Topology of Molecular Charge Distributions

Bader and his colleagues have developed topological arguments for molecular charge distributions. In particular Bader, Nguyen Dang, and Tal118 have emphasized that the concepts which are essential to the description of a chemical system are  

Bader and his co-workers have presented evidence that these concepts have 

We here summarize the results of Bader et a/.118 which are concerned with the definition of molecular structure and with the extension of this concept, together with the associated concept of a bond, to the dynamic case. A precise description and physical interpretation of the making and breaking of chemical bonds is presented by these workers in a quantitative analysis of the evolution of molecular structure. The topological analysis of the dynamic system, as pointed out by Collard and Hall,119 falls naturally into the realm of an existing and elegant mathematical theory, the catastrophe theory of Thom.120 

---

The theory of molecular structure based on the topology of molecular charge distribution, developed by Bader and co-workers (83MI2 85ACR9), enables certain features to be revealed that are characteristic of the systems with aromatic cyclic electron delocalization. To describe the structure of a molecule, it is necessary to determine the number and kind of critical points in its electronic charge distribution, i.e., the points where for the gradient vector of the charge density the condition Vp = 0 is fulfilled. 

Bader, R. F. W., T. T. Nguyen-Dang, and Y. Tal (1979). Quantum topology of molecular charge distributions. II. Molecular structure and its change.. /. Chem. Phys. 70, 4316-29. 

Bader RFW, Anderson SG, Duke AJ (1979) Quantum topology of molecular charge distributions. 1. J Am Chem Soe 101(6) 1389-1395... 

Bader RFW (1980) Quantum topology of molecular charge-distributions. 3. The mechanics of an atom in a molecule. J Chem Phys 73 2871-2883... 

Gatti, C., P. J. MacDougall, and R. F. W. Bader. 1988. Effect of Electron Correlation on the Topological Properties of Molecular Charge Distributions. J. Chem. Phys. 88, 3792. 

Boyd, R. J., Hydrogen bonding between nitriles and hydrogen halides and the topological properties of molecular charge distributions, Chem. Phys. Lett. 129, 62-65 (1986). 

Gatti C, MacDougall PJ, Bader RFW. Effect of electron correlation on the topological properties of molecular charge distributions. J Chem Phys 1988 88 3792-3804. 

This chapter, which describes the application of the theory of atoms in molecules to the chemistry of the alkanes, gives only a curtailed account of the quantum mechanical basis of the theory, as full accounts have been presented elsewhere The development of the theory of molecular structure is presented in somewhat more detail and the application begins with a review of the topological features of molecular charge distributions and the associated definitions of atoms, bonds and molecular structure. 

Clearly, the set of numbers (n, N, r, c) is a useful index of the major topological properties of a molecular charge distribution. 

Because of the dominant topological property exhibited by a molecular charge distribution—that it exhibits local maxima at the positions of the nuclei—the imposition of the quantum boundary condition of zero flux leads directly to the topological definition of an atom. Indeed, the interatomic... 

Molecular orbital theory has played the central role in the definition and understanding of problems of electronic structure. The charge density plays the corresponding role in the definition and understanding of the concepts associated with molecular structure. The previous chapters have shown that atoms, bonds, and structure are indeed consequences of the dominant topological property exhibited by a molecular charge distribution. What remains to be done is to demonstrate that the topological atom and its properties have a basis in quantum mechanics. 

---