S type orbital

The In-Phase ( 3s + 3s) Combination of Rydberg Orbitals Correlates to an s-type Orbital of the United Atom... 

HI) the only available hydrogen valence orbital is an isotropic s-type orbital with no angular nodes and,... 

We define a ten-function AO basis for the H2 molecule that has two different s -type orbitals and one />-type set on each H atom. It will be recalled that Weinbaum allowed the scale factor of the s orbital to adjust at each intemuclear distance. Using two different sized 5-type orbitals on each center accomplishes a similar effect by allowing the variation theorem to choose the amount of each in the mixture. Our orbitals are shown in Table 2.2. The 5-type orbitals are a split version of the Huzinaga 6-Gaussian H function and the p-type orbitals are adjusted to optimize the energy at the minimirm. It will be observed that the p and scale factors are different. We will present an interpretation of this below. 

Almost all the parameters yielded by the various types of radiofrequency spectroscopy arise from the interaction of nuclear magnetic or electrostatic moments with the magnetic or electrostatic fields produced by the surrounding electrons. A consideration of the way these interactions arise shows that they fall into two groups one of the groups contains terms proportional to the electron density at the nucleus, N, itself, Vn(0), and consequently reflects only the s-character of the wave-function centered on N, v>n while the other is proportional to the value for all or some of the electrons surroimding the nucleus N (Table 1). This latter term vanishes for s-type orbitals and for p, d, f orbitals of the same principal quantum number has values in the order p > > d > > f. In practice this means that in a first approximation, only p-electrons contribute to and that the direct effect of the d-orbitals is only... 

If a hydrogen is described by an s orbital, the electron cloud in its neighbourhood will have spherical symmetry. Thus the circled hydrogen can be described reasonably well with s-type orbitals in the reagent or in the product. In the transition state, however, this hydrogen is simultaneously bonded to C, and C5 and loses its spherical symmetry. Its electronic density is mostly localized along the CaH and the C5H axes. Such a broken line is impossible to represent with s orbitals, but poses no problem to p orbitals. In conclusion, to describe correctly the transition state of the ene reaction, polarization orbitals are mandatory, at least for the hydrogen to be transferred. 

Bonding in transition metal compounds can be analyzed analogously to that in transition metal complexes, by considering each oxygen or sulphur atom to contribute two electrons to the complex and an s-type orbital. The resulting orbital schemes are given in Fig. 4.13. 

Electron-spin-based phenomena are attracting attention for the possibility of logic devices based on spin rather than on the flow of charge for possible quantum information applications. Retention of a spin lifetime in the material is important for these considerations. The conduction-band states at the zone center are approximately spin eigenstates, and therefore, they have relatively long spin lifetimes because they are made up of s-type orbitals. This is in contrast to valence-band states that are made up of p-type orbitals for which the spin-orbit interaction mixes the orbital part of the p state with the spin part of the electron wave... 

The character of the lone pair of RjM, R = alkyl, aryl, M = P, As, Sb, changes from a p-type orbital in R3P towards more s-type orbitals when going to R3AS and R3Sb, and at the same time the basicity of R3M decreases down the group . ... 

If the metal, noted Mx, has not an occupied d orbital with an energy similar to that of the vacant py or s type orbital, the a coordination (a, Fig. 2) takes place whereas the back bonding it type (b, Fig. 2) is now impossible that is the case for Mg2+ and Cs- -+ derivatives. 

Because of the complexity of the PHF function, only very small electronic systems were initially considered. As first example, the electronic energy of some four electron atomic systems was calculated using the Brillouin procedure [8]. For this purpose, a short double zeta STO basis set. Is, Is , 2s and 2s , with optimized exponents was used. The energy values obtained are given in Table 1. In the same table, the RHF energy values calculated with the same basis are gathered for comparison. It is seen that the PHF model introduces some electronic correlation in the wave-function. Because of the nature of the basis set formed by only s-type orbitals, only radial correlation is included which account for about 30% of the electronic correlation energy. 

Interpretation of the first three terms in Eq.(2.229a) is straightforward. Term (1) results from the assumption that in the adsorbate no levels higher than Ef were occupied before adsorption. If such terms were occupied a correction to account for electron transfer from the adsorbate to the Fermi-level has to be introduced. Term (1) reflects electron transfer front the occupied undisturbed adsorbate levels to the Fermi level, term (2) electron transfer from a surface electronic state present before chemisorption to the Fermi level and term (3) electron transfer from the Fermi level to a surface molecule- or chemisorption- induced surface state level. In the surface molecule limit the contribution to the chemisorption energy is easy to calculate for s-type orbitals. If an orbital has Z" metal atom neighbors, the solutions cf become the solution of Ek. (2.215) ... 

Electrons fill up orbitals in shells. The innermost shell consists of just one s-type orbital and can hold just two electrons. The next shell consists of one s-type and three p-type orbitals, and can hold eight electrons. Higher shells consist of more and more orbitals and can thus hold more and more electrons. The valence shell of electrons is the highest occupied, or partially occupied, set of orbitals. 

Fig. 9.20. Predictmg the band structure ot (PtH )co- (a) The Bloch functions tor 1 = 0 and k = corresponding to the atomic orbitals 6p-(a type orbitals). Stl.ry (S type orbit s). 5J x- in type orbitals, similar for 5

The choice of the active space is the challenging aspect of these calculations. An appropriate active space should include the metal-metal bonding and antibonding orbitals and also the necessary hgand orbitals that interact with the metal d- and s-type orbitals. This active space comprises at least all the nd (n= 3, 4 or 5) and ( +l)s orbitals forming the M-M multiple bond, namely, 12 orbitals. From a G SSCF wavefunction it is possible to compute the effective bond order (EBO) [10, 11] which quantifies the formation of a chemical bond. For a single bond the EBO is defined as ... 

In the classical picture each dicoordinate chalcogen atoms bears two lone pair orbitals. It has been shown that a marked s-p separation is observed and that the nature of these two lone pair orbitals is mainly s and p ( = 3-5). The s -type orbital is usually not involved in the stereochemistry and it is clear that the structures of the species described in this chapter are determined by the repulsion between the adjacent occupied p lone pair orbitals. Thus, usually the systems try to minimize coulombic repulsion by adopting E-E-E-E torsion angles of about 90 20° (Figure 1). 

Ascent in symmetry tables have been provided by Boyle [4], Fowler and Quinn have listed the irreps that are induced by u-, n-, and S-type orbitals on molecular sites [5], These tables are reproduced below. They are useful for the construction of cluster orbitals. Geg always denotes the regular representation. r corresponds to the positional representation. The mechanical representation is the sum r a + r jt-... 

Fig. 9.19. Predicting the band structure of (PtH )co (a) the Bloch functions for k = 0 and k = - corresponding to the atomic orbitals 6p- (o- type orbitals), 5dxy (S type orbitals), 5dxz type orbitals, similarly for 5dy-), Sd 2 yi (o" type orbitals) (b) the band width is very sensitive to the overlap of the atomic...

For s-type orbitals the Pauli repulsion energy increases linear with the number of neighbors ... 

Figure 1.15. Symbolic representations for boron tribydride (monomeric borane), BH3 of the SCF-MO bonding orbitals (a) B 2s and positive Is H contributions (b) B 2p and one of two degenerate contributions from hydrogen (H) (c) B 2p and the other degenerate contribution from hydrogen (H) (d) boron trihydride (monomeric borane), BH3 where the s-type orbitals on the hydrogens (H) have been omitted for clarity. The boron is in the plane defined by the three hydrogens (H).

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