Bader s method

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.

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. 

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]. 

Several forms of wf have already been used within the field of MQS. These methods include the Hirshfeld partitioning [30], Bader s partitioning based on the virial theorem within atomic domains in a molecule [64], and the Mulliken approach [65]. For more information on all the three methods, refer to Chapter 15. 

The postulates of VSEPR theory are consistent with the partitioning of electron density according to Bader s atoms-in-molecules method [173], in which the electron pairs return as the valence shell charge concentration. 

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. 

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 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. 

---