Curing basis-set convergence of wave-function theory using density-functional theory: A systematically improvable approach

Giner, Emmanuel; Pradines, Barthélémy; Ferté, Anthony; Assaraf, Roland; Savin, Andreas; Toulouse, Julien

doi:10.1063/1.5052714

Cited by 56 publications

(116 citation statements)

References 49 publications

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“…Many techniques have been developed to accelerate the convergence to the complete basis-set limit including explicitly correlated methods, transcorrelated methods or simple yet less efficient basis-set extrapolation techniques [1][2][3][4][5][6][7][8]. More recently a density-functional theory based approach has also been employed to correct for basis set incompleteness errors [9].…”

Section: Introductionmentioning

confidence: 99%

Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theory

Irmler

Grüneis

2019

The Journal of Chemical Physics

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We investigate the basis-set convergence of electronic correlation energies calculated using coupled cluster theory and a recently proposed finite basis-set correction technique. The correction is applied to atomic and molecular systems and is based on a diagrammatically decomposed coupled cluster singles and doubles correlation energy. Only the second-order energy and the particle-particle ladder term are corrected for their basis-set incompleteness error. We present absolute correlation energies and results for a large benchmark set. Our findings indicate that basis set reductions by two cardinal numbers are possible for atomization energies, ionization potentials and electron affinities without compromising accuracy when compared to conventional CCSD calculations. In the case of reaction energies we find that reductions by one cardinal number are possible compared to conventional CCSD calculations. The employed technique can readily be applied to other many-electron theories without the need for three-or four-electron integrals.

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Section: Introductionmentioning

confidence: 99%

Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theory

Irmler

Grüneis

2019

The Journal of Chemical Physics

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“…As in Ref. 41, we consider here a speci c class of short-range correlation functionals known as correlation energy with multi-determinantal reference (ECMD) whose general de nition reads 42…”

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confidence: 99%

A Density-Based Basis-Set Correction for Wave Function Theory

Loos

Pradines

Scemama

et al. 2019

J. Phys. Chem. Lett.

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We report a universal density-based basis-set incompleteness correction that can be applied to any wave function method. e present correction, which appropriately vanishes in the complete basis set (CBS) limit, relies on short-range correlation density functionals (with multideterminant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis-set incompleteness error. Contrary to conventional RS-DFT schemes which require an ad hoc range-separation parameter µ, the key ingredient here is a range-separation function µ(r) that automatically adapts to the spatial non-homogeneity of the basis-set incompleteness error.As illustrative examples, we show how this density-based correction allows us to obtain CCSD(T) atomization and correlation energies near the CBS limit for the G2 set of molecules with compact Gaussian basis sets.Contemporary quantum chemistry has developed in two directions -wave function theory (WFT) 1 and density-functional theory (DFT). 2 Although both spring from the same Schrödinger equation, each of these philosophies has its own pros and cons.WFT is a ractive as it exists a well-de ned path for systematic improvement as well as powerful tools, such as perturbation theory, to guide the development of new WFT ansätze. e coupled cluster (CC) family of methods is a typical example of the WFT philosophy and is well regarded as the gold standard of quantum chemistry for weakly correlated systems. By increasing the excitation degree of the CC expansion, one can systematically converge, for a given basis set, to the exact, full con guration interaction (FCI) limit, although the computational cost associated with such improvement is usually high. One of the most fundamental drawbacks of conventional WFT methods is the slow convergence of energies and properties with respect to the size of the one-electron basis set. is undesirable feature was put into light by Kutzelnigg more than thirty years ago. 3 To palliate this, following Hylleraas' footsteps, 4 Kutzelnigg proposed to introduce explicitly the interelectronic distance r 12 = |r 1 − r 2 | to properly describe the electronic wave function around the coalescence of two electrons. 3,5,6 e resulting F12 methods yield a prominent improvement of the energy convergence, and achieve chemical accuracy for small organic molecules with relatively small Gaussian basis sets. [7][8][9][10][11][12] For example, at the CCSD(T) level, one can obtain quintuple-ζ quality correlation energies with a triple-ζ basis, 13 although computational overheads are introduced by the large auxiliary basis used to resolve three-and four-electron integrals. 14 To reduce further the computational cost and/or ease the transferability of the F12 correction, approximated and/or universal schemes have recently emerged. [15][16][17][18][19][20] Present-day DFT calculations are almost exclusively done within the so-called Kohn-Sham (KS) formalism, which corresponds to an exact dressed one-electron theory. 21 e a ractiveness of DFT originates from its very favor...

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“…It is de ned such that the long-range interaction of RS-DFT, w lr,µ (r 12 ) = erf(µr 12 )/r 12 , coincides, at coalescence, with an e ective two-electron interaction W B (r 1 , r 2 ) "mimicking" the Coulomb operator in an incomplete basis B, i.e. w lr,µ B (r) (0) = W B (r, r) at any r. 19 e explicit expression of W B (r 1 , r 2 ) is given by (11) and Γ rs pq = 2 Ψ B |â † r ↓â † s ↑â q ↑â p ↓ |Ψ B are the opposite-spin pair density associated with Ψ B and its corresponding tensor, respectively, φ p (r) is a (real-valued) molecular orbital (MO),…”

Section: A Range-separation Functionmentioning

confidence: 87%

“…As initially proposed in Ref. 19 and further developed in Ref. 20, we have shown that one can e ciently approxi-mateĒ B [n] by short-range correlation functionals with multideterminantal (ECMD) reference borrowed from RS-DFT.…”

Section: A Range-separation Functionmentioning

confidence: 99%

Chemically Accurate Excitation Energies With Small Basis Sets

Giner¹,

Scemama²,

Toulouse³

et al. 2019

Preprint

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By combining extrapolated selected con guration interaction (sCI) energies obtained with the CIPSI (Con guration Interaction using a Perturbative Selection made Iteratively) algorithm with the recently proposed shortrange density-functional correction for basis-set incompleteness [Giner et al., J. Chem. Phys. 2018, 149, 194301], we show that one can get chemically accurate vertical and adiabatic excitation energies with, typically, augmented double-ζ basis sets. We illustrate the present approach on various types of excited states (valence, Rydberg, and double excitations) in several small organic molecules (methylene, water, ammonia, carbon dimer and ethylene). e present study clearly evidences that special care has to be taken with very di use excited states where the present correction does not catch the radial incompleteness of the one-electron basis set.

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Curing basis-set convergence of wave-function theory using density-functional theory: A systematically improvable approach

Cited by 56 publications

References 49 publications

Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theory

Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theory

A Density-Based Basis-Set Correction for Wave Function Theory

Chemically Accurate Excitation Energies With Small Basis Sets

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