Bader analysis

Mulliken analysis is a quick and relatively simple way to break down the charge density into atomic contributions but it is dependent on the basis set used. In particular, if the number of basis functions is unevenly distributed between atoms, those with rich basis sets will tend to have too much charge assigned through the Mulliken procedure. To attempt to rectify this, methods based on the charge density alone have also been developed. For example, Bader analysis uses the minima in the density to define a region around each atom over which the density can be integrated numerically [41]. 

Bader and coworkers have shown that properties of the electron density distribution p(r) can be used to partition the molecular space into subspaces in a unique way [24]. This has been used by Cremer and Kraka (CK) to establish a model of the chemical bond that it easy to use, that allows a simple distinction between bonding and nonbonding situations, and that helps to characterize covalent bonds [19]. Therefore, the CK model has been applied when quantitatively describing chemical bonding in molecules containing light noble gas elements. In the following, we will briefly review the essentials of the Bader analysis and the CK bond model [25]. 

N-O and P-O Bond Nature in Hypervalent Compounds is Bader Analysis Basis-Set and Geometry Independent ... 

In the present work, the validity of the Bader analysis against the level/basis set and geometry variation will be tested in hypervalent amine and phosphine oxides (stractnres 1 H3PO, 2 F3PO, 3 H3NO, 4 F3NO) (see Fignre 1). 

In the Bader analysis of F-N bond nature, it is also important to include electron correlation, as pointed out in the geometry discussion. For example, the p r) values are... 

Bader analysis for the X-0 bond is mainly independent of the chosen level (HF, DFT or MP2). 

N-O and P-O bond nature in hypervalent compounds is Bader analysis basis-set and geometry independent ... 

It seems that at the essence of science is the fundamental question of why, and a clear answer to this question follows from a deep understanding the Nature s machinery. We cannot tell a student, Well, this is what the computer says, because it is more important for you and me to understand than that the computer cranks out an answer. Hence, interpretation of the results will be of crucial importance (a sort of Bader analysis cf.. Chapter 11). Progress in this realm seems to be rather modest for the time being. 

The model of molecule visualized in virtually all popular computer programs shows spherical atoms and chemical bonds as shining rods connecting them. First of aU, atoms are not spherical, as is revealed by Bader analysis (p. 667) or atomic multipole representations (see Appendix S available at booksite.elsevier.com/978-0-444-59436-5). Second, a chemical bond resembles more a rope (higher values) of electronic density than a cylindrical rod. The tope is not quite straight and is slimmest at a critical point (see p. 671). Moreover, the rope, when cut... 

This is a common fact of chemistry, but if you are wondering how you know this, then it turns out you have to quote your teachers. As to a more serious argument, this conclusion can he drawn either from an electronic population analysis described in Appendix S available at booksite.elsevier.com/978-0-444-59436-5 or by performing the Bader analysis (as described in Chapter 11). In the first case, we would get the positive (and equivalent) populations between atoms O and H, which will result from a net bonding interaction, while the population between H and H... 

In Bader analysis, in the critical point of the charge density for a covalent bond,... 

This is common knowledge in chemistry and is derived from experiments as well as from quantum mechanical calculations. The later provide the partial atomic charges from what is called population analysis (see Appendix S available at booksite.elsevier.com/978-0-444-59436-5). Despite its non-uniqueness, it would satisfy our needs. A unique and elegant method of calculation of atomic partial charges is related to the Bader analysis described on p. 669. 

Bader analysis, 667 balance, kinetic, 132 band, conduction, 533-534 band gap, 537 band structure, 523, 527 band, valence, 537, 610 bandwidth, 532 barrier as shell opening, 948 barrier of dissociation, 801 barriers of reaction, 948 basis, biorthogonal, 513 basis set, atomic, 428, 431,el37... 

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