Asymmetric Density Fitting with Modified Cholesky Decomposition Applied to Second-Order Electron Propagator

Lew-Yee, Juan Felipe Huan; Flores‐Moreno, Roberto; Morales, José Luís; Campo, Jorge M. del

doi:10.1021/acs.jctc.9b01215

Cited by 7 publications

(4 citation statements)

References 91 publications

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“…In parallel with the work of Folkestad et al, Lew‐Yee et al 68 reported two algorithms on the combination of asymmetric DF together with CD ERIs in a second‐order propagator implementation. Most recently, Zhang et al 69 reported a careful analysis of the computational costs of the two‐step procedure, and determined the optimal way to implement CD with respect to memory footprint and number of floating‐point operations.…”

Section: Cholesky Decompositionsmentioning

confidence: 99%

The versatility of the Cholesky decomposition in electronic structure theory

Pedersen,

Lehtola,

Fdez. Galván

et al. 2023

WIREs Comput Mol Sci

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The resolution‐of‐the‐identity (RI) or density fitting (DF) approximation for the electron repulsion integrals (ERIs) has become a standard component of accelerated and reduced‐scaling implementations of first‐principles Gaussian‐type orbital electronic‐structure methods. The Cholesky decomposition (CD) of the ERIs has also become increasingly deployed across quantum chemistry packages in the last decade, even though its early applications were mostly limited to high‐accuracy methods such as coupled‐cluster theory and multiconfigurational approaches. Starting with a summary of the basic theory underpinning both the CD and RI/DF approximations, thus underlining the extremely close relation of the CD and RI/DF techniques, we provide a brief and largely chronological review of the evolution of the CD approach from its birth in 1977 to its current state. In addition to being a purely numerical procedure for handling ERIs, thus providing robust and computationally efficient approximations to the exact ERIs that have been found increasingly useful on modern computer platforms, CD also offers highly accurate approaches for generating auxiliary basis sets for the RI/DF approximation on the fly due to the deep mathematical connection between the two approaches. In this review, we aim to provide a concise reference of the main techniques employed in various CD approaches in electronic structure theory, to exemplify the connection between the CD and RI/DF approaches, and to clarify the state of the art to guide new implementations of CD approaches across electronic structure programs.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry Quantum Computing > Theory Development

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Section: Cholesky Decompositionsmentioning

confidence: 99%

The versatility of the Cholesky decomposition in electronic structure theory

Pedersen,

Lehtola,

Fdez. Galván

et al. 2023

WIREs Comput Mol Sci

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“…In the authors’ experience, AZD3 makes it feasible to compute systems 1 order of magnitude bigger than those viable with PP2. Analysis of the formal scaling and timings for the second-order propagator and ADPT can be found in recent reports. , Systems with around 1000 atoms have been treated with ADPT. , …”

Section: Resultsmentioning

confidence: 99%

“…Analysis of the formal scaling and timings for the second-order propagator and ADPT can be found in recent reports. 29,58 Systems with around 1000 atoms have been treated with ADPT. 29,32 Connection with the h Function.…”

Section: ■ Resultsmentioning

confidence: 99%

Analytic Alchemical Derivatives for the Analysis of Differential Acidity Assisted by the h Function

et al. 2021

Self Cite

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Analytical calculation of alchemical derivatives based on auxiliary density perturbation theory is described, coded, and validated. For the case where the nucleus is a hydrogen atom and the nuclear charge is changed from 1 to 0, it turns out that a good estimate of the proton binding energies can be obtained very efficiently. First-order results correspond exactly to the molecular electrostatic potential evaluated at the hydrogen nucleus location (removing self-repulsion), in agreement with previously reported extensive studies. Therefore, the second-order results reported here are refinements in accuracy that finally allow a quantitative exploration of differential acidity. Furthermore, the recently reported h function is produced in its analytical form as a byproduct and local descriptor associated with the proton binding energy values found with this approach. In an example application, proton binding energies are computed for a family of imidazolium derivatives to demonstrate the capabilities and the stability of the method with respect to changes in basis set or exchange− correlation functional.

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“…Folkestad et al 67 have used this procedure in e T in CCSD calculations on systems with up to 80 000 AO basis functions, see fig. In parallel with the work of Folkestad et al, Lew-Yee et al 68 reported two algorithms on the combination of asymmetric DF together with CD ERIs in a second-order propagator implementation. Most recently, Zhang et al 69 reported a careful analysis of the computational costs of the two-step procedure, determining the optimal way to implement CD with respect to memory footprint and number of floatingpoint operations.…”

Section: Literature Reviewmentioning

confidence: 99%

The versatility of Cholesky decomposition in electronic structure theory

Pedersen

Lehtola

Galván

et al. 2023

Preprint

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The resolution-of-the-identity (RI) or density fitting (DF) approximation for the electron repulsion integrals (ERIs) has become a standard component of accelerated and reduced-scaling implementations of first-principles Gaussian- type orbital electronic-structure methods. The Cholesky decomposition (CD) of the ERIs has also become increasingly deployed across quantum chemistry packages in the last decade, even though its early applications were mostly limited to high-accuracy methods such as coupled-cluster theory and multi-configurational approaches. Starting with a summary of the basic theory underpinning both the CD and RI/DF approximations, thus underlining the extremely close relation of the CD and RI/DF techniques, we provide a brief and largely chronological review of the evolution of the CD approach from its birth in 1977 to its current state. In addition to being a purely numerical procedure for handling ERIs, thus providing robust and computationally efficient approximations to the exact ERIs that have been found increasingly useful on modern computer platforms, CD also offers highly accurate approaches for generating auxiliary basis sets for the RI/DF approximation on the fly, as the two approaches have a deep mathematical connection. In this review, we aim to provide a concise reference of the main techniques employed in various CD approaches in electronic structure theory, to exemplify the connection between the CD and RI/DF approaches, and to clarify the state of the art to guide new implementations of CD approaches across electronic structure programs.

show abstract

Asymmetric Density Fitting with Modified Cholesky Decomposition Applied to Second-Order Electron Propagator

Cited by 7 publications

References 91 publications

The versatility of the Cholesky decomposition in electronic structure theory

The versatility of the Cholesky decomposition in electronic structure theory

Analytic Alchemical Derivatives for the Analysis of Differential Acidity Assisted by the h Function

The versatility of Cholesky decomposition in electronic structure theory

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