Bader population analyses

Bader population analysis has shown (90JA1707) that the complex (115) is primarily formed through the tr-donation from the nonbonding cr-orbital of N2 to the low-lying vacant cr -orbital of borabenzene supplemented by the 7r-back-donation from the bt ir-orbital of borabenzene to the vacant 7r -orbital of N2. 

In Chapter 3, we studied the topic of population analysis. In population analysis, we attempt a rough-and-ready numerical division of the electron density into atom and bond regions. In Mulliken theory, the bond contributions are divided up equally between the contributing atoms, giving the net charges. The aim of the present section is to answer the questions Are there atoms in Molecules , and if so, How can they be defined . According to Bader and coworkers (Bader, 1990) the answers to both questions are affirmative, and the boundaries of these atoms are determined by a particular property of the electron density. 

The idea of Molecular Atoms can be traced back to Richard Bader s work in the 1960s. It didn t get a mention in the original Theoretical Chemistry SPR, but is now a widely used technique. It is now an option in packages such as Gaussian98. Consumers will have to get used to the atomic charges, which seem to make much more sense than those of conventional Population Analysis. I therefore asked Paul Popelier, Fiona Aicken and Sean O Brien to bring us up to speed. 

R. F. W. Bader, T. T. Nguyen-Dang, and Y. Tal, Rep. Progr. Phys., 44, 893 (1981). The Topological Theory of Molecular Structure. R. F. W. Bader, Atoms in Molecules, Oxford University Press, Oxford, 1990. See also, S. M. Bachrach, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, 1994, Vol. 5, pp. 171-227. Population Analysis and Electron Densities from Quantum Mechanics. 

This is a common fact of chemistry, but if you are wondering how you know this, then it turns out you have to quote your teachers. As to a more serious argument, this conclusion can he drawn either from an electronic population analysis described in Appendix S available at booksite.elsevier.com/978-0-444-59436-5 or by performing the Bader analysis (as described in Chapter 11). In the first case, we would get the positive (and equivalent) populations between atoms O and H, which will result from a net bonding interaction, while the population between H and H... 

This is common knowledge in chemistry and is derived from experiments as well as from quantum mechanical calculations. The later provide the partial atomic charges from what is called population analysis (see Appendix S available at booksite.elsevier.com/978-0-444-59436-5). Despite its non-uniqueness, it would satisfy our needs. A unique and elegant method of calculation of atomic partial charges is related to the Bader analysis described on p. 669. 

It has been recently shown [12] that the ELF topological analysis can also be used in the framework of a distributed moments analysis as was done for Atoms in Molecules (AIM) by Popelier and Bader [32, 33], That way, the Mo( 2) monopole term corresponds to the opposite of the population (denoted N) ... 

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