Valence dashes

Fig. 1.1 Structural formulas of ammonium cyanate left) and urea right) as examples of two different substances with the same composition above detailed valence dash formula, below condensed formula).

If in a polyatomic molecule built up from atoms in >S-states we let the electron spins of the constituent atoms compensate each other in pairs, we should be inchned, in analogy with the case of diatomic molecules, to write down as structure formula one in which to every electron pair there corresj)onds a valence dash. Thus if we take the four electrons outside the X-sheU of a quadrivalent 0-atom in the state and compensate the spm of one of them by the spin of the electron of an H-atom in its normal jS-state, the spin of the three others by the spins of the three 2 -electrons of an N-atom in its normal /S-state, we get the molecule hydrogen cyanide... 

New view-points were introduced into chemistry when one began to investigate systematically which compounds can occur in nature and which carmot be prepared, or in other words which combinations of atoms wiU give a stable molecule. Also the employment of thermochemical methods and the study of dissociation equilibria furnished a suitable measure for the stability of compounds in the reaction energies while independent evidence concerning chemical aflSnity was gained by measurements of reaction velocities. In order to systematise this field of experience, one spoke of chemical forces and one tried to describe their behaviour by means of the concept of valence. The use of valence dashes in chemical formulae and the notion of saturation of valences did much to clarify the general aspects of chemical union in spite of the numerous exceptions not amenable to this way of representation. 

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation [34], The volume is nonnalized to the experimental volume. The binding energy is the total electronic energy of the valence electrons. The slope of the dashed curve gives the pressure to transfomi silicon in the diamond structure to the p-Sn structure. Otlier polymorphs listed include face-centred cubic (fee), body-centred cubic (bee), simple hexagonal (sh), simple cubic (sc) and hexagonal close-packed (licp) structures.

Valenz, /. valence, valency, -betatigung, /. valence activity, -einlieit, /. valence unit, valence, -kraft,/. valence (or valency) force, -lehre, /. doctrine of valence, -richtung, /. valence direction, -strich, m. valence line or dash. -8 tufe,/. valence stage. 

Figure 4 The wind valence in A1 along the migration path. The initial and saddle point positions are at the origin and at 0.5 respectively. The lower curve is for Cu, the upper curves are for self-electromigration. The dashed and the dotted curve show the influence of a Cu atom at positions 1 and 2 of Fig. 3 respectively, on the wind force in pure A1 (thick curve).

Fig. 7. Schematic illustration of the pseudo dashed curves) and real q> solid curves) valence wave functions and associated potentials and Z/r as a function of r... 

Fig. 8. Scheme of the electronic structure of (A) [3Fe-4S] centers and (B) [4Fe-centers according to the standard model. The thin and thick dashed fines indicate the Emtiferromagnetic and double exchEmge coupling, respectively. Configurations a and b correspond to the two possible locations of the excess electron in the mixed-valence pair. In part (B), the local spin values are Sc = Sd = 2 in the case of [4Fe-4S] centers and Sc = Sd = i in the case of [4Fe-4S] + centers. 

Figure 18.5 Plausible sequence of steps responsible for rapid and selective reduction of O2 to H2O by mixed-valence CcO. The square frames signify the catalytic site (Fig. 18.4c) imidazole ligation of Cub is omitted for clarity in some or aU intermediates, Cub may additionally be ligated by an exogenous ligand, such as H2O (in Cu ) or OH (in Cu ) such ligation is not established, and hence is omitted in all but compound Pm and the putative hydroperoxo intermediate. The dashed frames signify the noncatalytic redox cofactors. Typically used phenomenological names of the spectroscopically observed intermediates (compounds A, E, H, etc.) are also indicated.

Fig. 5.6 Changes in the shape of the valence contribution due to geometric and electronic relaxation in [FeF4]" . Full line [FeF4] at its equilibrium geometry, dashed line [FeF4] at its equilibrium geometry. The square of the valence orbital that mainly contributes to p(0) along the Fe-F bond (distances are in units of the Bohr radius) is also drawn (from [19])...

Figures, l-Alanine.Fits to noisy data Calculations A (experimental noise) and B (10% experimental noise). MaxEnt, deformation and error density profiles along the Cl-01 bond. Solid line Model valence density. Dashed line MaxEnt density A. Dot-dashed line MaxEnt density B. Dotted line valence-shells non-uniform prior.

Figure 6. The valence-electron CPs of Cu calculated by the FLAPW-LDA (dashed) and the FLAPW-SIC (solid) schemes. The dots represent the experimental profiles measured by Sakurai etal. [24],... 

Figure 9. The valence-electron CPs of polycrystalline Na. The solid and dotted curves represent the FLAPW-GWA and FLAPW-LDA calculations, respectively. The dash-dotted and dashed curves represent the results calculated by the tree-electron and FLAPW-LDA including correlation effects according to Lundqvist and Lyden [27], respectively. The dots represent the experimental result by Sakurai et al. [28] (after Kubo [13]). 

Figure 11. Electron-energy-loss spectrum of crystalline boron nitride, showing the boron K-edge (at 190 eV) and the nitrogen K-edge (at 400 eV). The background intensity, delineated by the dashed curve arises from inelastic scattering by valence electrons. The hatched areas represent the measured values required for the quantitative analysis of boron ( see text) (50).

Figure 4.93 Orbital energies for s-type (left) and d-type (right) valence NAOs of group 4 (circles solid line), group 6 (squares dashed line), and group 10 (triangles dotted line) elements of the first three transition series.

A Lewis structure can show the bonding pattern in a covalent compound. In Lewis formulas, we show the valence electrons that are not involved in bonding as dots surrounding the element symbols. The valence electrons involved in bonding are present as dashes. There are several ways of deriving the Lewis structure, but here is one that works well for most compounds that obey the octet rule. 

With the exception of some unique symbols of William Higgins in 1789, generally, straight lines appeared in published chemical formulas only when Archibald Couper introduced them in 1858 to indicate valences (units of atomicity, saturation capacity, or quantivalence).77 Whereas innocent accent marks or superscript dashes had been used at midcentury to indicate valence or value, straight lines now suggested a less abstract meaning, despite disclaimers like Alexander Crum Brown s that the lines indicated the "chemical," not "physical," positions of atoms. 78... 

When, following Odling, we represent valency by dashes written after the elementary symbol, we give clear expression by means of a simple convention to certain ideas that are well understood by all among us who are versed in the fact to speak of electrons and use dots instead of dashes may serve to mislead the unwary. . . into a belief that we have arrived at an explanation of the phenomena.29... 

Figure 1.3 Normal distributions (solid lines) of the errors in the extrapolated valence-shell CCSD/cc-pV(X - 1,X)Z correlation energies relative to the R12 reference values (mEh). The corresponding CCSD/cc-pV6Z distribution (dashed line, see Fig. 1.2) is also shown for comparison.

Figure 4. Calculated HAB values as a function of Fe -Fe separation, based on the structural model given in Figure 1 and the diabatic wavefunctions I/a and f/B. Curves 1 and 2 are based on separate models in which the inner-shell ligands are represented, respectively, by a point charge crystal field model [Fe(H20)62 -Fe(HsO)63 ] and by explicit quantum mechanical inclusion of their valence electrons [Fe(HgO)s2 -Fe(H20)s3+] (as defined by the dashed rectangle in Figure 1). The corresponding values of Kei, the electronic transmission factor, are displayed for various Fe-Fe separations of interest.

Fig. 8-27. Polarization curves for transfer of redox electrons at n-type and p-type semiconductor electrodes solid curve near Egaxa = reaction with the Fermi level of redox electrons dose to the valence band edge dashed curve near F redok = reaction with the Fermi level of redox electrons dose to the conduction band edge dot-dash curve (FLP)= reaction in the state of Fermi level pinning.

Fig. 8-41. Electron transfer reaction of hydrated redox particles in equilibrium on a metal electrode covered with a thick film (F, solid curve) and with a thin film (F, dashed curve) >cs = electron transfer current via the conduction band >scl = tunneling electron current through a depletion layer in the conduction band >vb = hole transfer current via the valence band.

It has become increasingly popular to represent [C5H5]- by the structure shown in Fig. 6d. This representation is a valence bond structure notation it is intended to represent the five equivalent resonance structures (three of these are shown as Figs. 6c, /, and g the other two are similar), in which the negative charge is located at each carbon in turn. Each double bond is thus only a partial double bond and, if the usual notation of writing a partial double bond by a dashed line were applied, the structure would be written as 6h. The solid circle (6d) is a rapid way to write the 66 structure. In a completely analogous... 

The first satisfactory definition of crystal radius was given by Tosi (1964) In an ideal ionic crystal where every valence electron is supposed to remain localised on its parent ion, to each ion it can be associated a limit at which the wave function vanishes. The radial extension of the ion along the connection with its first neighbour can be considered as a measure of its dimension in the crystal (crystal radius). This concept is clearly displayed in figure 1.7A, in which the radial electron density distribution curves are shown for Na and Cl ions in NaCl. The nucleus of Cl is located at the origin on the abscissa axis and the nucleus of Na is positioned at the interionic distance experimentally observed for neighboring ions in NaCl. The superimposed radial density functions define an electron density minimum that limits the dimensions or crystal radii of the two ions. We also note that the radial distribution functions for the two ions in the crystal (continuous lines) are not identical to the radial distribution functions for the free ions (dashed lines). 

Figure 4. The characteristic ratio Coo calculated as a function of temperature T for values of the glycosidic valence angle 116 p < 124 . The dashed curve describes experimental results for cellulose triacetate.22...

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