Covalence energy

It is desirable to examine in greater detail the reasons for the thermodynamic instability (small dissociation energy) of the alkyl carbon-transition metal a bond, which appears to be so much less than the carbon-metal a bond of the nontransition metals. The reasons for the instability are (a) the very small covalent energy of the metal-carbon bond and (6) the relatively small difference in electronegativities between the trairsition metal and the carbon atom, which accounts for the small ionic resonance energy contribution to the total energy of the bond. 

The energies are usually expressed as electron volts. The IRE for the bond in ethane is zero and for CHgNa it is 2.56 ev. The stability of alkyl carbon-metal bonds for a variety of metals has been evaluated by Jaffe and Doak (5). They point out that not only is the (the measure of covalent energy) for the C—M bonds of transition metals appreciably smaller (perhaps one-half) than the corresponding values for other elements, but the ionic resonance energy of the alkyl-transition metal bonds is also appreciably smaller (perhaps one-third) than that of alkyl-alkali or alkyl-alkaline earth metal bonds. 

Catlow and Stoneham (1983) have shown that ionic term corresponds to the difference of the diagonal matrix elements of the Hamiltonian of an AB molecule in a simple LCAO approximation (Haa cf. section 1.18.1), whereas the covalent energy gap corresponds to the double of the off-diagonal term Hab—i e.,... 

Because of the complexity of the forces operating in the covalent bond, it is not possible to write a simple potential energy function as for the electrostatic forces such as ion—ion and dipole-dipole. Nevertheless, it is possible to describe the covalent energy qualitatively as a fairly short-range force (as the atoms are forced apart, the overlap decreases). 

The covalent energy, Ec, arising from electron sharing. It is a maximum in a homopolar bond and decreases with ionicity. 

Covalent energy, 340 Covalent radii, 291-296 Craig/Paddock model. 773 Cristobalite, 97-98 Crown ethers, 525 Cryptates, 530... 

To obtain a complete picture of bonding in acid-base interactions, three separate factors must be taken into account a) the electrostatic energy of the acid-base interaction b) the covalent energy of the acid-base interaction c) the energy involved when electron transfer takes place. These results were anticipated in principle on the basis of Mulliken-Jaffe electronegativity.37... 

The sum of (1) + (2) + (4) is very like the attractive energy of an ionic bond formed from atoms A and B and involving a partial charge, x, while (3) is a covalence energy for a bond of fractional order (1 — x). The... 

The results of these calculations are consistent with our earlier conclusions. As long as no 3-rings are present in the alumina-free material, differences in covalent energy are very small. The ab-initio calculations indicate that these differences do not exceed 1 kJ/mol. 

Wc found that hydrogen Is levels are split into bonding and antibonding levels when the two atoms form the molecule. The separation of those two levels is 2Kj, where is the covalent energy. To find the total energy of this system it is necessary to add a number of corrections to the simple sum of energies of the electrons. It will be convenient to postpone consideration of such corrections until systematic treatment in Chapter 7. 

A particularly important matrix element is that between hybrids pointed at each other, or into the bond, from two neighboring atoms. We call the magnitude of this matrix element the hybrid covalent energy,... 

Metallic energy and covalent energy (in cV), and metallicity for the homopolar semiconductors. 

Element Metallic energy F, Covalent energy Fj Metallicity m... 

The electronic structure in graphite may be understood in terms o(sp hybrids (see Problem 3-2) oriented in the direction of the bond and bond orbitals constructed from these hybrids. The shorter bond length and different composition of the hybrid lead to a covalent energy value, Fj. that is also different in graphite than it is in diamond. 

We may also imagine a system with p-state energy that is different for alternate atoms in the zig-zag structure, in order to have a polar as well as a covalent energy. This becomes the simplest structure to have essentially the same character as the tetrahedrally bonded structure, and it will be very useful for illustrating the theory of covalent solids Problems 8-1 and 8-2 are based on this system. 

The largest peak in Fig. 4-3, labelled 2. can be easily identified with the fairly parallel bands separated by between 4 and 6 eV over most of the region shown in Fig. 4-4. (A careful study of this was made recently by Kondo and Moritani, 1977.) These bands arise from the Jones Zone, which will be discussed in detail in the treatment of tetrahedral semiconductors with pseudopotentials in Chapter 18. The energy at which this peak occurs was used earlier as a basis for obtaining experimental values for the covalent energy Fj (Harrison and Ciraci, 1974). 

For homopolar semiconductors, we see from Eq. (4-17) that it is twice the covalent energy -in contrast to the hybrid covalent energy of Eq. (3-6)- defined by... 

Rederive an expression for the covalent energy (sec Eq. 4-18) for the graphite structure, and evaluate the corresponding polarity for hexagonal BN, assuming that it has the graphite bond length (see Problem 3-1). 

We may summarize the LCAO interpretation of the energy bands. Accurate bands were displayed initially in Fig. 6-1. The energy difference between the upper valence bands and the conduction bands that run parallel to them was associated with twice the covalent energy for homopolar semiconductors, or twice the bonding energy 2 Vl -1- in hetcropolar semiconductors. The broadening of those... 

In the last step, we used Eq. (3-6) to write the hybrid covalent energy as... 

A.31h / md ) and Fig. 6-5 to write F as 0.66h / md ), and then used Eq, (4-16) to write h / md ) as F2/2.I6. This result can be compared with that resulting from Eq. (6-19), which is written in the form 0 = 3.6OF2 — 4.44F, for the homopolar semiconductors. Neither is very accurate, but both correctly reflect a bondingantibonding splitting from the covalent energy, reduced by the band-broadening... 

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