Accurate Electronic Wave Functions for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Molecule

Kołos, W.; Roothaan, C. C. J.

doi:10.1103/revmodphys.32.219

Cited by 696 publications

(180 citation statements)

References 12 publications

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“…Ortho-and Para-H2 molecule Table I summarizes results for the binding energy of the H 2 molecule, using DFT/GGA and AF QMC for several supercells, and compares these to exact results [18] and experiment. The experimental bondlength of H 2 was used in all the calculations.…”

Section: Results Using Planewave Basis Setsmentioning

confidence: 99%

A study of H+H2 and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with plane wave and Gaussian basis sets

Al-Saidi

Krakauer

Zhang

2007

The Journal of Chemical Physics

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We present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H2 near the equilibrium geometry and in the van der Walls limit, as well as H2O, OH, and H2O2 molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a planewave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values.

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Section: Results Using Planewave Basis Setsmentioning

confidence: 99%

A study of H+H2 and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with plane wave and Gaussian basis sets

Al-Saidi

Krakauer

Zhang

2007

The Journal of Chemical Physics

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“…For reference, we show also some available E ∞ est , the estimated experimental non relativistic, infinite nuclear mass energy [36][37][38]. These represent the estimated exact results at the infinite basis size limit, and are thus significantly lower than the CCSD(T), FCI, or QMC energies because of the small basis size chosen in these benchmark calculations.…”

Section: All-electron Total Ground-state Energiesmentioning

confidence: 99%

Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis

Al-Saidi

Zhang

Krakauer

2006

The Journal of Chemical Physics

168

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We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis, and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with system size, as a low power. A QMC approach with auxiliary fields in principle allows an exact solution of the Schrödinger equation in the chosen basis. However, the well-known sign/phase problem causes the statistical noise to increase exponentially. The phaseless method controls this problem by constraining the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. In the present calculations, the trial wave function is a single Slater determinant from a Hartree-Fock calculation. The calculated all-electron total energies show typical systematic errors of no more than a few milli-Hartrees compared to exact results. At equilibrium geometries in the molecules we studied, this accuracy is roughly comparable to that of coupled-cluster with single and double excitations and with non-iterative triples, CCSD(T). For stretched bonds in H2O, our method exhibits better overall accuracy and a more uniform behavior than CCSD(T).

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“…It is well known that such gaussian geminal or orbital wave functions do not satisfy the electron-nucleus cusp condition, and it is for this reason we employ this wave function. Additionally, in contrast to wave functions such as the Kolos-Roothan type wave function [23,24], the calculations are analytical.…”

Section: Criticality Of Cusp Condition-application To the Hydro-gmentioning

confidence: 99%

Criticality of the electron-nucleus cusp condition to local effective potential-energy theories

Pan

Sahni

2003

Phys. Rev. A

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Local(multiplicative) effective potential energy theories of electronic structure comprise the transformation of the Schrödinger equation for interacting fermi systems to model noninteracting fermi or bose systems whereby the equivalent density and energy are obtained. By employing the integrated form of the Kato electron-nucleus cusp condition, we prove that the effective electron -interaction potential energy of these model fermions or bosons is finite at a nucleus. The proof is general and valid for arbitrary system whether it be atomic, molecular, or solid state, and for arbitrary state and symmetry. This then provides justification for all prior work in the literature based on the assumption of finiteness of this potential energy at a nucleus. We further demonstrate the criticality of the electron-nucleus cusp condition to such theories by example of the Hydrogen molecule. We show thereby that both model system effective electron-interaction potential energies, as determined from densities derived from accurate wave functions, will be singular at the nucleus unless the wave function satisfies the electron-nucleus cusp condition.

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Accurate Electronic Wave Functions for theH2Molecule

Cited by 696 publications

References 12 publications

A study of H+H2 and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with plane wave and Gaussian basis sets

A study of H+H2 and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with plane wave and Gaussian basis sets

Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis

Criticality of the electron-nucleus cusp condition to local effective potential-energy theories

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