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Convergence of Slater-Type Orbitals in Calculations of Basic Molecular Integrals

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Abstract

The relationship between real Slater-type orbitals with the distinct scaling constants is examined analytically via the Fourier transform method. The convergence of the formula that we have derived in terms of infinite sums of Slater-type orbitals is analyzed numerically. Subsequently, the analytical expression is applied to basic molecular integrals. Numerical calculations performed to demonstrate the accuracy of the obtained formulas are compared with results in the literature. Numerical results are also presented in tables.

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References

  • Antolovic D, Delhalle J (1980) Multipole and overlap integrals over reduced Bessel functions in molecular quantum mechanics. Phys Rev A 21:1815–1828

    Article  MathSciNet  Google Scholar 

  • Antolovic D, Silverstone HJ (2004) On the computation of (2-2) three-center Slater-type orbital integrals of 1/r 12 using Fourier-transform-based analytical formulas. Int J Quantum Chem 100:146–154

    Article  Google Scholar 

  • Aquilanti V, Cavalli S, Coletti C, Di Domenico D, Grossi G (2001) Hyperspherical harmonics as Sturmian orbitals in momentum space: a systematic approach to the few-body Coulomb problem. Int Rev Phys Chem 20:673–709

    Article  Google Scholar 

  • Arfken GB, Weber HJ (2001) Mathematical methods for physicists. Academic Press, San Diego

    MATH  Google Scholar 

  • Avery J (2000) Hyperspherical harmonics and general sturmians. Kluwer Academic Publishers, Dordrecht

    MATH  Google Scholar 

  • Avery JS, Avery JE (2015) Rapid evaluation of molecular integrals with ETOs. Int J Quantum Chem 115:930–936

    Article  Google Scholar 

  • Barnett MP (2001) Digital erosion in the evaluation of molecular integrals. Theor Chem Acc 107:241–245

    Article  Google Scholar 

  • Barnett MP (2003) Molecular integrals and information processing. Int J Quantum Chem 95:791–805

    Article  Google Scholar 

  • Bhattacharya AK, Dhabal SC (1986) Molecular overlap integrals with exponential-type orbitals. J Chem Phys 84:1598–1605

    Article  Google Scholar 

  • Bouferguene A, Rinaldi D (1994) A new single-center method to compute molecular integrals of quantum chemistry in Slater-type orbital basis of functions. Int J Quantum Chem 50:21–42

    Article  Google Scholar 

  • Bouferguene A, Fares A, Hoggan PE (1996) STOP: slater type orbital package for general molecular electronic structure calculations. Int J Quantum Chem 57:801–810

    Article  Google Scholar 

  • Calderini D, Cavalli S, Coletti C, Grossi G, Aquilanti V (2012) Hydrogenoid orbitals revisited: from slater orbitals to coulomb sturmians. J Chem Sci 124:187–192

    Article  Google Scholar 

  • Coletti C, Calderini D, Aquilanti V (2013) d-Dimensional Kepler–Coulomb Sturmians and hyperspherical harmonics as complete orthonormal atomic and molecular orbitals. Adv Quantum Chem 67:73–128

    Article  Google Scholar 

  • Edmonds AR (1960) Angular momentum in quantum mechanics. Princeton University Press, New Jersey

    MATH  Google Scholar 

  • Fernandez Rico J, Lopez R, Ramirez G (1988) Calculation of the one-electron two-center integrals with STOs using recurrence-based algorithms. J Comput Chem 9:790–797

    Article  Google Scholar 

  • Fernandez Rico J, Lopez R, Aguado A, Ema I, Ramirez G (1998) Reference program for molecular calculations with Slater-type orbitals. J Comput Chem 19:1284–1293

    Article  Google Scholar 

  • Fernandez Rico J, Lopez R, Aguado A, Ema I, Ramirez G (2001) New program for molecular calculations with Slater-type orbitals. Int J Quantum Chem 81:148–153

    Article  Google Scholar 

  • Fernandez Rico J, Lopez R, Ema I, Ramirez G (2004) Efficiency of the algorithms for the calculation of Slater molecular integrals in polyatomic molecules. J Comput Chem 25:1987–1994

    Article  Google Scholar 

  • Filter E, Steinborn EO (1978) Extremely compact formulas for molecular two-center one-electron integrals and Coulomb integrals over Slater-type atomic orbitals. Phys Rev A 18:1–11

    Article  Google Scholar 

  • Gaunt JA (1929) The triplets of Helium. Phil Trans R Soc Lond A 228:151–196

    Article  MATH  Google Scholar 

  • Geller M (1963) Two-center integrals over solid spherical harmonics. J Chem Phys 39:84–89

    Article  Google Scholar 

  • Gradshteyn IS, Ryzhik IM (2000) Tables of integrals, sums, series and products. Academic Press, New York

    Google Scholar 

  • Guidotti C, Salvetti O, Durante N, Lamanna UT, Arrighini GP (2003) Computational quantum chemistry in terms of multicenter Slater-type orbitals: entirely numerical procedure for the accurate evaluation of the basic integrals. Int J Quantum Chem 93:59–71

    Article  Google Scholar 

  • Guseinov II (1970) Analytical evaluation of two-centre Coulomb, hybrid and one-electron integrals for Slater-type orbitals. J Phys B 3:1399–1412

    Article  Google Scholar 

  • Guseinov II, Öztekin E, Hüseyin S (2001) Computation of molecular integrals over Slater-type Orbitals. Part VI. Calculation of overlap integrals with the same screening parameters using Gegenbauer coefficients. J Mol Struct 536:59–63

    Article  Google Scholar 

  • Guseinov II, Mamedov BA, Sünel N (2002) Computation of molecular integrals over Slater-type orbitals. X. Calculation of overlap integrals with integer and noninteger n Slater orbitals using complete orthonormal sets of exponential functions. J Mol Struct 593:71–77

    Article  Google Scholar 

  • Harris FE (2002) Analytic evaluation of two-center STO electron repulsion integrals via ellipsoidal expansion. Int J Quantum Chem 88:701–734

    Article  Google Scholar 

  • Jones HW (1997) Comprehensive strategy for the calculation of overlap integrals with Slater-type orbitals. Int J Quantum Chem 61:881–889

    Article  Google Scholar 

  • Kaijser P, Smith VH Jr (1977) Evaluation of momentum distributions and compton profiles for atomic and molecular systems. Adv Quantum Chem 10:37–76

    Article  Google Scholar 

  • Magnasco V, Rapolla A, Casanova M (1999) New translation method for STOs and its application to calculation of overlap integrals. Int J Quantum Chem 73:333–340

    Article  Google Scholar 

  • Özay S, Öztekin E (2013) Recurrence relations for radial parts of STOs and evaluation of overlap integrals via the Fourier transform methods. Adv Quantum Chem 67:245–265

    Article  Google Scholar 

  • Özcan S, Öztekin E (2009) Analytical evaluation for two-center nuclear attraction integrals over Slater type orbitals by using Fourier transform method. J Math Chem 45:1153–1165

    Article  MathSciNet  MATH  Google Scholar 

  • Özdoğan T, Orbay M (2002) Evaluation of two-center overlap and nuclear attraction integrals over Slater-type orbitals with integer and noninteger principal quantum numbers. Int J Quantum Chem 87:15–22

    Article  Google Scholar 

  • Öztekin E (2004) Overlap integrals with respect to quantum numbers over Slater-type orbitals via the Fourier-transform method. Int J Quantum Chem 100:236–243

    Article  Google Scholar 

  • Öztekin E, Özcan S, Orbay M, Yavuz M (2001) Calculation of nuclear-attraction and modified overlap integrals using Gegenbauer coefficients. Int J Quantum Chem 90:136–143

    Article  Google Scholar 

  • Prosser FP, Blanchard CH (1962) On the evaluation of two-center integrals. J Chem Phys 36:1112

    Article  Google Scholar 

  • Safouhi H (2004) Highly accurate numerical results for three-center nuclear attraction and two-electron Coulomb and exchange integrals over Slater-type functions. Int J Quantum Chem 100:172–183

    Article  Google Scholar 

  • Safouhi H, Hoggan PE (2003) New methods for accelerating the convergence of molecular electronic integrals over exponential type orbitals. Mol Phys 101:19–31

    Article  Google Scholar 

  • Silverstone HJ (1966) On the evaluation of two-center overlap and Coulomb integrals with noninteger-n Slater-type orbitals. J Chem Phys 45:4337–4341

    Article  Google Scholar 

  • Todd HD, Kay KG, Silverstone HJ (1970) Unified treatment of two-center overlap, Coulomb, and kinetic-energy integrals. J Chem Phys 53:3951–3956

    Article  Google Scholar 

  • Weniger EJ, Steinborn EO (1983a) Numerical properties of the convolution theorems of B functions. Phys Rev A 28:2026–2041

    Article  MathSciNet  Google Scholar 

  • Weniger EJ, Steinborn EO (1983b) The Fourier transforms of some exponential-type basis functions and their relevance to multicenter problems. J Chem Phys 78:6121–6132

    Article  Google Scholar 

  • Weniger EJ, Grotendorst J, Steinborn EO (1986) Unified analytical treatment of overlap, two-center nuclear attraction, and coulomb integrals of B functions via the Fourier-transform method. Phys Rev A 33:3688–3705

    Article  MathSciNet  Google Scholar 

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Correspondence to Selda Akdemir.

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Akdemir, S. Convergence of Slater-Type Orbitals in Calculations of Basic Molecular Integrals. Iran J Sci Technol Trans Sci 42, 1613–1621 (2018). https://doi.org/10.1007/s40995-017-0177-1

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