Performance and basis set dependence of density functional theory dipole and quadrupole moments  F. De Proft, F. Tielens, P. Geerlings * Faculteit Wetenschappen, Eenheid Algemene Chemie, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium Abstract A study is presented concerning the performance and basis set dependence of density functional methods in the calculation of dipole and quadrupole moments. A set of some small molecules was thereby used, together with seven commonly used exchange correlation functionals and Dunnings correlation consistent aug-cc-pVDZ, aug-cc-pVTZ, aug-cc-pVQZ and aug- cc-pV5Z basis sets. The results were compared with experiment and previously published values obtained with traditional ab initio molecular orbital methods. The best performance in the calculation of dipole and quadrupole moments is due to the hybrid functionals B3LYP and B3PW91. Moreover, the results seem to be essentially converged at the aug-cc-pVTZ level. Compar- ison of the LDA/aug-cc-pV5Z results with the numerical LDA results of Dickson and Becke, reveals that both sets of values are identical for most cases.  2000 Elsevier Science B.V. All rights reserved. Keywords: Density functional theory; Dipole and quadrupole moments; Basis set dependence 1. Introduction Multipole moments of molecules are of interest to theoretical chemists for a large number of reasons. One of them is that they are of utmost importance in describing molecular interactions. A central function in this field is the molecular electrostatic potential, defined as the interaction of the chemical system of interest with a unit positive charge at a position r [1– 3] V r X A Z A |r - R A | - Z rr |r - r 0 | dr 0 1 This electrostatic potential can be rewritten using a multipole expansion as [4] V r q r + mr r 3 + 1 2 X ij Q ij r i r j r 5 + … 2 where m represents the dipole moment and Q ij the elements of the quadrupole moment tensor. As can be seen, multipole moments thus constitute physically measurable properties related to the mole- cular charge distribution, necessary to describe chemical reactivity; moreover, they are found to be of great importance in the calculation of the interac- tion energy of small molecules with zeolites, neces- sary to obtain adsorption energies and separation constants [5–7]. In this work, we will focus on the performance and basis set dependence of density functional theory calculated dipole and quadrupole moments. Density Journal of Molecular Structure (Theochem) 506 (2000) 1–8 0166-1280/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S0166-1280(00)00397-3 www.elsevier.nl/locate/theochem  Presented at the 5th World Congress of Theoretically Oriented Chemists (WATOC), Imperial College, London, 1–6 August, 1999. * Corresponding author. Tel.: + 32-2-629-33-14; fax: + 32-2- 629-33-17. E-mail address: pgeerlin@vub.ac.be (P. Geerlings).