Abstract
A theorem, associated to the holographic nature of general Gaussian functions, is employed to describe holographic projections of electronic density model functions, both in position and momentum spaces, over the surface of a sphere.
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Boys S.F.: Proc. R. Soc. (London) A200, 542 (1950)
Shavitt I.: Meth. Comp. Phys., 2, 1. Academic Press, New York (1963)
Taketa H., Huzinaga S., ohata K.O.: J. Phys. Soc. (Japan) 21, 2313 (1966)
Saunders V.R.: Computational Techniques in Quantum Chemistry and Molecular Physics, ed. by G.H.F. Diercksen, B.T. Sutcliffe, A. Veillard (D. Reidel Pub. Co, Dordrecht, 1975), pp. 347– 424
Huzinaga, S. (eds): Gaussian Basis Sets for Molecular Calculations, Physical Sciences Data, Vol. 16. Elsevier, Amsterdam (1984)
’t Hooft G.: Dimensional Reduction in Quantum Gravity (Salam Fest). World Scientific, Singapore (1993)
Susskind L.: J. Math. Phys. 36, 6377 (1995)
Zwiebach B.: A First Course in String Theory. Cambridge University Press, Cambridge (2004)
Mezey P.G.: Mol. Phys. 96, 169 (1999)
Abramowitz M., Stegun I.A.: Handbook of Mathematical Functions. Dover Pub, New York (1972)
Constans P., Carbó R.: J. Chem. Inf. Comp. Sci. 35, 1046 (1995)
P. Constans, X. Fradera, Ll. Amat, R. Carbó, Quantum Molecular Similarity Measures (QMSM) and the Atomic Shell Approximation (ASA) in Proceedings of the 2nd. Girona Seminar on Molecular Similarity. July 1995. Advances in Molecular Similarity. JAI PRESS INC. Greenwich (Conn.) 1, 187 (1996)
Amat L.L., Carbó-Dorca R.: J. Comput. Chem. 18, 2023 (1997)
Amat L.L., Carbó-Dorca R.: J. Comput. Chem. 20, 911 (1999)
Carbó-Dorca R., Mercado L.D.: Commentaries on quantum similarity (1): density gradient quantum similarity. J. Comput. Chem. 31, 2195 (2010)
Carbó-Dorca E.: Besalú, Commentaries on quantum similarity (2): a geometric discussion on holographic electron density theorem (HEDT) and confined quantum similarity measures. J. Comput. Chem. 31, 2452 (2010)
R. Carbó-Dorca, E. Besalú, L.D. Mercado, Commentaries on quantum similarity (3):a geometric-quantum similarity molecular superposition (GQSMS) algorithm. J. Comput. Chem. (in press)
Kaijsser P., Smith V.H. Jr.: Evaluation of momentum distributions and compton profiles in atomic and molecular systems. Adv. Quantum. Chem. 10, 36–37 (1977)
Thakkar A.: The momentum density perspective of the electronic structure of atoms and molecules. Adv. Chem. Phys. 128, 303–352 (2004)
Vinogradov, I.M. (eds): Encyclopaedia of Mathematics, Vol. 4. Kluwer Academic Publishers, Dordrecht (1989)
Messiah A.: Quantum Mechanics. Dover Publications Inc, New York (1999)
Gröbner W., Hofreiter N.: Integraltafel, (II). Springer, Wien (1965)
Bowman G.E.: Essential Quantum Mechanics. Oxford University Press, Oxford (2008)
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Carbó-Dorca, R., Besalú, E. A Gaussian holographic theorem and the projection of electronic density functions into the surface of a sphere. J Math Chem 48, 914–924 (2010). https://doi.org/10.1007/s10910-010-9717-z
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DOI: https://doi.org/10.1007/s10910-010-9717-z