The geminal basis in explicitly correlated wave functions

Höfener, Sebastian; Tew, David P.; Klopper, Wim; Helgaker, Trygve

doi:10.1016/j.chemphys.2008.10.022

Cited by 25 publications

(12 citation statements)

References 56 publications

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“…Electron correlation is introduced via a Jastrow factor which can be optimised by Variational Monte Carlo methods. A novel aspect of the present method is adopting approximate nucleus‐electron pair (3‐body) terms based on a simple function studied by Helgaker and coworkers in Ref 49 with c j = 1/2 and γ j = 1 initially.…”

Section: Applying Qmc To Adsorbed Co Systems: Methodsmentioning

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: Applying Qmc To Adsorbed Co Systems: Methodsmentioning

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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“…Aside from its simplicity, its important virtues for interaction energy calculations are its size consistency and the absence of geminal basis set superposition error. 34,68 On the other hand, this Ansatz is known to be relatively sensitive 69,70 to the choice of the exponent β in the expression F (r 12 ) = − 1 β exp(−βr 12 ) for the F12 correlation factor. Therefore, throughout this work we employed the values of β recommended previously: 45 for aVDZ, aVTZ, aVQZ, and aV5Z, respectively (for the aV6Z basis, β was set to 1.4 a −1 0 as well).…”

Section: Details Of the Computational Proceduresmentioning

confidence: 99%

On the accuracy of explicitly correlated coupled-cluster interaction energies — have orbital results been beaten yet?

Patkowski¹

2012

The Journal of Chemical Physics

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The basis set convergence of weak interaction energies for dimers of noble gases helium through krypton is studied for six variants of the explicitly correlated, frozen geminal coupled-cluster singles, doubles, and noniterative triples [CCSD(T)-F12] approach: the CCSD(T)-F12a, CCSD(T)-F12b, and CCSD(T)(F12*) methods with scaled and unscaled triples. These dimers were chosen because CCSD(T) complete-basis-set (CBS) limit benchmarks are available for them to a particularly high precision. The dependence of interaction energies on the auxiliary basis sets has been investigated and it was found that the default resolution-of-identity sets cc-pVXZ/JKFIT are far from adequate in this case. Overall, employing the explicitly correlated approach clearly speeds up the basis set convergence of CCSD(T) interaction energies, however, quite surprisingly, the improvement is not as large as the one achieved by a simple addition of bond functions to the orbital basis set. Bond functions substantially improve the CCSD(T)-F12 interaction energies as well. For small and moderate bases with bond functions, the accuracy delivered by the CCSD(T)-F12 approach cannot be matched by conventional CCSD(T). However, the latter method in the largest available bases still delivers the CBS limit to a better precision than CCSD(T)-F12 in the largest bases available for that approach. Our calculations suggest that the primary reason for the limited accuracy of the large-basis CCSD(T)-F12 treatment are the approximations made at the CCSD-F12 level and the non-explicitly correlated treatment of triples. In contrast, the explicitly correlated second-order Mo̸ller-Plesset perturbation theory (MP2-F12) approach is able to pinpoint the complete-basis-set limit MP2 interaction energies of rare gas dimers to a better precision than conventional MP2. Finally, we report and analyze an unexpected failure of the CCSD(T)-F12 method to deliver the core-core and core-valence correlation corrections to interaction energies consistently and accurately.

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“…This is an expected result and is in agreement with previous work on explicitly correlated methods. [51,64,65] The negative values of geminal parameters indicate the role of the geminal function in providing a better description of the Coulomb hole. The analytical forms of the GTG functions are inherently approximate and are not capable of describing the cusp correctly because their first derivative vanishes in the limit of r ee = 0…”

Section: Discussionmentioning

confidence: 99%

“…[43] Recently, Hofener and coworkers have also derived the geminal integrals by extending the ObaraSaika techniques for calculating the GTG integrals. [51] The solution for the CI coefficients requires diagonalization of the CI Hamiltonian matrix. However, the lowest eigenvalue and eigenfunction can be obtained without explicit construction and storage of the CI matrix.…”

Section: B Optimization Of the Trial Wavefunctionmentioning

confidence: 99%

Variational solution of the congruently transformed Hamiltonian for many-electron systems using a full-configuration-interaction calculation

2012

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The congruent transformation of the electronic Hamiltonian is developed to address the electron correlation problem in many-electron systems. The central strategy presented in this method is to perform transformation on the electronic Hamiltonian for approximate removal of the Coulomb singularity. The principle difference between the present method and the transcorrelated method of Handy and Boys is that the congruent transformation preserves the Hermitian property of the Hamiltonian. The congruent transformation is carried out using explicitly correlated functions and the optimum correlated transform Hamiltonian is obtained by performing a search over a set of transformation functions. The ansatz of the transformation functions are selected to facilitate analytical evaluation of all the resulting integrals. The ground state energy is obtained variationally by performing a full configuration interaction (FCI) calculation on the congruent transformed Hamiltonian. Computed results on well-studied benchmark systems show that for the identical basis functions, the energy from the congruent transformed Hamiltonian is significantly lower than the conventional FCI calculations. Since the number of configuration state functions in the FCI calculation increases rapidly with the size of the 1-particle basis set, the results indicate that the congruent transformed Hamiltonian provides a viable alternative to obtain FCI quality energy using a smaller underlying 1-particle basis set.

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The geminal basis in explicitly correlated wave functions

Cited by 25 publications

References 56 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

On the accuracy of explicitly correlated coupled-cluster interaction energies — have orbital results been beaten yet?

Variational solution of the congruently transformed Hamiltonian for many-electron systems using a full-configuration-interaction calculation

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