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Yıl 2022, Cilt: 43 Sayı: 4, 721 - 725, 27.12.2022

Ercan Şahin

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

Öz

Kaynakça

  • [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

Yıl 2022, Cilt: 43 Sayı: 4, 721 - 725, 27.12.2022

Ercan Şahin

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • [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.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Klasik Fizik (Diğer)
Bölüm Natural Sciences
Yazarlar

Ercan Şahin 0000-0002-4588-1257

Yayımlanma Tarihi 27 Aralık 2022
Gönderilme Tarihi 28 Haziran 2022
Kabul Tarihi 17 Ekim 2022
Yayımlandığı Sayı Yıl 2022Cilt: 43 Sayı: 4

Kaynak Göster

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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