Quasi-atoms

The factor A has been measured for a variety of samples, indicating that the approximation can be applied up to quasi-atomic resolution. In the case of biological specimens typical values of are of the order of 5-7%, as detemiined from images with a resolution of better than 10 A [37,38]- For an easy interpretation of image contrast and a retrieval of the object infomiation from the contrast, such a combination of phase and amplitude hifomiation is necessary. 

At first sight, we are foreed to solve this equation numerically, but its overall form allows a qualitative insight into the number of solutions and their approximate values. For example, one easily see that S represents a sum of two identical quasi-atomic (onedimensional) functions each centered on the corresponding hydrogen nucleus. The functions are quite similar to 2pz Gaussian functions, but they differ by their one-dimensionality and by a different radial dependence. Indeed, instead of the usual... 

It was also observed, in 1973, that the fast reduction of Cu ions by solvated electrons in liquid ammonia did not yield the metal and that, instead, molecular hydrogen was evolved [11]. These results were explained by assigning to the quasi-atomic state of the nascent metal, specific thermodynamical properties distinct from those of the bulk metal, which is stable under the same conditions. This concept implied that, as soon as formed, atoms and small clusters of a metal, even a noble metal, may exhibit much stronger reducing properties than the bulk metal, and may be spontaneously corroded by the solvent with simultaneous hydrogen evolution. It also implied that for a given metal the thermodynamics depended on the particle nuclearity (number of atoms reduced per particle), and it therefore provided a rationalized interpretation of other previous data [7,9,10]. Furthermore, experiments on the photoionization of silver atoms in solution demonstrated that their ionization potential was much lower than that of the bulk metal [12]. Moreover, it was shown that the redox potential of isolated silver atoms in water must... 

A different approach for extracting relevant information is to define quasi-atomic quantities the sum of which yields the value of Jp [43], This can be done even though a decomposition into transferable additive terms, a long standing pipe dream in optical activity, is not possible. To this end, the dinuclear terms in Equation (2.156) have to be split between two atoms, in proportion to the motion of their nuclei and the size of the gradients of the electronic tensors. For an atom with nucleus a in its molecular environment, a quasi-atomic contribution J(a) can then be defined as... 

Chapman et al.12061 recently reported the construction of polycules (197) which were generated from quasi-atoms , in this case substituted 1,3,5,7-tetraphenyladamantanes, and the related diadamantanes. This assembly process can be demonstrated (Scheme 4.54) by the treatment of core 1951207 209] with building block 196. 

We may re-define the active orbitals utilizing the invariance of the active orbital space. In the CASVB with nonorthogonal LMOs, we employ Rueden-berg s procedure of projected localized MOs [6-8] and obtain quasi-atomic CASSCF MOs that have maximal overlaps with atomic orbitals (AOs) of the free atoms. Consider an AO, Xa, centered on a nucleus A. Diagonalizing the matrix,... 

The full configuration space that is spanned by all possible configurations generated from these quasi-atomic CASSCF MOs is identical to that of full Cl space that is constructed from the canonical CASSCF MOs. Thus, we use (p as orbitals from which a CASVB wave function is constructed. To obtain the corresponding VB structures, we project a canonical CASSCF wave function onto a VB wave function. The projection does not modify the original wave function but simply re-expresses it in the VB language. Let Vt/CASSCF be a CASSCF wave function,... 

Martin, C. S., Burnett, R. M., de Haas, F., Heinkel, R., Rutten, T., Fuller, S. D., Butcher, S. J., and Bamford, D. H. (2001). Combined EM/X-ray imaging yields a quasi-atomic model of the adenovirus-related bacteriophage PRDl and shows key capsid and membrane interactions. Structure 9, 917-930. 

We suggest that the expansion transformation involves a subunit rotation mechanism, as visualized at the level of a quasi-atomic model for phage HK97 (Conway et al, 2001). Specifically, rotation of gplO subunits about axes in the plane of the capsid shell and extending radially outward from the local symmetry axis may bring densities that were formerly on the inner surface into the plane of the shell. To accommodate these densities, the centers of adjacent capsomers are pushed further apart. Concomitantly, the gp9 scaffold protein subunits are released. Both of these effects have the effect of making the mature capsid thinner walled and smoother surfaced than its precursor. 

The quadrupole splitting of a suitably oriented sample represents the angle of the deuterated C—segment relative to the axis of alignment. Thus, quasi-atomic coordinates within the molecule can be determined, and the angular distribution of the sample estimated (see Section 6.2.4). 

The symmetry of an isolated atom is that of the full rotation group R+ (3), whose irreducible representations (IRs) are D where j is an integer or half an odd integer. An application of the fundamental matrix element theorem [22] tells that the matrix element (5.1) is non-zero only if the IR DW of Wi is included in the direct product x of the IRs of ra and < f. The components of the electric dipole transform like the components of a polar vector, under the IR l)(V) of R+(3). Thus, when the initial and final atomic states are characterized by angular momenta Ji and J2, respectively, the electric dipole matrix element (5.1) is non-zero only if D(Jl) is contained in Dx D(j 2 ) = D(J2+1) + T)(J2) + )(J2-i) for j2 > 1 This condition is met for = J2 + 1, J2, or J2 — 1. However, it can be seen that a transition between two states with the same value of J is allowed only for J 0 as DW x D= D( D(°) is the unit IR of R+(3)). For a hydrogen-like centre, when an atomic state is defined by an orbital quantum number , this can be reduced to the Laporte selection rule A = 1. This is of course formal, as it will be shown that an impurity state is the weighted sum of different atomic-like states with different values of but with the same parity P = ( —1) These states are represented by an atomic spectroscopy notation, with lower case letters for the values of (0, 1, 2, 3, 4, 5, etc. correspond to s, p, d, f, g, h, etc.). The impurity states with P = 1 and -1 are called even- and odd-parity states, respectively. For the one-valley EM donor states, this quasi-atomic selection rule determines that the parity-allowed transitions from Is states are towards np (n > 2), n/ (n > 4), nh (n > 6), or nj (n > 8) states. For the acceptor states in cubic semiconductors, the even- and odd-parity states labelled by the double IRs T of Oh or Td are indexed by + or respectively, and the parity-allowed transition take place between Ti+ and... 

Fabry CMS, Rosa-Calatrava M, Conway J F, et al. (2005). A quasi-atomic model of human adenovirus type 5 capsid. EMBO J. 24 1645-1654. 

Giant quasi-atoms and spontaneous positron formation 142... 

The embedded-atom method (EAM) overcomes the limitations of the pair potential technique. It is considered to be practical enough for calculations of defects, impurities, fractures, and surfaces in metals. In this model, an impurity (that is, a quasi-atom) is assumed to experience a locally uniform or only slightly nonuni-form, environment. The energy of the quasi-atom can be expressed as... 

In sect. 1, we considered how particular mechanisms affect the behaviour of d and f orbitals in free atoms. We now turn to the question of how these atomic properties are modified when dealing with the atom in the solid. A crucial aspect of rare earth physics is the persistence of quasi-atomic spectral multiplet structure in the solid. To explain this, we first note that a collapsed orbital, localized in the inner reaches of the atom, will tend to survive as a localized atomic orbital in the solid, whereas an orbital which lies in the outer reaches of the atom (or in the outer well of the double-well potential described above) will be completely modified, and may hybridize with the conduction band. 

We are thus faced with a complex situation. Orbital collapse survives in the solid, but the orbitals are only truly atomic in the fiilly collapsed condition. This provides us with a very useful experimental tool to probe the spectra of rare-earth elements, but is also a formidable challenge when one has to account for the complete situation. For the moment, the important point to note is that orbitals recover their atomic character even in the solid once collapse has occurred. It also follows that the depth and width of the inner well of the quasi-atomic double-well potential continue to play a crucial role in the solid. 

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