The cohesive energy and associated PV relation for fcc neon have been calculated in the muNn-tin approximation via the augmented-plane-wave statistical-exchange (APW-Xa) method. Exchange parameters of 0.72997 (Schwarz's avT), 0.66667 (the Kohn-Sham-Gaspar value) and 0.500 were used. In all cases, the static lattice is significantly overbound, the amount of overbinding lessening with decreasing a. The introduction of a simple radial independence (a = 0.7772 for r g r"a = 2/3 for r p r, with r, some suitable change point inside the APW sphere) into the model does not cure the overbinding. I. BACKGROUND AND INTRODUCTORY REMARKSOver the last several years, the Xn statistical exchange model' has enjoyed considerable success as a procedure for the calculation of metallic and ionic crystalline cohesive energies and zero-temperature equations of state in the static-lattice limit. Recently, the model has been applied to the fcc rare-gas crystals' Ar, Kr, and Xe. In this latter work (hereafter referred to as I), it was found that a popular criterion for selecting the value of n [the "virial-theorem" o. , see Sec. II of I] enabled the calculation of static-lattice constants which were in surprisingly good agreement with experiments. The calculated PV relations were in fairly good agreement with experiment. A trend noted in I was that the best system so far as agreement of calculated cohesive energy and lattice constant with experiment was argon, while the worst was xenon (about 30% underbound).However, the best calculated PV relation was that for xenon.Extrapolation of the trends found in I suggests that fcc neon should be overbound when. the same criterion for the choice of n is used. In this paper we report confirmation of the prediction and, further, the inability of either a simple adjustment in the value of n or a simple radial dependence of a (Ref. 11) to improve matters. II. SUMMARY OF THE AI.&uMENTED-PLANE-WAVE STATISTICAL-EXCHANGE (APW-Xn ) METHODThe Xe scheme takes the total energy of the electrons in a solid (in the static-lattice approximation) to be the same as the exact expression except for the replacement of the exchange-correlation contribution by a local exchange-correlation operator which, in the non-spin-polarized case, is assumed to be U"(1) =-9n(3/8m)'~p'~(1)Here p is the charge density (see I for details). It is this assumption which determines all the prop-r& r.Here r is the distance from the nuclear site and r, is the solitary parameter.This alternative was intended to provide a more appropriate Z dependence of a than that provided by Xn/1. We found that direct calculations of z,by matching the Xo/2 atomic total energy to the Xo/I result) yields r, =0. 37 bohr, the value we used. [Wood'~has reported z, = 3. 30/(Z -l. 65) which gives 0. 395 bohr for neon. ]Whether we employ the Xn/I or Xo/2 choice of localexchange-correlation potential, the method of solution of the ensuing one-electron equations for the orbitals u; which we have used is the APW method in its traditional muffin-tin form (see Appendix...
The local-density (Xu) calculation of insulator band gaps is re-examined. Both new and extant data show the calculated gaps to be systematically small by substantial percentages (35 to 50%) while cohesive energies, valence band widths, and PV curves are in satisfactory agreement with experiment. The Slater transition state cannot be invoked directly to resolve the dilemma and its periodic generalization is unsuccessful. The simple periodic excitation calculation of AESCF can be interpreted usefully in terms of the first exciton absorption, a fact we illustrate in f.c.c. Ar. It is argued that the numerical results indicate strongly that Xa calculations of metal-insulator transition pressures yield lower bounds to that pressure.Die Lokaldichte-(Xa)-Berechnung von Isolatorbandgaps wird erneut uberpriift. Sowohl neue als schon vorhandene Werte zeigen, da13 die berechneten Gaps systematisch urn einen wesentlichen Prozentsatz (35 bis 50%) zu klein sind, wiihrend Kohasionsenergien, Breiten dervalenzbiinder und PV-Kurven mit dem Experiment befriedigend iibereinstimmen. Der Slater-tfbergangszustand laBt sich nicht direkt zur Losung des Dilemmas einsetzen, und seine periodische Verallgemeinerung ist nicht erfolgreich. Die simple Berechnung der periodischen Anregung des AESCF lafit sich erfolgreich mit der ersten Absorption des Exzitons interpretieren; diese Tatsache wird an k.f.z.-Ar illustriert. Es wird angenommen, daB die numerischen Ergebnisse starke Hinweise dafur geben, daB die Xa-Berechnungen der Metall-Isolator-ubergangsdriicke untere Grenzwerte fur diesen Druck ergeben.
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