Atomic energy level mismatch

For homonuclear diatomic molecules the atomic energy-level mismatch vanishes so that aj = 0 and ac = 1. Hence, the change in the electronic... 

For hetercnuclear diatomic molecules, the atomic energy-level mismatch does not vanish, so that <5 0. Hence, the electronic charge distribution... 

Fig. 4.12 The normalized eigenvalues, , of the triatomic molecule AH2 as a function of the bond angle, 2/3, for the particular choice of normalized atomic energy level mismatch, 5 = 1. The symmetries of the eigenfunctions are also shown for the bent and linear configurations.

Fig. 4.13 Examples of nearest-neighbour paths of length four that contribute to the fourth moment of the AH2 eigenspectrum for the case of vanishing atomic energy-level mismatch. The solid atom indicates the site from which the path starts and to which it eventually returns. The number prefactor under each trimer gives the total number of such paths starting and ending on the solid atom. The three-atom paths involve the square of cos 2/7 due to a reduction in magnitude of the p, orbital on rotation through 2/7 as in Fig. 4.11.

The heats of formation of equiatomic AB transition-metal alloys may be predicted by generalizing the rectangular d band model for the elements to the case of disordered binary systems, as illustrated in the lower panel of Fig. 7.13. Assuming that the A and transition elements are characterized by bands of width WA and WB, respectively, then they will mix together in the disordered AB alloy to create a common band with some new width, WAB. The alloy bandwidth, WAB may be related to the elemental bond integrals, hAA and , and the atomic energy level mismatch, AE — EB — EAt by evaluating the second moment of the total alloy density of states per atom ab( ), namely... 

Thus, for bands that are nearly half-full with N 5, we have that the atomic energy-level mismatch for LCN will be given by... 

The second contribution inside the curly brackets of eqn (7.79) represents the loss of bonding due to the atomic energy-level mismatch in the alloy. Since from eqs (7.73) and (7.42) = (3b2/5a)N(10 — N to the zeroth... 

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