The Rotational g Tensor as a Benchmark for Density-Functional Theory Calculations of Molecular Magnetic Properties David J. D. Wilson,* ,† Chris E. Mohn, and Trygve Helgaker Department of Chemistry, UniVersity of Oslo, P. O. Box 1033 Blindern, N-0315 Oslo, Norway Received April 15, 2005 Abstract: The rotational g factor for a large number of organic compounds has been investigated with density-functional theory. Rapid convergence toward the basis-set limit is ensured by the use of London atomic orbitals. A statistical analysis of the results has been carried out in comparison with accurate experimental data. It is shown that gradient-corrected and hybrid functionals reproduce experimental results most closely, with the Keal-Tozer KT2 functional being the most accurate. I. Introduction Calculations of rotational g tensors constitute a particular challenge to ab initio theory, with the errors introduced in the description of the electronic system often being much larger than the experimental standard deviations obtained in highly accurate molecular-beam 1 and microwave Zeeman experiments. 2,3 Still, theoretical studies of the rotational g tensor have been presented at various levels of ab initio theory, including Hartree-Fock theory, 4-6 second-order Møller-Plesset (MP2) theory, 7-9 linearized coupled-cluster doubles theory, 9 the second-order polarization propagator approximation, 10-12 multiconfigurational self-consistent field (MCSCF) theory, 13-15 and, for small systems, full configu- ration-interaction theory. 16,17 However, although the results presented in these wave-function studies are mostly in qualitative agreement with experimental results, they often differ by more than 10 experimental standard deviations from the experimental values, especially at lower levels of theory. In recent years, density-functional theory (DFT) has emerged as the most popular quantum-mechanical method for studying molecular properties. While the standard local- density approximation (LDA) Slater-Vosko-Wilk-Nusair (SVWN) functional 18 typically gives results of intermediate quality, generalized gradient approximation (GGA) func- tionals such as the Becke-Lee-Yang-Parr (BLYP) func- tional 19,20 and hybrid functionals such as the Becke three- parameter Lee-Yang-Parr (B3LYP) functional 21-23 often describe electron correlation effects of molecular properties with an accuracy comparable to that of MP2 24 and coupled- cluster single-and-doubles 25-27 theories. In view of the accurate experimental measurements of g tensors, it is therefore of considerable interest to apply DFT to the calculation of this property and, in particular, to benchmark DFT g tensors against the available experimental data. In common with all properties that involve interactions with an external magnetic field, the calculation of rotational g factors suffers from the gauge-origin problem and slow basis-set convergence. Despite the many treatments of the gauge-origin problem proposed over the years, 10,28-34 it was, in principle, already solved in 1937 by London, who proposed attaching field-dependent complex phase factors to the atomic orbitals. 35 In London’s scheme, each atomic orbital has its own gauge origin: the nucleus to which it is attached. These London orbitals, which are also known as gauge invariant atomic orbitals, are correct to the first order in the magnetic field for a one-electron, one-center problem. 36 Their use in ab initio theory was pioneered by Hameka 37-39 in the 1950s and 1960s and by Ditchfield 40 in the 1970s, but the efficient implementation of London orbitals was not achieved until the 1990s, with the work of Wolinski and co- workers. 41 London orbitals are now widely used in quantum chemistry, with Hartree-Fock, 42 MP2, 43 MCSCF, 44 and * Corresponding author phone: +47 228 55432; fax: +47 228 55441; e-mail: d.j.wilson@kjemi.uio.no. † Current affiliation: Chemistry Department, La Trobe University, Australia. 877 J. Chem. Theory Comput. 2005, 1, 877-888 10.1021/ct050101t CCC: $30.25 © 2005 American Chemical Society Published on Web 08/16/2005