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Year 2022, Volume: 43 Issue: 4, 721 - 725, 27.12.2022

Ercan Şahin

https://doi.org/10.17776/csj.1136963

Abstract

References

  • [1] Carbo R., Leyda L., Arnau M., How Similar is a Molecule to Another? An Electron Density Measure of Similarity Between Two Molecular Structures, Int. J. Quantum Chem., 17 (1980) 1185-1189.
  • [2] Carbo-Dorca R., Besalu E., A General Survey of Molecular Quantum Similarity, J. Mol. Struct. (Theochem), 451 (1998) 11-23.
  • [3] Robert D., Girones X., Carbo-Dorca R., Molecular Quantum Similarity Measures As Descriptors for Quantum QSAR, Polycycl. Aromat. Comp., 19 (2000) 51-71.
  • [4] Carbo-Dorca R., Robert D., Amat L., Girones X., Besalu E., Molecular quantum similarity in QSAR and drug design. 1st ed. Berlin, (2000) 26-38.
  • [5] Carbo-Dorca R., Girones X., Mezey P.G., Fundamentals of molecular similarity. 1st ed. New York, (2001) 187-320.
  • [6] Bultinck P., Girones X., Carbo-Dorca R., Molecular Quantum Similarity: Theory and Applications. In: Lipkowitz K.B., Larter R., Cundari T., (Eds). Reviews in computational chemistry. 1st ed. Hoboken: Wiley, (2005) 127–207.
  • [7] Borgoo A., Godefroid M., Sen K.D., De Profit F., Geerlings P., Quantum Similarity of Atoms: A Numerical Hartree–Fock and Information Theory Approach, Chem. Phys. Lett., 399 (2004) 363-367.
  • [8] Robert D., Carbo-Dorca R., On the Extension of Quantum Similarity to Atomic Nuclei: Nuclear Quantum Similarity, J. Math. Chem., 23 (1998) 327-351.
  • [9] Amat L., Carbo-Dorca R., Quantum Similarity Measures Under Atomic Shell Approximation: First Order Density Fitting Using Elementary Jacobi Rotations, J. Comput. Chem., 18 (1997) 2023-2039.
  • [10] Amat L., Carbo-Dorca R., Molecular Electronic Density Fitting Using Elementary Jacobi Rotations Under Atomic Shell Approximation, J. Chem. Inf. Comput. Sci., 40 (2000) 1188-1198.
  • [11] Hoggan P.E., How Exponential Type Orbitals Recently Became a Viable Basis Set Choice in Molecular Electronic Structure Work and When to Use Them. In: Russo N., Antonchenko V.Y., Kryachko E.S., (Eds). Self-organization of molecular systems. 1st ed. Dordrecht: Springer, (2009) 199-219.
  • [12] Sola M., Mestres J., Oliva J.M., Duran M., Carbo R., The Use of Ab Initio Quantum Molecular Self-Similarity Measures to Analyze Electronic Charge Density Distributions, Int. J. Quantum Chem., 58 (1996) 361-372.
  • [13] Berlu L., Hoggan P.E., Useful Integrals for Ab Initio Molecular Quantum Similarity Measurements Using Slater Type Atomic Orbitals, J. Theor. Comput. Chem., 2 (2003) 147-161.
  • [14] Berlu L., A Fourier Transform Approach for Two-Center Overlap-Like Quantum Similarity Integrals Over Slater Type Orbitals, J. Theor. Comput. Chem., 3 (2004) 257-267.
  • [15] Berlu L., Safouhi H., Analytical Development of Multicenter Overlap-Like Quantum Similarity Integrals Over Slater Type Orbitals and Numerical Evaluation, J. Theor. Comput. Chem., 4 (2005) 787-801.
  • [16] Safouhi H., Analytical and Numerical Development for The Two-Centre Overlap-Like Quantum Similarity Integrals Over Slater Type Functions, J. Phys. A, 38 (2005) 7341-7361.
  • [17] Safouhi H., Berlu L., The Fourier Transform Method and The SD Approach for The Analytical and Numerical Treatment of Multicenter Overlap-Like Quantum Similarity Integrals, J. Comput. Phys., 216 (2006) 19-36.
  • [18] Guseinov I.I., New Complete Orthonormal Sets of Exponential Type Orbitals and Their Application to Translation of Slater Orbitals, Int. J. Quantum Chem., 90 (2002) 114-118.
  • [19] Guseinov I.I., New Complete Orthonormal Sets of Exponential Type Orbitals in Standard Convention and Their Origin, Bull. Chem. Soc. Jpn., 85 (2012) 1306-1309.
  • [20] Mamedov B.A., Israfil I. Guseinov: A Pioneer of The Quantum Theory of Atomic, Molecular, and Nuclear Systems, Int. J. Quantum Chem., 114 (2014) 361-366.
  • [21] Guseinov I.I., Unified Treatment of Complete Orthonormal Sets of Functions in Coordinate, Momentum and Four-Dimensional Spaces and Their Expansion and One-Range Addition Theorems, J. Math. Chem., 42 (2007) 991-1001.
  • [22] Arfken G.B., Weber H.J., Mathematical methods for physicists. 6th ed. Amsterdam, (2005) 499-533.
  • [23] Guseinov I.I., Sahin E., Evaluation of One-Electron Molecular Integrals Over Complete Orthonormal Sets of ψα-ETO Using Auxiliary Functions, Int. J. Quantum Chem., 110 (2010) 1803-1808.

Calculation of One- and Two-Center Overlap Like Quantum Similarity Integrals over ψ^((α)) Exponential Type Functions

Year 2022, Volume: 43 Issue: 4, 721 - 725, 27.12.2022

Ercan Şahin

https://doi.org/10.17776/csj.1136963

Abstract

One- and two-center overlap like quantum similarity integrals over ψ^((α)) functions are evaluated using the one-center expansion method. These integrals are expressed through expansion coefficients and usual two-center overlap integrals. The expressions derived in this work have no restrictions for the values of orbital parameters, quantum numbers and internuclear distances. Since these integrals of ψ^((α)) functions are calculated for the first time, the comparison is made with literature values obtained from Slater type functions. The computation results are in good agreement with literature values. The algorithm presented in this study could be useful when exponential type functions are employed in quantum similarity measures of atomic and molecular systems.

Keywords

ψ^((α)) function expansion theorem overlap-like quantum similarity integral exponential type function

References

  • [1] Carbo R., Leyda L., Arnau M., How Similar is a Molecule to Another? An Electron Density Measure of Similarity Between Two Molecular Structures, Int. J. Quantum Chem., 17 (1980) 1185-1189.
  • [2] Carbo-Dorca R., Besalu E., A General Survey of Molecular Quantum Similarity, J. Mol. Struct. (Theochem), 451 (1998) 11-23.
  • [3] Robert D., Girones X., Carbo-Dorca R., Molecular Quantum Similarity Measures As Descriptors for Quantum QSAR, Polycycl. Aromat. Comp., 19 (2000) 51-71.
  • [4] Carbo-Dorca R., Robert D., Amat L., Girones X., Besalu E., Molecular quantum similarity in QSAR and drug design. 1st ed. Berlin, (2000) 26-38.
  • [5] Carbo-Dorca R., Girones X., Mezey P.G., Fundamentals of molecular similarity. 1st ed. New York, (2001) 187-320.
  • [6] Bultinck P., Girones X., Carbo-Dorca R., Molecular Quantum Similarity: Theory and Applications. In: Lipkowitz K.B., Larter R., Cundari T., (Eds). Reviews in computational chemistry. 1st ed. Hoboken: Wiley, (2005) 127–207.
  • [7] Borgoo A., Godefroid M., Sen K.D., De Profit F., Geerlings P., Quantum Similarity of Atoms: A Numerical Hartree–Fock and Information Theory Approach, Chem. Phys. Lett., 399 (2004) 363-367.
  • [8] Robert D., Carbo-Dorca R., On the Extension of Quantum Similarity to Atomic Nuclei: Nuclear Quantum Similarity, J. Math. Chem., 23 (1998) 327-351.
  • [9] Amat L., Carbo-Dorca R., Quantum Similarity Measures Under Atomic Shell Approximation: First Order Density Fitting Using Elementary Jacobi Rotations, J. Comput. Chem., 18 (1997) 2023-2039.
  • [10] Amat L., Carbo-Dorca R., Molecular Electronic Density Fitting Using Elementary Jacobi Rotations Under Atomic Shell Approximation, J. Chem. Inf. Comput. Sci., 40 (2000) 1188-1198.
  • [11] Hoggan P.E., How Exponential Type Orbitals Recently Became a Viable Basis Set Choice in Molecular Electronic Structure Work and When to Use Them. In: Russo N., Antonchenko V.Y., Kryachko E.S., (Eds). Self-organization of molecular systems. 1st ed. Dordrecht: Springer, (2009) 199-219.
  • [12] Sola M., Mestres J., Oliva J.M., Duran M., Carbo R., The Use of Ab Initio Quantum Molecular Self-Similarity Measures to Analyze Electronic Charge Density Distributions, Int. J. Quantum Chem., 58 (1996) 361-372.
  • [13] Berlu L., Hoggan P.E., Useful Integrals for Ab Initio Molecular Quantum Similarity Measurements Using Slater Type Atomic Orbitals, J. Theor. Comput. Chem., 2 (2003) 147-161.
  • [14] Berlu L., A Fourier Transform Approach for Two-Center Overlap-Like Quantum Similarity Integrals Over Slater Type Orbitals, J. Theor. Comput. Chem., 3 (2004) 257-267.
  • [15] Berlu L., Safouhi H., Analytical Development of Multicenter Overlap-Like Quantum Similarity Integrals Over Slater Type Orbitals and Numerical Evaluation, J. Theor. Comput. Chem., 4 (2005) 787-801.
  • [16] Safouhi H., Analytical and Numerical Development for The Two-Centre Overlap-Like Quantum Similarity Integrals Over Slater Type Functions, J. Phys. A, 38 (2005) 7341-7361.
  • [17] Safouhi H., Berlu L., The Fourier Transform Method and The SD Approach for The Analytical and Numerical Treatment of Multicenter Overlap-Like Quantum Similarity Integrals, J. Comput. Phys., 216 (2006) 19-36.
  • [18] Guseinov I.I., New Complete Orthonormal Sets of Exponential Type Orbitals and Their Application to Translation of Slater Orbitals, Int. J. Quantum Chem., 90 (2002) 114-118.
  • [19] Guseinov I.I., New Complete Orthonormal Sets of Exponential Type Orbitals in Standard Convention and Their Origin, Bull. Chem. Soc. Jpn., 85 (2012) 1306-1309.
  • [20] Mamedov B.A., Israfil I. Guseinov: A Pioneer of The Quantum Theory of Atomic, Molecular, and Nuclear Systems, Int. J. Quantum Chem., 114 (2014) 361-366.
  • [21] Guseinov I.I., Unified Treatment of Complete Orthonormal Sets of Functions in Coordinate, Momentum and Four-Dimensional Spaces and Their Expansion and One-Range Addition Theorems, J. Math. Chem., 42 (2007) 991-1001.
  • [22] Arfken G.B., Weber H.J., Mathematical methods for physicists. 6th ed. Amsterdam, (2005) 499-533.
  • [23] Guseinov I.I., Sahin E., Evaluation of One-Electron Molecular Integrals Over Complete Orthonormal Sets of ψα-ETO Using Auxiliary Functions, Int. J. Quantum Chem., 110 (2010) 1803-1808.
There are 23 citations in total.

Details

Primary Language English
Subjects Classical Physics (Other)
Journal Section Natural Sciences
Authors

Ercan Şahin 0000-0002-4588-1257

Publication Date December 27, 2022
Submission Date June 28, 2022
Acceptance Date October 17, 2022
Published in Issue Year 2022Volume: 43 Issue: 4

Cite

APA Şahin, E. (2022). Calculation of One- and Two-Center Overlap Like Quantum Similarity Integrals over ψ^((α)) Exponential Type Functions. Cumhuriyet Science Journal, 43(4), 721-725. https://doi.org/10.17776/csj.1136963
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