Hybrid polar energy table

For any compound, the hybrid polar energy can be estimated by using the term values given in Table 2-2 or the Solid State Table. 

Consider hexagonal boron nitride, shown in Fig. 3-10. Define a hybrid covalent and hybrid polar energy for this structure, in analogy with the corresponding definitions for tetrahedral solids in Eqs. (3-4) and (3-6). Compare the polarity obtained from these values with that of tetrahedral BN, listed in Table 7-2. Take d = 1.42 A as in graphite. Notice that many values arc modified by having sp hybrids rather than sp hybrids. 

Bond orbitals are constructed ft om s/r hybrids for the simple covalent tetrahedral structure energies are written in terms of a eovalent energy V2 and a polar energy K3. There are matrix elements between bond orbitals that broaden the electron levels into bands. In a preliminary study of the bands for perfect crystals, the energies for all bands at k = 0 arc written in terms of matrix elements from the Solid State Tabic. For calculation of other properties, a Bond Orbital Approximation eliminates the need to find the bands themselves and permits the description of bonds in imperfect and noncrystalline solids. Errors in the Bond Orbital Approximation can be corrected by using perturbation theory to construct extended bond orbitals. Two major trends in covalent bonds over the periodic table, polarity and metallicity, arc both defined in terms of parameters from the Solid State Table. This representation of the electronic structure extends to covalent planar and filamentary structures. 

The last form is obtained by using the expressions for the interatomic matrix elements from the Solid State Table. For polar semiconductors the splitting becomes 2(Vl+ with the polar energy- m contrast to the hybrid polar... 

Table 4.14. Relative energies (/srei) and NBO characteristics of optimized pi and tw isomers o/Ir(CH2)H, Os(CH2)2, and W(CH2)3 (see Fig. 4.18), showing Lewis densities (pf), hybridizations (Iim), and bond polarizations (100cm2)...

Boron nitride forms the same structure that graphite does, as indicated in Fig. 3-10. The sp -hybrid energy-difference may be evaluated by using the Solid State Table and used to estimate the corresponding. It is possible to treat the counterparts of all the properties of polar tetrahedral semiconductors also for the... 

Extension of the calculation to the polar counterparts of Si02, such as aluminum phosphate, is also quite direct and can be made without the introduction of any new parameters. The energies of the two hybrids in the bonding unit now differ, - = 21/j, but the hybrid energies arc just those given in Table 2-2. We must generalize the bond orbital by allowing different coefficients for /i,> and j/jj) in Eq. (11-2), and must solve a cubic rather than a quadratic equation. 

Comparison of these with (13.182) shows the simple LCAO functions to be reasonable first approximations to the minimal-basis-set SCF MOs. TTie approximation is best for the la-g and MOs, whereas the 2a-g MO has substantial Iptr AO contributions in addition to the 2s AO contributions. For this reason the notation of the third column of Table 13.1 (Section 13.7) is preferable to the separated-atoms MO notation. The substantial amount of 2s-2pa- hybridization is to be expected, since the 2s and 2p AOs are close in energy [see Eq. (9.27)] the hybridization allows for the polarization of the 2s AOs in forming the molecule. 

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