Bond Orbital Energies

Molecule Interatomic Distance (A) Homopolar Splitting 2V, CeV) Chemical Splitting, 2C (eV) Bond Energy, 2A(eV) Minimum 300 K Energy Gap (eV) 

Values from D.K. Ferry, Ref. 2. Minimum energy saps from Ref. 3.  

Here the crystallographic indices in the subscripts refer to the hybrid molecular orbital directions. Because the Schrbdinger Equation governing electron motion is linear, any combination of wave functions that solve it will also be a solution. In other words, choosing the hybrid orbitals or the atomic orbitals as a starting point for the calculation must yield identical results. The most flexible and general approaeh is not to be restricted to specific hybrid orbitals but rather to consider all possible orbital-by-orbital interactions of the fundamental atomic states. These states apply to a given atom in any environment. Thus, their use is valid for any material in which the atom occurs. As an example of a specific interaction, one can ask how does the Px orbital on one atom interact with the orbital on another atom. 

It is through the phase factors that a given electron momentum is defined. One might have expected this as, from the discussion of Chapter 2, band structures represent the interference of electron waves with the periodic potential of the lattice. For the wave functions in Equation 5.10, the corresponding phase factors are  

An examination of the terms for the g values will show that these simply represent the interference behavior of the electron waves with given wave vectors k interacting with atoms at positions defined by the real-space vectors d and at the origin. The g values include the free-electron-like behavior of Chapter 2. The calculation of the g factors becomes more complex when second-nearest neighbors and beyond are included, but the method is the same. The energy of an electron with wave vector k is the determinant of a matrix representing the energies of all possible orbital pairs. For example, for a zincblende semiconductor with no d-orbitals the LCAO matrix is [c.f Ref 4]  

---

The mixing parameters, a and A, may be obtained from the first and second moments of the densities of states. The first moment of njj (e) gives the bond orbital energy with respect to E0 of — h, so that from eqn (7.94)... 

---