated orbital on each site, this work extends the CMR theory and the computational algorithm to more complex periodic bulk systems with multiple atoms in a unit cell and multiple correlated orbitals on each atom. Such a development enables, for the first time, applications of the CMR calculations to real world solid state systems with complex multiple correlated orbitals.…”