Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations

Goings, Joshua J.; Caricato, Marco; Frisch, Michael J.; Li, Xiaosong

doi:10.1063/1.4898709

Cited by 51 publications

(52 citation statements)

References 39 publications

(63 reference statements)

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“…Finally, P–EOM–CCSD is missing, but its CCSD(2) variant is featured among the results. Based on the data in Table , the P–EOM–CCSD(2) method shows the worst performance for valence states, although it performs much better for Rydberg states, in accordance with the findings of Goings et al The remaining methods can be assigned to two groups based on the similarity of the results, EOM–CCSD and EOM–CCSD(2) on one hand and CC2 and CIS(D ∞ ) on the other. EOM–CCSD(2) and CIS(D ∞ ) are obtained from EOM–CCSD and CC2 by replacing the ground state solution with MP2 amplitudes (and hence they also lack the singles transformation in the excited state).…”

Section: Benchmarkssupporting

confidence: 84%

“…The relevant methods discussed in these papers are CCSD and CC2, while ADC(2) data are supplied by Dreuw and coworkers for Thiel's test set . The work of Goings et al also provides a comparison between some of the second‐order methods discussed here. Kánnár and Szalay revisited Thiel's work, adding some missing CC3 results and CCSDT reference data for the small molecules using the TZVP basis .…”

Section: Benchmarksmentioning

confidence: 99%

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Single‐reference coupled cluster methods for computing excitation energies in large molecules: The efficiency and accuracy of approximations

Izsák

2019

WIREs Comput Mol Sci

110

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While methodological developments in the last decade made it possible to compute coupled cluster (CC) energies including excitations up to a perturbative triples correction for molecules containing several hundred atoms, a similar breakthrough has not yet been reported for excited state computations. Accurate CC methods for excited states are still expensive, although some promising candidates for an efficient and accurate excited state CC method have emerged recently. This review examines the various approximation schemes with particular emphasis on their performance for excitation energies and summarizes the best state-of-the-art results which may pave the way for a robust excited state method applicable to molecules of hundreds of atoms.Among these, special attention will be given to exploiting the techniques of similarity transformation, perturbative approximations as well as integral decomposition, local and embedding techniques within the equation of motion CC framework. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Structure and Mechanism > Molecular Structures K E Y W O R D S accuracy, coupled cluster, efficiency, excited states, single reference | INTRODUCTIONIn their lucid review written a few years ago, 1 Sneskov and Christiansen discussed the various coupled cluster (CC) methods available for excited states. Using the systematic machinery of response theory, they described a hierarchy of methods, established a link between response theory and equation of motion (EOM) methods, and finished by discussing a number of approaches that might be used to reduce the computational cost. The present review aims at providing an overview of efficient methods available primarily for large molecules, and hence the emphasis will be laid more upon recent methodological advances which reduce the cost and on the extent this affects the accuracy of these methods. For ground state calculations, choosing a reference method for benchmarks is quite easy, since the CC singles doubles and perturbative triples, or CCSD(T), ansatz 2 is not only widely regarded as the gold standard of quantum chemistry, but it has also recently become possible to compute CCSD(T) energies for molecules containing several hundred atoms. 3 For excited states, progress has been

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Section: Benchmarkssupporting

confidence: 84%

Section: Benchmarksmentioning

confidence: 99%

Single‐reference coupled cluster methods for computing excitation energies in large molecules: The efficiency and accuracy of approximations

Izsák

2019

WIREs Comput Mol Sci

110

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“…Some of these approximations have been investigated and compared for charged excitations [57][58][59] and for neutral electronic excitations. 60,61…”

Section: Application Of Eom-ccsd To the Gw100 Test Setmentioning

confidence: 99%

On the Relation between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation

Lange

Berkelbach

2018

J. Chem. Theory Comput.

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We discuss the analytic and diagrammatic structure of ionization potential (IP) and electron affinity (EA) equation-ofmotion coupled-cluster (EOM-CC) theory, in order to put it on equal footing with the prevalent GW approximation. The comparison is most straightforward for the time-ordered one-particle Green's function, and we show that the Green's function calculated by EOM-CC with single and double excitations (EOM-CCSD) includes fewer ring diagrams at higher order than does the GW approximation, due to the former's unbalanced treatment of time-ordering. However, the EOM-CCSD Green's function contains a large number of vertex corrections, including ladder diagrams, mixed ringladder diagrams, and exchange diagrams. By including triple excitations, the EOM-CCSDT Green's function includes all diagrams contained in the GW approximation, along with many high-order vertex corrections. In the same language, we discuss a number of common approximations to the EOM-CCSD equations, many of which can be classified as elimination of diagrams. Finally, we present numerical results by calculating the principal charged excitations energies of the molecules contained in the so-called GW100 test set [J. Chem. Theory Comput. 2015, 11, 5665-5687]. We argue that (in molecules) exchange is as important as screening, advocating for a Hartree-Fock reference and second-order exchange in the self-energy. EOM GW EO EOM-CCSDT EOM-CCSD GW Number of diagrams included in the one-particle Green's functionTable of contents figure.Within the molecular physics and quantum chemistry communities, a number of perturbative schemes have been proposed to directly construct the self-energy, 12,13 including the outer-valence Green's function approach, 12 the two-particlehole Tamm-Dancoff approximation 14 and its extended variant, 15 and the algebraic diagrammatic construction. 16 More recently the second-order Green's function 17,18 has been studied, especially in its self-consistent 19 and finite-temperature 20 variations. In wavefunction-based techniques, ionization potentials and electron affinities can either be calculated as a difference in ground-state energies (between the neutral and ionic systems) or via the equation-of-motion framework, which directly results in an eigensystem whose eigen-arXiv:1805.00043v1 [physics.chem-ph]

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“…Recently, Schütz and coworkers have implemented a linear scaling CC2 method for IP. Goings et al have investigated the effect of perturbative truncation to EOM‐CCSD on various kind of excited states …”

Section: Introductionmentioning

confidence: 99%

Lower scaling approximation to EOM‐CCSD: A critical assessment of the ionization problem

Dutta

Vaval

Pal

2018

Int J of Quantum Chemistry

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In this article, we investigate the performance of different approximate variants of the EOM‐CCSD method for calculation of ionization potential (IP), as compared to EOM‐CCSDT reference values. None of the lower scaling approximations to the EOM‐CCSD method give a consistent performance for valence, inner valence, and core ionization, favoring one, or the other depending on the nature of the approximation used. The parent EOMIP‐CCSD method gives superior performance for valence IP but can show large errors for inner valence and core ionization. The problem is particularly severe for core‐ionization, where even the EOMIP‐CCSDT method cannot provide quantitative accuracy.

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Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations

Cited by 51 publications

References 39 publications

Single‐reference coupled cluster methods for computing excitation energies in large molecules: The efficiency and accuracy of approximations

Single‐reference coupled cluster methods for computing excitation energies in large molecules: The efficiency and accuracy of approximations

On the Relation between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation

Lower scaling approximation to EOM‐CCSD: A critical assessment of the ionization problem

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