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Refinement of Crystallographic Disorder in the Tetrafluoroborate Anion

Module by: John J. Allen, Andrew R. Barron. E-mail the authors

Introduction

Through the course of our structural characterization of various tetrafluoroborate salts, the complex cation has nominally been the primary subject of interest; however, we observed that the tetrafluoroborate anion (BF4-) anions were commonly disordered (13 out of 23 structures investigated). Furthermore, a consideration of the Cambridge Structural Database as of 14th December 2010 yielded 8,370 structures in which the tetrafluoroborate anion is present; of these, 1044 (12.5%) were refined as having some kind of disorder associated with the BF4- anion. Several different methods have been reported for the treatment of these disorders, but the majority was refined as a non-crystallographic rotation along the axis of one of the B-F bonds.

Unfortunately, the very property that makes fluoro-anions such good candidates for non-coordinating counter-ions (i.e., weak intermolecular forces) also facilitates the presence of disorder in crystal structures. In other words, the appearance of disorder is intensified with the presence of a weakly coordinating spherical anion (e.g., BF4- or PF6-) which lack the strong intermolecular interactions needed to keep a regular, repeating anion orientation throughout the crystal lattice. Essentially, these weakly coordinating anions are loosely defined electron-rich spheres. All considered it seems that fluoro-anions, in general, have a propensity to exhibit apparently large atomic displacement parameters (ADP's), and thus, are appropriately refined as having fractional site-occupancies.

Refining disorder

In crystallography the observed atomic displacement parameters are an average of millions of unit cells throughout entire volume of the crystal, and thermally induced motion over the time used for data collection. A disorder of atoms/molecules in a given structure can manifest as flat or non-spherical atomic displacement parameters in the crystal structure. Such cases of disorder are usually the result of either thermally induced motion during data collection (i.e., dynamic disorder), or the static disorder of the atoms/molecules throughout the lattice. The latter is defined as the situation in which certain atoms, or groups of atoms, occupy slightly different orientations from molecule to molecule over the large volume (relatively speaking) covered by the crystal lattice. This static displacement of atoms can simulate the effect of thermal vibration on the scattering power of the "average" atom. Consequently, differentiation between thermal motion and static disorder can be ambiguous, unless data collection is performed at low temperature (which would negate much of the thermal motion observed at room temperature).

In most cases, this disorder is easily resolved as some non-crystallographic symmetry elements acting locally on the weakly coordinating anion. The atomic site occupancies can be refined using the FVAR instruction on the different parts (see PART 1 and PART 2 in Figure 1) of the disorder, having a site occupancy factor (s.o.f.) of x and 1-x, respectively. This is accomplished by replacing 11.000 (on the F-atom lines in the “NAME.INS” file) with 21.000 or -21.000 for each of the different parts of the disorder. For instance, the "NAME.INS" file would look something like that shown in Figure 1. Note that for more heavily disordered structures, i.e., those with more than two disordered parts, the SUMP command can be used to determine the s.o.f. of parts 2, 3, 4, etc. the combined sum of which is set at s.o.f. = 1.0. These are designated in FVAR as the second, third, and fourth terms.

Figure 1: General layout of the SHELXTL "NAME.INS" file for treatment of disordered tetrafluoroborate. a For more than two site occupancies “SUMP = 1.0 0.01 1.0 2 1.0 3 1.0 4” is added in addition to the FVAR instruction.
Figure 1 (Fig22.jpg)

In small molecule refinement, the case will inevitably arise in which some kind of restraints or constraints must be used to achieve convergence of the data. A restraint is any additional information concerning a given structural feature, i.e., limits on the possible values of parameters, may be added into the refinement, thereby increasing the number of refined parameters. For example, aromatic systems are essentially flat, so for refinement purposes, a troublesome ring system could be restrained to lie in one plane. Restraints are not exact, i.e., they are tied to a probability distribution, whereas constraints are exact mathematical conditions. Restraints can be regarded as falling into one of several general types:

  • Geometric restraints, which relates distances that should be similar.
  • Rigid group restraints.
  • Anti-bumping restraints.
  • Linked parameter restraints.
  • Similarity restraints.
  • ADP restraints (Figure 2).
  • Sum and average restraints.
  • Origin fixing and shift limiting restraints.
  • Those imposed upon atomic displacement parameters.
Figure 2: Consequence of the anisotropic displacement parameter (ADP) restraints DELU, SIMU, and ISOR on the shape and directionality of atomic displacement parameters. Adapted from P. Müller, Crystal Structure Refinement, A Crystallographer's Guide to SHELXL, Oxford University Press, UK (2006).
Figure 2 (graphics2.jpg)

Geometric restraints

  • SADI - similar distance restraints for named pairs of atoms.
  • DFIX - defined distance restraint between covalently bonded atoms.
  • DANG - defined non-bonding distance restraints, e.g., between F atoms belonging to the same PART of a disordered BF4-.
  • FLAT - restrains group of atoms to lie in a plane.

Anisotropic displacement parameter restraints

  • DELU - rigid bond restraints (Figure 2).
  • SIMU - similar ADP restraints on corresponding Uij components to be approximately equal for atoms in close proximity (Figure 2).
  • ISOR - treat named anisotropic atoms to have approximately isotropic behavior (Figure 2).

Constraints (different than "restraints")

  • EADP - equivalent atomic displacement parameters.
  • AFIX - fitted group; e.g., AFIX 66 would fit the next six atoms into a regular hexagon.
  • HFIX - places H atoms in geometrically ideal positions, e.g., HFIX 123 would place two sets of methyl H atoms disordered over two sites, 180° from each other.

Classes of disorder for the tetrafluoroborate anion

Rotation about a non-crystallographic axis along a B-F bond

The most common case of disorder is a rotation about an axis, the simplest of which involves a non-crystallographic symmetry related rotation axis about the vector made by one of the B-F bonds; this operation leads to three of the four F-atoms having two site occupancies (Figure 3). This disorder is also seen for tBu and CF3 groups, and due to the C3 symmetry of the C(CH3)3, CF3 and BF3 moieties actually results in a near C2 rotation.

Figure 3: Schematic representation of the rotational relationship between two disordered orientations of the BF4- anion.
Figure 3 (graphics3.jpg)

In a typical example, the BF4- anion present in the crystal structure of [H(Mes-dpa)]BF4 (Figure 4) was found to have a 75:25 site occupancy disorder for three of the four fluorine atoms (Figure 5). The disorder is a rotation about the axis of the B(1)-F(1) bond. For initial refinement cycles, similar distance restraints (SADI) were placed on all B-F and F-F distances, in addition to similar ADP restraints (SIMU) and rigid bond restraints (DELU) for all F atoms. Restraints were lifted for final refinement cycles. A similar disorder refinement was required for [H(2-iPrPh-dpa)]BF4 (45:55), while refinement of the disorder in [Cu(2-iPrPh-dpa)(styrene)]BF4 (65:35) was performed with only SADI and DELU restraints were lifted in final refinement cycles.

Figure 4: Structures of (a) substituted bis(2-pyridyl)amines (R-dpa) and (b) substituted bis(2-quinolyl)amines [R-N(quin)2] ligands.
Figure 4 (graphics4.jpg)
Figure 5: Structure for the BF4- anion in compound [H(Mes-dpa)]BF4 with both parts of the disorder present. Thermal ellipsoids are shown at the 20% level. Adapted from J. J. Allen, C. E. Hamilton, and A. R. Barron, Dalton Trans., 2010,11451.
Figure 5 (graphics5.jpg)

In the complex [Ag(H-dpa)(styrene)]BF4 use of the free variable (FVAR) led to refinement of disordered fluorine atoms F(2A)-F(4A) and F(2B)-F(4B) as having a 75:25 site-occupancy disorder (Figure 6). For initial refinement cycles, all B-F bond lengths were given similar distance restraints (SADI). Similar distance restraints (SADI) were also placed on FF distances for each part, i.e., F(2A)F(3A) = F(2B)F(3B), etc. Additionally, similar ADP restraints (SIMU) and rigid bond restraints (DELU) were placed on all F atoms. All restraints, with the exception of SIMU, were lifted for final refinement cycles.

Figure 6: Structure of the disordered BF4- anion in [Ag(H-dpa)(styrene)]BF4 viewed down the axis of disorder. Thermal ellipsoids are shown at the 30% probability level. Adapted from J. J. Allen and A. R. Barron, J. Chem. Cryst., 2009, 39, 935.
Figure 6 (graphics6.jpg)

Rotation about a non-crystallographic axis not along a B-F bond

The second type of disorder is closely related to the first, with the only difference being that the rotational axis is tilted slightly off the B-F bond vector, resulting in all four F-atoms having two site occupancies (Figure 7). Tilt angles range from 6.5° to 42°.

Figure 7: Molecular structure for the anion in [Cu(H-dpa)(cis-3-octene)]BF4 with both parts of the disordered BF4- present. Thermal ellipsoids are shown at the 20% level. Adapted from J. J. Allen and A. R. Barron, Dalton Trans., 2009, 878.
Figure 7 (graphics7.jpg)

The disordered BF4- anion present in the crystal structure of [Cu(Ph-dpa)(styrene)]BF4 was refined having fractional site occupancies for all four fluorine atoms about a rotation slightly tilted off the B(1)-F(2A) bond. However, it should be noted that while the U(eq) values determined for the data collected at low temperature data is roughly half that of that found at room temperature, as is evident by the sizes and shapes of fluorine atoms in Figure 8, the site occupancies were refined to 50:50 in each case, and there was no resolution in the disorder.

Figure 8: Comparison of the atomic displacement parameters observed in the disordered BF4- anion from [Cu(Ph-dpa)(styrene)]BF4 at data collection temperature (a) T = 213 K and (b) T = 298 K. Thermal ellipsoids are set at the 25% level.
Figure 8 (graphics8.jpg)

An extreme example of rotation off-axis is observed where refinement of more that two site occupancies (Figure 9) with as many as thirteen different fluorine atom locations on only one boron atom.

Figure 9: Structure for the tetrafluoroborate anion with twelve fluorine atom locations. Adapted from S. Martinez-Vargas, R. Toscano, and J. Valdez-Martinez, Acta Cryst., 2007, E63, m1975.
Figure 9 (graphics9.jpg)

Constrained rotation about a non-crystallographic axis not along a B-F bond

Although a wide range of tilt angles are possible, in some systems the angle is constrained by the presence of hydrogen bonding. For example, the BF4- anion present in [Cu(Mes-dpa)(μ-OH)(H2O)]2[BF4]2 was found to have a 60:40 site occupancy disorder of the four fluorine atoms, and while the disorder is a C2-rotation slightly tilted off the axis of the B(1)-F(1A) bond, the angle is restricted by the presence of two B-FO interactions for one of the isomers (Figure 10).

Figure 10: Structure of the disordered BF4- in [Cu(Mes-dpa)(μ-OH)(H2O)]2[BF4]2 showing interaction with bridging hydroxide and terminal water ligands. Thermal ellipsoids are shown at the 20% level. Adapted from J. J. Allen, C. E. Hamilton, and A. R. Barron, Dalton Trans., 2010, 11451.
Figure 10 (graphics10.jpg)

An example that does adhere to global symmetry elements is seen in the BF4- anion of [Cu{2,6-iPr2C6H3N(quin)2}2]BF4.MeOH (Figure 11), which exhibits a hydrogen-bonding interaction with a disordered methanol solvent molecule. The structure of R-N(quin)2 is shown in Figure 4b. By crystallographic symmetry, the carbon atom from methanol and the boron atom from the BF4- anion lie on a C2-axis. Fluorine atoms [F(1)-F(4)], the methanol oxygen atom, and the hydrogen atoms attached to methanol O(1S) and C(1S) atoms were refined as having 50:50 site occupancy disorder (Figure 11).

Figure 11: H-bonding interaction in [Cu{2,6-iPr2C6H3N(quin)2}2]BF4.MeOH between anion and solvent of crystallization, both disordered about a crystallographic C2-rotation axis running through the B(1)C(1S) vector. Adapted from J. J. Allen, C. E. Hamilton, and A. R. Barron, Dalton Trans., 2010, 11451.
Figure 11 (graphics11.jpg)

Non crystallographic inversion center at the boron atom

Multiple disorders can be observed with a single crystal unit cell. For example, the two BF4- anions in [Cu(Mes-dpa)(styrene)]BF4 both exhibited 50:50 site occupancy disorders, the first is a C2-rotation tilted off one of the B-F bonds, while the second is disordered about an inversion centered on the boron atom. Refinement of the latter was carried out similarly to the aforementioned cases, with the exception that fixed distance restraints for non-bonded atoms (DANG) were left in place for the disordered fluorine atoms attached to B(2) (Figure 12).

Figure 12: Structure for the disordered BF4- anion due to a NCS-inversion center, in compound [Cu(Mes-dpa)(styrene)]BF4 with both parts of the disorders present. Thermal ellipsoids are shown at the 20% level. Adapted from J. J. Allen, C. E. Hamilton, and A. R. Barron, Dalton Trans., 2010, 11451.
Figure 12 (graphics12.jpg)

Disorder on a crystallographic mirror plane

Another instance in which the BF4- anion is disordered about a crystallographic symmetry element is that of [Cu(H-dpa)(1,5-cyclooctadiene)]BF4. In this instance fluorine atoms F(1) through F(4) are present in the asymmetric unit of the complex. Disordered atoms F(1A)-F(4A) were refined with 50% site occupancies, as B(1) lies on a mirror plane (Figure 13). For initial refinement cycles, similar distance restraints (SADI) were placed on all B-F and F-F distances, in addition to similar ADP restraints (SIMU) and rigid bond restraints (DELU) for all F atoms. Restraints were lifted for final refinement cycles, in which the boron atom lies on a crystallographic mirror plane, and all four fluorine atoms are reflected across.

Figure 13: Molecular structure for the anion in [Cu(H-dpa)(1,5-cyclooctadiene)]BF4 with both parts of the disordered BF4- present. For clarity, thermal ellipsoids are shown at the 20% level. Adapted from J. J. Allen and A. R. Barron, Dalton Trans., 2009, 878.
Figure 13 (graphics13.jpg)

Disorder on a non-crystallographic mirror plane

It has been observed that the BF4- anion can exhibit site occupancy disorder of the boron atom and one of the fluorine atoms across an NCS mirror plane defined by the plane of the other three fluorine atoms (Figure 14) modeling the entire anion as disordered (including the boron atom).

Figure 14: Disordered anion across the plane of three fluorine atoms. Adapted from J. T. Mague and S. W. Hawbaker, J. Chem. Cryst., 1997, 27, 603.
Figure 14 (graphics14.jpg)

Disorder of the boron atom core

The extreme case of a disorder involves refinement of the entire anion, with all boron and all fluorine atoms occupying more than two sites (Figure 15). In fact, some disorders of the latter types must be refined isotropically, or as a last-resort, not at all, to prevent one or more atoms from turning non-positive definite.

Figure 15: An example of a structure of a highly disordered BF4- anion refined with four site occupancies for all boron and fluorine atoms. Adapted from P. Szklarz, M. Owczarek, G. Bator, T. Lis, K. Gatner, and R. Jakubas, J. Mol. Struct., 2009, 929, 48.
Figure 15 (graphics15.jpg)

Bibliography

  • J. J. Allen and A. R. Barron, J. Chem. Cryst., 2009, 39, 935.
  • J. J. Allen and A. R. Barron, Dalton Trans., 2009, 878.
  • J. J. Allen, C. E. Hamilton, and A. R. Barron, Dalton Trans., 2010, 11451.
  • W. Clegg, Crystal Structure Determination, Oxford University Press, NY (1998).
  • IUCr Monographs on Crystallography, Ed. E. Domenicano and I. Hargittai, Oxford University Press, NY, (1992).
  • Crystallographic Computing 6: A Window on Modern Crystallography, Ed. H. D. Flack, L. Parkanyi, and K. Simon, Oxford University Press, NY (1993).
  • F. L. Hirshfield, Acta Cryst., 1976, A32, 239.
  • J. T. Mague and S. W. Hawbaker, J. Chem. Cryst., 1997, 27, 603.
  • S. Martinez-Vargas, R. Toscano, and J. Valdez-Martinez, Acta Cryst., 2007, E63, m1975.
  • P. Müller, Crystal Structure Refinement, A Crystallographer's Guide to SHELXL, Oxford University Press, UK (2006).
  • D. F. Mullica, S. L. Gibson, E. L. Sappenfield, C. C. Lin, and D. H. Leschnitzer, Inorg. Chim. Acta, 1990, 177, 89.
  • P. Szklarz, M. Owczarek, G. Bator, T. Lis, K. Gatner, and R. Jakubas, J. Mol. Struct., 2009, 929, 48.

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