Bader decomposition

Henkelman G, Amaldsson A, Jonsson H (2006) A fast and robust algorithm for Bader decomposition of charge density. Comput Mater Sci 36 354-360... 

The diffusivities of ozone in mucus, tissue, and water are unknown. As an approximation, the diffusivity of oxygen in water (2.5 x 10 cm /s) may be used for the diffusivity of ozone in water and in the mucus layer. Although reactivities of ozone in mucus and tissue are unknown, the results of Alder and Hill and Hoigne and Bader, which describe the decomposition of ozone in aqueous solutions, may be used as a first approximation. 

Bader treated the decomposition of an azo compound, R—N=N—R, in the same way. The Walsh diagram (Fig. 4) indicates the appropriate levels ... 

It seems clear that in molecules with one type of atom only, say ozone, one should have a similar sort of decomposition. In independent work and from a different direction, Bader and his co-workers have likewise insisted on the importance of Vp in dividing a molecule into fragments which are localized and transferable. As one example, the work of Bader and Beddall58 effects such a partitioning into fragments based on the virial theorem, and the interested reader is referred to this and various other papers which throw very considerable light on electron densities in specific molecules and on partitioning the electron cloud.59-85... 

Bader and Gatti [38] suggested a decomposition scheme that divides the total ED into atomic sources on the basis of the local source function (LS)... 

Bader s paper dealt primarily with the modes of decomposition of activated complexes, a special kind of unimolecular reaction. Several early papers by Salem 9) and Pearson also dealt with unimolecular reactions. Recently several papers have discussed bimolecular and termolecular reactions (Pearson ii)). Before presenting the theory in a formal sense. 

For an activated complex (point B) there must necessarily be at least one excited state of low energy. The symmetry of this state and the ground state then determines the mode of decomposition of the activated complex. This was the subject of the first application of Eq. (3) to chemical reactions by Bader 8). 

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 its emphasis on the the coupling of molecular orbitals by means of coordinates for nuclear motion, OCAMS resembles treatments based on the second-order Jahn-Teller effect [23, pp. 17-25], such as that of Bader [21] and developments ensuing from it [63, 64], in which a vibrational coordinate of appropriate symmetry couples occupied and unoccupied MOs of the same molecule and determines the manner of its decomposition. 

Consider first the concept of atom in molecule. Several definitions can be proposed which depend upon choices such as the nature of the space, the required properties of the atom in the molecule. Richard Bader s definition is based on (i) a space filling non overlapping partition of the density and (ii) on the fulfillment of an energy decomposition requirement the electronic energy of the molecule is the sum of atomic and interatomic contributions having a definite value. Condition (i) can be written as ... 

Keywords Halogen bonds Bader s atoms-in-molecules theory Energy decomposition Interacting quantum atoms scheme Electrostatic interactions Electronic quantum exchange... 

In this chapter, we provided evidence that Bader s atoms-in-molecules provides deep physical insight into the formation mechanism of halogen bonds. Within this framework, the interacting quantum atoms decomposition enables to cure the deficiencies of the local approach based on critical points, and to rigorously assess the importance of classical electrostatics and quantum effects in terms of energetic quantities. It was notably shown that even if classical electrostatics (that can be further decomposed into charge points and multipolar components) generally... 

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