Interbond matrix elements

The energy bands of tetrahedral solids have been studied in terms of LCAO s for many years the first study was that of Hall (1952), who used a Bond Orbital Approximation, keeping only nearest-neighbor interbond matrix elements in order to obtain analytic expressions for the bands over the entire Brillouin Zone. The recent study by Chadi and Cohen (1975), which did not use either of Hall s approximations, is the source of the interatomic matrix elements between. v and p orbitals, which appear in the Solid Stale Table. Pantelides and Harrison (1975) used the Bond Orbital Approximation but not the nearest-neighbor approximation and found that accurate valence bands could be obtained by adjusting a few matrix elements at the same time very clear interpretations of many features of the bands were achieved. The main features of the Pantiledes-Harrison interpretation will be presented here. 

Comparison of interbond matrix elements (eV) obtained in different ways. The first entry in each list is based upon the parameters of the Solid State Table. The second entry is the matrix clement based upon the Chadi-Cohen parameters (1975). The third entry is the value for extended bond orbitals obtained by Sokel (1976) by using perturbation theory and the Chadi-Cohen parameters. The fourth entry is the value obtained by Pantclides and Harrison by fitting the observed bands. 

Consider first = < 4 H Xi - Let one of the bond orbitals from the Bloch sum for the wave function on the right be the orbital labelled 3 in the center of Fig. 6-2. There arc then matrix elements with nearest-neighbor bonds of type 4 lying above and below the central orbital 3 in the figure, and both of these have phase factors e" the same as the phase factor for the central orbital (that is, for this choice of wave number). One is coupled through an atom of type A and one through an atom of type C we call these interbond matrix elements B and respectively. Thus if we retain only nearest-neighbor matrix elements, we obtain immediately... 

The hybrid energy and Vj were obtained in Problem 3-2, where a value of the bond energy Cb was found. A value for the matrix element between two hybrids on the same atom, — Ki, was also obtained, and only its contribution, — V, jl, to the interbond matrix element need be retained. 

Simple metals Transition metals Interatomic interaction. See Overlap interaction Interatomic matrix elements. See Matrix elements Interbond matrix elements, 1441f Interfaces. See also Surfaces... 

In a similar way one can compute matrix elements of any interbond interaction. The use of recoupling techniques (Racah algebra) allows one to reduce calculations of properties of molecules with n bonds to those of molecules with 2 bonds. 

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