Raman optical activity spectra of chiral transition metal complexes Sandra Luber, Markus Reiher * Laboratorium fu ¨ r Physikalische Chemie, ETH Zu ¨ rich, Wolfgang-Pauli-Str. 10, CH-8093 Zu ¨ rich, Switzerland Received 30 November 2007; accepted 21 January 2008 Available online 1 February 2008 Dedicated to Professor P. Botschwina on the occasion of his 60th birthday. Abstract We present calculated vibrational Raman optical activity (ROA) spectra for the transition metal complexes K-tris(acetylacetonato)- cobalt(III), K-tris(acetylacetonato)rhodium(III), dichloro-(6R,7S,9S,11S-()-sparteine)zinc(II) and D(ddd)-tris(ethylenediaminato)- cobalt(III). For this study, it was necessary to benefit from density-fitting techniques to a large extent. Necessary implementations are described and the gauge origin problem is addressed. The importance of the electric-dipole–electric-quadrupole polarizability tensor for ROA intensity differences is investigated and found to be small, especially at lower wavenumbers where no C–H stretching vibrations occur. Furthermore, the basis set and density functional dependence is examined. Ó 2008 Elsevier B.V. All rights reserved. Keywords: Optical activity; Raman spectroscopy; Density functional calculations; Vibrational spectroscopy 1. Introduction Stereochemistry is an important aspect in chemistry, influencing strongly certain properties of molecules. There are several techniques in order to gain information about the chirality of systems, among them being the promising, quite young technique of vibrational Raman optical activity (ROA) spectroscopy [1–4]. Usually, the intensity differences of the Raman intensities scattered by the molecules in inci- dent right- and left-circularly polarized light are measured [5]. For the assignment of ROA spectra [6,7], quantum chemical calculations are required (see Ref. [8] for a recent review on the first-principles calculation of vibrational spec- tra), because no universal relationship between molecular structure and intensity differences is known yet [9–12]. ROA experiments have been performed for polymers, peptides, and even for large systems like proteins and viruses (see, e.g. Refs. [13–21]), which can be studied in their natural environment. ROA calculations, however, are very time-consuming and therefore full ROA spectra have only been evaluated for quite small organic molecules (compare, for example, Refs. [22–30]). The largest molecule investi- gated so far with density functional theory (DFT) is deca- alanine [29]. ROA spectra of chiral metal complexes have not been reported at all, in contrast to vibrational circular dichroism (VCD) spectra [31–33]. Motivated by these VCD measurements and the expectation that ROA mea- surements will follow, we present the first ROA calculations of metal complexes. Our goal is to assess the feasibility of such calculations and to uncover possible pitfalls. We have chosen several closed-shell complexes with different ligands and metal atoms (see Fig. 1): first, K-tris(acetylacetona- to)cobalt(III) and K-tris(acetylacetonato)rhodium(III), for which recently VCD measurements have been reported [31], furthermore dichlorosparteinezinc(II) (sparteine is an abbreviation for 6R,7S,9S,11S-()-sparteine (compare Ref. [32]) and D(ddd)-tris(ethylenediaminato)cobalt(III) (for an explanation of the nomenclature and for references to VCD measurements and calculations, see Ref. [34]). In order to reduce the computational effort, we will rely on density-fitting techniques [35] for the calculation of the 0301-0104/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2008.01.046 * Corresponding author. Tel.: +41 44 63 34308; fax: +41 44 63 31594. E-mail address: markus.reiher@phys.chem.ethz.ch (M. Reiher). www.elsevier.com/locate/chemphys Available online at www.sciencedirect.com Chemical Physics 346 (2008) 212–223