Abstract
In this chapter, the elementary basis of Quantum Similarity framework is presented in an elementary way. Here, by defining in a rigorous way the concept of quantum object, the quantum mechanical concept of Quantum Similarity is described. This leads to a discussion about the role of density functions in the chemical description of molecular structures. Some definitions -tagged, Boolean and functional tagged sets, as well as vector semispaces- are previously introduced, in order to produce the adequate formalism from where Quantum Similarity can be easily deduced and after this computational algorithms can be developed.
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Reference
Von Neumann J (1955) Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton
Bohm D (1989) Quantum Theory. Dover Publications, New York
Goldstein S (1988) Quantum Theory without Observers-Part One. Physics Today March: 42–46, Part Two, April:38-42
Bell JS (1993) Speakable and Unspeakable in Quantum Mechanics-Cambridge University Press, Cambridge
Vinogradov IM (ed) (1987) Encyclopaedia of Mathematics. Vol. 8. Reidel-Kluwer, Dordrecht, p 249
Carbó-Dorca R, Besalú E, Gironés X (1999) Extended Density Functions. Adv Quantum Chem, in press
Carbó-Dorca R (1997) Fuzzy sets and Boolean Tagged Sets. J Math Chem 22:143–147
Carbó-Dorca R (1998) Fuzzy sets and boolean tagged sets; vector semispaces and convex sets; quantum similarity mesures and ASA density functions; diagonal vector spaces and quantum chemistry. In: Carbó-Dorca R, Mezey PG (eds) Advances in Molecular Similarity. JAI Press, Greenwich, Vol 2, pp 43–72
Carbó-Dorca R (1998) Tagged Sets, Convex Sets and Quantum Similarity Measures. J Math Chem 23:353–364
Carbó R, Besalú E, Amat L, Fradera X (1996) On molecular quantum similarity measures (QMSM) and indices (QMSI). J Math Chem 19:47–56
Robert D, Carbó-Dorca R (1998) A formal comparison between molecular quantum similarity indices. J Chem Inf Comput Sci 38:469–475
Besalü E, Carbó R, Mestres J, Solà M (1995) Foundations and Recent Developments on Quantum Molecular Similarity. Top Curr Chem 173:31–62
Arsenin VY (1968) Basic Equations and Special Functions of Mathematical Physics. Iliffe Books, London
Matsuoka O (1973) Int J Quantum Chem 7:365–381
Bethe AH, Salpeter EE (1957) Quantum mechanics of one-and two-electron Systems. Springer-Verlag, Berlin
Dunlap BI, Connnolly JWD, Sabin JR (1979) On some approximations in applications of some Xα theory. J Chem Phys 71:3396–3402
Mestres J, Solà M, Duran M, Carbó R (1994) On the calculation of ab initio quantum molecular similarities for large systems: fitting the electron density. J Comput Chem 15:1113–1120
Cioslowski J, Piskorz P, Rez P (1997) Accurate analytical representations of the core electron densities of the elements 3 through 118. J Chem Phys 106:3607–3612
Constans P, Carbo R (1995) Atomic shell approximation: electron density fitting algorithm restricting coefficients to positive values J Chem Inf Comput Sci 35:1046–1053
Constans P, Amat L, Fradera X, Carbô-Dorca R (1996) Quantum molecular similarity measures (QMSM) and the atomic shell approximation (ASA). In: Carbo-Dorca R, Mezey PG (eds) Advances in Molecular Similarity. JAI Press, Greenwich, Vol 1, pp 187–211
Amat L, Carbó-Dorca R (1997) Quantum similarity measures under atomic shell approximation: first order density fitting using elementary Jacobi rotations. J Comput Chem 18:2023–2039
Amat L, Carbó-Dorca R (1999) Fitted electronic density functions from H to Rn for use in quantum Similarity measures: Cis-diamminedichloroplatinum(II) complex as an application example. J Comput Chem 20:911–920
Ruedenberg K, Schwarz WHE (1990) Nonspherical atomic ground-state densities and chemical deformation densities from x-ray scattering. J Chem Phys 42:4956–4969
Coppens P (1992) In: International Tables for Crystallography. Kluwer, Amsterdam, Vol B, p 10
Coppens P, Becker (1992) In: International Tables for Crystallography. Kluwer, Amsterdam, Vol C, p 628
Ruedenberg K, Raffenetti RC, Bardon D (1973) Energy, structure and reactivity. Proceedings of the 1972 Boulder Conference on Theoretical Chemistry. Wiley, New York, p 164
Schmidt MW, Ruedenberg K (1979) Effective convergence to complete orbital bases and to the atomic Hartree-Fock limit through systematic sequences of Gaussian primitives. J Chem Phys 71:3951–3962
Feller DF, Ruedenberg K (1979) Systematic approach to extended even-tempered orbital bases for atomic and molecular calculations. Theor Chim Acta 52:231–251
Jacobi CGJ (1846) Ober ein leichtes Verfahren, die in der Theorie der Säkularstörungen vorkommenden Gleichungen numerisch aufzulösen. J Reine Angew Math (Crelle’s Journal) 30:51–94
Wilkinson JH, Reinsch C (1971) Linear algebra. Springer-Verlag, Berlin, pp 202–211
Pierre DA (1969) Optimization theory With applications. Wiley, New York
Carbó-Dorca R, Amat L, Besalú E, Gironés X, Robert D (1999) Quantum molecular similarity: theory and applications to the evaluation of molecular properties, biological activities and toxicity. In: Carbó-Dorca R, Mezey PG (eds) The Fundamentals of Molecular Similarity. Kluwer, New York, in press
McLean AD, Chandler GS (1980) Contracted gaussian basis sets for molecular calculations. I. Second row atoms, Z=l 1-18. J Chem Phys 72:5639–5648
Krishnan B, Binkley JS, Seeger R, Pople JA (1980) Self-consistent orbital methods. XX. A basis set for correlated wave functions. J Chem Phys 72:650–654
These coefficients and exponents can be downloaded from http://iqcudg-es/cat/similarity/ASA/func6311.html
Gironés X, Amat L, Carbô-Dorca R (1998) A comparative study of isodensity surfaces using “ab initio” and ASA density functions. J Mol Graph Model 16:190–196
Atai A, Tomioka N, Yamada M, Inoue A, Kato Y (1993) Molecular superposition for rational drug design. In: Kubinyi H (ed) 3D QSAR in drug design. ESCOM, Leiden, pp 200–225
Nyburg SC (1974) Some uses of a best molecular fit routine. Acta Cryst B 30:251–253
Martin YC (1992) 3D database searching in drug design. J Med Chem 35:2145–2154
Constans P, Amat L, Carbó-Dorca R (1997) Toward a global maximization of the molecular similarity function: superposition of two molecules. J Comput Chem 18:826–846
See, for example: Bayada DM, Simpson RW, Johnson AP, Laurenco C (1992) An algorithm for the multiple common subgraph problem. J Chem Inf Comput Sci 32:680–685
Gavuzzo E, Pagliuca S, Pavel V, Quagliata C (1972) Generation and best fitting of molecular models. Acta Cryst B 28:1968–1969
McLachlan AD (1972) A mathematical procedure for superimposing atomic coordinates of proteins. Acta Cryst A 28:656–657
Gerber PR, Muller K (1987) Superimposing several sets of atomic coordinates. Acta Cryst A 41:426–428
Redington PK (1992) Molfit: A computer program for molecular superposition. Comput Chem 16:217–222
Kearsley SK, Smith GM (1990) An alternative method for the alignment of molecular structures: maximizing electrostatic and steric overlap. Tetrahedron Comput Method 3:615–633
Manaut M, Sanz F, Jose J, Milesi M (1991) Automatic search for maximum similarity between molecular electrostatic potential distributions. J Comput-Aided Mol Design 5:371–380
Clark M, Cramer III RD, Jones DM, Patterson DE, Simeroth PE (1990) Comparative molecular field analysis (CoMFA). 2. Towards its use with 3D-structural databases. Tetrahedron Comput Method 3:47–59
Good AC, Hodgkin EE, Richards WG (1992) Utilization of Gaussian functions for the rapid evaluation of molecular similarity. J Chem Inf Comput Sci 32:188–191
Mestres J, Rohrer DC, Maggiora GM (1997) MIMIC: A molecular-field matching program, exploiting applicability of molecular similarity approaches. J Comput Chem 18:934–954
Parretti MF, Kroemer RT, Rothman JH, Richards WG (1997) Alignment of molecules by the Monte Carlo optimization of molecular similarity indices. J Comput Chem 18:1344–1353
McMahon AJ, King PM (1997) Optimization of Carbó molecular similarity index using gradient methods. J Comput Chem 18:151–158
Dean PM, Callow P, Chau PL (1988) Molecular recognition: blind-searching for regions of strong structural match on the surfaces of two dissimilar molecules. J Mol Graph 6:28–34
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Carbó-Dorca, R., Robert, D., Amat, L., Gironés, X., Besalú, E. (2000). Quantum objects, density functions and molecular quantum similarity measures. In: Molecular Quantum Similarity in QSAR and Drug Design. Lecture Notes in Chemistry, vol 73. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57273-9_2
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DOI: https://doi.org/10.1007/978-3-642-57273-9_2
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