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1 DOI: /NCHEM.1896 Unusual Structure, Bonding and Properties in a Californium Borate Matthew J. Polinski, 1 Edward B. Garner, III, 2 Rémi Maurice, 3,4 Nora Planas, 3 Jared T. Stritzinger, 1 T. Gannon Parker, 1 Justin N. Cross, 1 Thomas D. Green, 1 Evgeny V. Alekseev, 5 Shelley M. Van Cleve, 6 Wulf Depmeier, 7 Laura Gagliardi, 3 Michael Shatruk, 1 Kenneth L. Knappenberger, 1 Guokui Liu, 8 S. Skanthakumar, 8 Lynda Soderholm, 8 David A. Dixon, 2 Thomas E. Albrecht-Schmitt 1,* Affiliations: 1 Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida Department of Chemistry, The University of Alabama, Shelby Hall, Tuscaloosa AL Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota SUBATECH, UMR CNRS 6457, IN2P3/EMN Nantes/Université de Nantes, 4 rue Alfred Kastler, BP20722, Nantes Cédex 3, France 5 Institute for Energy and Climate Research (IEK-6), Forschungszentrum Jülich GmbH, Jülich, Germany and Institut für Kristallographie, RWTH Aachen University, Aachen, Germany 6 Nuclear Materials Processing Group, Oak Ridge National Laboratory, One Bethel Valley Rd, Oak Ridge, Tennessee Institut für Geowissenschaften, Universität Kiel, Kiel, Germany 8 Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, IL *albrecht-schmitt@chem.fsu.edu. Supplementary Materials Computational Methods The first step is to build a realistic cluster model of the Cf-borate complex. All of the Cf sites are equivalent by symmetry in the reported (periodic) crystallographic structure. The shortest Cf-Cf distance in the crystal is Å, which prevents efficient direct (through space) exchange between the Cf sites. Four bonds, Cf-O, O-B, B-O and O-Cf, connect two nearest Cf neighbors. As a consequence only weak antiferromagnetic interactions can occur between the two nearest Cf neighbors. Thus, one can consider the Cf sites as nearly independent, and a cluster approach that considers explicitly only one Cf(III) ion can be used to characterize the Cf- O bonds. In order to define an adequate cluster, it is necessary to include several layers of atoms surrounding the central Cf atom and the Cf-O bonds to be characterized. We explicitly treat the atoms belonging to the first, second, and third coordination spheres of the Cf(III) ion, such that the bonding with the first coordination sphere is not dramatically affected by the truncation. At this stage, a negatively charged cluster would be obtained. We then model the B and Cf atoms of 1 NATURE CHEMISTRY 1

2 the fourth coordination sphere by protons, which were added to ensure a global neutral charge for the here defined cluster (Supplementary Figure 2). Additional calculations were done as follows. The PBE geometry was optimized with the hybrid B3LYP functional 1,2 with the Stuttgart basis set and ECP on Cf and the DZVP2 basis set 3 on the remaining atoms. A single point calculation with the same geometry and basis set was done with the generalized gradient approximation (GGA) functional PW91 4,5 to examine the difference between the GGA and hybrid functionals. We further tested the cluster approximation by modeling a cluster with a -2 charge and a -6 charge by removing symmetry related protons. In addition, the same set of calculations was done for Cm(III) with an f7 electronic structure to test for issues with the spin in the f 9 Cf(III). No issues were found. These calculations were done with the G09 program system. ELF allows for the determination of basins of chemical interest, namely core basins C(X), non-bonding valence basins V(X), and bonding valence basins V(X,X ), referred to as covalent basins. By integrating the electron density over the ELF basins, one obtains the number of electrons present in each basins, i.e. a measure of the covalency can be proposed by counting the total number of electrons belonging to covalent basins between a pair of atoms. The number of bonding electrons was obtained by summing over all the covalent basins belonging to a given Cf-O pair and having a maximum value of ELF, ELFmax>0.7. Some basins with a low value of ELFmax, close to 0.6, were discarded from this analysis, since a low value of ELFmax is not necessarily associated with clearly defined basins. Note that the C2 symmetry was not considered in the ELF analysis, resulting in slightly different numbers of bonding electrons for equivalent Cf-O bonds. A minimal active space for computing states belonging to the f 9 manifold is considered, consisting of 9 electrons in 7 orbitals is considered, i.e. only the f electrons are active. Three calculations are performed, (i) a state-average calculation on the 21 (high-spin) sextet spin states, (ii) a state-average calculation on 11 sextet spin states, and (iii) a state-specific calculation on the ground state. For (i) and (ii), the crystal-field splitting of the ground free-ion term(s) is estimated, and for (iii) the Mulliken charges and spin populations are determined. Since the lowest-energy states have a similar nature (crystal-field f 9 states corresponding to a same free-ion term), the spin-orbit coupling is not expected to significantly change the electronic structure of 2 NATURE CHEMISTRY 2

3 the ground state, and thus has not been considered in the present work dealing with atomic charges and spin populations. References 1. Becke, A. D., Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, Lee, C.; Yang, W.; Parr, R. G., Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B: Condens. Matter. 1988, 37, Godbout, N.; Salahub, D. R.; Andzelm, J.; Wimmer, E., Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through neon, optimization technique and validation. Can. J. Chem. 1992, 70, Perdew, J. P.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C., Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B: Condens. Matter. 1992, 46, Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, NATURE CHEMISTRY 3

4 Supplementary Table 1. Crystallographic information for Cf[B6O8(OH)5]. Compound Cf[B6O8(OH)5] Formula Mass Color and habit Space group Pale green, plate C2/c a (Å) (14) b (Å) (4) c (Å) (15) a ( ) 90 β ( ) (7) γ( ) 90 V (Å 3 ) 910.9(3) Z 4 T (K) 130(2) λ (Å) Maximum 2θ (deg.) ρcalc(g/cm 3 ) μ(mo Ka) (cm 1 ) R(F) for Fo 2 > 2s(Fo 2 ) a Rw(Fo 2 ) b R F F F F a o c o b 2 2 w o o R F w F F wf c2 2 4 o NATURE CHEMISTRY 4

5 Supplementary Table 2. Selected bond distances for Cf[B6O8(OH)5]. Cf-O Å B-O Å Cf(1)-O(3) 2.414(5) B(1)-O(2) 1.469(8) Cf(1)-O(3)' 2.414(5) B(1)-O(5) 1.466(8) Cf(1)-O(5) 2.411(5) B(2)-O(1) 1.338(10) Cf (1)-O(5)' 2.411(5) B(2)-O(2) 1.370(9) Cf (1)-O(6) 2.432(5) B(2)-O(3) 1.392(10) Cf (1)-O(6)' 2.432(5) B(3)-O(6) 1.476(8) Cf (1)-O(7) 2.463(5) B(3)-O(7) 1.473(8) Cf (1)-O(7)' 2.463(5) B(4)-O(3) 1.484(9) B(4)-O(4) 1.532(9) B(4)-O(5) 1.454(8) B(4)-O(7) 1.421(10) Supplementary Figure 1. Cluster of microcrystals of Cf[B6O8(OH)5]. 5 NATURE CHEMISTRY 5

6 Supplementary Figure 2. Cluster design. Top: illustration of the immediate coordination of a Cf atom. Central: illustration of the truncation and H substitution of the Boron (red) and Cf (blue) atoms in the cluster. Bottom: schematic representation of the cluster after proton optimization. 6 NATURE CHEMISTRY 6

7 Supplementary Figure 3. Fragment representation of the cluster structure. Left: front view perpendicular to the C2 axis. Right: top view parallel to the C2 axis. Ligand fragment with 4 coordinating O (tan), ligand fragments with 2 coordinating O (blue and purple) and Cf ( cyan), H atoms have been omitted for clarity. Supplementary Figure 4. Cf[B6O8(OH)5]. T/T and -1 /T plots of the magnetic susceptibility of 7 NATURE CHEMISTRY 7

8 Supplementary Figure 5. Representation of the optimized cluster model and atom labeling scheme. Left: front view perpendicular to the C2 axis. Right: top view parallel to the C2 axis. Cf: pink, O: red, B: light cream, H atoms have been omitted for clarity. Ball and sick represent the central Cf and its first coordination sphere, capped sticks second and third sphere. 8 NATURE CHEMISTRY 8

9 Supplementary Figure 6. Front view (perpendicular to the C2 axis) plot of the spin density (top figure in blue, isovalue=0.04) and f orbitals from a restricted open-shell DFT single point calculation (center and bottom figures in yellow and black, isovalue=0.01), using the PBE functional. 9 NATURE CHEMISTRY 9

10 Supplementary Figure 7. Plot of representative Cf-O bonding orbitals from Cf (from a restricted open-shell PBE calculation). Left, front view perpendicular to the C2 axis. Right, top view parallel to the C2 axis. 10 NATURE CHEMISTRY 10

11 Supplementary Table 3. Molecular charges for the Cf atom obtained at various levels of theory. Method f occ Mulliken Cf NBO Cf Mulliken Spin Cf PBE f /1.67 a 4.90 PBE0 f /1.85 a 4.98 B3LYP f b PW91 f b a Unrestricted/spin restricted open-shell calculations. b Unrestricted open-shell calculations. Supplementary Table 4. Orbital populations (in electrons) in the valence s, p, d, and f orbitals of Cf obtained at various levels of theory. Functional Pop 7s Pop 5f Pop 6d Pop 7p B3LYP a PW91 a PBE b PBE0 b a NBO orbital populations b Mulliken orbital populations Supplementary Table 5. Number of electrons involved in covalent V(Cf,O) ELF basins. The V(Cf,O) basins for which the maximum value of ELF was lower than 0.7 have been discarded from this analysis. Atom O3 O3 O5 O5 O6 O6 O7 O7 UPBE UPBE NATURE CHEMISTRY 11

12 Supplementary Table 6. Comparison of Cf and Cm model clusters with different charges. Functional f occ Spin pop NBO charge Mulliken charge 6 CfB11O34H32 Pop 7s Pop 5f Pop 6d Pop 7p B3LYP f PW91 f CmB11O34H32 B3LYP f PW91 f Functional f occ Spin pop NBO charge Mulliken charge 6 CfB11O34H30-2 Pop 7s Pop 5f Pop 6d Pop 7p B3LYP f PW91 f CmB11O34H30-2 B3LYP f PW91 f Functional f occ Spin pop NBO charge Mulliken charge 6 CfB11O34H26-6 Pop 7s Pop 5f Pop 6d Pop 7p B3LYP f PW91 f CmB11O34H26-6 B3LYP f PW91 f NATURE CHEMISTRY 12

13 Supplementary Table 7. Energies of the 21 (high-spin, S=5/2) sextet spin state from a stateaveraged CASSCF calculation with a 9 electrons in 7 orbitals active space. The molecular orbitals have been averaged over the 21 roots in the calculation. Free-ion term E (a.u.) ΔE (ev) H F P NATURE CHEMISTRY 13

14 Supplementary Table 8. Energies of 11 (high-spin, S=5/2) sextet spin state from a stateaveraged CASSCF calculation with a 9 electrons in 7 orbitals active space. The molecular orbitals have been averaged over the 11 roots. Free-ion term E (a.u.) ΔE (ev) H NATURE CHEMISTRY 14

15 Supplementary Table 9. PBE Optimized Cartesian X,Y,Z Coordinates in Å. Cf O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B B B B B NATURE CHEMISTRY 15

16 B B B B B H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H NATURE CHEMISTRY 16

17 Supplementary Table 10. B3LYP Optimized Cartesian X,Y,Z Coordinates in Å 6 CfB11O34H32 CF O O B B O O B B O O O O O B B B O O O O O H H B H H O O O O O O H H B H H O O H H H NATURE CHEMISTRY 17

18 B H B O O H H O O O O H H H H H H O H H O H H O H H O H H H O H H O H CmB11O34H32 CM O O B B O O B B NATURE CHEMISTRY 18

19 O O O O O B B B O O O O O H H B H H O O O O O O H H B H H O O H H H B H B O O H H O O O O H NATURE CHEMISTRY 19

20 H H H H H O H H O H H O H H O H H H O H H O H CfB11O34H30-2 CF O B B O O O O O H H B B H O O O O O B H NATURE CHEMISTRY 20

21 H H H O O O H H H O B H O O B H O O O H H B O O H H O B H O O B H O O O H H B O O H H O H H NATURE CHEMISTRY 21

22 O H H O H H O H H CmB11O34H30-2 CM O B B O O O O O H H B B H O O O O O B H H H H O O O H H H O B H O O NATURE CHEMISTRY 22

23 B H O O O H H B O O H H O B H O O B H O O O H H B O O H H O H H O H H O H H O H H CfB11O34H26-6 CF O O NATURE CHEMISTRY 23

24 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B B B B B B B B B B H H H NATURE CHEMISTRY 24

25 H H H H H H H H H H H H H H H H H H H H H H H CmB11O34H26-6 CM O O O O O O O O O O O O O O O O O O O O NATURE CHEMISTRY 25

26 O O O O O O O O O O O O O O B B B B B B B B B B B H H H H H H H H H H H H H H H H H H H H H NATURE CHEMISTRY 26

27 H H H H H NATURE CHEMISTRY 27