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It is necessary to employ quasi-particle calculations to correct band gapproblems in LDA. As an expedient way for the reliable but massive GWA,Quasi-Particle-LDA (QPLDA) is proposed by several authors, where the totalcomputational cost scales with N. Historically, Sham and Kohn introduced theidea of the local mass operator based on local wavenumber similar to WKB, butdid not execute actual numerical calculations. They took into account exchangeinteraction only, from which we could not expect precise treatments anyway.Later, Pickett and Wang had proposed a more qualitative method and had shownits potentiality in examples of semiconductors, such as silicon, diamond andGaP. They used a model analytic formula for the dialectic function and adopteda model energy dispersion, which is free-electron like one, except that, beingaccompanied with an artificial band-gap discontinuity. The latter method hastwo shortcomings. First, to execute the calculation, several parameters areneeded, such as the macroscopic dielectric constant and the band gap, whichshould be evaluated by the calculation itself, rather than being prepared asparameters. Second, in their computation of the mass operator, two or threedimensional numerical integrations are needed on each point of the direct spacemesh, which demand large computational costs in iterative procedures indetermining local wavenumbers and quasi-particle energies. This may be thereason why QPLDA has not been widely used until now. The present work proposesa qualitative way of QPLDA which does not need any experimental parameters,being much speedier than the formalism of Picket and Wang, and more precisethan that of Sham and Kohn. The computational method adopted by the presentwork is a modification of the original proposal by Sham and Kohn, rather thanthat of Picket and Wang.

Simplification of QPLDA: A practical method to the correction for the LDA band gap problem