Bader

Figure C3.5.6 compares the result of this ansatz to the numerical result from the Wiener-Kliintchine theorem. They agree well and the ansatz exliibits the expected exponential energy-gap law (VER rate decreases exponentially with Q). The ansatz was used to detennine the VER rate with no quantum correction Q= 1), with the Bader-Beme hannonic correction [61] and with a correction based [83, M] on Egelstaff s method [62]. The Egelstaff corrected results were within a factor of five of experiment, whereas other corrections were off by orders of magnitude. This calculation represents the present state of the art in computing VER rates in such difficult systems, inasmuch as the authors used only a model potential and no adjustable parameters. However the ansatz procedure is clearly not extendible to polyatomic molecules or to diatomic molecules in polyatomic solvents.

Bader J S and Berne B J 1994 Quantum and olassioal rates for olassioal simulations J. Chem. Phys. 100 8359-66... 

R F W Bader s theory of atoms in molecules [Bader 1985] provides an alternative way to partition the electrons between the atoms in a molecule. Bader s theory has been applied to many different problems, but for the purposes of our present discussion we will concentrate on its use in partitioning electron density. The Bader approach is based upon the concept of a gradient vector path, which is a cuiwe around the molecule such that it is always perpendicular to the electron density contours. A set of gradient paths is drawn in Figure 2.14 for formamide. As can be seen, some of the gradient paths terminate at the atomic nuclei. Other gradient paths are attracted to points (called critical points) that are... 

R. F. W. Bader, Atoms in Molecules, A Quantum Theory Oxford, Oxford (1990). 

The individual gauges for atoms in molecules (IGAIM) method is based on Bader s atoms in molecules analysis scheme. This method yields results of comparable accuracy to those of the other methods. However, this technique is seldom used due to large CPU time demands. 

J. Ficini, N. Lumbroso-Bader and J. Pouliquen, Tetrahedron Lett., (196B), 4i39. 

Bader, M. A Systematic Approach to Standard Addition Methods in Instrumental Analysis, /. Chem. Educ. 1980, 57, 703-706. 

Although Saran is a generic name for VDC copolymers in the United States, it is a Dow trademark in most foreign countries. Other trade names include Daran (Hampshire Chemical Corporation) and Serfene (Morton Chemical) in the United States, and Haloflex (Zeneca Resins), Diofan (BASE), Ixan (Solvay SA), and Polyidene (Scott-Bader) in Europe. The monomer is of particular economic interest because it is only 27 wt % hydrocarbon. In addition, B. E. Goodrich Chemicals (GEON) supply non-barrier VDC copolymers. 

E. E. Bader, Proceedings of the 11th International Conference on Electric Contact Phenomena, West Berlin, Germany, 1982, pp. 133—137. 

RA Kuharski, JS Bader, D Chandler, M Sprik, ML Klein, RW Impey. Molecular model for aqueous ferrous-ferric electron transfer. J Chem Phys 89 3248-3257, 1988. 

Fig. 1.6. Charge distributions in strained cyclic hydrocarbons in comparison with cyclohexane. Data are from K. B. Wiherg, R. F. W. Bader, and C. D. H. Lau, J. Am. Chem. Soc. 109 1001 (1987).

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