Orbital structures

Methfessel M, Rodriguez C O and Andersen O K 1989 Fast full-potential calculations with a converged basis of atom-centered linear muffIn-tIn orbitals structural and dynamic properties of silicon Phys. Rev. B 40 2009-12... 

In this section, we briefly discuss spectroscopic consequences of the R-T coupling in tiiatomic molecules. We shall restrict ourselves to an analysis of the vibronic and spin-orbit structure, detennined by the bending vibrational quantum number o (in the usual spectroscopic notation 02) and the vibronic quantum numbers K, P. 

For c/rwo-boranes and for the larger open-cluster boranes it becomes increasingly difficult to write a simple satisfactory localized orbital structure, and a full MO treatment is required. Intermediate cases, such a.s B5H9, require several resonance hybrids in the localized orbital... 

Fig. 13. Change in the metal Pi orbital structure in square- planar substitution.

On the other hand, the XPS data near the Fermi level provide us the valuable information about the band structures of nanoparticles. XPS spectra near the Fermi level of the PVP-protected Pd nanoparticles, Pd-core/ Ni-shell (Ni/Pd = 15/561, 38/561) bimetallic nanoparticles, and bulk Ni powder were investigated by Teranishi et al. [126]. The XPS spectra of the nanoparticles become close to the spectral profile of bulk Ni, as the amount of the deposited Ni increases. The change of the XPS spectrum near the Fermi level, i.e., the density of states, may be related to the variation of the band or molecular orbit structure. Therefore, the band structures of the Pd/Ni nanoparticles at Ni/Pd >38/561 are close to that of the bulk Ni, which greatly influence the magnetic property of the Pd/Ni nanoparticles. 

Figure 6.8 (a) A stylized orbital structure of the methyl cation. The bonds are... 

The present perturbative treatment is carried out in the framework of the minimal model we defined above. All effects that do not crucially influence the vibronic and fine (spin-orbit) structure of spectra are neglected. The kinetic energy operator for infinitesimal vibrations [Eq. (49)] is employed and the bending potential curves are represented by the lowest order (quadratic) polynomial expansions in the bending coordinates. The spin-orbit operator is taken in the phenomenological form [Eq. (16)]. We employ as basis functions... 

Atomic Orbitals Hybrid Type Number of Orbitals Structure... 

On a more qualitative level, the bonding in the more stable isomer lb can be explained on the basis of the general molecular orbital scheme for bent (C2v) metallocenes containing 14 valence electrons, as shown in Fig. 5. The localization of three electron pairs in bonding orbitals (lal, 2 i, 2b2) is primarily responsible for the Si-Cp interaction the absence of a silicon orbital of a2 symmetry imposes the presence of a ligand-based non-bonding orbital. Structural adjustment from D5d (ferrocene type) to C2v... 

Figure 4.1 Copper sulfate pentaquo complex. In solution, CuS04 exists as a Cu2 + ion in octahedral co-ordination surrounded by the S042- ion and five water molecules orientated so that the oxygen atom points towards the copper ion. It is the effect of this hydration sphere on the electronic orbital structure of the copper which gives rise to d-d band transitions, and hence the blue color of the solution.

It is seen from their orbital structures that hydrogen and fluorine both need to share 1 electron to complete their outer shells. Therefore the orbital representation of HF molecule is ... 

Correspondence between Canonical and Localized Orbital Structures. 48... 

In the following we shall discuss these localized orbital structures and those of some heteronuclear diatomics on the basis of accurate diagrams which were obtained from minimal basis set ab initio calculations. The numerical results on which these diagrams are based have been reported elsewhere. 35 ... 

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