Contour charged densities

Fig. 7. Maps of the electronic charge density in the (110) planes In the ordered twin with (111) APB type displacement. The hatched areas correspond to the charge density higher than 0.03 electrons per cubic Bohr. The charge density differences between two successive contours of the constant charge density are 0.005 electrons per cubic Bohr. Atoms in the two successive (1 10) planes are denoted as Til, All, and T12, A12, respectively, (a) Structure calculated using the Finnis-Sinclair type potential, (b) Structure calculated using the full-potential LMTO method.

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.

A map of the electron density distribution around these atoms provides important information. It tells us to what distance from the adatom the surface is perturbed or, in catalytic terms, how many adsorption sites are promoted or poisoned by the adatom. The charge density contours in Fig. 6.27 are lines of constant electron density. 

Figure 6.27. Charge density contours for the adsorption of Cl, Si, and Li on jellium. (a) Total charge and (b) induced charge solid lines indicate an increase in electron density, dashed...

Figure 4.6 Left STM image of a stoichiometric 1 x 1 Ti02(l 1 0) surface, 14A x 14 A. Sample bias + 1.6 V, tunneling current 0.38 nA. The inset shows a ball-and-stick model of the unrelaxed 1 x 1 Ti02(l 1 0) surface. Rows of bridging oxygen atoms are labeled A and rows of fivefold coordinated titaniums B . Right contour plots of [0 1 l]-averaged charge densities associated with electron states within...

Fig. 7. (a) Contour plot of the charge density in the (110) plane through the atoms for neutral H at the bond center. The Si atoms in their relaxed positions are indicated with black dots and connected with solid lines. Dashed lines connect the unrelaxed atomic positions. The contour interval is 50 units are electrons per unit cell (for a supercell containing 1 H and 32 Si atoms), (b) Contour plot of the difference between spin-up and spin-down densities in the (110) plane through the atoms for neutral H at the bond center. The contour interval is 2.5 electrons/(unit cell). (Reprinted with permission from the American Physical Society, Van de Walle et al., 1989.)... 

Fig. 14.4. The valence electron charge density of silicon. Contour spacings are in units of electrons per unit cell volume. Shaded circles represent atomic cores.

Fig. 14.7 Total valence electron charge density for the ideal Si(111) surface shown in Fig. 14.6. Charge contours are plotted in the (110) plane and normalized to one-electron charge per primitive cell. Shaded circles represent atomic cores.

The surface charge density of Al(lll) has been well characterized by first-principles calculations as well as helium scattering experiments. The asymptote of the corrugation amplitude Az of equal-LDOS surface contours follows an exponential law, as obtained from a first-principles calculation of the electronic structure of the Al(l 11) surface (Mednick and Kleinman, 1980) ... 

As we have mentioned, the results of first-principles calculations are usually presented in the form of charge-density contours. The following are the commonly used forms of presenting results of first-principles calculations. 

Fig. 4.15. Contours of constant charge density for Si(lll). The occupied portion of the dangling-bond surface state on Si(lll) is shown. Dots locate nuclei of surface atoms, the vacuum is above, and the charge density is in a.u.X lOL (Reproduced from Appelbaum and Hamann, 1976, with permission.)...

Fig. 4.16. Charge density of surface states on W(OOl) and Mo(OOl). (a) Charge-density contours of a localized surface state on W(OOl), located 0.3 eV below the Fermi level. Contours are in units of electrons per unit cell. (Reproduced from Posternak et al., 1980, with permission.) (b) A d localized surface state on Mo(OOl) 0.2 eV below the Fermi level. The contour plane is perpendicular to the surface. Dots indicate nuclei of surface atoms. The charge density is in units of electrons per unit cell. (Reproduced from Kcrkcr ct al., 1978, with permission.)...

Fig. 4.17. Electronic states of W clusters near the Fermi level. Charge-density contours for several states on W clusters, (a) and (c) The highest occupied molecular orbitals (HOMO) of Wi and Wi. (b) and (d) The eigenstates just below HOMO. (Reproduced from Ohnishi and Tsukada, 1989, with permission.)...

Therefore, the corrugation amplitude arising from a p, tip state gains a factor of [l over that of the charge-density contour see Fig. 5.2. This is... 

Therefore, the constants Q and C can be obtained from the charge-density contours of first-principles calculations. 

Fig. 5.4. The corrugation amplitude of the STM images for Cu(OOl). Calculated for different m = 0 lip states and different tip-sample distances. The corrugation amplitude of charge density contours is obtained from Gay ct al. (1977).

Fig. 5.7. Charge-density contour plot of Al(lll) film. Results of a first-principles calculation of a nine-layer Al(lll) film. The contours are in steps of 0.27 electrons per atom. (Reproduced from Wang et al., 1981, with permission.)...

Similarly, 3 = 7 - 2k. The ratio (Ci/Cq) can be determined by comparing Eq. (5.49) with the corrugation amplitudes of the charge-density contours obtained from first-principles calculations. For example, from Fig. 5.7, averaged from five contours ranging from three contours of thinnest densities, we find (C /Co) 5.7 1.0. Following the procedure for the one-dimensional ca,se, the STM image for the p- tip state is... 

Figure 6.9 is a comparison of the results discussed previously with the first-principles calculation of the AI(lll) surface as well as the experimental results of STM images on Al(lll) by Wintterlin et al. (1989). A very simple model of the Al(lll) surface is used On each surface Al atom, there is an independent Is state near the Fermi level. The charge density contour (i.e., the image with an. r-wave tip state) agrees with the extrapolated corrugation amplitudes of the first-principles calculation (Mednick and Kleinman, 1980 ... 

Fig. 8.1. Local modification of the electronic structure in the gap. Charge-density contours of a system with an A1 tip and an A1 sample. (a) Free Al(ll 1) surface, (b) At a tip-sample distance 8 bohr (4.2 A) (c) 7 bohr (3.6 A) and (d) 5 bohr (2.6 A). (Reproduced from Ciraci et al., 1990a, with permission.)...

See Atomic force microscope Al(lll) 33, 135, 136, 169 charge-density contours 135 experimental STM images 33 theoretical STM images 136, 169 AMIE... 

See Surface Brillouin zone Cantilever 314—317 fahrication 316 requirements 314 Charge-density contours 117 Chemical hond 13, 172... 

Figure 1.17. Electron charge density difference contour map for CO on Ni(100) and CO on Ni(100)/H in atop sites, derived from DFT calculations.

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