Extended electron distribution

J G 1994. Extended Electron Distributions Applied to the Molecular Mechanics of Some termolecular Interactions. Journal of Computer-Aided Molecular Design 8 653-668. el A and M Karplus 1972. Calculation of Ground and Excited State Potential Surfaces of anjugated Molecules. 1. Formulation and Parameterisation. Journal of the American Chemical Society 1 5612-5622. 

The extended Electron Distribution (XED) force field was first described by Vinter [96]. This force field proposes a different electrostatic treatment of molecules to that found in classical molecular mechanics methods. In classical methods, charges are placed on atomic centers, whereas the XED force field explicitly represents electron anisotropy as an expansion of point charges around each atom. The author claims that it successfully reproduces experimental aromatic ji stacking. Later, others made similar observations [97]. This force field is now available in Cresset BioMoleculaf s software package [95]. Apaya et al. were the first to describe the applicability of electrostatic extrema values in drug design, on a set of PDE III inhibitors [98]. 

Vinter J G 1994. Extended Electron Distributions Applied to the Molecular Mechanics of Some Intermolecular Interactions Journal of Computer-Aided Molecular Design 8 653-668. 

Similarly to ROCS, the Cresset FieldScreen approach [31, 32] considers multiple 3D conformations. These are generated with a force field based on nonatom-centered extended electron distribution charges (XED). From the interaction energy with molecular probes, four 3D field properties are then calculated steric, hydrophobic. 

J.G. Vinter, Extended electron distributions applied to the molecular mechanics of some intermolecular interactions. J. Comput.-Aided Mol. Des. 8, 653-668 (1994)... 

The quantity p2 as a function of the coordinates is interpreted as the probability of the corresponding microscopic state of the system in this case the probability that the electron occupies a certain position relative to the nucleus. It is seen from equation 6 that in the normal state the hydrogen atom is spherically symmetrical, for p1M is a function of r alone. The atom is furthermore not bounded, but extends to infinity the major portion is, however, within a radius of about 2a0 or lA. In figure 3 are represented the eigenfunction pm, the average electron density p = p]m and the radial electron distribution D = 4ir r p for the normal state of the hydrogen atom. 

This model of the hydrogen atom accordingly consists of a nucleus embedded in a ball of negative electricity—the electron distributed through space. The atom is spherically symmetrical. The electron density is greatest at the nucleus, and decreases exponentially as r, the distance from the nucleus, increases. It remains finite, however, for all finite values of r, so that the atom extends to infinity the greater part of the atom, however, is near the nucleus—within 1 or 2 A. 

Since every atom extends to an unlimited distance, it is evident that no single characteristic size can be assigned to it. Instead, the apparent atomic radius will depend upon the physical property concerned, and will differ for different properties. In this paper we shall derive a set of ionic radii for use in crystals composed of ions which exert only a small deforming force on each other. The application of these radii in the interpretation of the observed crystal structures will be shown, and an at- Fig. 1.—The eigenfunction J mo, the electron den-tempt made to account for sity p = 100, and the electron distribution function the formation and stability D = for the lowest state of the hydr°sen of the various structures. 

In this chapter, we develop a model of bonding that can be applied to molecules as simple as H2 or as complex as chlorophyll. We begin with a description of bonding based on the idea of overlapping atomic orbitals. We then extend the model to include the molecular shapes described in Chapter 9. Next we apply the model to molecules with double and triple bonds. Then we present variations on the orbital overlap model that encompass electrons distributed across three, four, or more atoms, including the extended systems of molecules such as chlorophyll. Finally, we show how to generalize the model to describe the electronic structures of metals and semiconductors. 

The number and type of basis functions strongly influence the quality of the results. The use of a single basis function for each atomic orbital leads to file minimal basis set. In order to improve the results, extended basis sets should be used. These basis sets are named double-f, triple-f, etc. depending on whether each atomic orbital is described by two, three, etc. basis functions. Higher angular momentum functions, called polarization functions, are also necessary to describe the distortion of the electronic distribution due... 

Besides uracil-6-iminophosphorane, the iminophosphorane component was extended to pyrazole 3 and pyrazolon-4-iminophosphoranes 363 (94JOC3985). In its electron distribution, 363 can be compared with uracil 346. With arylisocyanates, pyridine, or y-picoline, zwitterionic pyrazolo [3, 4 4,5]pyrido[6,l-a]pyrimidines (364) are obtained and with isoquinoline, 365 is formed (Scheme 131). Again, both systems show a typical negative solvatochromism (94JOC3985). 

Since the electron distribution function for an ion extends indefi-finitely, it is evident that no single characteristic size can be assigned to it. Instead, the apparent ionic radius will depend upon the physical property under discussion and will differ for different properties. We are interested in ionic radii such that the sum of two radii (with certain corrections when necessary) is equal to the equilibrium distance between the corresponding ions in contact in a crystal. It will be shown later that the equilibrium interionic distance for two ions is determined not only by the nature of the electron distributions for the ions, as shown in Figure 13-1, but also by the structure of the crystal and the ratio of radii of cation and anion. We take as our standard crystals those with the sodium chloride arrangement, with the ratio of radii of cation and anion about 0.75 and with the amount of ionic character of the bonds about the same as in the alkali halogenides, and calculate crystal radii of ions such that the sum of two radii gives the equilibrium interionic distance in a standard crystal. 

One could easily extend these relations to crystals in which the electron distribution is degenerate by using Fermi statistics instead of Boltzmann statistics. 

A wavefunction ip and its eigenvalue E define an orbital. The orbital is therefore an energy level available for electrons and it implies the relevant electron distribution. In mathematical models, these distributions extend to infinity, but in a pictorial representation it is sufficient to draw the volume in which the probability of presence of the electron is rather arbitrarily around 90%. The spatial distribution of atomic and molecular orbitals have implications for processes of electron tunneling (section 4.2.1). 

Ionic Size. The size of an ion is a somewhat hazy concept because the modern notion of atoms pictures the electron distribution to extend to infinity. Nevertheless, it is true that there are definite distances established between the centers of atoms in a compound. It is thus natural to attempt to conceive of the distance between, say, Na+ and CT in solid sodium chloride as being made up as a sum of two contributions, one from the negative ion and the other the positive ion. This amounts to defining the sizes of ions in such a manner that in each ionic compound the sum of the ionic radii equals the observed interionic distance at equilibrium. 

An obvious question is, when does one need symmetry correct orbitals The HaO example illustrates that the symmetry correct orbitals will usually extend over a larger region of the molecule than did the symmetry incorrect orbitals from which they were made. The symmetry correct model corresponds to a more highly delocalized picture of electron distribution. We believe that electrons are actually able to move over the whole molecule, and in this sense the delocalized symmetry correct pictures are probably more accurate than their localized counterparts. Nevertheless, for most purposes we are able to use the more easily obtained localized model. The reason the localized model works is illustrated in Figure 10.6. The interaction that produced the delocalized symmetry correct orbitals made one electron pair go down in energy and another go up by an approximately equal amount. Thus the total energy of all the electrons in the molecule is predicted to be about the same by the localized and by the more correct delocalized model. 

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