Virtual atoms

Temary and quaternary semiconductors are theoretically described by the virtual crystal approximation (VGA) [7], Within the VGA, ternary alloys with the composition AB are considered to contain two sublattices. One of them is occupied only by atoms A, the other is occupied by atoms B or G. The second sublattice consists of virtual atoms, represented by a weighted average of atoms B and G. Many physical properties of ternary alloys are then expressed as weighted linear combinations of the corresponding properties of the two binary compounds. For example, the lattice constant d dependence on composition is written as ... 

Levitt Warshel [17, 18] were the first to show that reduced representations may work they used Ca atoms and virtual atoms at side chain centroids. OOBATAKE Crippen [24] simplified further by only considering the Ca atoms. This is snfficient since there are reasonably reliable methods (Holm Sander [11, 12]) that compute a full atom geometry from the geometry of the Ca atoms. (All atom representations are used as well, but limited to the prediction of tiny systems such as enkephalin.)... 

Various ion-optical tricks have to be used to compensate for the spread of energies of the extracted ions, which limit mass resolution unless corrected for. In the latest version of the atom probe (Cerezo et at. 1988), spatial as well as compositional information is gathered. The hole in the imaging screen is dispensed with and it is replaced by a position-sensitive screen that measures at each point on the screen the time of flight, and thus a compositional map with extremely high (virtually atomic) resolution is attained. Extremely sophisticated computer control is needed to obtain valid results. 

Of the parameters which occur in Eqns. 11.24 and 11.25, M and M are in the particular position that they are of virtually atomic character. Furthermore, the initial assumptions concerning M and M have indi-... 

Notice that the number NA of atoms is usually small compared to the number NS of species, and hence the RAND algorithm is very effective in terms of computational effort. The rank of the atom matrix, however, must be equal to the number NA of atoms. At this point it is interesting to remark that instead of the atom matrix we can use a virtual atom matrix, i.e., the matrix of reaction invariant coefficients if the atom matrix is not available or we are interested in a restricted equilibrium. For details see Section 1.8.1. 

Jets can be collided frontal, i.e. at a 180° angle [52]. Here, the energy input is maximal. The fluid can be virtually atomized in this way and has to be surrounded by a mixing chamber to be re-collected. In a Y-type flow configuration, a softer contact can be achieved [39,136]. The two jets simply merge to a third one. Under unfavorable conditions, however, a separated, bi-laminated fluid system is achieved. 

LCVAO linear combination of virtual atomic orbitals... 

Dynamics). The field of molecular simulations grew up independently from that of NMR structural studies and developed its own level of molecular detail. Many such force fields use the united atom representation of a molecule, in which all heavy atoms are present but only polar hydrogens are treated explicitly.12-14 An NMR restraint, however, may well refer to an aliphatic proton not explicitly treated. To handle this situation, van Gunsteren et al., applied what was called the virtual atom.ls With this method, one can take the force that one would want to impose on the proton and redistribute it on to the atoms present. For example, one may have a potential V defined in terms of the coordinates of a proton H. The force as a function of that proton s coordinates would be written as follows ... 

Fig. 4. Three structural fragments corresponding to the notion of synthon, the bond lines which stick out are conventionally terminated by virtual atoms (vertices). We see that the synthon B is a subsynthon of A, but that synthon C is not a subsynthon of A...

Due to the existence of the virtual atoms without unique mutual mapping, there may be more than one SR-graph for the specified transformation. The unique internal part of the SR-graph is a graph GR defined as follows ... 

The London theory uses second-order perturbation theory in its usual (R.S.) form an infinite sum over a complete basis set. The set taken for the composite system of two interacting molecules a and b consists of all products of the complete set of eigenfunctions of a and b separately. Thus, the London theory not only assumes that there is no overlap between the ground-state atoms but also that there is no overlap between any of the virtual atomic excited states. ... 

If the electronegativity of the atoms is low enough, interstitial holes behave as virtual atoms that have their own electronegativity and hardness and can accept valence electrons. In the phlogiston model, as in the Johnson model, metals are substances that have a cation lattice and interstitial valence electrons. 

The kinetic temperature cannot be directly measured from the observations but can be deduced from the analysis of the line profiles and molecular excitatiOTi as the level populations are also sensitive to the temperature. For an accurate determination of the physical conditions, including the kinetic temperature, the full set of the statistical equilibrium calculations must be solved. There are some freely available numerical codes, such as RADEX ([38], http //www.strw.leidenuniv.nl/moldata/ radex.html). They make use of extensive data bases of collisional cross sections, LAMDA (Leiden Atomic and Molecular DAtabase http //www.strw.leidenuniv.nl/ moldata/), and BASECOL (http //basecol.obspm.fr/), that are now part of the European initiative VAMDC (Virtual Atomic and Molecular Data Center http // www.vamdc.eu/). 

Conventionally, the sticking out bond lines are terminated by "virtual" atoms denoted by, R2> The fragment B for example, looks like... 

The electrofugal (with respect to the ith atom) dissociation of a bond between the ith and Jth atoms is represented by the operator. The same type of dissociation between the ith atom and a virtual atom is represented by the operator In this notation the index k... 

The formation of a nitrilium ion (a ) occurs (in a similar way as in the previous path), the charge is shifted to the bond between the atom m and the virtual atom w, then the virtual atom is removed as... 

Table 5.3 Correspondence between operators a, B, y, S and ANCOD strings (X = virtual atom)...

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