Bader’s theory

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... 

A modem description of a conventional hydrogen bond as well as its older, more accurate definition are based on Bader s theory of atoms in molecules (AIM theory) [4]. Bader considers matter a distribution of charge in real space of point-like nuclei embedded in the diffuse density of electron charge, p(r). All the properties of matter are manifested in the charge distribution and the topology... 

In another paper by C.N. Ramachandran, D. Roy, and N. Sathyamurthy (Chem. Phys. Fetters, 461, 87 (2008)),which was issued after our paper was submitted, the host-guest interaction between C60 fullerene and inserted H+, H-, Pie, and Li ions and atoms, and the Fp molecule was also examined within the MP2 approximation and using Bader s theory of atoms-in-molecules. 

The outline of this chapter is as follows The chapter begins with the classical definition of H-bonding. Its importance in molecular clusters, molecular solvation, and biomolecules are also presented in the first section. A brief overview of various experimental and theoretical methods used to characterize the H-bonding is presented in the second section with special emphasis on Bader s theory of AIM [6]. Since AIM theory has been explained in numerous reviews and also in other chapters of this volume, the necessary theoretical background to analyze H-bonding interactions is described here. In the last section, the salient results obtained from AIM calculations for a wide variety of molecular systems are provided. The power of AIM theory in explaining the unified picture of H-bonding interactions in various systems has been presented with examples from our recent work. 

Bader s theory of AIM offers a convenient means of looking at H-bonding interaction in various intermolecular and intramolecular systems [6]. One of the advantages of the AIM theory is that one can obtain information on changes in the electron distribution as a result of either bond formation or complex formation. In the following section, the significant features of theory of AIM are discussed from the point of view of characterization of H-bonding interactions. 

Bader s theory, based upon the topological analysis of the electron density, is now nsed to describe many different types of compounds [37-39]. The phosphonic acid derivatives [40,41] are among these, hi our group the Atoms in Molecules Theory has also been used in the field of intermolecular interactions [42,43] and transition metal complexes [44,45],... 

Non-covalent interactions have been characterized using Bader s theory of Atoms In Molecules (AIM) [24] which has been used successfully to under-... 

Knowledge of the accurate electron density is decisive especially for the development of chemical concepts that are based on the analysis of this observable. Such concepts are Gillespie s valence-shell electron-pair repulsion model [1149] or the ligand-induced charge concentrations [880,1150-1152] that are designed to predict molecular structures and even chemical reactivity. Both approaches can be related to Bader s theory of atoms in molecules [1153], for which relativistic generalizations have been discussed in the literature [1154,1155]. 

It has also been shown that in the atomic regions the virial theorem holds [27, 33]. That is why Bader s partitioning of the electron density is often cited as the virial partitioning method [35, 36]. Bader s theory leads to an unequivocal formulation of the transferability idea the ensemble of atomic properties, in particular the contribution of an atom to the total energy, may be the same in different molecules, provided the charge density of the atomic region is identical [27]. The chemical bonds can be identified with the paths of maximal electron density, which interconnect the various nuclei. This point and several other chemical applications of Bader s theory have been recently reviewed by Wiberg [37]. 

Mohallem, J. R. (2002). Molecular structure and Bader s theory. Theor. Chem. Acc. 107, 372-374. 

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