Beyond the LUC‐CNDO k = 0 approximation
Brian I. Craig, Phillip V. Smith · physica status solidi (b) · 1987
Abstract In applying the periodic LUC‐CNDO method it has been customary to employ the so‐called k = O approximation to represent the rather complex Brillouin zone (BZ) density matrix summations which arise within that formalism. The inability of this simplifying approximation to accurately describe these terms has, however, led to somewhat disappointing results. In this paper the periodic LUC‐CNDO formalism is extended beyond the k = O approximation by employing LUC special k‐point sets of progressively increasing size to evaluate these BZ density matrix summations to essentially arbitrary precision. This enables one, for the first time, to actually assess the accuracy of this semi‐empirical formalism without the imposition of additional approximations. Carrying the calculations through to full convergence in the BZ density matrix summations it is found that the periodic LUC‐CNDO method provides insufficient flexibility within its parameterization scheme to result in quantitatively accurate values for all of the properties of the homopolar covalent solids which are of interest. Whilst extension of this work to incorporate the additional contributions of INDO produced little improvement, recent work employing the MINDO method within the LUC periodic formalism appears promising.