Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory

Garniron, Yann; Scemama, Anthony; Loos, Pierre‐François; Caffarel, Michel

doi:10.1063/1.4992127

Cited by 148 publications

(221 citation statements)

References 43 publications

(88 reference statements)

Supporting

Mentioning

217

Contrasting

Order By: Relevance

“…where κ denotes a determinant outside R. To reduce the cost of the evaluation of the second-order energy correction, the semi-stochastic multi-reference approach of Garniron et al 47 was used, adopting the technical specifications recommended in that work. The CIPSI energy is systematically refined by doubling the size of the CI reference space at each iteration, selecting the determinants κ with the largest |e (2) κ |.…”

Section: The Cipsi Algorithm In a Nutshellmentioning

confidence: 99%

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

Giner

Pradines

Ferté

et al. 2018

The Journal of Chemical Physics

105

View full text Add to dashboard Cite

The present work proposes to use density-functional theory (DFT) to correct for the basis-set error of wavefunction theory (WFT). One of the key ideas developed here is to define a range-separation parameter which automatically adapts to a given basis set. The derivation of the exact equations are based on the Levy-Lieb formulation of DFT, which helps us to define a complementary functional which corrects uniquely for the basis-set error of WFT. The coupling of DFT and WFT is done through the definition of a realspace representation of the electron-electron Coulomb operator projected in a one-particle basis set. Such an effective interaction has the particularity to coincide with the exact electron-electron interaction in the limit of a complete basis set, and to be finite at the electron-electron coalescence point when the basis set is incomplete. The non-diverging character of the effective interaction allows one to define a mapping with the long-range interaction used in the context of range-separated DFT and to design practical approximations for the unknown complementary functional. Here, a local-density approximation is proposed for both fullconfiguration-interaction (FCI) and selected configuration-interaction approaches. Our theory is numerically tested to compute total energies and ionization potentials for a series of atomic systems. The results clearly show that the DFT correction drastically improves the basis-set convergence of both the total energies and the energy differences. For instance, a sub kcal/mol accuracy is obtained from the aug-cc-pVTZ basis set with the method proposed here when an aug-cc-pV5Z basis set barely reaches such a level of accuracy at the near FCI level.

show abstract

Section: The Cipsi Algorithm In a Nutshellmentioning

confidence: 99%

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

Giner

Pradines

Ferté

et al. 2018

The Journal of Chemical Physics

105

View full text Add to dashboard Cite

show abstract

“…E PT2 is efficiently computed with a recently proposed hybrid stochastic-deterministic algorithm. 18 In order to extrapolate the sCI results to the FCI limit, the method recently proposed by Holmes, Umrigar and Sharma in the context of the HBCI method 5 is employed. It consists in extrapolating the sCI energy, E sCI , as a function of E PT2 , i.e E sCI E FCI − E PT2 .…”

Section: B Application To Atomic and Molecular Systemsmentioning

confidence: 99%

“…Table VI presents the HF and 1s 2 -frozen-core exFCI energies of CH 4 . The geometry of the molecule -close to the experimental one-is given in the Supporting Information.…”

Section: Chmentioning

confidence: 99%

Evaluating two-electron-repulsion integrals over arbitrary orbitals using zero variance Monte Carlo: Application to full configuration interaction calculations with Slater-type orbitals

Caffarel

2019

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

A Monte Carlo method for evaluating multi-center two-electron-repulsion integrals over any type of orbitals (Slater, Sturmian, finite-range, numerical, etc.) is presented. The approach is based on a simple and universal (orbital-independent) gaussian sampling of the two-electron configuration space and on the use of efficient zero-variance Monte Carlo estimators. Quite remarkably, it is shown that the high level of accuracy required on two-electron integrals to make Hartree-Fock (HF) and configuration interaction (CI) calculations feasible can be achieved. A first zero-variance estimator is built by introducing a gaussian approximation of the orbitals and by evaluating the two-electron integrals using a correlated sampling scheme for the difference between exact and approximate orbitals. A second one is based on the introduction of a general coordinate transformation. The price to pay for this simple and general Monte Carlo scheme is the high computational cost required. However, we argue that the great simplicity of the algorithm, its embarrassingly parallel nature, its ideal adaptation to modern computational platforms and, most importantly, the possibility of using more compact and physically meaningful basis sets make nevertheless the method attractive. HF and near full CI (FCI) calculations using Slater-type orbitals (STO) are reported for Be, CH 4 and [H 2 N(CH)NH 2 ] + (a simple model of cyanine). To the best of our knowledge, our largest FCI calculation involving 18 active electrons distributed among 90 orbitals for the cyanine molecule, is the most extensive molecular calculation performed so far using pure STO orbitals (no gaussian approximation, even for the challenging four-center two-electron integrals).

show abstract

“…where D σ I and R σ are determinants and coordinates of the spin-σ electrons, respectively. The fermionic nature of the wave function is imposed using a single-or multi-determinant expansion of Slater determinants [17,18,19,20,21,22] made of Hartree-Fock (HF) or Kohn-Sham (KS) molecular orbitals (MOs) φ i (r) = N µ c µi χ µ (r) (2) built as a linear combination of N Gaussian basis functions χ µ (r). J(R) is called the Jastrow factor and its main purpose is to catch the bulk of the dynamic electron correlation.…”

Section: Introductionmentioning

confidence: 99%

Self-consistent electron–nucleus cusp correction for molecular orbitals

Loos

Scemama

Caffarel

2019

State of the Art of Molecular Electronic Structure Computations: Correlation Methods, Basis Sets and More

Self Cite

View full text Add to dashboard Cite

We describe a method for imposing the correct electron-nucleus (e-n) cusp in molecular orbitals expanded as a linear combination of (cuspless) Gaussian basis functions. Enforcing the e-n cusp in trial wave functions is an important asset in quantum Monte Carlo calculations as it significantly reduces the variance of the local energy during the Monte Carlo sampling. In the method presented here, the Gaussian basis set is augmented with a small number of Slater basis functions. Note that, unlike other e-n cusp correction schemes, the presence of the Slater function is not limited to the vicinity of the nuclei. Both the coefficients of these cuspless Gaussian and cusp-correcting Slater basis functions may be self-consistently optimized by diagonalization of an orbital-dependent effective Fock operator. Illustrative examples are reported for atoms (H, He and Ne) as well as for a small molecular system (BeH 2 ). For the simple case of the He atom, we observe that, with respect to the cuspless version, the variance is reduced by one order of magnitude by applying our cusp-corrected scheme.

show abstract

Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory

Cited by 148 publications

References 43 publications

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

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

Evaluating two-electron-repulsion integrals over arbitrary orbitals using zero variance Monte Carlo: Application to full configuration interaction calculations with Slater-type orbitals

Self-consistent electron–nucleus cusp correction for molecular orbitals

Contact Info

Product

Resources

About