Bader’s atoms

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. 

Cioslowski et al. used fragment similarity indices to compute the degree of similarity between atoms of the same element in different molecules, where the atoms were those derived from Bader s atoms in molecules theory [68,69]. They introduced a novel atomic similarity index for atom A in molecule X and atom B in molecule Y defined as [70]... 

An analysis of the topological characteristics of electron density was performed for the studied Sarin-magnesium oxide complexes following Bader s Atoms in Molecules Theory (AIM).82 This analysis can be used to characterize hydrogen bonding solely from the charge density. There have been formulated several effects... 

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. 

Occasionally, he has approached an experimentalist with a computationally inspired problem. In working with Bader s Atoms-In-Molecules theory, Grimme was interested in whether bond paths really correlate with bonds. Grimme proposed to Erker to synthesize 4,5-dideuterated phenanthrene and we got spectroscopists to measure this ... 

In order to produce qualitative information about bonding patterns and lone pairs, MO theory has to resort to orbital localisation procedures or more complicated interpretation techniques such as, for example, Bader s Atoms in Molecules (AIM) approach.However, orbital localisation procedures can be applied only to wavefunctions which remain invariant with respect to non-singular linear transformations of the orbitals, i.e. single-configuration and complete-active-space (CAS) MO wavefunctions and even for these, the use of orthogonal localised orbitals is not sufficient to reproduce all of the chemically-important information included in modern VB wavefunctions. Evidence of the superiority of the interpretational facilities offered by VB wavefunctions is provided by the continuing efforts to transform CAS wavefunctions to VB-style... 

In order to compare the global hardness as an all-metal aromaticity descriptor, we determine other quantities employed to evaluate aromaticity. The delocalization index (DI, 8 in Equation i)35,36 is derived from Bader s atoms-in-molecules (AIM) theory37 from the exchange-correlation density matrix (Txc) ... 

In addition, we used Bader s atoms-in-molecules (AIM) theory [56,57] to help analyze some of the results. For convenience, we give here a very brief overview of this approach. According to the AIM theory, every chemical bond has a bond critical point at which the first derivative of the charge density, p(r), is zero. The (> r) topology is described by a real, symmetric, second-rank Hessian-of-/3(r) tensor, and the tensor trace is related to the bond interaction energy by a local expression of the virial theorem ... 

P. Kolandaivel and V. Nirmala, Study of proper and improper hydrogen bonding using Bader s atoms in molecules (AIM) theory and NBO analysis, J. Mol. Struct. 694, 33-38 (2004). 

Table 5 Bader s atomic charges for structures 1-4 at the different theoretical levels...

Alternative approaches to the many-electron problem, working in real space rather than in Hilbert space and with the electron density playing the major role, are provided by Bader s atoms in molecule [11, 12], which partitions the molecular space into basins associated with each atom and density-functional methods [3,13]. These latter are based on a modified Kohn-Sham form of the one-electron effective Hamiltonian, differing from the Hartree-Fock operator for the inclusion of a correlation potential. In these methods, it is possible to mimic correlated natural orbitals, as eigenvectors of the first-order reduced density operator, directly... 

If such a partition scheme is to be employed, the atomic domains 2 need to be defined exphdtly. The most frequently apphed decomposition is Bader s Atoms in Molecules (AIM) approach [174,175] where the atomic domains 2 are divided by surfaces that are determined on the basis of the topology of the electron density. As the atomic volumes (or domains) are determined from the properties of the electron density, the AIM scheme can be apphed to any electron density calculated from a general wave function. In AIM theory, the boundary condition for an atom in a molecule requires the gradient vector field of the electron density Vp(r) to have zero flux [174,176],... 

In fact, this feature of Laplacian was extensively employed by Bader s atoms in molecules theory at the purely electronic density level in order to quantum rationalize the previous Gillespie s geometrical VSEPR (Valence Shell Electron Pair Repulsion) description of the molecular bonds (Gillespie, 1972 Bader etal., 1988). 

Another procedure that yields atomic charges is Bader s atoms-in-molecules (AIM) theory [Bader, R. F. W. Bader, Chem. Rev., 91, 893 (1991)]. Here, one first calculates an approximate wave function for the molecule, and from this wave function one calculates the electron probability density p x,y,z). One now imagines drawing all the contour surfaces of constant p (isodensity surfaces). Then one draws lines (called gradient paths) throughout three-dimensional space such that at every point on a given line, that line is perpendicular to the isodensity surface that passes through the point. (A simple example is... 

Bader s atoms are defined through the partitioning of (r) in three-dimensional real space. The atomic regions are bounded by atomic surfaces, which satisfy the following zero flux condition ... 

Hall and coworkers [9] described this mechanistic spectrum by an analysis of the geometry computed for the transition state. To do so, they used the reaction coordinate middle point defined by Bader s atoms in molecules (AIM) approach [10], which describes the bond critical points... 

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