The application of cholesky decomposition in valence bond calculation

Gong, Xiping; Chen, Zhenhua; Wu, Wei

doi:10.1002/jcc.24442

Cited by 6 publications

(6 citation statements)

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“…[38][39][40] Similarly, Hohenstein et al have presented impressive implementations of CD ERI methods in connection with reduced-rank CC theory on GPUs, 41 and combined with tensor hypercontraction of the doubles amplitudes. 42 To this list of implementations of CD ERIs in ab initio methods one can also add a variational two-particle reduced-density-matrix driven CASSCF method, 43 a self-consistent-field valence bond (VBSCF) method, 44 and an implementation in density matrix renormalization group (DMRG) second-order N -electron valence state perturbation theory (NEVPT2). 45 Further developments of the CD method itself have been reported recently.…”

Section: Eris and Related Tensorsmentioning

confidence: 99%

The versatility of Cholesky decomposition of electron repulsion integrals

Pedersen

Galván

Lindh

2023

Preprint

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Over the past three decades, the resolution-of-the-identity (RI) approximation of electron repulsion integrals (ERIs) over Gaussian-type orbitals has become a stan- dard component of accelerated and reduced-scaling implementations of first-principles electronic-structure methods. For the first two decades, the closely related approach based on Cholesky decomposition (CD) of the ERIs lived a more secluded life, fo- cusing mainly on high-accuracy methods such as coupled-cluster theory and multi- configurational approaches. In the past decade, however, the CD technique has been increasingly deployed across quantum chemistry as a numerically robust, computation- ally efficient, and highly accurate approach to on-the-fly generation of auxiliary basis sets for the RI approximation. Starting with a summary of the basic theory underpin- ning both the CD and RI approximations, we provide a brief and largely chronological review of the evolution of the CD approach from its birth in 1977 as a purely numerical procedure for handling ERIs to its current state as the perhaps most powerful on-the-fly generator of auxiliary basis sets.

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Section: Eris and Related Tensorsmentioning

confidence: 99%

The versatility of Cholesky decomposition of electron repulsion integrals

Pedersen

Galván

Lindh

2023

Preprint

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“…All VB calculations were performed at the optimized geometries with the Xiamen Valence Bond (XMVB) package, which is a quantum chemistry program designed for ab initio VB calculations. The latest version is XMVB 3.0, where Cholesky decomposition is implemented to prepare the electronic repulsion integrals . The adoption of the Cholesky decomposition enables the current version of XMVB to handle more than 1000 basis functions.…”

Section: Computational Detailsmentioning

confidence: 99%

“…The second category focuses on the spin coupling patterns in VB structures and uses delocalized AOs to pursue the compactness of wave functions. Spin‐couple valence bond and generalized valence bond methods are two outstanding examples in this category, where the former uses nonorthogonal overlap‐enhanced AOs while the latter imposes strong orthogonality condition on delocalized orbitals. The third category is based on MOs and retraces VB concepts quantitatively by imposing the localization on MOs (thus orbitals are essentially semi‐delocalized).…”

Section: Introductionmentioning

confidence: 99%

“…Few VB applications aim to pursue computational accuracy due to the much higher costs than MO‐based calculations. Nevertheless, the applicability of ab initio VB methods has been significantly strengthened over the last two decades, expanding the extent from the qualitative aspect to the quantitative one, due to notably novel algorithms implemented for VB methods . Thus, it becomes necessary and timely to assess the performance of VB methods by using some well‐defined standard sets.…”

Section: Introductionmentioning

confidence: 99%

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Performance of the VBSCF method for pericyclic and π bond shift reactions

Zhang

Zhou

et al. 2018

J Comput Chem

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The performance of the valence bond self-consistent field (VBSCF) method was investigated in this paper by predicting the activation barriers and reaction energies in pericyclic and π bond shift reactions for hydrocarbons. The benchmarking set includes 3 electrocyclic reactions, 3 sigmatropic shifts, 3 cycloadditions, 2 cycloreversions, and 7 π bond shift reactions, where the first 11 reactions are taken from Houk's standard set (J. Phys. Chem. A 2003, 107, 11445). Computational results reveal that the VB(CI) method, which performs VBSCF calculations first with full covalent structures and then includes all mono-and di-ionic structures to compute the total energy without further orbital optimization, matches the accuracy of the complete active space SCF (CASSCF) method very well. The mean absolute error values (the deviations from the CASSCF data) are 0.01 kcal/mol for the reaction energy, and 0.26 and 0.32 kcal/ mol for the activation energy with the 6-31G and 6-31G(d) basis sets, respectively.

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“…[14,15] Parallel implementations are also available and they recently improved the efficiency of the codes. [16][17][18] In this paper, we discuss convergence issues related to an optimizer for Valence Bond non-orthogonal orbitals, with a special focus on excited states. [19][20][21] The super CI optimizer that we used is based on the Generalized Brillouin theorem [21,22]The paper is organized as follows: in the section 3, some equations are reminded, our notation is introduced, and our implementation is briefly explained.…”

Section: Introductionmentioning

confidence: 99%