Bader’s theory of atoms in molecules

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. 

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]. 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

The final part is devoted to a survey of molecular properties of special interest to the medicinal chemist. The Theory of Atoms in Molecules by R. F.W. Bader et al., presented in Chapter 7, enables the quantitative use of chemical concepts, for example those of the functional group in organic chemistry or molecular similarity in medicinal chemistry, for prediction and understanding of chemical processes. This contribution also discusses possible applications of the theory to QSAR. Another important property that can be derived by use of QC calculations is the molecular electrostatic potential. J.S. Murray and P. Politzer describe the use of this property for description of noncovalent interactions between ligand and receptor, and the design of new compounds with specific features (Chapter 8). In Chapter 9, H.D. and M. Holtje describe the use of QC methods to parameterize force-field parameters, and applications to a pharmacophore search of enzyme inhibitors. The authors also show the use of QC methods for investigation of charge-transfer complexes. 

The TAE/RECON method, developed by Breneman and co-workers based on Bader s quantum theory of Atoms In Molecules (AIM). The TAB method of molecular electron density reconstruction utilizes a library of integrated atomic basins , as defined by the AIM theory, to rapidly reconstruct representations of molecular electron density distributions and van der Waals electronic surface properties. RECON is capable of rapidly generating 6-31-I-G level electron densities and electronic properties of large molecules, proteins or molecular databases, using TAB reconstruction. A library of atomic charge density fragments has been assembled in a form that allows for the rapid retrieval of the fragments, followed by rapid molecular assembly. Additional details of the method are described elsewhere. ... 

Qm QM RECON Mean absolute atomic charge Quantum mechanics An algorithm for the rapid reconstruction of molecular charge densities and charge density-based electronic properties of molecules, using atomic charge density fragments precomputed from ab initio wave functions. The method is based on Bader s quantum theory of atoms in molecules. 

Parallel to the exciting reports about new types of hydrogen-hydrogen interactions, a paradigm shift was (and is) taking place in interpretative theoretical chemistry. Since the publication of Bader s classic monograph in 1990 [63], the quantum theory of atoms in molecules (QTAIM) has become a standard tool for the interpretation of theoretical and experimental [65-69] electron density distribution maps. The theory and its applications have been reviewed on a number of occasions by its principal author [63, 70-78] and by others [65-67, 69, 79-84]. A brief reminder of some of the basic concepts of QTAIM will be presented here with the sole purpose of keeping this chapter self-contained, but the interested reader is referred to the previously cited literature for in-depth treatments. 

Other quantum-chemical descriptors are TAE descriptors based on the Bader s quantum theory of —> Atoms In Molecules (AIM). 

Shghtly earher than the appearance of NICS, attempts to construct numerical characteristics of the electron delocalization based on Bader s quantum theory of atoms in molecules (QTAIM) (1990MI) or electron localization function (ELF) (1990JCP5397) had begun. The most important for aromaticity description are electron sharing indices. For example, the delocalization index (DI) provides a value 6(A,B) which is the number of electrons delocalized or shared between atoms A and B. The next useful aromaticity... 

This report follows on from the first report in the RSC Specialist Periodical Report series, this time with a slightly more adventurous title that specifies more precisely the character of the theory of Atoms in Molecules (AIM) pioneered by Bader and co-workers. In the first report we reviewed AIM from its very origin up to June 1999. The reader is referred to the first report for information on what AIM is and on software that implements it. Very recently two new books have appeared that may help the uninitiated to learn AIM or to deepen one s level of understanding. A recent popular account may also be of interest. 

Bader RFW (2(K)7) Everyman s derivation of the theory of atoms in molecules. J Phys Chem A 111 7966-7972... 

The most widely used approach is Bader s quantum theory of atoms in molecules (QTAIM), which depicts AIM as nonoverlapping [3, 7-10], Other popular models, such as those of Stewart [4, 11] and Hirshfeld [5], depict AIM as overlapping spherical fuzzy electron densities. Both the advantages and disadvantages of these methods have been previously discussed [1]. 

Bader s density-based topological theory [7] of Atoms in Molecules (AIM) has become a standard interpretive tool of electronic structure studies. There are obvious reasons for the popularity of this method it provides—on a firm physical basis—a relatively simple, real-space analysis of atomic interactions. Most importantly, the method is applicable to both theoretical and experimental EDs. 

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