Automated Selection of Active Orbital Spaces

Abstract

One of the key challenges of quantum-chemical multi-configuration methods is the necessity to manually select orbitals for the active space. This selection requires both expertise and experience and can therefore impose severe limitations on the applicability of this most general class of ab initio methods. A poor choice of the active orbital space may yield even qualitatively wrong results. This is obviously a severe problem, especially for wave function methods that are designed to be systematically improvable. Here, we show how the iterative nature of the density matrix renormalization group combined with its capability to include up to about 100 orbitals in the active space can be exploited for a systematic assessment and selection of active orbitals. These benefits allow us to implement an automated approach for active orbital space selection, which can turn multi-configuration models into black box approaches.

On the multi-reference nature of plutonium oxides: PuO22+, PuO2, PuO3 and PuO2(OH)2

“…One possibility to define stable and reliable active spaces in correlation calculations was proposed by some of us [36,39] and recently applied to facilitate black-box DMRG calculations. [79] In contrast to ref. 79, which uses the singleorbital entropy as exclusive selection criterion, we will exploit the orbital-pair mutual information in defining an optimal active space, primarily because I i|j allows us to quantify the correlation between orbital pairs and thus represents an immediate measure for electron correlation effects between orbital pairs embedded in an active space.…”

“…[79] In contrast to ref. 79, which uses the singleorbital entropy as exclusive selection criterion, we will exploit the orbital-pair mutual information in defining an optimal active space, primarily because I i|j allows us to quantify the correlation between orbital pairs and thus represents an immediate measure for electron correlation effects between orbital pairs embedded in an active space. Since we are only interested in reproducing the largest orbital-pair correlations I i|j > 10 −2 that are important for nondynamic/static electron correlation, the orbital-pair correlation-based active space will be constructed by excluding all orbitals for which all values of the orbital-pair mutual information are smaller than 10 −2 .…”

Second-Order Self-Consistent-Field Density-Matrix Renormalization Group

“…The CAS (12,28) active orbital space is a superposition of the CAS (12,12) space with the addition of the 4p as well as the so-called double-d shell for each Cr atom.…”

Polarizable Embedding Density Matrix Renormalization Group

“…These orbital-based entities have become popular as descriptors to classify multiconfigurational character. [63,64,139, 140] Figure 5 shows the PE-DMRG entanglement plots of the ground-state S 0 (left) and the first excited state S 1 (right The π orbitals are labeled 5,7-10 and the π * orbitals 11-13,16,17.…”

“…As an active-space method, DMRG relies on the selection of a proper orbital space from frontier molecular orbitals [63,64]. As a consequence, dynamical electron correlation must be considered either a posteriori, for instance by perturbation the-ory [61,[65][66][67][68][69][70][71]] (diagonalize-and-then-perturb [72]), or a priori from the outset (in a perturb-and-then-diagonalize approach [72]).…”