Atomic Shell Approximation: Electron Density Fitting Algorithm Restricting Coefficients to Positive Values

Journal of Chemical Information and Computer Sciences

Volumn 35, Issue 6, 1995, Pages 1046-1053

  Constans, Pere ^a   Carbó, Ramon ^a  

^a UNIVERSITY OF GIRONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ATOMS; COMPUTATIONAL METHODS; ELECTRON ENERGY LEVELS; ELECTRONS; MATHEMATICAL TRANSFORMATIONS; OPTIMIZATION; PROBABILITY DENSITY FUNCTION;

ATOMIC ORBITALS; ATOMIC SHELL APPROXIMATION; ATOMIC SHELLS; BASIS FUNCTIONS; ELECTRON DENSITY FUNCTIONS; GAUSSIAN FUNCTIONS; GAUSSIAN TRANSFORMS; QUANTUM MOLECULAR SIMILARITY MEASURES; VARIATIONAL COEFFICIENTS;

MOLECULAR STRUCTURE;

EID: 0029404423     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci00028a015     Document Type: Article

References (23)

1. Carbó, R.; Leyda, L.; Amau, M. How Similar is a Molecule to Another? An Electron Density Measure of Similarity between two Molecular Structures. Int. J. Quantum Chem. 1980,17, 1185-1189.
2. Carbó, R.; Calabuig, B. Molecular Quantum Similarity Measures and A'-Dimensional Representation of Quantum Objects. I. Theoretical Foundations. Int. J. Quantum Chem. 1992, 42, 1681-1693.
3. Carbó, R.; Calabuig, B. Molecular Quantum Similarity Measures and N-Dimensional Representation of Quantum Objects. II. Practical Applications. Int. J. Quantum Chem. 1992, 42, 1595-1709.
4. Carbó, R.; Calabuig, B.; Vera, L.; Besalú, E. Molecular Quantum Similarity; Theoretical Framework, Ordering Principles, and Visualization Techniques. Adv. Quantum Chem. 1994, 25, 253-313.
5. Besalu, E.; Carbó, R.; Mestres, J.; Sola, M. Foundations and Recent Developments on Molecular Quantum Similarity. Top. Curr. Chem. 1995, 173, 31-62.
6. Mestres, J.; Solá, M.; Duran, M.; Carbó, R. On the Calculation of Ab Initio Quantum Molecular Similarities for Large Systems: Fitting the Electron Density. 7. Comput. Chem. 1994, 15, 1113-1120.
7. Löwdin, P. O. Quantum Theory of Many-Particle Systems. I. Physical Interpretation by Means of Density Matrices, Natural SpinOrbitals, and Convergence Problems in the Method of Configurational Interaction. Phys. Rev. 1955, 97, 1474-1489.
8. McWeeny, R. The Density Matrix in Many-Electron Quantum Mechanics. I. Generalized Product Functions. Factorization and Physical Interpretation of the Density Matrices. Proc. R. Soc. London, 1959, A253, 242-259.
9. Unsold, A. Beiträge zur Quantenmechanik de Atome. Ann. Physik. 1927, 82, 355-393.
10. Coppens, P.; Pautler, D.; Griffm, J. F. Electron Population Analysis of Accurate Diffraction Data. II. Application of One-Center Formalisms to Some Organic and Inorganic Molecules. J. Am. Chem. Soc. 1971, 93, 1051-1058.
11. Schwarz, W. H. E.; Lagenbach, A.; Birlenbach, L. Density Matrices from position and momentum densities. Theor. Chim. Acta 1994, 88, 437-445.
12. Hirschfelder, J. O.; Curtiss, Ch. F.; Bird, R. B. Molecular Theory of Gases and Molecules; John Wiley & Sons: New York, 1964.
13. Paoloni, L.; Giambiagi, M. S.; Giambiagi, M. On the symmetry properties of the AO basis for the semiempirical MO-LCAO description of aromatic systems. Atti Soc. Nat. Mat. Modena 1969, C. 89105.
14. Frost, A. A. Floating Spherical Gaussian Model of Molecular Structure. I. Computational Procedure. LiH as an Example. J. Chem. Phys. 1967, 47, 3707.
15. Moncrieff, D.; Wilson, S. Distributed basis sets of s-type Gaussian functions in molecular electronic structure calculations. Mol. Phys. 1994, 82, 523-530.
16. Reeves, C. M.; Harrison, M. C. Use of Guassian Functions in the Calculation of Wavefunctions for Small Molecules. II. The Ammonia Molecule. J Chem. Phys. 1963, 39, 11-17.
17. Ruedenberg, K.; Raffenetti, R. C.; Bardon, D. Energy, Structure and Reactivity, Proceedings of the 1972 Boulder Conference on Theoretical Chemistry; Wiley: New York, 1973; 164 pp.
18. Schmidt, M. W.; Ruedenberg, K. Effective convergence to complete orbital bases and to the atomic Hartree-Fock limit through systematic sequences of Gaussian primitives. J. Chem. Phys. 1979, 71, 3951-3962.
19. Feller, D. F.; Ruedenberg, K. Systematic Approach to Extended Even-Tempered Orbital Bases for Atomic and Molecular Calculations. Theor. Chim. Acta 1979, 52, 231-251.
20. Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K. Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J. Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92, Revision B Gaussian, Inc.: Pittsburgh, PA, 1992.
21. Dunning, T. H.; Hay, P. J. Mod. Theor. Chem. 1976, J. 1-28.
22. Flörke, U.; Haupt, H. J. The First Dinuclear Cobalt-Rhenium Cluster Compound: Hexacatbonylbis(µ-dicyclohexylphosphanido)cobaltihenium. Acta Crystallogr. 1993, C49, 1906-1908.
23. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetteriing, W. T. Numerical Recipes. The Art of Scientific Computing; Cambridge University Press: New York, 1988; Chapter 10.