Abstract
A postulate is enunciated involving the construction of the quantum mechanical linear momentum vector in position space. This proposal leads to a coherent Heisenberg uncertainty relation for a Gaussian model density function. Such result is then used as starting point to obtain algorithms to perform kinetic energy calculations, when only the density function of a given system is known. The general theoretical framework is described and several density function types, including ab initio formulation, are used as application examples.
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References
P.W. Ayers, R.G. Parr, A. Nagy, Intl. J. Quantum Chem. 90, 309–326 (2002)
J.S.M. Anderson, P. W. Ayers, J. I. Rodriguez Hernandez, J. Phys. Chem. 114, 8884–8895 (A 2010)
D. Chakraborty, P.W. Ayers, Kinetic energy functionals of the electron density and pair density. In Concepts and Methods in Modern Theoretical Chemistry, vol. 1: Electronic Structure and Reactivity, eds. S.K. Ghosh, P.K. Chattaraj, (CRC Press, Boca Raton, Florida, 2013), pp. 1–42 (2013)
W. Kohn, L.J. Sham, Phys. Rev 140, A1133A1138 (1965)
R. Carbó-Dorca, J. Math. Chem. 51, 420–426 (2013)
E. Besalú, R. Carbó-Dorca, J. Math. Chem. 49, 1769–1784 (2011)
D. Andrae, Phys. Rep. 336, 413–525 (2000)
R. Carbó-Dorca, J. Math. Chem. 38, 671–676 (2005)
E. Besalú, R. Carbó-Dorca, J. Math. Chem. 51, 1771–1783 (2013)
Ll Amat, R. Carbó-Dorca, J. Comput. Chem 18, 2023–2029 (1997)
Ll Amat, R. Carbó-Dorca, J. Comput. Chem 20, 911–920 (1999)
Ll Amat, R. Carbó-Dorca, J. Chem. Inf. Comput. Chem. Sci. 40, 1188–1198 (2000)
R. Carbó, E. Besalú, B. Calabuig, L. Vera, Molecular quantum similarity: theoretical framework, ordering principles and visualization techniques. Adv. Quantum Chem. 25, 253–313 (1994)
R. Carbó-Dorca, E. Besalú, J. Molec, Struct. Theochem 451, 11–23 (1998)
R. Carbó-Dorca, Ll. Amat, E. Besalú, X. Gironés, D. Robert, Quantum Molecular Similarity: Theory and Applications to the Evaluation of Molecular Properties, Biological Activity and Toxicity. Mathematical and Computational Chemistry: Fundamentals of Molecular Similarity. Kluwer/Plenum Publishers, pp. 187–320 (2001)
P. Bultinck, X. Gironés, R. Carbó-Dorca, Molecular Quantum Similarity: Theory and Applications; Rev. Comput. Chem. vol. 21, Eds. K.B. Lipkowitz, R. Larter, T. Cundari, Wiley, Hoboken, pp. 127–207 (2005)
P. Bultinck, S. Van Damme, R. Carbó-Dorca, Molecular quantum similarity, in Theory of Chemical Reactivity (A Density Functional View), ed. by P. Chattaraj (Taylor & Francis, Boca Raton, 2009), pp. 229–242
R. Carbó-Dorca, E. Besalú, L.D. Mercado, J. Comput. Chem. 32, 582–599 (2011)
R. Carbó-Dorca, Soft Nuclear Density and Nuclear Repulsion. IQCC Technical Report TC-2014-2. Ind. J. Chem. A (to be published)
R. Carbó-Dorca, J. Math. Chem. 51, 1681–1683 (2013)
Acknowledgments
This manuscript was developed while one of us (R. C-D.) was invited professor at the China University of Petroleum - Beijing. The received support from this institution is deeply acknowledged. The authors also want to acknowledge the support of the University of Girona by means of the grant: ASING12/05.
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Carbó-Dorca, R., Besalú, E. A postulate involving quantum mechanical momentum in position space, density function expression of the kinetic energy and Heisenberg’s uncertainty relation. J Math Chem 52, 1949–1967 (2014). https://doi.org/10.1007/s10910-014-0358-5
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DOI: https://doi.org/10.1007/s10910-014-0358-5