Orbitals Terms Links

The q = 1 terms link the fine structure states the importance of this mixing is maximised when the separation between the fine-structure states is small (i.e. small spin-orbit splitting), and when the rotational constant B is large. Consequently molecules like CIO, BrO and 10 are good case (a)2 n systems, whereas CH obeys case (b) coupling, even in its lowest rotational levels. The OH radical approximates more closely to case (a) in its lowest rotational levels, but goes over to case (b) as the rotational quantum number increases. As we mentioned above, the transition from case (a) to case (b) is discussed in detail in chapter 9 it is not, of course, confined to 2n molecules. 

The case of boron as a network former cation is somewhat specific in that this element has no available d orbitals. However, a p orbital is available when the boron has a coordination number of 3, which allows stabilisation of an electronic doublet of the oxygen or sulphur introduced by the modifier. This oxygen or sulphur giving up a doublet to another boron atom increases the cross-linking by the formation of two BO4 tetrahedra. In hybridisation terms, the boron is altered from the sp configuration to the sp configuration. The coordination change of boron has been especially well observed by NMR (Bray and O Keefe, 1963 Muller-Warmuth and Eckert, 1982). 

Nakatsuji and Yasuda [56, 57] focused on the term appearing in A, which according to the perturbative expansion could be interpreted as a linked diagram of two A elements. In analogy to the Dyson equation, they proposed to estimate the A with a procedure whose main step, expressed in a spin-orbital basis, may be written... 

FIGURE 3.18 The valence-bond description of the bonding in an ethane molecule, CjHf,. Only two of the bonds are shown in terms of their boundary surfaces. Each pair of neighboring atoms is linked by a cr-bond formed by the pairing of electrons in either Hls-orbitals or C2sp3 hybrid orbitals. All the bond angles are close to 109.5° (the tetrahedral angle). 

APIPAT. This is the patent database produced by the American Petroleum Institute and covers patents from 1964 of interest to the petrochemical industry, including petroleum refining, pollution control, uses of petrochemicals, and catalysts. Enhanced indexing includes terms applied from a hierarchical thesaurus with automatic posting to the broader terms in the hierarchy. Fragments called chemical aspects are linked to describe each compound, and the compounds are further linked to roles (eg, reactant or product) and use (eg, antioxidant or lubricant). ORBIT provides access to a merged APIPAT/WPI file, which allows searchers to draw on the strengths of both databases without the need to search them separately (95). 

Classical anharmonic spring models with or without damping [9], and the corresponding quantum oscillator models seem well removed from the molecular problems of interest here. The quantum systems are frequently described in terms of coulombic or muffin tin potentials that are intrinsically anharmonic. We will demonstrate their correspondence after first discussing the quantum approach to the nonlinear polarizability problem. Since we are calculating the polarization of electrons in molecules in the presence of an external electric field, we will determine the polarized molecular wave functions expanded in the basis set of unperturbed molecular orbitals and, from them, the nonlinear polarizability. At the heart of this strategy is the assumption that perturbation theory is appropriate for treating these small effects (see below). This is appropriate if the polarized states differ in minor ways from the unpolarized states. The electric dipole operator defines the interaction between the electric field and the molecule. Because the polarization operator (eq lc) is proportional to the dipole operator, there is a direct link between perturbation theory corrections (stark effects) and electronic polarizability [6,11,12]. 

In the parametrization of equ. (4.68) the terms associated with the Legendre polynomials Pk(cos ab) represent that part of the angular correlation which is independent of the light beam, while the terms associated with the bipolar harmonics are due to the multipole expansion of the interactions of the electrons with the electric field vector. The link between geometrical angular functions and dynamical parameters is made by the summation indices ku k2 and k. These quantities are related to the orbital angular momenta of the two individual emitted electrons, and they are subject to the following conditions ... 

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