Difference electronic charge density

The isomer shift is caused because the emitter and the absorber 57Fe nuclei in the Mossbauer experiment have different electronic charge densities at the position of the nucleus [137-140], Consequently, we get a small shift in the difference of the energy levels given by [137-140]... 

Figure 8.26 (a) Difference electronic charge density map (calculated bulk minus isolated ion densities), displayed in the crystallographic plane containing the central Mo and the vertices 0(1)0(2 )0(3 )0(2) of one isolated MoOs octahedron. Continuous, dashed and dot-dashed lines correspond to positive, negative and zero difference respectively. The interval between the isodensity lines is 0.005 a.u. (electrons ao ). 

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.

The electric monopole interaction between a nucleus (with mean square radius k) and its environment is a product of the nuclear charge distribution ZeR and the electronic charge density e il/ 0) at the nucleus, SE = const (4.11). However, nuclei of the same mass and charge but different nuclear states isomers) have different charge distributions ZeR eR ), because the nuclear volume and the mean square radius depend on the state of nuclear excitation R R ). Therefore, the energies of a Mossbauer nucleus in the ground state (g) and in the excited state (e) are shifted by different amounts (5 )e and (5 )g relative to those of a bare nucleus. It was recognized very early that this effect, which is schematically shown in Fig. 4.1, is responsible for the occurrence of the Mossbauer isomer shift [7]. 

Some n-electron charge density differences between the ground and first excited states calculated by the PPP-MO method for 4-aminoazobenzene,... 

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.

Figure 2.8. Electron density contours for atomic chemisorption on jellium with electron density that corresponds to A1 metal. Upper row Contours of constant electron density in the plane normal to the surface. Center row Difference in charge density between isolated adatom and metal surface, full line gain and dashed line loss of charge density. Bottom row Bare metal electron density profile. Reproduced from [30].

The different behavior of tertiary and quaternary carbon atoms seems to be due to either the complete neglect of overlap in these calculations or to polarization effects of the carbon-nitrogen bonds, Similar results are obtained for a series of 5-halouracils by plotting the 13C NMR chemical shifs versus 7r-electron charge densities calculated by the extended Hiickel theory [756], Though for several nitrogen heterocycles a better correla-... 

A large number of 13C NMR studies on proline derivatives and proline peptides have appeared in the literature [815-830]. As the electron charge density of cis-proline carbons is different from that of franx-prolinc carbons, these isomers can be differentiated by nCNMR spectroscopy [826, 830]. On the basis of calculations Tonelli [831] predicted four conformations for the dipeptide Boc-Pro-Pro-OBzl, three of which could be detected by 13C NMR spectroscopy [826, 830], In proline-containing peptides the stereochemistry of the proline residue plays an important role for the conformation of these oligomers. The 13C chemical shift data of cis and trans proline derivatives, collected in Table 5.29, are useful to determine the stereochemistry of the amino acid-proline bond, e.g. in cyclo-(Pro-Gly)3, melanocyte-stimulating hormone release-inhibiting factor or thyrotropin-releasing hormone. 

Here Aq = qv (X) — q (CeHgF) is the -electron charge density on the fluorine atom in X relative to fluorobenzene Aq c is the corresponding difference in jt-electron bond order for the FC bond Aqc is the corre-... 

It is important to note that whilst only those electrons at the Fermi level can contribute to tunneling, all the electrons below the Fermi level contribute to the charge density. The STM therefore measures the electronic charge density at the Fermi level outside the surface (put another way — it images the spatial locations of the molecular orbitals) rather than the true positions of the atoms in the surface. The imaging of Si(100) surfaces provides a simple example of this difference and will be discussed later in the chapter. Whilst this electronic charge density at the Fermi level is directly related to the positions of the atoms on the surface, the theory relating these is rather complex and remains the subject of intensive debate. 

In the DFT, as in the Hartree-Fock approach, an effective independent-particle Hamiltonian is arrived at, and the electronic states are solved for self consistency. The many-electron wave function is still written as a Slater determinant. However, the wave functions used to construct the Slater determinant are not the one-electron wave functions of the Hartree-Fock approximation. In the DFT, these wave functions have no individual meaning. They are merely used to construct the total electron-charge density. The difference between the Hartree-Fock and DFT approaches lies in the dependence of the Hamiltonian in DFT on the exchange correlation potential, Vxc[ ](t), a functional derivative of the exchange correlation energy, Exc, that, in turn, is a functional (a function of a function) of the electron density. In DFT, the Schrodinger equation is expressed as ... 

Electron charge densities (ECHD) presented in the paper are calculated as the difference between the optimised Pd/Pt-Zr02 interface and the free Zirconia surface and Pd/Pt adlayer, respectively ... 

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