BFW: A Density Functional for Transition Metal Clusters Matthew A. Addicoat, Mark A. Buntine, and Gregory F. Metha* Department of Chemistry, UniVersity of Adelaide, Adelaide, SA 5005, Australia Andrew T. B. Gilbert and Peter M. W. Gill* Research School of Chemistry, Australian National UniVersity, Canberra, ACT 0200, Australia ReceiVed: NoVember 22, 2006; In Final Form: January 9, 2007 Ionization potentials (IPs) or electron affinities (EAs) for transition metal clusters are an important property that can be used to identify and differentiate between clusters. Accurate calculation of these values is therefore vital. Previous attempts using a variety of DFT models have correctly predicted trends, but have relied on the use of scaling factors to compare to experimental IPs. In this paper, we introduce a new density functional (BFW) that is explicitly designed to yield accurate, absolute IPs for transition metal clusters. This paper presents the numerical results for a selection of transition metal clusters and their carbides, nitrides, and oxides for which experimental IPs are known. When tested on transition metal clusters, the BFW functional is found to be significantly more accurate than B3LYP and B3PW91. 1. Introduction The past decade has seen an explosion in the experimental and theoretical study of transition metal clusters. 1-11 Due to the size-dependent variation of each cluster’s electronic and geometric structure, the interaction of a molecule with a specific cluster is unique, yielding species with novel chemical and physical properties. 5-7 Consequently, considerable effort has gone into understanding the physical and chemical properties of molecules, both experimentally and computationally. How- ever, the partially filled d-shells of the metal atoms that constitute the clusters make this a difficult task. For transition metal clusters, two of the most readily determined physical properties are the ionization potential (IP) or electron affinity (EA). These are easily obtained experimen- tally over a large range of sizes and their importance in understanding cluster properties has been documented in several reviews. 1-5,7 It has been shown that the IP and EA can provide information about electronic and geometric structure as well as chemical reactivity with other molecules. Therefore, the ability to accurately calculate IPs and EAs, and compare them with experiment, can provide an important component to understand- ing the physical and chemical properties of metal clusters. The reaction between Ag clusters and ethylene is an example where the use of IP information has been instrumental in determining the structure. For Ag 3 -C 2 H 4 , DFT calculations predict two close-lying minima where the μ-bonded ethylene is either μ 1 or μ 2 bonded. Relative to Ag 3 , the two isomers were predicted to have lower and higher IPs, respectively, the former being in better agreement with experiment. 5,11 More recent work by some of the present authors has shown that the reaction of CO with Nb 3 and Nb 4 yields a product with an IP that is consistent with DFT calculations in which the CO is dissociated. 12 Hence, it is important to have the best possible computational tool for calculating absolute IPs and EAs for transition metal clusters and the relative changes that occur upon binding to a variety of molecules. However, accurately calculating these values has been shown to be problematic. 13 Due to the large number of electronic states that must be considered, ab initio methods require multiconfigurational approaches and calcula- tions are largely intractable for all but the very smallest clusters. Present DFT methods give values that vary dramatically with the chosen functional and basis set, which is not surprising since metal cluster species are not included in their parametrization. Therefore, by optimizing a specific functional for cluster species, it may be possible to improve the performance of DFT for calculating such parameters. In this paper we present a simple DFT functional for cal- culating IPs and EAs of transition metal clusters (and their car- bides, nitrides and oxides). Following the procedure used to optimize the EDF1 22 and EDF2 23 functionals, we have devel- oped a density functional specifically for IPs and EAs of metal clusters. The training set consists of 47 metal atoms and metal- containing diatomic molecules. We apply our functional to a set of larger metal clusters and find that it yields results that are significantly improved over those of the popular B3LYP and B3PW91 functionals. 2. Method A common strategy in forming new density functionals, is the recombination of existing functionals into a compound functional. B3LYP, 14 one of the most successful and widely used functionals, is of this form and comprises exact (or Fock 15 ) exchange, the Dirac 17 and Becke’88 16 exchange functionals, and the Vosko-Wilk-Nusair 18 and Lee-Yang-Parr 19 correlation functionals. Other functionals of this form include the family of empirical density functionals; EDF1 and EDF2. The determination of the linear mixing coefficients in these functionals is usually achieved by minimizing the residual error between the predicted and experimentally measured values for a set of training data. This results in a functional that depends not only on the choice of component functionals, but also on the choice of training data. In practice this choice of data is dictated by the availability of accurately determined experi- * Corresponding authors. (G.F.M) E-mail: greg.metha@adelaide.edu.au. Telephone: +61 8 8303 5943. Fax: +61 8 8303 4358. (P.M.W.G.) peter.gill@anu.edu.au. Telephone: +61 2 6125 4258. Fax: +61 2 6125 0750. 2625 J. Phys. Chem. A 2007, 111, 2625-2628 10.1021/jp067752l CCC: $37.00 © 2007 American Chemical Society Published on Web 03/14/2007