On the effectiveness of exponential type orbitals with hyperbolic cosine functions in atomic calculations

Şahin, E.; Özdoğan, Telhat; Orbay, Metin

doi:10.1007/s10910-017-0764-6

Cited by 10 publications

(11 citation statements)

References 24 publications

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“…There are many important studies with respect to accuracy of results and computation time when the basis functions modified with an additional parameters. In view of accuracy, as reported [9][10][11][12][13], it is shown that the accuracy of the total HFR energies increase with an increasing atomic number. In order to develop an efficient method in view of computation time, the integral bottleneck in evaluating electronic energies arises from the two-electron contributions are difficult and time-consuming, especially over ETFs used to ensure the correct analytical behavior of atomic orbitals.…”

Section: Introductionmentioning

confidence: 74%

“…In the literature, there are many attempts to reduce to computational time consumed for calculating the matrix elements of atomic and molecular systems in basis set approaches. Despite many difficulties arising from analytical evaluation of multicenter integrals over ETFs, the use of modified BTFs as basis function in atomic and molecular HFR calculations has advantages for the improvement of accuracy of quantum chemical calculations [4,12,13]. There is also continuing interest to increase the computational efficiency of calculation of atomic and molecular matrix elements over all ETFs [14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

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Comparative performance of different hyperbolic cosine functions and generalized B functions basis sets for atomic systems

Coşkun¹,

Ertürk²

2022

Phys. Scr.

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Recently, we reported a new set of Bessel type orbitals, which include the radial part of generalized Bessel functions for LCAO calculations of atomic systems. In this study, to achieve further improvement of the performance of generalized Bessel type basis sets in the Hartree-Fock-Roothaan calculations, different hyperbolic cosine functions inserted into the radial part of those generalized Bessel functions. For this purpose, three different generalized hyperbolic cosine functions have been used to construct the generalized Bessel type hyperbolic cosine basis sets. The accuracies of generalized Bessel type hyperbolic cosine orbitals within the minimal basis sets approach are compared to show their superiority to conventional approaches those in the literature. The performance of the presented basis functions is also compared to the numerical Hartree-Fock results. Our virial ratios are in good agreement to within 8-digits of the -2. It is shown that the results obtained by the new basis sets surpass the quality and accuracy of existing BTOs basis sets

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Section: Introductionmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Comparative performance of different hyperbolic cosine functions and generalized B functions basis sets for atomic systems

Coşkun¹,

Ertürk²

2022

Phys. Scr.

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“…A hyperbolic cosine factor can be associated to ETO to provide a "double zeta" character to a minimal basis set 14 . This can be considered for DHO, as well.…”

Section: Discussionmentioning

confidence: 99%

Smeared Coulomb potential orbitals for the electron-nucleus mean field configuration interaction method

Cassam-Chenaï,

Lebeau

2017

Preprint

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We propose to use the eigenfunctions of a one-electron model Hamiltonian to perform electron-nucleus mean field configuration interaction (EN-MFCI) calculations.The potential energy of our model Hamiltonian corresponds to the Coulomb potential of an infinite wire with charge Z distributed according to a Gaussian function. The time independent Schrödinger equation for this Hamiltonian is solved perturbationally in the limit of small amplitude vibration (Gaussian function width close to zero).

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“…A hyperbolic cosine factor can be associated to ETO to provide a "double zeta" character to a minimal basis set 22 . This can be considered for DHO, as well.…”

Section: Dhomentioning

confidence: 99%

Smeared Coulomb potential orbitals: I—asymptotic expansion

Cassam-Chenaı̈

Lebeau

2021

J Math Chem

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We consider an 1-electron model Hamiltonian, whose potential energy corresponds to the Coulomb potential of an infinite wire with charge Z distributed according to a Gaussian function. The time independent Schrödinger equation for this Hamiltonian is solved perturbationally in the asymptotic limit of small amplitude vibration (Gaussian function width close to zero). We propose to use the naturally polarized functions soobtained, as orbital basis sets for quantum chemical calculations. In particular, they should be well suited to perform electron-nucleus mean field configuration interaction calculations. Since the free-parameters of the model have the remarkable property to factorize the perturbative corrections to the eigenfunctions, these corrective part in factor can be simply added as additional functions to standard basis sets, leaving it to the molecular orbital calculation to optimize the free parameters within molecular orbital coefficients.

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On the effectiveness of exponential type orbitals with hyperbolic cosine functions in atomic calculations

Cited by 10 publications

References 24 publications

Comparative performance of different hyperbolic cosine functions and generalized B functions basis sets for atomic systems

Comparative performance of different hyperbolic cosine functions and generalized B functions basis sets for atomic systems

Smeared Coulomb potential orbitals for the electron-nucleus mean field configuration interaction method

Smeared Coulomb potential orbitals: I—asymptotic expansion

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