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Advances in Quantum Chemistry by Per-Olov Lowdin

By Per-Olov Lowdin


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62a) This we should now compare with the results from the simple three-term function Y = I + c1u + c2t2 (63) with the much more convenient linear variational parameters. In this case we have the formulas + 2 . 1 7 . 5 ~+~2 . 2 4 ~ ~ L = 4 + 2 . 1 5 ~+~2 . 154C1c2 + 72c: + 2 . 1 4 0 ~ ~ ~ ~ + 576c$, + 576c$, (63a) M = 2 -+- 2 . 6 . 2 5 ~+~2 . 625 + 2 . 2 ~ -t~2 . 2 . 2 5 ~ ~ + 3 2 ~ : + 2 . 7 3 ~ ~ ~ ~ + 8 . 7 5 ~ :+ 2 . 1 2 ~ ~ ~ ~ +480~:~ +394, N =4 which as above have to be used in connection with the scale parameter k= L - C/Z 2M from which E = - ( L - L'/Z)2 4MN (63b) In varying only one parameter the result is c, = O .

Is working on certain compounds having the @-wolframstructure. The method is as well adapted to the investigation of compounds as of elements, and the limited number of results obtained so far is oniy an indication of the limited amount of manpower which we have available for the study. The general conclusion which we come to about the APW method is that it shares with the Green's function method the distinction of being the most accurate procedure available for calculating energy bands in the type of periodic potential found in a solid.

The characteristic here is of course the bands of 3d character interposed in the middle of the 4s-like band. Wood’s calculations are made for a nonmagnetic potential; that is, the same potential is used for electrons of both spin. However, Wood has also estimated the effect of using different potentials for the two spins, to give an energy band description of ferromagnetism. By using two different P ’ ’ ~exchange potentials, that of each spin being derived from the charge density of electrons of the corresponding spin, as proposed by the present author (Slater 1951b), one brings about a separation of the energy bands for the electrons of the two spins.

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