Solid State Communications, Vol. 79, No. 5, pp. 457-460, 1991. Printed in Great Britain. 0038-1098/91 $3.00 + .OO Pergamon Press plc NON-LOCAL CORRECTIONS IN DENSITY FUNCTIONAL THEORY Dipartimento di Fisica, Universita di Padova, Via Marzolo 8, I-35131 Padova, Italy (Received 2 May 1991 by M. Tosi) We have studied the non-local corrections to the local density approxi- mation (LDA) using a many-body perturbative method. By splitting the total energies into terms corresponding to different orders of self- energy perturbation, we obtain a clear picture of how inclusion of non-local interactions improve LDA total energy. Up to second order (which is equivalent to the same order of the configuration interaction expansion), this formulation gives the correct asymptotic behaviour of the exchange-correlation potential. Numerical calculations for the first two rows atoms give very good ground state energies. X.J. Chen* and F. Toigo I. INTRODUCTION THE STUDY of non-local corrections to the local density approximation (LDA) of the density func- tional theory (DFT) [ I] is receiving renewed interest. Many efforts have recently been made using many- body approaches such as the GW approximation [2], which successfully accounts for properties where a good accuracy in the calculation of quasi-particle energies is required, and where the simple LDA fails. Among these we mention band gaps in semiconduc- tors and insulators [3], and surface states [4]. Since many of these efforts have used a LDA basis as the starting point to construct the unperturbed Green function, it is important to study to which extent results obtained with the use of a LDA basis differ from those obtained from a somewhat more accurate but much more complicated selfconsistent non-local calculation. In this paper we pursue such a goal by using a many-body perturbation method, i.e., by treating screening effects on the coulomb interaction to various orders, while keeping the LDA basis in the construction of the Green function. Besides being simple, our approach exhibits the desirable feature of treating separately exchange and correlations, and therefore it allows to analyze them separately. In view of the increasing interest in the construc- tion of first principle pseudopotentials, we have applied our analysis to atomic systems. A natural way of introducing perturbation theory within the framework of DFT is to model the system * Present address: TCM, Cavendish laboratory, Madingley Road CB3 OHE, Cambridge, UK. by a non-interacting Hamiltonian gO, characterized by some local effective potential r?,,, and treat pertur- batively the correction H, = P - o,, + UC,,,,where Pis Coulomb interaction and rl,,, is the external field. By choosing oc, such that the ground state electronic density distribution no(r) of the non-interacting model system is the same as the exact distribution n(r), then, following Sham [5], we may write the ground state energy of the Hamiltonian A = fiO + A, as: E = E, + i Tr [In (1 - CC,) + CC] -I- Y’, (1) where E, is the ground state energy of fi,,, Z is the self-energy, G, and G are the unperturbed and the full Green functions respectively, and iY’ indicates the sum of all skeleton diagrams [5]. Since it is known that LDA is a rather good Table 1. Contributions to the total energy (in eV) in d@erent order ofperturbation, compared with the LDA and HF results. LDA calculated with the Gunnarsson and Lundqvist [II] parametrization of the exchange- correlation energy density. The HF results are obtained from [I21 AtOm ELDAeHF ELDA EHF Ej” Ej2, He - 77.8 - 77.8 - 77.9 0.0 - 1.2 Li - 202.2 - 200.5 -202.2 -0.1 - 1.3 Be - 396.4 - 394.5 -396.5 -0.1 -1.5 B - 667.3 - 664.2 -667.4 -0.2 -2.0 C - 1024.9 - 1020.6 - 1025.5 -0.5 -2.1 N - 1478.3 - 1472.9 - 1480.2 -0.6 -2.7 0 -2034.7 -2029.8 -2035.6 -0.5 -3.7 F -2704.2 -2700.5 -2704.9 -0.4 - 5.6 Ne -3497.4 -3493.9 -3497.8 -0.3 -8.9 457