Efficient Implementation of Block-Correlated Coupled Cluster Theory Based on the Generalized Valence Bond Reference for Strongly Correlated Systems

Abstract

An optimized implementation of block-correlated coupled cluster theory based on the generalized valence bond wave function (GVB-BCCC) for the singlet ground state of strongly correlated systems is presented. The GVB-BCCC method with two-pair correlation (GVB-BCCC2b) or up to three-pair correlation (GVB-BCCC3b) will be the focus of this work. Three major techniques have been adopted to dramatically accelerate GVB-BCCC2b and GVB-BCCC3b calculations. First, the GVB-BCCC2b and GVB-BCCC3b codes are noticeably optimized by removing redundant calculations. Second, independent amplitudes are identified by constraining excited configurations to be pure singlet states and only independent amplitudes need to be solved. Third, an incremental updating scheme for the amplitudes in solving the GVB-BCCC equations is adopted. With these techniques, accurate GVB-BCCC3b calculations are now accessible for systems with relatively large active spaces (50 electrons in 50 orbitals) and GVB-BCCC2b calculations are affordable for systems with much larger active spaces. We have applied GVB-BCCC methods to investigate three typical kinds of systems: polyacenes, pentaprismane, and [Cu2O2]2+ isomers. For polyacenes, we demonstrate that GVB-BCCC3b can capture more than 94% of the total correlation energy even for 12-acene with 50 π electrons. For the potential energy curve of simultaneously stretching 15 C–C bonds in pentaprismane, our calculations show that the GVB-BCCC3b results are quite close to the results from the density matrix renormalization group (DMRG) over the whole range. For two dinuclear copper oxide isomers, their relative energy predicted by GVB-BCCC3b is also in good accord with the DMRG result. All calculations show that the inclusion of three-pair correlation in GVB-BCCC is critical for accurate descriptions of strongly correlated systems.

ipie: A Python-Based Auxiliary-Field Quantum Monte Carlo Program with Flexibility and Efficiency on CPUs and GPUs

“…We expect our estimate of the isomerization energy for 32- and 52-electron correlation spaces in the CBS limit to be nearly within its statistical error bar from the exact theoretical answer. We emphasize that such reliable high-level calculations have never been possible with other single- and multireference methods such as density matrix renormalization group , or high-order coupled-cluster theory in such large correlation spaces. ,, Finally, Table provides some comparison between ph-AFQMC, ph-AFQMC, and CCSD­(T) in these larger correlation spaces.…”

“…We emphasize that such reliable high-level calculations have never been possible with other single-and multireference methods such as density matrix renormalization group 62,63 or highorder coupled-cluster theory in such large correlation spaces. 55,64,65 Finally, Table 4 provides some comparison between ph-AFQMC, ph-AFQMC, and CCSD(T) in these larger correlation spaces.…”

Geminal-Based Strategies for Modeling Large Building Blocks of Organic Electronic Materials

“…At the same time, the applicability of standard wave function-based method is very limited, mainly due to unfavorable computational scaling of multireference approaches. Geminal-based methods are a promising alternative to conventional quantum chemistry models, providing a more compact representation of the correlated wave function. − Commonly used examples are the wave function classes based on the Antisymmetric Product of 1-reference orbital Geminal (AP1roG), , also known as pair Coupled Cluster Doubles (pCCD), the Antisymmetrized Product of Strongly orthogonal Geminals (APSG), the Generalized Valence Bond (GVB), and their orbital optimized variants (for a recent review, see ref ). ,− Combined with a reliable a posteriori correction to account for the missing dynamic correlation effects, − they allow us to model electron correlation effects effectively and in a balanced way . Except for perturbation-based approaches, which might break size-extensivity, these geminal-based models can be upscaled to model OPV-devices.…”

Equation-of-Motion Block-Correlated Coupled Cluster Method for Excited Electronic States of Strongly Correlated Systems

“…We should mention that EOM-GVB-BCCC2b is an excellent approximation to EOM-GVB-BCCC2, since only the intrapair excitation is neglected in the ground-state wave function and its contribution was demonstrated to be quite small in our previous studies. 31,32 For a system with only 2 GVB pairs, a GVB(2) calculation automatically determines an active space with 4 electrons in 4 GVB orbitals. Hence, the corresponding exact wave function is CASCI (4,4).…”

“…To treat excited states from a GVB (or APSG) reference, the time-dependent GVB (or APSG) formalism was established. , However, the GVB wave function only takes static correlation in each pair of electrons in 2 orbitals (bonding and antibonding) into consideration, which is insufficient to provide accurate electron correlation descriptions for general molecules. In our previous work, we developed a post-GVB method called GVB-based block-correlated coupled cluster (GVB-BCCC), − in which the GVB wave function is taken as the reference function and the correlation between different pairs is recovered via a coupled-cluster ansatz. In addition, other cluster-based methods with a similar direct product reference wave function have been developed to describe the ground and excited states of strongly correlated systems.…”