Cusps and derivatives for wave‐functions expanded in Slater orbitals: A density study

Reinhardt, Peter; Hoggan, Philip E.

doi:10.1002/qua.22156

Cited by 19 publications

(10 citation statements)

References 27 publications

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“…It is assumed that the rate limiting step is the initial concerted bond‐stretch and charge re‐arrangement (shown in the scheme and Fig. 1: All the molecules involved have near‐Hartree‐Fock‐limit wave functions available from the STOP (QCPE 667)16 code using basis sets due to I. Ema,52 which are triple‐zeta STOs with one d and one f orbital on O and C. The works on water and CO 2 are referenced below, and those on diatomic molecules are unpublished tests 53, 54. An extensive QMC study showing improvements obtained using STO was recently carried out on Bluegene/P calculators 55…”

Section: Application: Describing the System And Its Usefulnessmentioning

confidence: 99%

Quantum Monte Carlo simulation of carbon monoxide reactivity when adsorbed at metal and oxide catalyst surfaces: Trial wave‐functions with exponential type basis and quasi‐exact three‐body correlation

Hoggan

2012

Int J of Quantum Chemistry

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Review publications show the advantages of using quantum Monte Carlo (QMC) methods when bonding interactions are modified and consequently, where the electron correlation energy varies and needs to be evaluated accurately. This article considers a model efficient metal catalyst for reactions of carbon monoxide. The ultimate aim is to help design industrially useful catalysts, since the reaction with water produces hydrogen gas selectively, that is, a clean fuel and a sustainable energy source. To narrow the gap between the industrial process and calculation, a model of platinum/oxide is studied. It is mimicked here by copper with and without adsorbed oxygen. Periodicity as well as a validated pseudo-potential are used to limit the number of active electrons considered. A suitable code to carry out this task is CASINO. Furthermore, this code scales linearly to 100,000 processors and possesses a shared memory facility so that it is well-suited to runs on the Blugene/P. It has been in production on such computers since early in 2011. A mixed plane-wave/exponential type orbitals (ETO) basis is used for the systems studied. Plane waves are well-suited to periodic solid substrates and a linear combination of ETOs for molecules. The atomic orbitals have direct physical interpretation, i.e., Coulomb Sturmians and hydrogen-like orbitals. Their radial nodes are shown to be essential in obtaining the vitally important accurate QMC trial wave-functions. Until 2008,ETO products on different atoms were difficult to manipulate for the evaluation of two-electron integrals. Coulomb resolutions provide an excellent approximation that reduces these integrals to a sum of one-electron overlap-like integral products that each involve orbitals on at most two centers. They are thus readily evaluated. Only these integrals need to be re-evaluated to change basis functions. In this article, QMC-VMC variational optimisation is used with a quasi analytic two-electron and nucleus correlation factor. The QMC diffusion Monte Carlo methodology is applied to adsorbed carbon monoxide and some of its reactions.

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Section: Application: Describing the System And Its Usefulnessmentioning

confidence: 99%

Quantum Monte Carlo simulation of carbon monoxide reactivity when adsorbed at metal and oxide catalyst surfaces: Trial wave‐functions with exponential type basis and quasi‐exact three‐body correlation

Hoggan

2012

Int J of Quantum Chemistry

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“…One solution would be to use a different set of basis functions [30] as, for instance, Slater basis functions [31,32,33]. However, they are known to be troublesome, mainly due to the difficulty of calculating multicentric twoelectron integrals which require expensive numerical expansions or quadratures.…”

Section: ∂ φ I (R)mentioning

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

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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.

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“…As stressed above, cusp conditions are better satisfied as nuclear charge increases, and poor results are generally attained for hydrogen, a fact previously noted by Reinhardt and Hoggan. [2] As an illustrative example, we present in Table 4 the nuclear cusps of hydrogen in formaldehyde and methanol. It can be seen that, while the cusps of spherical terms are not too bad, inaccurate values are obtained for the cusps of the dipole-type terms.…”

Section: Full Papermentioning

confidence: 99%

“…Cusp conditions for wave functions and densities have been considered useful in different contexts such as basis set optimizations, calculations of Fermi contact terms or hyperfine coupling constants, numerical calculations of atomic wave functions, Quantum Monte Carlo methods and so forth.…”

Section: Introductionmentioning

confidence: 99%

Nuclear cusp conditions and their fulfillment in molecular calculations with SLATER basis sets

Rico

López

Ema

et al. 2014

Int J of Quantum Chemistry

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A short revision of the main antecedents on the nuclear cusp conditions is followed by a derivation of the general expressions of the conditions which must be accomplished by wave functions and densities. It is stressed that in case of the molecular densities, besides Kato's cusp condition, there are also simple cusp conditions for the three dipole‐type terms of the densities but not for terms of order higher than dipole. The degree of fulfillment of standard atomic and molecular calculations with Slater basis sets is tested, concluding that errors of spherical terms usually affect the third or fourth significant figures, being smaller as nuclear charges increase, and the errors of dipole‐type components are greater than those of the spherical terms. In practice, improvements in the computational method or in the basis set do not guarantee a better fulfillment of the cusp conditions. Hydrogen is a special case which can yield poor results. © 2014 Wiley Periodicals, Inc.

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Cusps and derivatives for wave‐functions expanded in Slater orbitals: A density study

Cited by 19 publications

References 27 publications

Quantum Monte Carlo simulation of carbon monoxide reactivity when adsorbed at metal and oxide catalyst surfaces: Trial wave‐functions with exponential type basis and quasi‐exact three‐body correlation

Quantum Monte Carlo simulation of carbon monoxide reactivity when adsorbed at metal and oxide catalyst surfaces: Trial wave‐functions with exponential type basis and quasi‐exact three‐body correlation

Self-consistent electron–nucleus cusp correction for molecular orbitals

Nuclear cusp conditions and their fulfillment in molecular calculations with SLATER basis sets

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