Structure of Endohedral Fullerene Eu@C74 W
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View Online / Journal Homepage / Table of Contents for this issue PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics Structure of endohedral fullerene Eu@C74w Dmitrij Rappoport* and Filipp Furche Received 2nd February 2009, Accepted 12th May 2009 First published as an Advance Article on the web 10th June 2009 DOI: 10.1039/b902098e Structure determination of endohedral fullerenes in the absence of X-ray data is difficult and often controversial. Here we show that the structure of endohedral fullerene Eu@C74 may be determined by density functional theory aided interpretation of its electronic, infrared and Raman spectra. The use of recently developed analytical polarizability gradient methods to simulate resonance-enhanced Raman spectra is crucial for this approach and allows for a nearly complete assignment of the experimental spectra. Eu@C74 is assigned a pear-shaped C2v symmetric structure and shows strong ionic interaction between the encapsulated metal and the fullerene p system. 1. Introduction spectrum of Eu@C74 to predictions from time-dependent density functional theory (TDDFT) to identify the frontier Endohedral metallofullerenes constitute a large class of molecular orbitals, specifically the electronic configuration of fullerene inner complexes with metal atoms or small metal europium. The structure of the carbon cage is inferred from an clusters.1,2 Group 2 and 3 metals and lanthanides form a assignment of infrared and Raman spectra of Eu@C74. number of endohedral fullerene complexes notable for their An important tool in the structure elucidation of endohedral electronic absorption in the near infrared and for their large fullerenes is 13C nuclear magnetic resonance (NMR) spectro- 1–3 third-order nonlinear susceptibilities. Lanthanide endohedral scopy. 13C NMR was used in conjunction with density fullerenes have recently attracted attention as high-relaxivity functional calculations to determine the structures of the 4,5 contrast agents for magnetic resonance imaging and as spin closed-shell endohedral fullerenes Ca@C 14 and Yb@C .15 6 74 74 qubits for quantum computing. 13 However, no C NMR data have been reported for Eu@C74 A major challenge in endohedral fullerene chemistry is the which makes the present theory-aided interpretation of complicated preparation and purification procedure yielding electronic and vibrational spectra particularly useful. The 1,7 only milligrams or less of substance. Structure determination present approach is applicable to other paramagnetic endohedral by X-ray crystallography is further complicated by the low fullerenes. crystallization tendency of fullerenes and crystal disorder.8 Downloaded by University of California - Irvine on 23 February 2012 Published on 10 June 2009 http://pubs.rsc.org | doi:10.1039/B902098E These difficulties may be alleviated by co-crystallization with 9 10 metalloporphyrins, e.g., for Tb3N@C80 or Ba@C74 or using 11 2. Computational details covalent adducts such as La@C74C6H3Cl3. Nevertheless, experimental structural data are still unavailable for many The theoretical tools for prediction of the vibrational proper- fullerene metal complexes including all europium endohedral ties of Eu@C74 are based on analytical derivative methods in fullerenes. Eu@C74 was the first isolated endohedral europium the framework of density functional theory (DFT). Molecular fullerene and was characterized spectroscopically and electro- force constants of large molecules are efficiently computed 12 chemically ten years ago. However, the structure of Eu@C74 from analytical second energy derivatives with respect to has not been established to date. nuclear displacements.16,17 However, due to the large number In a pioneering study, Vietze, Seifert and Fowler (VSF) of vibrations and the low symmetry of Eu@C74, vibrational applied semi-empirical density functional tight-binding theory frequencies alone contain too little information for a complete 13 (DFTB) methods to Eu@C74. Their work focused on vibrational band assignment. Infrared intensities and Raman tentative structures and relative energies of low-lying isomers. scattering cross sections provide additional characterization VSF did not provide predictions of experimentally accessible and are essential for correlating computed vibrational modes properties of Eu@C74, and thus a conclusive assignment of the to observed bands in vibrational spectra of Eu@C74. structure was not possible. Here we show how modern density The present structural assignment of Eu@C74 became possible functional methods can help to extract structural information by the recently developed efficient method for computing from electronic, infrared and Raman spectra of Eu@C74. This Raman scattering cross sections in the framework of leads to the first definitive structure assignment of this TDDFT.18 Within polarizability theory, Raman scattering endohedral fullerene. We compare the electronic excitation cross sections are determined from first-order derivatives of the frequency-dependent polarizability with respect to normal-mode displacements.19,20 Efficient computation of Department of Chemistry, University of California, Irvine, polarizability derivatives has long been the time-limiting CA 92697-2025, USA. E-mail: [email protected] w Electronic supplementary information (ESI) available: Atomic step in Raman calculations. Methods based on numerical coordinates. See DOI: 10.1039/b902098e differentiation of frequency-dependent polarizabilities were This journal is c the Owner Societies 2009 Phys.Chem.Chem.Phys., 2009, 11, 6353–6358 | 6353 View Online 21 applied to the molecules as large as buckminsterfullerene C60, 3. Results and discussion exploiting its high point group symmetry. The major drawback of numerical derivative methods is that they require a large 3.1 Minimum energy structure number of polarizability evaluations that increases with the The empty C74 cage is known to have a D3h symmetric 38 number of nuclear degrees of freedom. In contrast, the recently structure. In Eu@C74 the carbon cage is distorted from proposed analytical derivative method based on a Lagrangian D3h symmetry along one of the three equivalent dihedral formulation of frequency-dependent polarizabilities18 yields all axes. The resulting three degenerate energy minima have Cartesian polarizability derivatives at approximately 2–3 times symmetry-equivalent C2v symmetric structures one of which the cost of a single polarizability calculation, independent of the is depicted in Fig. 1. The europium atom is symmetrically number of nuclear degrees of freedom. In contrast to the coordinated to a [6,6]-bond of a pyracyclene unit with widely used analytical Hartree–Fock-based implementation of europium–carbon distances of 254 pm. Four carbon atoms Frisch and co-workers,22 the Lagrangian method18 includes adjacent to the coordinated [6,6]-bond are at a distance of the frequency-dependence of polarizability derivatives in a 267 pm from europium, which is even shorter than the natural way. This is particularly important for molecules europium–carbon distances of 277–282 pm found in 40–42 with low excitation energies such as fullerenes because the europium cyclopentadienyl complex Eu(C5Me5)2. resonance enhancement is significant at experimental excitation The carbon cage is visibly distorted near the encapsulated frequencies.23,24 metal: the cage surface is bulged out at the coordination site The structures of the energy minima and transition states of while the coordinated C–C bond is elongated by 6 pm Eu@C74 were optimized in C2v point group symmetry using compared to the empty C74 cage. 25,26 the BP86 exchange–correlation functional and the resolution The formation of the Eu@C74 endohedral complex from of the identity approximation (RI-J).27 Basis sets were of neutral species is associated with a large binding energy of À1 split-valence quality with polarization (SVP) for carbon28 359 kJ mol . The counterpoise correction for the basis set and of triple-zeta valence quality with two sets of polarization superposition error (BSSE) reduces the binding energy to À1 functions (TZVPP) for europium29 together with corresponding 324 kJ mol . The three energy minima of Eu@C74 are auxiliary basis sets.27,29 Effective core potentials (ECP) were symmetry-equivalent, in agreement with only one Eu@C74 12 used for europium.30 Reoptimization of the energy minimum fraction found in the HPLC separation procedure. The structure using triple-zeta valence quality basis set on all atoms degenerate interconversion of neighboring energy minima resulted in changes in bonding distances of 1 pm or less. Thus, proceeds via a C2v-symmetric transition state with a sizeable À1 À1 SVP basis sets were used for carbon atoms, and TZVPP basis activation barrier of 46 kJ mol (42 kJ mol including the sets were used for europium for all structure optimizations and BSSE correction). As a consequence, the diffusional motion of the europium atom throughout the carbon cage is strongly force constant calculations in this study. Electronic excitation 13 energies and oscillator strengths were obtained from TDDFT hindered. C-NMR experiments on Ca@C74 showed that the 31,32 33 site-hopping motion of the calcium atom is observable at the calculations using the RI-J approximation. The exchange– 14 Downloaded by University of California - Irvine on 23 February 2012 time scale of the NMR experiment. An activation barrier of Published on 10 June 2009 http://pubs.rsc.org | doi:10.1039/B902098E correlation functional and basis sets were the same