On the inclusion of cusp effects in expectation values with explicitly correlated Gaussians

Jeszenszki, Péter; Ireland, Robbie T.; Ferenc, Dávid; Mátyus, Edit

doi:10.1002/qua.26819

Cited by 25 publications

(44 citation statements)

References 34 publications

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“…In this direction, the computation of a precise representation of the electronic wave function is a necessary first step that was demonstrated in this work to be feasible. The adiabatic, non-adiabatic and (regularized) relativistic and QED corrections can be evaluated at a couple of points using currently existing procedures [41,46,35,47]. At the same time, for a complete description of a polyatomic system like H 3 , these corrections must be computed over hundreds or thousands of nuclear configurations.…”

Section: Summary Conclusion and Outlookmentioning

confidence: 99%

Benchmark potential energy curve for collinear H$_3$

Ferenc,

Mátyus

2022

Preprint

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A benchmark-quality potential energy curve is reported for the H 3 system in collinear nuclear configurations. The electronic Schrödinger equation is solved using explicitly correlated Gaussian (ECG) basis functions using an optimized fragment initialization technique that significantly reduces the computational cost. As a result, the computed energies improve upon recent orbital-based and ECG computations. Starting from a well-converged basis set, a potential energy curve with an estimated sub-parts-per-billion precision is generated for a series of nuclear configurations using an efficient ECG rescaling approach.

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Section: Summary Conclusion and Outlookmentioning

confidence: 99%

Benchmark potential energy curve for collinear H$_3$

Ferenc,

Mátyus

2022

Preprint

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“…To obtain precise correction values, regularization techniques [41,44,45] have been used to pinpoint the value of the non-relativistic expectation value of the singular terms, δ(r iA ), δ(r ij ), and (∇ 2 i ) 2 . Furthermore, we have noticed in earlier work [29,30] that the 'non-radiative QED' corrections of the perturbative scheme are 'visible' at the current ppb convergence level already for Z = 1.…”

Section: A Perturbative Energy Expressionsmentioning

confidence: 99%

Variational versus perturbative relativistic energies for small and light atomic and molecular systems

Ferenc¹,

Jeszenszki²,

Mátyus³

2022

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Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called nonradiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac-Coulomb-Breit (DCB) equation to all orders of the α fine-structure constant. The analysis of the polynomial α dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the nonrelativistic energy to high precision without regularization. Contributions from the Breit-Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The α dependence of the no-pair DCB energy shows that the higher-order (α 4 E h ) non-radiative QED correction is 5 % of the leading-order (α 3 E h ) non-radiative QED correction for Z = 2 (He), but it is 40 % already for Z = 4 (Be 2+ ), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.

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“…( 59), is implemented in the QUANTEN computer program [57] (for recent applications of the program see Refs. [7,10,19,[58][59][60][61][62]). QUANTEN was written using the Fortan90 programming language and contains several analytic ECG integrals.…”

Section: Implementation Of the Dirac-coulomb Matrix-eigenvalue Equationmentioning

confidence: 99%

“…The expectation values used to calculate the correction terms were taken from Refs. [75], [79], [5], and [19]. b The full non-radiative correction of order α 4 for He (1 1 S0 and 2 1 S0) and H2 (ground state, Rpp = 1.4 bohr) were taken from Refs.…”

Section: Comparison With Literature Datamentioning

confidence: 99%

“…The explicitly correlated Gaussian functions (ECGs) [8,14,15] have the advantage that they preserve the analytic formulation for a variety of systems [15][16][17]. Although, they fail to correctly describe the exact wave function near the coalescence point and at large separations of the particles [8,15], additional treatments exist to correct for this failure at the coalescence points and to enhance the convergence rate of selected expectation values [18,19].…”

Section: Introductionmentioning

confidence: 99%

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Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules

Jeszenszki,

Ferenc,

Mátyus

2021

Preprint

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The Dirac-Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting point for further comparison and further developments in relation with high-resolution atomic and molecular spectroscopy. Besides a detailed discussion of the implementation of the fundamental spinor structure, permutation and point-group symmetries, various options for the positive-energy projection procedure are presented. The no-pair Dirac-Coulomb energy converged to a parts-per-billion precision is compared with perturbative results for atomic and molecular systems with small nuclear charge values. The subsequent paper [Paper II: D. Ferenc, P. Jeszenszki, and E. Mátyus (2021)] describes the implementation of the Breit interaction in this framework.

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On the inclusion of cusp effects in expectation values with explicitly correlated Gaussians

Cited by 25 publications

References 34 publications

Benchmark potential energy curve for collinear H$_3$

Benchmark potential energy curve for collinear H$_3$

Variational versus perturbative relativistic energies for small and light atomic and molecular systems

Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules

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