Z. Phys. B 91, 463466 (1993) ZEITSCHRIFT FORPHYSIK B 9 Springer-Verlag 1993 On the accuracy of the wavefunctions calculated by LAPW method E.E. Krasovskii 1, V.V. Nemoshkalenko 1, V.N. Antonov 2' * Institute of Metal Physics,Academyof Sciences of Ukraine, Vernadskogo 36, 252142 Kiev, Ukraine 2Max-Planck Institut fiir Festk6rperforschung,W-7000 Stuttgart 80, Germany Received: 9 October 1992 / Revised version: 1 March 1993 Abstract. The accuracy and the convergence properties of LAPW wavefunctions are studied using Be metal as an example. We show that radial part of the s-component of wavefunction inside the muffin-tin sphere differs substan- tially from the exact solution to the radial Schrodinger equation. We find that LAPW method underestimates the energy expectation value in the interstitial region. The inaccuracy of the well-converged wavefunctions oc- casionally produces significant errors in momentum ma- trix elements. PACS: 71.25 T n 1. Introduction Although the linear augmented plane wave (LAPW) method introduced by Andersen [ 1] has been widely used in electronic energy band structure calculations and in studying the physical properties of crystals, the accuracy of the LAPW wavefunctions has not been yet carefully examined. Some authors (Andersen [1], Koelling and Arbman [2], Singh [3]) consider the properties of LAPW method to be similar to those of standard Slater's APW, provided that energy parameters E~I are close to the eigenvalue in question, Ekx. It is also assumed that if E~I are not close to Eka (but still within the energy interval of I Evt-Ekzl< 0.5 Ry) the desired accuracy can be achieved by increasing the number of basis functions. In this work we show that the convergence properties of LAPW wavefunctions are quite different from those of APW wavefunctions, with well-converged LAPW ones being often far from exact solutions of the crystal Schr6- dinger equation. Using the standard APW method it is possible to ob- tain eigenenergies of any desired accuracy. With any set of basis functions, the wavefunction is an exact solution of the crystal Schr6dinger equation inside the muffintin * Permanent address: Institute of Metal Physics, Academyof Sci- ences of Ukraine, Vernadskogo 36, 252142 Kiev, Ukraine spheres. In Sect. 2 we examine the accuracy of the s- component of LAPW-wavefunction inside the muffin-tin sphere. The wavefunction calculated by standard APW method has a discontinuity in slope at the sphere bound- ary. From the APW formalism it follows at once that if the discontinuity diminishes as the number of basis func- tions increases, the wavefunction in the interstitial region will converge to the exact solution. As has been shown by Harmon et al. [4], the discontinuity does diminish with extending the basis set and the energy expectation value in the interstitial region rapidly approaches the eigen- energy. In Sect. 3 we study the accuracy of the LAPW- wavefunction in the interstitial region. The accuracy of crystal wavefunctions is of particular importance in the calculation of optical properties, which involves momentum matrix elements (MME). In our ear- lier works [5, 6, 7] we have used LAPW method to cal- culate the optical conductivity spectra of transitional metals and their compounds, and obtained a very good agreement with experiment. There we employed MME converged to within few per cent, however their accuracy was not estimated directly. In the Sect. 3 the accuracy of diagonal MME for HCP beryllium is studied. Beryllium is a simple metal, hence the wavefunctions of valence states are delocalized ones, having s-p character. Because the plane waves are a good representation of s-p functions in the interstitial region, one may expect the LAPW method to yield a minimal error in this case. We used a self-consistent crystal potential obtained in the framework of Local Density Approximation with ex- change-correlation term in form of Hedin and Lundqvist [8]. The partial /-projected densities of states (DOS) at each iteration were obtained with 196 k-points in 1/24-th part of Brillouin zone (BZ) (the irreducible part of BZ is divided into 648 tetrahedra). The linear inter- polation of energies Ek~ ~ and/-projected partial charges Qua (l) in a tetrahedron was employed. The LAPW basis set of about 100 functions was used in the self-consistent procedure.