Summary
The applicability to crystals of the Slater and of the Kohn and Sham approximations to the exchange has been investigated through the behaviour of thed-bands of zinc and cadmium within the framework of the APW method. Both approximations were found to give correctly the features of the Fermi surface in both metals. However, the Slater approximation locates thed-bands very deeply. On the contrary in the Kohn and Sham approximation thed-bands appear as resonances of the muffin-tin potential, within the width of thes-like conduction band. Such a strong rising could possibly not be entirely attributed to inadequacy of the exchange approximations but, more probably, to the lack of dynamical correlation in the crystal potential.
Riassunto
Si è studiata l`applicabilità ai cristalli delle approssimazioni di Slater e di Kohn e Sham mediante Pesame del eomportamento delle banded dello zinco e del cadmio, nel contesto del metodo APW. Ambedue le approssimazioni danno correttamente le caratteristiche fondamentali della superficie di Fermi in entrambi i metalli. Mentre però l’approssimazione di Slater porta a banded troppo profonde, quella di Kohn e Sham porta le banded a mescolarsi con le bandes. In questo caso le banded appaiono come risonanze del Potenziale « a scatole di focaccine ». Lo spostamento osservato non può essere interamente attribuito all’inadeguatezza dell’approssimazione per lo scambio ma, più probabilmente, all’assenza di correlazione dinamica nel potenziale di cristallo.
Резюме
В рамках APW метода по по ведению d-зон цинка и кадмия была исследована примени мость к кристаллам об менных приближений Слетера и Кона и Шема. Обнаружено, что оба приближения прав ильно описывают особеннос ти поверхности Ферми в о боих металлах. Однако, приближение Слетера размещает d-зоны очень глубоко. На против, в приближении Кона и Шема d-зоны появляются как резонансы потенц иала, внутри ширины s-по добной зоны проводимости. Та кое сильное возрастание, вероятно, не может пол ностью быть приписано неадекват ности обменных приближени й, но, более вероятно, о тсутствию динамической коррел яции в кристаллическом по тенциале.
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Borghese, F., Denti, P. Effects of exchange on the band structure of zinc and cadmium. Nuov Cim B 3, 34–44 (1971). https://doi.org/10.1007/BF02899939
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DOI: https://doi.org/10.1007/BF02899939