Abstract. A new method based on linear response theory is proposed for the determination of the Kohn- Sham potential corresponding to a given electron density. The method is very precise and aords a comparison between Kohn-Sham potentials calculated from correlated reference densities expressed in Slater- (STO) and Gaussian-type orbitals (GTO). In the latter case the KS potential exhibits large oscillations that are not present in the exact potential. These oscillations are related to similar oscillations in the local error function d i r ^ h e i u i r when SCF orbitals (either Kohn- Sham or Hartree-Fock) are expressed in terms of Gaussian basis functions. Even when using very large Gaussian basis sets, the oscillations are such that extreme care has to be exercised in order to distinguish genuine characteristics of the KS potential, such as intershell peaks in atoms, from the spurious oscillations. For a density expressed in GTOs, the Laplacian of the density will exhibit similar spurious oscillations. A previously proposed iterative local updating method for generating the Kohn-Sham potential is evaluated by comparison with the present accurate scheme. For a density expressed in GTOs, it is found to yield a smooth ``average'' potential after a limited number of cycles. The oscillations that are peculiar to the GTO density are constructed in a slow process requiring very many cycles. Keywords: Density functional theory ± Kohn-Sham potentials ± Gaussian basis functions Introduction Quantum chemical calculations can be performed very conveniently in terms of single-particle orbitals within the Kohn-Sham formalism of density functional theory (DFT). Kohn and Sham postulate the existence of a local potential V s with the property that non-interacting electrons moving in this potential will yield exactly the same electron density as the actual (interacting) many- electron system characterized by the local external potential. In atomic units h e m 1, the Kohn- Sham orbitals fu i g given by ^ H s u i r 1 2 r 2 V s r u i r e i u i r 1:1 generate the many-electron density q by occupying the N orbitals with the lowest orbital energy e i , qr X N i1 f i ju i rj 2 ; 1:2 where f i denotes the occupation number. The Kohn- Sham potential V s , which according to the Hohen- berg-Kohn theorem [1] must be uniquely related to the density q, can be subdivided into the external potential ®eld V ext (the Coulomb ®eld of the nuclei), the Hartree potential V H of the electrostatic electron repulsion and the exchange-correlation potential V xc ; V s r V ext r V H r V xc r : 1:3 Since V ext is known and V H can be calculated straight- forwardly for any given density, the construction of V s amounts to that of the unknown potential V xc . Although the exchange-correlation potential is formally de®ned through the relation V xc r dE xc n=dnr, approxima- tions have to be used since the energy functional E xc n R nre xc n; rd r is unknown. Determination of an accurate KS potential (in particular the exchange- correlation part) from an accurate electron density q allows us to judge approximations to the energy functional E xc n by comparing the approximate model potential V model xc r dE model xc n=dnr with the accurate one. A more direct test is of course a comparison between approximate and exact exchange-correlation energy densities. It has been demonstrated, however, that in order to calculate the exact (a very accurate) exchange-correlation energy density e xc r from an accurate wavefunction, a necessary step is the determi- nation of the KS orbitals, and hence, the KS potential, from the diagonal density qr corresponding to the given wavefunction [2, 3]. Correspondence to: P.R.T. Schipper Kohn-Sham potentials corresponding to Slater and Gaussian basis set densities P.R.T. Schipper, O.V. Gritsenko, E.J. Baerends Scheikundig Laboratorium der Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands Received: 24 February 1997 / Accepted: 18 June 1997 Theor Chem Acc (1997) 98:16±24