Charge density, total

This equation is usually solved self-consistently . An approximate charge is assumed to estimate the exchange-correlation potential and to detennine the Flartree potential from equation Al.3.16. These approximate potentials are inserted in the Kolm-Sham equation and the total charge density is obtained from equation A 1.3.14. The output charge density is used to construct new exchange-correlation and Flartree potentials. The process is repeated nntil the input and output charge densities or potentials are identical to within some prescribed tolerance. 

You can also plot ihe electrostatic polenlial. the total charge density. or the total spin density determined during a semi-enipincal or ah initio calculation. This information is useful in determining reactivity and correlating calculalional results with experimental data. Th ese examples illustrate uses of lb ese plots ... 

To obtaiti the total charge density r, at atom C we must sum over all occupied or partially occupied orbitals and subtract the I esult from 1,0. the n charge density of the carbon atom alone... 

Dioxolan-2-ylium cation INDO optimized geometry, 6, 750 total charge density, 6, 750... 

Based on electrochemical experiments combined with ex situ analysis by AES, LEED, and RHEED, Wang et al. (2001) suggested the formation of a (2 x 2) (2CO + O) adlayer on Ru(OOOl) at = 0.2 V in CO-samrated HCIO4, similar to the phase formed in UHV after CO adsorption on a (2 x 2)0-covered surface [Schiffer et al., 1997]. Erom the total charge density transferred after a potential step to 1.05 V in a CO-free electrolyte, they concluded that only 60% of the CO content in such an adlayer can be oxidized under these conditions [Wang et al., 2001]. 

At a certain stage in the refinement, the electron density map is interpreted using a model representation of the charge density distribution to extract the atomic coordinates. A commonly used scattering formalism is the independent-atom model (IAM), in which the total charge density in the crystal is approximated by the superposition... 

The requirements that n and its slope be continuous at z0 allow the expression of A and B in terms of a, b, and z0 a third condition, that the total charge density of the interface be equal to zero, gives... 

Z)(r) is the total charge density its sign can vary as a function of r. 

It should be noted that the electrostatic potential V(r) is related rigorously to the total charge density D(r) through Poisson s equation, Eq. (3.4). 

SCHEME 6. Charge distribution in two different sulfenamide cations (total charge densities as revealed by MNDO calculation H. -U. Wagner in Reference 56)... 

Fig. 25. Total charge density and charge-density differences in the HOH-F -HOH complex in the plane of the water molecules (maps taken from Ref. 208))...

Figure 2. (a) Density of water oxygens and hydrogens, (b) The water dipole density profile and the associated potential drop, (c) The total charge density profile and the potential drop, as a function of the distance between two parallel slabs of the Pt( 100) surface at T = 300 K. 

The calculations of Feibelman and Hamann have expressly addressed the surface electronic perturbation by sulfur as well as by Cl and The sulfur-induced total charge density vanishes beyond the immediately adjacent substrate atom site. However, the Fermi-level density of states, which is not screened, and which governs the ability of the surface to respond to the presence of other species, is substantially reduced by the sulfur even at nonadjacent sites. Finally, the results for several impurities indicate a correlation between the electronegativity of the impurity and its relative perturbation of the Fermi-level density of states, a result which could be very relevant to the poisoning of H2 and CO chemisorption by S,C1, and as discussed above. 

In the presence of the static imposed external potential, which couples to the total charge density, the energy of the electron gas is shifted by an amount... 

Space Partitioning and Topological Analysis of the Total Charge Density... 

In analogy to the definition of the total charge density, we define the total structure factor Ftotal(H), which includes both the nuclei and the electrons, and is, excluding thermal effects, given by... 

The study of the nature of the Si—O bond through analysis of its charge density is based on net ionic charges, heights of peaks in atom deformation density maps, and, more recently, topological analysis of the total charge density. 

With the topological analysis of the total charge density, the distinction between a covalent and a closed-shell ionic interaction can be based on the value of the Laplacian and its components at the bond critical point. Such an analysis will be most conclusive when done on a series of related compounds, analyzed with identical basis sets, as the topological values of the model density from experimental data have been found to be quite dependent on the choice of basis functions. 

This form of information is particularly common for the surface states, units used are similar to that of the total charge density. 

Local density of states (continued) definition 119 s-wave-tip model, and 29 Sommerfeld metal 93 STM corrugation, and 142 total charge density, and 120 Local modification of sample wavefunctions 195 Local-density approximation 114 Logarithmic amplifier 257 Louse 269... 

For the repulsion energy, the total charge density overlap integral between molecules A and B, 5ab> is calculated and is subdivided into contributions from pairs of atomic species m and n, S n- Then... 

Figure 2.1. Schematic picture illustrating the local probe character in XES for N2 adsorbed on a Ni surface. From the total charge density (gray envelope) valence electrons with p-angular momentum (contour lines) decay into the N Is core hole. From Ref. [3].

---