Atom charge superposition

A crude estimation of the charge-density distribution on simple metal surfaces can be made by assuming that the electron charge for each atom is spherical. Especially, as shown by Cabrera and Goodman (1972), by representing the atomic charge distribution with a Yukawa function. 

After some modification, the method of atomic charge superposition of Haneman and Heydock (1982), together with the analytic summation of Cabrera and Goodman (1972), can be applied to calculate STM and AFM images. We will discuss it in Chapter 6. 

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See Atomic metallic ion emission Anomalous corrugation theory 31, 142 breakdown 146 graphite, and 31, 144 Apparent barrier height 63,171 anomalously low 171 attractive force, and 49, 209 definition 7 image force, and 72 repulsive force, and 171, 198, 209 square-barrier problem, in 63 Apparent radius of an atomic state 153 Atom charge superposition I 11 analytic form 111 Au(lll), in 138 in atomic beam scattering 111 Atom-beam diffraction 107 apparatus 109... 

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.

Autocorrelation coefficients are used to transform a pattern of atom properties into a representation that allows comparison of molecules without needing to find the correct atom-by-atom superposition [60, 61]. Any atom property P (atomic charge, Hpophilicity parameter, topological or electrotopological index, etc.) can be used as input... 

The STM simulations are based on a simplified atomic charge model [31], in which a spherical shape of the valence charge density is assumed for the atoms. These spherical shells of fixed radius (solid sphere) are superimposed in three dimensions for all atomic positions considered in the simulation. From this superposition the z(x,y) (z parallel to the plane normal) contour of the uppermost shells is... 

Figure 5.8b. Pseudo valence charge density contour plots of the (a) RuO2(110) surface in comparison with (b) the RuO2(001) surface cut through the cus-Ru atoms. These plots are defined as the difference between the total valence electron density and a linear superposition of radially symmetric atomic charge densities. Contours of constant charge density are separated by 0.15 eV/A. Electron depletion and accumulation are marked by dashed and solid lines, respectively. In addition, regions of electron accumulation are shadowed...

The LCAO total energy was evaluated using the variational expression (Eq. 7) with n obtained from a potential generated using superposition of carbon sp atomic charges. This and the fact that only 12 basis functions per atom were used account for the slight difference in the cohesive energy between the two calculations. We note that because of the localized nature of the carbon bond in diamond approximately 250 plane waves per atom were used for the plane wave basis. 

In these lectures we will present the theory of atomic scattering focusing in particular on the atom surface potential. This potential is separated in an attractive part of the Van der Waals type and in a repulsive part related to the surface charge which is approximate as a superposition of atomic charges. The lateral Fourier trasform of this potential, which enters in the cross sections, has a gaussian form which is essential in order to explain the falling off of the Rayleigh peaks at the zone boundary. 

The aim of this chapter is to show, on the basis of several examples, how the location of the bond path may be useful to characterize, define and/or verify the specific, considered interaction. Mainly the QTAIM approach [4-7] is considered here however sometimes there are also references to other methods and concepts as for example the Namral Bond Orbitals (NBO) method [21, 22] or the o-hole concept [25-27]. This is worth to note that the results presented hereafter are mainly based on the MP2/aug-cc-pVTZ level of calculations those results are taken from earlier studies or the calculations were carried out especially for the purposes of this chapter. Consequently the QTAIM calculations were performed on the MP2/aug-cc-pVTZ wave functions. The binding energies (Ebin s) were calculated as differences between the energy of the complex and the sum of energies of monomers optimized separately and they were corrected for the basis set superposition error (BSSE) by the counterpoise method [28]. Since the NBO method is based on the Hartree-Fock method thus the corresponding NBO results, i.e. orbital-orbital interactions or atomic charges, if presented, are based on the HF/aug-cc-pVTZ//MP2/aug-cc-pVTZ level. Hence there is rather not indicated the level of calculations for the next systems discussed hereafter unless the results presented were obtained within other levels of calculations. 

In the trapped-ion system, the qubit levels are two electronic states of the trapped charged atom. Using superpositions, states in which the qubit is in 0 and 1, one can process all possible input states at once with a given algorithm (quantum parallelism). The only catch is that once the algorithm terminates, the answer must be read out. Similar to Schrddinger s cat, which, upon looking, is... 

The formation of chemical bonds between atoms brings about a redistribution of electronic charge relative to a simple superposition of atomic charge densities. One may characterize many of the properties of an atom in two ways by its ground-state charge distribution (which determines the atomic size), and by the accessibility of its first... 

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