Charge densities, atomic

Sum of the squared atomic charge densities Sum of the absolute values of charges Absolute hardness... 

Figure 1. The charge-density difference (bonding charge density) between NiaX and the superposition of neutral Ni and X atomic charge densities on the (001) planes for (a) X = A1 and (b) X = Si. The solid (dotted) contours denote contours of increased (decreased) density as atoms are brought together to form the NiaX (X = Al, Si) crystal. Contours start from 4.0 X 10 e/(a.u.) cind increase successively by a factor of root 2.

Deviation includes, in fact, the summation of steric and electronic effects, and basicity is somewhat a useful predictor for properties of complex dyes (solvent sensitivity, isomeric forms of trinuclear dyes) and gives also semiquantitative data for color structure relation charge density, redox properties. 

In discussing gross atomic charges it must be realized that a given pattern of atomic charge densities in a molecule can be imposed by several factors. We identify three effects responsible for a molecular charge distribution ... 

The shortness of these bonds may be attributed, in part, to their polar nature as indicated by the strong intensity of the S—S stretching vibrations at ca. 590 and 565 cm" in the infrared spectrum of and supported by ab initio calculations of the atomic charge densities in the anion (see Sects. 3, 3.4) In contrast to PhjPNSNSS, the S—N bonds of the central SNS unit in the two S N structures are unequal and the inequality is in opposite senses, presumably as a result of interactions with the cation. 

Neutron diffraction is especially important for the location of hydrogen atoms, as the pronounced effect of bonding on the hydrogen-atom charge density leads to a systematic bias in the X-ray positions, as discussed in chapter 3. If the charge density in a hydrogen-containing molecule is to be studied, independent information on positions and thermal vibrations of the H atoms is invaluable. 

Transferability of atomic densities was tested by Brock et al. (1991), who applied atomic charge density parameters from an accurate low-temperature study of perylene (I) to data collected at five and six different temperatures on naphthalene (II) and anthracene (III), respectively. The molecules are all aromatic hydrocarbons. To reduce the number of variables, all H atoms were assigned... 

Embedded atom potentials have been extensively used for performing atomistic simulations of point, line and planar defects in metals and alloys (e.g. Vitek and Srolovitz 1989). The pair potential ( ), atomic charge density pBtom(r), and embedding function F(p) are usually fitted to reproduce the known equilibrium atomic volume, elastic moduli, and ground state structure of the perfect defect-free lattice. However, the prediction of ground state structure, especially the competition between the common metallic structure types fee, bcc, and hep, requires a more careful treatment of the pair potential contribution ( ) than that provided by the semiempirical embedded atom potential. This is considered in the next chapter. 

Figure 2.6. Molecule-atom charge density differences for H2 and H 2 molecules. From Ref. [29].

The regioselectivity associated with the nitration of the 7-bromo-l,5-benzodiazepinone 9, which occurred at C-8 and C-9, was examined by considering the relative atomic charge densities, total pz electron population, and the electron population density of the highest occupied molecular orbital (HOMO) at each site. The it-localization energy of the two C-8 and C-9 nitration transition state cr-complexes was better able to predict the observed ratio of products, which favors nitration at C-9 by 3 1 <2003M1629, 2004HAC263>. 

When the charge distributions correspond to molecules such as proteins that are composed of discrete segments, i.e., atoms, the charge distribution function can be expressed as the sum of atomic charge densities given by... 

The calculation of log P (octanol) is facilitated by the availability of computer programs that use the group contribution method (27,28). The derivation of log P (octanol) values from relative HPLC retention times (29-31), and from atomic charge densities calculated using semi-empirical molecular orbital methods has also been described (32). 

Fig 7 a-f. Shake-up and shake-off processes in photoionization (a) Real space picture illustrating contraction of the atomic charge density in response to the creation of a core hole (b, d) Shake-up (c, f) Conjugate shake-up and (e) inelastic scattering... 

A CNDO study on benzo[l,2-c 4,5-c ]dithiophene predicted that it would be more polar than thieno[3,4-c]thiophene, and that excess electron density would be distributed at the bridgehead carbon atoms. A singlet ground state was also predicted <75ACR139>. The heats of atomization, charge densities, and resonance energies of a series of benzodithiophenes were calculated <80T27il>. A [c] fusion led to less resonance stabilization of a system than a [b] fusion. 

Table 9-1. Mulliken atomic charge densities in all states in Figure 9-10. The positions of the three S atoms and two H atoms are shown in Figure 9-9, distinguished by the suffixes...

C NMR spectra of five separate series of mono-, di-, and polysubstituted chloro-, bromo-, iodo-, benzoyl-, and nitrocarbazoles substituted at the T,3-, 6-, and 8-positions have been recorded <2005JHC867>. C chemical shifts of carbons ipso, ortho, and para show good linear correlations with net atomic charge density values, suggesting that charge density nicely predicts the substituent effects. 

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. ... 

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