By Per-Olov Löwdin
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Extra info for Advances in quantum chemistry. Vol. 6: 1972
2) for both modifications, and should find which of these has the lower energy. It requires a very accurate Calculation of the energies to determine this, since the energy difference between the modifications must be very small, and no such calculations have yet been made. With the accuracy which is now being attained in the calculation of total energy, however, it does not seem impossible that during the next years such calculations should prove to be practical. The magnetic questions which we have been considering have been a determination of the ground state of a magnetic crystal.
Thus let us calculate the energy difference between an initial state, and a final state in which q ihas decreased by one unit, qj has increased by one unit, so that an electron has had a tliansition from the ith to thejth state. First, we carry the calculation through using the initial state as the standard state around which we make our power series expansion. Thus we assume that in the initial state qi = q i l ,qj = q j l , while in the final state qi = qil - 1, q j = qjl + 1. Let us find the energies of initial and final states from Eq.
It is in these cases that the familiar energy-band calculation of optical properties, from densities of states, is appropriate. Even in such a case, one can have an incipient discrete level, what Friedel (1954; see also references to Blandin and Daniel) refers to as a virtual excited state, which will modify the wave functions and transition probabilities profoundly. We possess the mathematical machinery for studying perturbed crystals of the sort met with excitons, as well as those resulting from impurity atoms.
Advances in quantum chemistry. Vol. 6: 1972 by Per-Olov Löwdin