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The Theoretical Account of the Ligand Field Bonding PCCP Accepted Manuscript This is an Accepted Manuscript, which has been through the Royal Society of Chemistry peer review process and has been accepted for publication. Accepted Manuscripts are published online shortly after acceptance, before technical editing, formatting and proof reading. Using this free service, authors can make their results available to the community, in citable form, before we publish the edited article. We will replace this Accepted Manuscript with the edited and formatted Advance Article as soon as it is available. You can find more information about Accepted Manuscripts in the Information for Authors. Please note that technical editing may introduce minor changes to the text and/or graphics, which may alter content. The journal’s standard Terms & Conditions and the Ethical guidelines still apply. In no event shall the Royal Society of Chemistry be held responsible for any errors or omissions in this Accepted Manuscript or any consequences arising from the use of any information it contains. www.rsc.org/pccp Page 1 of 11 Physical Chemistry Chemical Physics PCCP RSC Publishing ARTICLE The Theoretical Account of the Ligand Field Bonding Regime and Magnetic Anisotropy in the DySc 2N@C 80 Cite this: DOI: 10.1039/x0xx00000x Single Ion Magnet Endohedral Fullerene Manuscript Fanica Cimpoesu,*a Nita Dragoe, b Harry Ramanantoanina,c Werner Urland,c Received 0-th December 2012, and Claude Daul*c Accepted 0-th December 2012 DOI: 10.1039/x0xx00000x www.rsc.org/ Considering the DySc 2N@C 80 system as prototype for Single Ion Magnets (SIMs) based on endohedral fullerenes, we present methodological advances and state-of-the art computations analysing the electronic structure and its relationship with the magnetic properties due to the Accepted Dy(III) ion. The results of the quantum chemical calculations are quantitatively decrypted in the framework of Ligand Field (LF) theory, extracting the full parametric sets and interpreting in heuristic key the outcome. An important result is the characterization of the magnetic anisotropy in the ground and excited states, drawing the polar maps of the state-specific magnetization functions that offer a clear visual image of the easy axes and account the pattern of response to perturbations by magnetic field applied from different space directions. The state-specific magnetization functions are derivatives with respect of the magnetic field, taken for a given eigenvalue of the computed spectrum. The methodology is based on the Physics exploitation of the data from the black box of the ab initio Spin-Orbit (SO) calculations. The ground state is characterized by the Jz=±15/2 quantum numbers with easy axis along the Dy-N bond. The implemented dependence on the magnetic field allowed the first-principles simulation of the magnetic properties. The computational approach to the properties of endohedral fullerenes is an important goal, helping to complement the scarcity of the experimental data on such systems, determined by the limited amount of samples. Chemical Introduction Ln@C 82 species confirmed the trivalent state of lanthanides incorporated into the cage.8 The above briefing refers to the The physical chemistry of fullerene-lanthanide endohedral classical part of fullerenes encapsulating lanthanides story, the complexes occurs at the confluence of two large streams of further history showing extreme diversification of the 9 scientific fundamental interests, on lanthanide 1 and fullerene 2 encountered species, going up to the recent entries, such as 10 compounds, each class having rich manifestations, relevant to crystallographic resolution of Yb@C 80 , the structural 11 the quest of finding special properties and potential applications characterization of the series Sm 2@C 88 , Sm 2@C 90 , Sm 2@C 92 , in future technologies. The inclusion of lanthanide atoms inside or the Gd 2@C 79 N hetero-fullerene with a magnetic S = 15/2 12 fullerene cages started with the detection of La@C 82 in mass spin state. A remarkable class is represented by the C 80 spectra (while, initially, no evidence of smaller systems icosahedral cage incorporating a triangle of metal ions, triply 3 bridged by a central nitrogen atom, various Ln N@C systems La@C 60 or La@C 70 ). Further evidences by EPR spectra 3 80 Chemistry showed that the La@C system is ionic, with La (3+) and C (3-) with trivalent lanthanide ions (Ln= Gd, Tb, Dy, Ho) being 82 82 13 components. 4 Soon after, Ln@C adducts with many other investigated. Hetero-metallic compounds with this topology 82 14 lanthanide ions (e.g. Ln= La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho) and mixed composition Ln xM3-xN@C 80 , are also known, an 5 15 were reported. Molecules with two inner lanthanide ions, such important case being the DySc 2N@C 80 system, which was 6 as Ce 2@C 82 , were also obtained. Later on, the Ln@C 60 (e.g., revealed with the special Single Ion Magnet (SIM) behaviour, Ln = Eu, Gd, Dy) species appeared. 7 Synchrotron X-ray similar to the previously evidenced properties of the Ishikawa’s - - diffraction, EPR spectra, electrochemical measurements, bis (phthalo-cyaninato) lanthanide [Pc 2Tb] , [Pc 2Dy] or - 16 ultraviolet photoemission spectroscopy (UPS) data on various [Pc 2Ho] mononuclears. Physical This journal is © The Royal Society of Chemistry 2013 Phys. Chem. Chem. Phys. , 2013, 00 , 1-3 | 1 Physical Chemistry Chemical Physics Page 2 of 11 ARTICLE Journal Name The SIM property is an astonishing facet of the Single C3' C2' 17 Molecule Magnet (SMM) paradigm, that initially was Sc Sc 18 N developed on coordination compounds with large nuclearity C3 C2 and progressively shifted to smaller systems, down to Sc binuclears. 19, 25b Although relatively new, the SIM C4' Ln manifestation receives full attention, including illuminating C4 C1 C1' theoretical treatments. 20 The physical chemistry of lanthanide Sc C5 C6 ions inside fullerenes is a new world, yet at the initial stages of C4' C3' exploration, showing promising prospects for a new kind of molecular magnetism, pointing towards the in-vogue topics of C4 C1 C5' C6' C3 C2 the spintronics, as future technology. 21 Reported calculations devoted to endohedral lanthanide 12, 22, 23 Scheme 1 complexes were confined till now to the Density Manuscript Functional Theory (DFT) 24 methods, which, in general, offer We used, along with the optimization procedure, the facility of reliable information on ground states. However, in the routine ADF code to work with Average of Configuration (AOC), computational forms, the DFT approach is incomplete with smearing the nine electrons from the f 9 configuration of Dy(III) respect of intrinsic features of lanthanide compounds, such as over seven MOs having predominant f character (i.e. having the the multi-configuration nature of the wave functions and the 9/7=1.2857 population). Recalling that fractional occupations occurrence of quasi-degenerate states. are allowed in DFT, 29 we point that this non-standard option We enter this topic with a different perspective on the improves the convergence and leads to a reference with theoretical approach, in response to many opened questions to convenient physical meaning, mimicking the barycentre of the f experiment and prospect to special properties due to charge and orbital split. Since the f-type LF gap is expected in the order spin combined effects. We claim pioneering contributions in 2 3 -1 25 10 -10 cm , i.e. negligible in the scale of molecular bonding the ab initio multi-configuration wave function and DFT Accepted and thermochemical effects, this conventional choice does not treatment of lanthanide complexes, 26, 27 after pointing and impinge upon the quality of the geometry optimization itself. solving hidden technical and conceptual problems related with The optimization can be done, in principle, without this the weakly interacting nature of the f shell. As consequence of constraint, but leads to doubly occupied f-type orbitals smeared the radial part, contracted inside the atomic body, the f atomic in small fractions among the ligand-type MOs and distant in orbitals (AOs) are weakly perturbed by the environment. This energy from the single occupied f-type MOs, if the calculation sort of electronic structure is problematic in single-determinant is of restricted type. If the unrestricted way is followed, the f methods, like Hartree-Fock of DFT. 25 In the ab initio wave function theory, we resolved the issue orbitals from α and β sets are, after convergence, separated by going directly into multi-configuration calculations with large gaps, the situation being inappropriate for LF starting orbitals assembled from fragments, computed considerations. The AOC option is a rational manner to conduct Physics individually, in advance, i.e. the lanthanide ions and the calculations that are further devoted to the f-shell LF problems. remainder of the molecule. On the other hand, some of us The optimized Dy-N bond length is 2.225 Å, sensibly shorter than the usual coordination bonds in lanthanide complexes. For approached non-routine strategies in the DFT frame, by (-) 28 instance, in the [Pc 2Ln] units, the averaged Ln-N distances controlling the orbital occupations or dichotomizing the 32 interaction scheme, keeping only the electrostatic effects.26 are about 2.38 Å. It seems then that the DySc 2N moiety is Such procedures, and the subsequent Ligand Field (LF) constrained to compressed bond lengths inside the fullerene analysis, consecrated under the LFDFT acronym,27 are cage. In an approximate description, suggested in Scheme 1, the encompassing limitations of the standard DFT. The LFDFT N-Ln bond points towards the middle of a hexagonal face of the exploits the subtleties of the conceptual DFT, that allows and C80 cage, the corresponding C1-C6 carbon atoms forming the assigns a clear physical meaning to the systems with fractional first environment.
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