Evaluation of two‐center overlap and nuclear attraction integrals over Slater‐type orbitals with integer and noninteger principal quantum numbers

Özdoğan, Telhat; Orbay, Metin

doi:10.1002/qua.10052

Cited by 34 publications

(20 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One can easily derive these formulas by means of the simple algebra in our papers. The published formulas in 1 can be obtained from the following equations from our articles 2–4—expansion formulas (see Eqs. (10), (16), and (38) of 2, Eq.…”

Section: Theorymentioning

confidence: 99%

“…Let us first show that Eq. (9) of 1 can be derived from Eq. (1) by means of changing the summation indices.…”

Section: Theorymentioning

confidence: 99%

“…Now we are in a position to obtain the formulas published in Ref. 1 for the two‐center overlap and nuclear‐attraction integrals in terms of auxiliary functions. Finally, substituting Eq.…”

Section: Theorymentioning

confidence: 99%

“…Özdogan and Orbay 1 published the formulas for the expansion of the product of two normalized associated Legendre functions in ellipsoidal coordinates and the two‐center overlap and nuclear‐attraction integrals over Slater‐type orbitals (STOs).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Comment on “Evaluation of Two‐Center Overlap and Nuclear‐Attraction Integrals over Slater‐Type Orbitals with Integer and Noninteger Principal Quantum Numbers”

Guseinov¹

2002

Int J of Quantum Chemistry

View full text Add to dashboard Cite

ABSTRACT:Recently published formulas for the evaluation of two-center overlap and nuclear-attraction integrals (Ö zdogan, T.; Orbay, M. Int J Quantum Chem 2002, 87, 15) are critically analyzed. It is proved that the general formula presented in this work for the expansion of the product of two normalized associated Legendre functions in ellipsoidal coordinates is obtained from the expansion relationships contained in our articles (Guseinov, I. I. J Phys B 1970, 3, 1399 Phys Rev A 1985, 32, 1864 J Mol Struct THEOCHEM 1995, 336, 17) by changing the summation indices. It is demonstrated that the formulas published by these authors results in two-center overlap and nuclearattraction integrals that are also derived from our formulas.

show abstract

Section: Theorymentioning

confidence: 99%

“…Let us first show that Eq. (9) of 1 can be derived from Eq. (1) by means of changing the summation indices.…”

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Comment on “Evaluation of Two‐Center Overlap and Nuclear‐Attraction Integrals over Slater‐Type Orbitals with Integer and Noninteger Principal Quantum Numbers”

Guseinov¹

2002

Int J of Quantum Chemistry

View full text Add to dashboard Cite

show abstract

“…The usefulness of non-Gaussian basis sets with improved cusp properties is illustrated most starkly by considering the current use 18 of Slater basis sets [19][20][21] for specific purposes despite the very long integral evaluation times, 22,23 as well as more generally in the Amsterdam Density Functional (ADF) program. 24 Thus, despite more than 80 yr of investigation, [25][26][27][28] research is still undertaken [29][30][31][32][33][34][35][36][37][38][39][40][41] to improve integral evaluation for Slatertype orbitals to make these calculations competitive with all-Gaussian calculations. Given this, mixed ramp-Gaussian basis sets arguably encapsulate the best of both worlds: characteristics similar to all-Slater basis sets with the potential to match or better all-Gaussian calculation speeds.…”

Section: Introductionmentioning

confidence: 99%

Efficient calculation of integrals in mixed ramp-Gaussian basis sets

McKemmish

2015

The Journal of Chemical Physics

View full text Add to dashboard Cite

Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RampItUp. These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density functional theory quantum chemistry calculations, replacing all-Gaussian basis sets, and (2) give very large speed-ups for calculations of core-dependent properties, such as electron density at the nucleus, NMR parameters, relativistic corrections, and total energies, replacing the current use of Slater basis functions or very large specialised all-Gaussian basis sets for these purposes. This initial implementation already demonstrates roughly 10% speed-ups in HF/R-31G calculations compared to HF/6-31G calculations for large linear molecules, demonstrating the promise of this methodology, particularly for the second application. As well as the reduction in the total primitive number in R-31G compared to 6-31G, this timing advantage can be attributed to the significant reduction in the number of mathematically complex intermediate integrals after modelling each ramp-Gaussian basis-function-pair as a sum of ramps on a single atomic centre.

show abstract

Hartree‐Fock‐Roothaan calculations for ground states of some atoms using minimal basis sets of integer and noninteger n‐STOs

Gümüş

Özdoğan

2004

Chin. J. Chem.

View full text Add to dashboard Cite

Hartree-Fock-Roothaan (HFR) calculations for ground states of some atoms, i.e. He, Be, Ne, Ar, and Kr have been performed using minimal basis sets of Slater type orbitals (STOs) with integer and noninteger principal quantum numbers (integer n-STOs and noninteger n-STOs). The obtained total energies for these atoms using minimal basis sets of integer n-STOs are in good agreement with those in the previous literature. On the other hand, for the case of minimal basis sets of noninteger n-STOs, although the calculated total energies of these atoms agree well with the results in Literature, some striking results have been obtained for atoms Ar and Kr. Our computational results for the energies of atoms Ar and Kr are slightly better than those in literature. by amount of 0.00222 and O.oooO54 a.u., respectively. The improvement in the energies of atoms Ar and Kr may result from the efficient calculations of one-center two-electron integrals over noninteger n-STOs. For some atomic ions in their ground state, HFR calculations have been canied out using minimal basis sets of noninteger n-STOs. The obtained total energies for these atomic ions are substantially lower than those available in literature.

show abstract

Evaluation of two‐center overlap and nuclear attraction integrals over Slater‐type orbitals with integer and noninteger principal quantum numbers

Cited by 34 publications

References 55 publications

Comment on “Evaluation of Two‐Center Overlap and Nuclear‐Attraction Integrals over Slater‐Type Orbitals with Integer and Noninteger Principal Quantum Numbers”

Comment on “Evaluation of Two‐Center Overlap and Nuclear‐Attraction Integrals over Slater‐Type Orbitals with Integer and Noninteger Principal Quantum Numbers”

Efficient calculation of integrals in mixed ramp-Gaussian basis sets

Hartree‐Fock‐Roothaan calculations for ground states of some atoms using minimal basis sets of integer and noninteger n‐STOs

Contact Info

Product

Resources

About