Descriptors and probability distributions in MO theory: Weighted Mulliken matrices and molecular quantum similarity measures

Journal of Mathematical Chemistry

Volumn 39, Issue 3-4, 2006, Pages 551-591

  Carbó Dorca, Ramon ^a,b  

^a GHENT UNIVERSITY   (Belgium)

^b UNIVERSITY OF GIRONA   (Spain)

Author keywords

Molecular descriptors; Molecular discrete probability distributions; Mulliken population analysis; Weighted Mulliken matrices; Weighted Mulliken populations

Indexed keywords

EID: 33746894556     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10910-005-9049-6     Document Type: Article

References (45)

1. (a) R.S. Mulliken, J. Chem. Phys. 23 (1955) 1833;
2. (b) R.S. Mulliken, J. Chem. Phys. 23 (1955) 1841;
3. (c) R.S. Mulliken, J. Chem. Phys. 23 (1955) 2338;
4. (d) R.S. Mulliken, J. Chem. Phys. 23 (1955) 2343.
5. See, for example: (a) M. Giambiagi, M.S. de Giambiagi and K.C. Mundim, Struct. Chem. 1 (1990) 423;
6. (b) K.C. Mundim, M. Giambiagi and M.S. de Giambiagi, J. Phys. Chem., 98 (1994) 6118;
7. (c) M. Giambiagi, M.S. de Giambiagi, C.D. dos Santos Silva and A. Paiva de Figueredo, Phys. Chem. Chem. Phys. 2 (2000)3381;
8. (d) J. Pipek, J. Mol. Struct. (Theochem) 501-502 (2000)395;
9. (e) I. Mayer, Simple Theorems, Proofs and Derivations in Quantum Chemistry, Mathematical and Computational Chemistry Series, Vol. 3 (Kluwer Academic/Plenum Publishers, New York, 2003).
10. (a) R. Carbó-Dorca and P. Bultnick, J. Math. Chem. 36 (2004) 201;
11. (b) R. Carbó-Dorca, P. Bultnick; J. Math. Chem. 36 (2004) 231.
12. P. Bultnick, R. Carbó-Dorca and R. Ponec; Int. J. Quantum Chem. (submitted)
13. See, for example: F. L. Pilar, Elementary Quantum Chemistry (Dover Ed., New York, 2001).
14. V. Fock, Z. Phys. 61 (1930) 126.
15. D.R. Hartree; Proc. Camb. Phil. Soc. 24 (1928) 89.
16. W. Kohn and L.J. Sham, Phys. Rew. 140 (1965) A1133.
17. See, for example: P.W. Ayers and W. Yang; Density functional theory, in: Computational Medicinal Chemistry for Drug Discovery, eds. P. Bultinck, H. de Winter, W. Langenaeker and J.P. Tollenaere (Marcel Dekker, Inc., New York, 2004) pp. 89-118.
18. J.W. Demmel, Applied Numerical Linear Algebra (SIAM, Philadelphia, 1997).
19. G.W. Stewart, Matrix Algorithms. Vol.: Basic Decompositions (SIAM, Philadelphia 1998).
20. J.H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon Press, Oxford, 1965).
21. See, for example: (a) R. Carbó-Dorca, J. Mol. Struct. (Teochem), 537 (2001) 41;
22. (b) R. Carbó-Dorca, J. Math. Chem. 32 (2002) 201;
23. (c) R. Carbó-Dorca, J. Math. Chem. 30 (2001) 227.
24. See, for example: (a) J.E. Lennard-Jones and J.A. Pople, Proc. Roy. Soc. (London), A202 (1950) 166;
25. (b) S.F. Boys, Rev. Mod. Phys. 32 (1960) 296;
26. (c) C. Edminston and K. Ruedenberg, Rev. Mod. Phys. 35 (1963) 457;
27. (d) J. Pipek and P.G. Mezey, J. Chem. Phys. 90 (1989) 4916.
28. See, for example: (a) R.G. Parr and L.J. Bartolotti, J. Phys. Chem. 87 (1983) 2810;
29. (b) P. Geerlings, F. De Proft and W. Langenaeker, Chem. Rev. 103 (2003) 1793.
30. P. Bultinck and R. Carb́o-Dorca, J. Math. Chem. 36 (2004) 191.
31. See, for example: I.M. Vinogradov (Ed.), Encyclopaedia of Mathematics (Reidel-Kluwer Academic Publishers, Dordrecht, 1987).
32. R. Carbó-Dorca, Advances Molec Simil. Vol. 2, (JAI Press, Greenwhich, Conn., 1998) pp. 43-72.
33. R. Carbó-Dorca, J. Math. Chem. 32 (2002) 201.
34. R. Ahlrichs, Phys. Chem. Chem. Phys. 6 (2004) 5119.
35. R. Carbó-Dorca; Adv. Quantum Chem. (in press)
36. P. Bultinck, X. Gironés and R. Carbó-Dorca, Molecular quantum similarity: theory and applications, Rev. Comput. Chem. Vol. 21, eds. K.B. Lipkowitz, R. Larter and T. Cundari, (John Wiley & Sons, Inc., Hoboken, USA, 2005) pp. 127-207.
37. R.F.W. Bader, Atoms in Molecules, A Quantum Theory (Clarendon Press, Oxford, 1990).
38. See, for example: D. Bohm, Quantum Theory (Dover Publications, Inc., New York, 1989).
39. R. Carbó, B. Calabuig, E. Besalú and A. Martínez, Mol. Eng. 2 (1992) 43.
40. P.O. Löwdin, Phys. Rew. 97 (1955) 1474.
41. See, for example: (a) R. Carbó, and E. Besalú, J. Math. Chem. 13 (1993) 331;
42. (b) R. Carbó and E. Besalú, Comput. & Chem. 18 (1994) 117;
43. (c) R. Carbó and E. Besalú, J. Math. Chem. 18 (1995) 37;
44. (d) R. Carbó and E. Besalú, in: Strategies and Applications in Quantum Chemistry: from Astrophysics to Molecular Engineering. M. Defranceschi y Y. Ellinger (Eds.), pp 229-248. Kluwer Academic Pub. Amsterdam (1996).
45. R. Carbó-Dorca, Int. J. Quantum Chem. 91 (2003) 607.