Minimal Auxiliary Basis Set Approach for the Electronic Excitation Spectra of Organic Molecules

Zhou, Zehao; Sala, Fabio Della; Parker, Shane M.

doi:10.1021/acs.jpclett.2c03698

Cited by 11 publications

(19 citation statements)

References 82 publications

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“…Single-point energies were, however, found to be prone to the errors introduced by the lacking handling of the mixed Cartesian/spherical auxiliary functions used in the aCD scheme, in agreement to the findings of Lehtola. 114 However, it is interesting to compare the findings of Hellmann et al to the recent work of Zhou et al, 137 who found that TDDFT excitation energies of organic molecules can be captured to 0.06 eV error with just a single(!) s-type auxiliary basis function per atom.…”

Section: Auxiliary Basis Setsmentioning

confidence: 94%

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: Auxiliary Basis Setsmentioning

confidence: 94%

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 LT-G 0 W 0 /BSE calculations, we have shown that the computational time is now dominated by the BSE calculation. Based on our three guiding principles, we aim to achieve similar improvements also for the BSE in the future by making use of, for example, minimal auxiliary basis sets 72 or simplified integrals. 73,74 ■ ASSOCIATED CONTENT * sı Supporting Information…”

Section: Discussionmentioning

confidence: 99%

Accelerating Analytic-Continuation GW Calculations with a Laplace Transform and Natural Auxiliary Functions

Tölle,

Niemeyer,

Neugebauer

2024

J. Chem. Theory Comput.

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We present a simple and accurate GW implementation based on a combination of a Laplace transform (LT) and other acceleration techniques used in post-self-consistent field quantum chemistry, namely, natural auxiliary functions and the frozen-core approximation. The LT-GW approach combines three major benefits: (a) a small prefactor for computational scaling, (b) easy integration into existing molecular GW implementations, and (c) significant performance improvements for a wide range of possible applications. Illustrating these advantages for systems consisting of up to 352 atoms and 7412 basis functions, we further demonstrate the benefits of this approach combined with an efficient implementation of the Bethe−Salpeter equation.

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“…Single-point energies were, however, found to be prone to the errors introduced by the lacking handling of the mixed Cartesian/spherical auxiliary functions used in the aCD scheme, in agreement to the findings of Lehtola 112 . However, it is interesting to compare the findings of Hellmann et al to the recent work of Zhou et al 135 , who found that TDDFT excitation energies of organic molecules can be captured to 0.06 eV error with just a single(!) s-type auxiliary basis function per atom.…”

Section: Auxiliary Basis Setsmentioning

confidence: 92%

The versatility of Cholesky decomposition in electronic structure theory

Pedersen

Lehtola

Galván

et al. 2023

Preprint

View full text Add to dashboard Cite

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

Minimal Auxiliary Basis Set Approach for the Electronic Excitation Spectra of Organic Molecules

Cited by 11 publications

References 82 publications

The versatility of the Cholesky decomposition in electronic structure theory

The versatility of the Cholesky decomposition in electronic structure theory

Accelerating Analytic-Continuation GW Calculations with a Laplace Transform and Natural Auxiliary Functions

The versatility of Cholesky decomposition in electronic structure theory

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