A mathematical discussion on density and shape functions, vector semispaces and related questions

Journal of Mathematical Chemistry

Volumn 36, Issue 2, 2004, Pages 191-200

  Bultinck, Patrick ^a   Carbó Dorca, Ramon ^b  

^a GHENT UNIVERSITY   (Belgium)

^b UNIVERSITY OF GIRONA   (Spain)

Author keywords

convex sets; Density function; DFT; fukui functions; Pseudo wave functions; quantum similarity; shape function; space shell structure; variational DFT theorem; vector semispaces

Indexed keywords

ARTICLE; ATOMIC PARTICLE; CHEMICAL ANALYSIS; CHEMICAL STRUCTURE; DENSITY FUNCTIONAL THEORY; MATHEMATICAL ANALYSIS; QUANTUM CHEMISTRY; THEORETICAL STUDY; THERMODYNAMICS;

EID: 4444375547     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOMC.0000038793.21806.65     Document Type: Article

References (29)

1. R.G. Parr and L.J. Bartolotti, J. Phys. Chem. 87 (1983) 2810.
2. P. Geerlings, F. De Proft and W. Langenaeker, Chem. Rev. 103 (2003) 1793.
3. R. Carbó-Dorca, Fuzzy sets and boolean tagged sets; vector semispaces and convex sets; quantum similarity measures and ASA density functions; diagonal vector spaces and quantum chemistry, in: Advances in Molecular Similarity Vol. 2, eds. R. Carbó-Dorca and P.G. Mezey (JAI Press, London, 1998).
4. (a) R. Carbó-Dorca, E. Besalú and X. Gironés, Extended density functions, in: Advances in Quantum Chemistry, ed. P.O. Löwdin (Academic Press, New York, 2000)
5. (b) R. Carbó-Dorca, Mathematical elements of quantum electronic density functions institute of computational chemistry technical report: IT-IQC-00-3 (University of Girona).
6. (a) R. Carbó, E. Besalú, L. Amat and X. Fradera, J. Math. Chem. 18 (1995) 237;
7. (b) R. Carbó-Dorca, E. Besalú, Ll. Amat and X. Fradera, Quantum molecular similarity measures: concepts, definitions, and applications to QSAR, in: Advances in Molecular Similarity, Vol. 1, eds. R. Carbó-Dorca and P. G. Mezey (JAI Press, London, 1996);
8. (c) R. Carbó-Dorca, L. Amat, E. Besalú, X. Gironés and D. Robert. J. Mol. Struct. (Theochem) 504 (2000) 181;
9. (d) R. Carbó-Dorca, L. Amat, X. Gironés and D. Robert, Quantum molecular similarity: Theory and applications to the evaluation of molecular properties, biological activities and toxicity, in: Fundamentals of Molecular Similarity, eds. R. Carbó-Dorca, X. Gironés and P. G. Mezey, (Kluwer Academic / Plenum Publishers, New York, 2001);
10. (e) R. Carbó-Dorca and E. Besalú, Contrib. to Sci. 1 (2000) 399.
11. R. Carbó-Dorca, Density functions and generating wave functions, in: Reviews in modern quantum chemistry: a celebration of the contributions of R. G. Parr., ed. K.D. Sen (World Scientific, Singapore, 2002) p. 401.
12. I.M. Vinogradov, Encyclopaedia of Mathematics (Kluwer Academic Publishers, Dordrecht, 1992).
13. R. Carbó-Dorca, J. Math. Chem. 32 (2002) 201.
14. R.G Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1989).
15. (a) K. Fukui, T. Yonezawa and H. Shingu, J. Chem. Phys. 20 (1952) 722;
16. (b) K. Fukui, T. Yonezawa, C. Nagata and H. Shingu, J. Chem. Phys. 22 (1954) 1433.
17. P.W. Ayers, R.C. Morrison and R.K. Roy, J. Chem. Phys. 116 (2002) 8731.
18. P. Bultinck, R. Carbó-Dorca and W. Langenaeker, J. Chem. Phys. 118 (2003).
19. P. Bultinck and R. Carbó-Dorca, J. Math. Chem. 34 (2003) 67.
20. R. Carbó-Dorca, J. Math. Chem. 33 (2003) 227.
21. R. Carbo, J. Arnau and L. Leyda, Int. J. Quantum Chem. 17 (1980) 1185.
22. P. Constans, Ll. Amat, X. Fradera and R. Carbó-Dorca, Advances in Molecular Similarity, eds. R. Carbó-Dorca, and P.G Mezey, (JAI Press, London, 1996) Chapter 8.
23. (a) P. Constants and R. Carbó, J. Chem. Inf. Comput. Sci. 35 (1995) 1046;
24. (b) Ll. Amat and R. Carbó-Dorca, J. Comput. Chem. 18 (1997) 2039;
25. Ll. Amat and R. Carbó-Dorca, J. Comput. Chem. 20 (1999) 911.
26. J.P. Perdew, R.G Parr, M. Levy and J.L. Balduz Jr., Phys. Rev. Lett. 49 (1982) 1691.
27. (a) M. Born, Atomic Physics (Blackie & Son, London, 1944);
28. (b) J. Von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, 1955).
29. P. Hohenberg and W. Kohn, Phys. Rev. B 136 (1964) 864.