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Valence approximation

Variability in metallic valency is also made possible by the resonance of atoms among two or more valence states. In white tin the element has valency approximately 2-5, corresponding to a resonance state between bicovalent tin, with a metallic orbital, and quadricovalent tin, without a metallic orbital, in the ratio 3 to 1 and copper seems similarly in the elementary state to have metallic valency 5-5. [Pg.231]

Its counterpart, the first-order ( y") valence molecular connectivity index, is also calculated from the non-hydrogen part of the molecule and was suggested by several authors [103,276,277]. In the valence approximation, non-hydrogen atoms are described by their atomic valence <5 "values, which are calculated from their electron configuration by the following equation ... [Pg.261]

If lattice QCD (see Section 27.2) is used to calculate QCD in the so-called quenched or valence approximation, one obtains a hnear potential at large distances between quark and antiqum k. [Pg.243]

Nearly all semiempirical methods used for calculating the PES s are the valence approximation methods in contrast to the nonempirical procedures they take account of only the valence electrons and the atomic orbitals of valence shells. The influence of the non-valence (core) electrons is included in empirical parameters. [Pg.77]

Figure 7 The Gouy-Chapman potential profile for a negatively charged plane with a surface charge density = —0.01 eo/A in a mixed asymmetric 1 1-2 1 electrolyte (solid line Eq. [39]) for mono- and divalent salt concentrations Ci = 0.1 M and C2 = 0.02 M, respectively. The exact GC profile (circles) is compared with three approximate profiles based on the effective-valence approximation (solid line Eq. [70]), the high charge density approximation (dotted-dashed line Eq. [57]), and the apparent (dotted line Eq. [93]) and actual (dashed line Eq. [89]) DH approximations. Figure 7 The Gouy-Chapman potential profile for a negatively charged plane with a surface charge density = —0.01 eo/A in a mixed asymmetric 1 1-2 1 electrolyte (solid line Eq. [39]) for mono- and divalent salt concentrations Ci = 0.1 M and C2 = 0.02 M, respectively. The exact GC profile (circles) is compared with three approximate profiles based on the effective-valence approximation (solid line Eq. [70]), the high charge density approximation (dotted-dashed line Eq. [57]), and the apparent (dotted line Eq. [93]) and actual (dashed line Eq. [89]) DH approximations.
The first reliable energy band theories were based on a powerfiil approximation, call the pseudopotential approximation. Within this approximation, the all-electron potential corresponding to interaction of a valence electron with the iimer, core electrons and the nucleus is replaced by a pseudopotential. The pseudopotential reproduces only the properties of the outer electrons. There are rigorous theorems such as the Phillips-Kleinman cancellation theorem that can be used to justify the pseudopotential model [2, 3, 26]. The Phillips-Kleimnan cancellation theorem states that the orthogonality requirement of the valence states to the core states can be described by an effective repulsive... [Pg.108]

There are also very reliable approximate methods for treating the outer core states without explicitly incorporating them in the valence shell. [Pg.112]

Under the assumption that the matrix elements can be treated as constants, they can be factored out of the integral. This is a good approximation for most crystals. By comparison with equation Al.3.84. it is possible to define a fiinction similar to the density of states. In this case, since both valence and conduction band states are included, the fiinction is called the joint density of states ... [Pg.119]

It is accurate for simple low valence electrolytes in aqueous solution at 25 °C and for molten salts away from the critical point. The solutions are obtained numerically. A related approximation is the following. [Pg.479]

The osmotic coefficients from the HNC approximation were calculated from the virial and compressibility equations the discrepancy between ([ly and ((ij is a measure of the accuracy of the approximation. The osmotic coefficients calculated via the energy equation in the MS approximation are comparable in accuracy to the HNC approximation for low valence electrolytes. Figure A2.3.15 shows deviations from the Debye-Htickel limiting law for the energy and osmotic coefficient of a 2-2 RPM electrolyte according to several theories. [Pg.497]

Anisimov V I, Kuiper P and Nordgren J 1994 First-principles calculation of NIG valence spectra in the impurity-Anderson-model approximation Phys. Rev. B 50 8257-65... [Pg.2230]

The simplest example is that of tire shallow P donor in Si. Four of its five valence electrons participate in tire covalent bonding to its four Si nearest neighbours at tire substitutional site. The energy of tire fiftli electron which, at 0 K, is in an energy level just below tire minimum of tire CB, is approximated by rrt /2wCplus tire screened Coulomb attraction to tire ion, e /sr, where is tire dielectric constant or the frequency-dependent dielectric function. The Sclirodinger equation for tliis electron reduces to tliat of tlie hydrogen atom, but m replaces tlie electronic mass and screens the Coulomb attraction. [Pg.2887]

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). [Pg.300]

As ab initio MD for all valence electrons [27] is not feasible for very large systems, QM calculations of an embedded quantum subsystem axe required. Since reviews of the various approaches that rely on the Born-Oppenheimer approximation and that are now in use or in development, are available (see Field [87], Merz ]88], Aqvist and Warshel [89], and Bakowies and Thiel [90] and references therein), only some summarizing opinions will be given here. [Pg.14]

As mentioned above, HMO theory is not used much any more except to illustrate the principles involved in MO theory. However, a variation of HMO theory, extended Huckel theory (EHT), was introduced by Roald Hof nann in 1963 [10]. EHT is a one-electron theory just Hke HMO theory. It is, however, three-dimensional. The AOs used now correspond to a minimal basis set (the minimum number of AOs necessary to accommodate the electrons of the neutral atom and retain spherical symmetry) for the valence shell of the element. This means, for instance, for carbon a 2s-, and three 2p-orbitals (2p, 2p, 2p ). Because EHT deals with three-dimensional structures, we need better approximations for the Huckel matrix than... [Pg.379]

This approximation leads to the CNDO/2 scheme, ft remains to explore the valiiesoflf l vvhich are closely related to valence state... [Pg.275]

T orbital for benzene obtained from spin-coupled valence bond theory. (Figure redrawn from Gerratt ], D L oer, P B Karadakov and M Raimondi 1997. Modem valence bond theory. Chemical Society Reviews 87 100.) figure also shows the two Kekule and three Dewar benzene forms which contribute to the overall wavefunction Kekuleform contributes approximately 40.5% and each Dewar form approximately 6.4%. [Pg.146]

Whereas the tight-binding approximation works well for certain types of solid, for other s. items it is often more useful to consider the valence electrons as free particles whose motion is modulated by the presence of the lattice. Our starting point here is the Schrodinger equation for a free particle in a one-dimensional, infinitely large box ... [Pg.165]


See other pages where Valence approximation is mentioned: [Pg.355]    [Pg.102]    [Pg.102]    [Pg.552]    [Pg.655]    [Pg.269]    [Pg.237]    [Pg.242]    [Pg.257]    [Pg.110]    [Pg.355]    [Pg.102]    [Pg.102]    [Pg.552]    [Pg.655]    [Pg.269]    [Pg.237]    [Pg.242]    [Pg.257]    [Pg.110]    [Pg.204]    [Pg.108]    [Pg.480]    [Pg.484]    [Pg.492]    [Pg.496]    [Pg.500]    [Pg.512]    [Pg.1323]    [Pg.1858]    [Pg.2202]    [Pg.2209]    [Pg.2210]    [Pg.2219]    [Pg.2222]    [Pg.2392]    [Pg.2624]    [Pg.2890]    [Pg.511]    [Pg.207]    [Pg.107]    [Pg.160]   
See also in sourсe #XX -- [ Pg.102 , Pg.103 , Pg.104 ]




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