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Valence bond functions for the hydrogen molecule

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Abstract

Valence bond wavefunctions were constructed for H2. Use of Slater exponents resulted in very slow convergence to the ground state energy. Convergence was improved by optimizing exponents which were found to increase as the principal quantum number n. However, this gave problems of linear dependence since optimum orbitals were strikingly similar for all n. The best function without angular correlation contained 27 terms constructed from 1s, 3s, 2p 0, 3d 0, 4f 0, and 5g 0 orbitals and gave an energy of −1.1594a.u. The best function with angular correlation gave E=-1.1656 a.u.

Zusammenfassung

Für das H2-Molekül werden Wellenfunktionen nach der Valenzstrukturmethode konstruiert. Die Benutzung von Exponenten nach Slater führt zu einer sehr langsamen Konvergenz zur Grundzustandsenergie. Die Konvergenz wurde durch Optimierung der Exponenten verbessert, wobei diese mit der Hauptquantenzahl ansteigen. Dabei ergab sich jedoch das Problem linearer Abhängigkeit der Funktionen, da die optimalen Orbitale sehr ähnlich für alle n waren. Die beste Funktion ohne Winkelkorrelation enthielt 27 Terme, die aus den Orbitalen 1s, 3s, 2p 0, 3d 0, 4f 0 und 5g 0 konstruiert waren, und ergab eine Energie von −1,1594A.E. Die beste Funktion mit Winkelkorrelation ergab E=−1,1656 A.E.

Résumé

Des fonctions d'onde de liaison de valence sont construites pour H2. L'emploi d'exposants de Slater entraîne une très faible convergence vers l'énergie de l'état fondamental. La convergence a été améliorée par optimisation des exposants qui croissent comme le nombre quantique principal n. Cependant, ceci crée des problèmes de dépendance linéaire car les orbitales optimales sont étonnement similaires pour tous les n. La meilleure fonction sans corrélation angulaire contient 27 termes construits à partir d'orbitales 1s, 3s, 2p 0,3d 0,4f 0 et 5g 0 et donne une énergie de −1,1594 u.a. La meilleure fonction avec corrélation angulaire donne E= −1,1656 u.a.

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References

  1. Heitler, W., London, F.: Z. Physik 44, 455 (1927).

    Google Scholar 

  2. Sugiura, Y.: Z. Physik 45, 484 (1927).

    Google Scholar 

  3. Coulson, C. A.: Trans. Faraday Soc. 33, 1479 (1937).

    Google Scholar 

  4. Cohen, E. R., DuMond, J. W.: Rev. mod. Physics 37, 537 (1965).

    Google Scholar 

  5. Wang, S. C.: Physic. Rev. 31, 579 (1928).

    Google Scholar 

  6. Rosen, N.: Physic. Rev. 38, 2099 (1931).

    Google Scholar 

  7. Weinbaum, S.: J. chem. Physics 1, 593 (1933).

    Google Scholar 

  8. Eckart, C.: Physic. Rev. 36, 878 (1930).

    Google Scholar 

  9. Bowen, H. C.: Molecular Physics 10, 299 (1966).

    Google Scholar 

  10. McLean, A. D., Weiss, A., Yoshimine, M.: Rev. mod. Physics 32, 211 (1960).

    Google Scholar 

  11. Kolos, W., Wolniewicz, L.: J. chem. Physics 49, 404 (1968).

    Google Scholar 

  12. Herzberg, G.: J. Mol. Spect. 33, 147 (1970).

    Google Scholar 

  13. Thomas, I. L.: Ph. D. Thesis in chemistry, Vanderbilt University, January, 1968.

  14. Kotani, M., Amemiya, A., Ishiguro, E., Kimura, T.: Tables of molecular integrals. Tokyo: Maruzen Co., Ltd. 1963.

    Google Scholar 

  15. Miller, J., Gerhauser, J. M., Matsen, F. A.: Quantum chemistry integrals and tables. Austin: University of Texas Press 1959.

    Google Scholar 

  16. Sahni, R. C., Cooley, J. W.: Derivation and tabulation of molecular integrals, supplement I, II. Washington: National Aeronautics and Space Administration Technical Note D-146 1959.

  17. Lofthus, A.: Molecular Physics 5, 105 (1962).

    Google Scholar 

  18. Wahl, A. C., Cade, P. E., Roothaan, C. C. J.: J. chem. Physics 41, 2578 (1964).

    Google Scholar 

  19. Givens, W.: Numerical computation of the characteristic values of a real symmetric matrix. Oak Ridge National Laboratory Report ORNL-1574 1954.

  20. Prosser, F.: GIVENS, program 62, Quantum Chemistry Program Exchange, Indiana University.

  21. Slater, J. C.: Physic. Rev. 36, 57 (1930).

    Google Scholar 

  22. Shull, H., Löwdin, P. O.: J. chem. Physics 23, 1362 (1955).

    Google Scholar 

  23. Schwartz, M. E., Schaad, L. J.: J. chem. Physics 46, 4112 (1967).

    Google Scholar 

  24. Fraga, S., Ransil, B. J.: J. chem. Physics 35, 1967 (1961).

    Google Scholar 

  25. Hagstrom, S., Shull, H.: Rev. mod. Physics 35, 624 (1963).

    Google Scholar 

  26. Wilde, D. J.: Optimum seeking methods. Englewood Cliffs, N. J.: Prentice-Hall, Inc. 1964.

    Google Scholar 

Download references

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Author notes

  1. I. L. Thomas

    Present address: Chemical Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tenn.

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  1. Department of Chemistry, Vanderbilt University, Nashville, Tennessee

    L. J. Schaad & I. L. Thomas

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  1. L. J. Schaad
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  2. I. L. Thomas
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N.I.H. Predoctoral Fellow 1964–1967.

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Schaad, L.J., Thomas, I.L. Valence bond functions for the hydrogen molecule. Theoret. Chim. Acta 21, 115–126 (1971). https://doi.org/10.1007/BF00530209

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