Molecular structures of two metal tetrakis(tetrahydroborates), Zr(BH4)4 and U(BH4)4: Equilibrium conformations and barriers to internal rotation of the triply bridging BH4 groups

Article abstract of DOI:10.1021/ic020357z

The molecular structures of Zr[(μ-H)₃BH]₄ and U[(μ-H)3BH]4 have been investigated by density functional theory (DFT) calculations and gas electron diffraction (GED). The triply bridged bonding mode of the tetrahydroborate groups in the former is confirmed, but both DFT calculations and GED structure refinements indicate that the BH₄ groups are rotated some 12° away from the orientation in which the three bridging B-H bonds are staggered with respect to the opposing ZrB₃ fragment. As a result the symmetry of the equilibrium conformation is reduced from T_d to T. Bond distances and valence angles are as follows (DFT/GED): Zr-B = 232.2/232.4(5) pm; Zr-H_b = 214.8/214.4(6) pm; B-H_b = 125.3/127.8(8) pm; B-H_t = 119.4/118.8(17) pm; 〈ZrBH_b 66.2/65.6(3)°; the smallest dihedral angle of type τ(BZrBH_b) = 48/45(2)°. DFT calculations on Hf(BH₄)₄ indicate that the structure of this molecule is very similar to that of the Zr analogue. Matrix-isolation IR spectroscopy and DFT calculations on U(BH₄)₄ show that while the polymeric solid-state structure is characterized by terminal triply bridging and metal-metal bridging bidentate BH₄ groups, all BH₄ groups are triply bridging in the gaseous monomer. Calculations with one of the two nonbonding 5f electrons on U occupying an a₁ and the other distributed equally among the three t₂ orbitals indicate that the equilibrium conformation has T_d symmetry, i.e. that the three B-H_b bonds of each tetrahydroborate group are exactly staggered with respect to the opposing UB₃ fragment with τ(BUBH_b) = 60°. Calculations including spin-orbit interactions indicate that Jahn-Teller distortions from T_d symmetry are either absent or very small. The best agreement between observed and calculated GED intensity data was obtained for a model of T_d symmetry, but models of T symmetry with dihedral angles τ(BUBH_b) > 42° cannot be ruled out. Bond distances and valence angles are as follows (DFT/GED): U-B = 248.8/251.2(4) pm; U-H_b = 227.7/231.5(6) pm; B-H_b = 126.0/131.6(5) pm, B-H_t = 119.5/117.8(11) pm; 〈UBH_b = 65.6/63.1(3)°. It is suggested that the different equilibrium conformations of the three molecules are determined primarily by repulsion between bridging H atoms in different tetrahydroborate groups.

Full text of DOI:10.1021/ic020357z

Inorg. Chem. 2002, 41, 6646−6655
Molecular Structures of Two Metal Tetrakis(tetrahydroborates), Zr(BH )
4 4
and U(BH ) : Equilibrium Conformations and Barriers to Internal
4 4
Rotation of the Triply Bridging BH Groups
4
Arne Haaland,* Dmitry J. Shorokhov, Andrey V. Tutukin, and Hans Vidar Volden
Department of Chemistry, UniVersity of Oslo, Box 1033 Blindern, N-0315 Oslo, Norway
Ole Swang*
SINTEF, Applied Chemistry, Department of Hydrocarbon Process Chemistry, Box 124 Blindern,
N-0314 Oslo, Norway
G. Sean McGrady*
Department of Chemistry, King’s College London, Strand, London WC2R 2LS, U.K.
Nikolas Kaltsoyannis
Department of Chemistry, UniVersity College London, 20 Gordon Street, London WC1H 0AJ, U.K.
Anthony J. Downs,* Christina Y. Tang, and John F. C. Turner
Inorganic Chemistry Laboratory, UniVersity of Oxford, South Parks Road, Oxford, OX1 3QR, U.K.
Received May 20, 2002
The molecular structures of Zr[(µ-H)3BH]4 and U[(µ-H)3BH]4 have been investigated by density functional theory (DFT)
calculations and gas electron diffraction (GED). The triply bridged bonding mode of the tetrahydroborate groups in the
former is confirmed, but both DFT calculations and GED structure refinements indicate that the BH groups are rotated
4
some 12° away from the orientation in which the three bridging B−H bonds are staggered with respect to the opposing
ZrB fragment. As a result the symmetry of the equilibrium conformation is reduced from Td to T. Bond distances and
3
valence angles are as follows (DFT/GED): Zr−B ) 232.2/232.4(5) pm; Zr−H ) 214.8/214.4(6) pm; B−H ) 125.3/
b
b
127.8(8) pm; B−H ) 119.4/118.8(17) pm; ZrBH ) 66.2/65.6(3)°; the smallest dihedral angle of type τ(BZrBH ) )
t
b
b
48/45(2)°. DFT calculations on Hf(BH ) indicate that the structure of this molecule is very similar to that of the Zr
4 4
analogue. Matrix-isolation IR spectroscopy and DFT calculations on U(BH ) show that while the polymeric solid-state
4 4
structure is characterized by terminal triply bridging and metal−metal bridging bidentate BH groups, all BH groups are
4
4
triply bridging in the gaseous monomer. Calculations with one of the two nonbonding 5f electrons on U occupying an a1
and the other distributed equally among the three t2 orbitals indicate that the equilibrium conformation has Td symmetry,
i.e. that the three B−H bonds of each tetrahydroborate group are exactly staggered with respect to the opposing UB
b
3
fragment with τ(BUBH ) ) 60°. Calculations including spin−orbit interactions indicate that Jahn−Teller distortions from
b
Td symmetry are either absent or very small. The best agreement between observed and calculated GED intensity data
was obtained for a model of Td symmetry, but models of T symmetry with dihedral angles τ(BUBH ) > 42° cannot be
b
ruled out. Bond distances and valence angles are as follows (DFT/GED): U−B ) 248.8/251.2(4) pm; U−H ) 227.7/
b
231.5(6) pm; B−H ) 126.0/131.6(5) pm, B−H ) 119.5/117.8(11) pm; UBH ) 65.6/63.1(3)°. It is suggested that the
b
t
b
different equilibrium conformations of the three molecules are determined primarily by repulsion between bridging H
atoms in different tetrahydroborate groups.
Introduction
screening of the metal atom and the limited bridging ability
of the BH4 ligands results in remarkable volatility. This
-
Homoleptic tetrakis(tetrahydroborate) derivatives, M(BH4)4,
of the heavier transition metals, e.g. M ) Zr or Hf, and
actinides, e.g. M ) Th or U, are noteworthy on at least two
counts. First, the combination of high-symmetry, efficient
has led U(BH4)4, for example, to be considered as a means
of separating uranium isotopes or processing uranium-
containing materials.1-3 Second, the structures pose several
questions. (i) Given the variety of coordination modes and
6646 Inorganic Chemistry, Vol. 41, No. 25, 2002
10.1021/ic020357z CCC: $22.00 © 2002 American Chemical Society
Published on Web 11/14/2002

Molecular Structures of Zr(BH4)4 and U(BH4)4
the fluxionality of the BH4- ligands,4.5 how exactly are these
ligands linked to the metal center? (ii) How is the geometry
of the MB4 skeleton affected by the size of M or the presence
of more or less nonbonding electrons [e.g. 5f2 for U(IV)]?
(iii) How are the BH4- ligands oriented with respect to one
another and what sorts of barriers oppose their internal
rotation or changes of the coordination mode?
hedral arrangement. Two boron atoms (in cis positions) were
found at a distance of 253 pm from the uranium atom, while
the remaining four were approximately equidistant from two
metal atoms with an average U-B distance of 287 pm. The
positions of H atoms were determined in a later investigation
by neutron diffraction:12 the two B atoms at the shorter
distance belong to terminal BH4 groups bonded to the metal
atom through triple H bridges, while the four B atoms at the
longer distance belong to bridging BH4 groups bonded to
each of the two metal atoms through double H bridges. Each
uranium atom is thus surrounded by fourteen bridging
hydrogen atoms. Several years later, Charpin and co-workers
described a second crystalline form in which the U atom
and the B atoms of the four bridging, bidentate BH4 groups
are coplanar, while the terminal, tridentate BH4 groups
occupy trans positions.13
The molecular structure of zirconium(IV) tetrakis(tetrahy-
droborate), Zr(BH4)4, was first determined by X-ray crystal-
lography at -160 °C.6 The compound was found to be
monomeric in the solid phase with each tetrahydroborate
group bonded to the metal atom through triple H bridges,
M[(µ-H)3BH]4. The positions of the bridging hydrogen atoms
could not be determined with accuracy, but it was noted that
the molecules occupy crystal sites of Td symmetry, whichs
barring disordersimplies that each (µ-H)3BH group is
oriented in such a manner that the three bridging B-H bonds
are staggered with respect to the U-B bonds of the opposing
UB3 fragment. A neutron diffraction study of the hafnium
analogue at 110 K showed that the crystal structures of Hf-
(BH4)4 and Zr(BH4)4 are isomorphous; there were no
indications of disorder, and the bridging hydrogen atoms
were located at positions corresponding to staggered BH4
groups and molecular Td symmetry.7 A subsequent gas
electron diffraction study of Zr(BH4)4 showed that the
molecule retains the M[(µ-H)3BH]4 structure in the gas
phase.8 The thermal average orientation of the tetrahydrobo-
rate groups was, however, found to deviate from the
staggered, and the symmetry of the average structure was
consequently T rather than Td. Since no corrections were
made for thermal motion, the apparent symmetry lowering
may be due to large-amplitude librational motion of the
tetrahydroborate groups rather than distortion of the equi-
librium structure. Subsequent careful studies of the IR and
Raman spectra failed to settle unequivocally whether the
equilibrium structure of Zr(BH4)4 has T or Td symmetry.9,10
Despite its polymeric crystal structure, U(BH4)4 vaporizes
at near-ambient temperatures. On the evidence of molecular
weight14 and mass spectrometric15 measurements, the vapor
consists of monomeric U(BH4)4 molecules. Similarities in
the IR spectra of U(BH4)4 and Zr(BH4)4 vapors have been
taken to imply that the two molecules have analogous
structures in the gas phase,9,10,15,16 and the same inference
has been drawn from the UV photoelectron spectra of the
gaseous molecules M(BH4)4, where M ) Zr, Hf, or U.17
A
slightly different view comes from the optical spectra of
molecular crystals of Hf(BH4)4 doped with U(BH4)4, which
have been interpreted18 on the basis of discrete U(BH4)4
molecules with overall Td symmetry.
-
The coordination of BH4 is a matter of some relevance
to the activation of the isoelectronic but much less basic CH4
molecule.19 That the issue is far from straightforward,
however, is demonstrated by the discovery that the crystal
11-13
structures of U(BH4)4
and several other tetrahydrobo-
rates, e.g. Ti(BH4)3(PMe3)2,19 reveal molecular units in which
the metal atom is surrounded by BH4 groups linked to it
-
through different coordination modes. In view of this and
other uncertainties, closer examination of U(BH4)4 vapor
appeared warranted to establish the structure of the gaseous
monomer. At the same time, differences in the size and
electronic makeup of Zr(IV) and U(IV) (with its two 5f
electrons) urged a comparison of U(BH4)4 with Zr(BH4)4.
Accordingly we present the results (i) of quantum chemical
density functional theory (DFT) calculations for the three
molecules Zr(BH4)4, Hf(BH4)4, and U(BH4)4 and (ii) of a
new gas electron diffraction study of Zr(BH4)4 plus the first
A single-crystal X-ray diffraction study of uranium(IV)
tetrakis(tetrahydroborate), U(BH4)4, published by Bernstein
and co-workers11 30 years ago, showed that this compound
is associated in the solid state; each uranium atom is
surrounded by six boron atoms in an approximately octa-
(1) Gmelin Handbuch der Anorganischen Chemie, Uran; Erga¨nzungsband;
Teil C1; System-Nummer 55; Springer-Verlag: Berlin and Heidelberg,
1977; pp 73-79.
(2) Katz, J. J., Seaborg, G. T., Morss, L. R., Eds. The Chemistry of the
Actinide Elements, 2nd ed.; Chapman and Hall: London and New
York, 1986; pp 255-258, 1432.
(3) See, for example: Batelle-Institut, E. V. Fr. Demande 2 1972, 119,
214. Bernstein, E. R. U.S. Pat. 4,032,419, 1977. Coleman, J. H.; Marks,
T. J. Fr. Demande 2 1979, 408, 382.
(12) Bernstein, E. R.; Hamilton, W. C.; Keiderling, T. A.; La Placa, S. J.;
Lippard, S. J.; Mayerle, J. J. Inorg. Chem. 1972, 11, 3009.
(13) Charpin, P.; Nierlich, M.; Vigner, D.; Lance, M.; Baudry, D. Acta
Crystallogr. 1987, C43, 1465.
(14) Schlesinger, H. I.; Brown, H. C. J. Am. Chem. Soc. 1953, 75, 219.
(15) Paine, R. T.; Light, R. W.; Nelson, M. Spectrochim. Acta, Part A
1979, 35, 213.
(16) Cunha, R. D.; Kaimal, V. N. P.; Kartha, V. B. Spectrochim. Acta,
Part A 1980, 36, 907.
(17) Downs, A. J.; Egdell; R. G.; Orchard, A. F.; Thomas, P. D. P. J. Chem.
Soc., Dalton Trans. 1978, 1755.
(4) Marks, T. J.; Kolb, J. R. Chem. ReV. 1977, 77, 263.
(5) Ephritikhine, M. Chem. ReV. 1997, 97, 2193.
(6) Bird, P. H.; Churchill, M. R. J. Chem. Soc., Chem. Commun. 1967,
403.
(7) Broach, R. W.; Chuang, I.-S.; Marks, T. J.; Williams, J. M. Inorg.
Chem. 1983, 22, 1081.
(8) Plato, V.; Hedberg, K. Inorg. Chem. 1971, 10, 590.
(9) Davies, N.; Wallbridge, M. G. H.; Smith, B. E.; James, B. D. J. Chem.
Soc., Dalton Trans. 1973, 162.
(10) Smith, B. E.; Shurvell, H. F.; James, B. D. J. Chem. Soc., Dalton
Trans. 1978, 710.
(11) Bernstein, E. R.; Keiderling, T. A.; Lippard, S. J.; Mayerle, J. J. J.
Am. Chem. Soc. 1972, 94, 2552.
(18) Bernstein, E. R.; Keiderling, T. A. J. Chem. Phys. 1973, 59, 2105.
(19) Jensen, J. A.; Girolami, G. S. J. Chem. Soc., Chem. Commun. 1986,
1160. Jensen, J. A.; Wilson, S. R.; Girolami, G. S. J. Am. Chem. Soc.
1988, 110, 4977.
Inorganic Chemistry, Vol. 41, No. 25, 2002 6647

Haaland et al.
by Wallbridge et al.27 Freshly recrystallized, finely ground LiBH4
(2.20 g, 110 mmol, ex Aldrich) and ZrCl4 (3.75 g, 16.2 mmol, ex
Aldrich) were mixed gently under vacuum until reaction occurred
(after about 10 min) with the evolution of heat and the formation
of what appeared to be a sticky white mass. The mixture was then
stirred for 1 h at room temperature with the aid of a glass-coated
magnetic “flea”. After cooling to 77 K, any noncondensable gas
was removed; the reaction mixture was then warmed to room
temperature under continuous pumping through a trap cooled to
163 K where the Zr(BH4)4 condensed as a white solid. The crude
product was purified by revaporization at 273 K and trapping at
195 K. The yield (1.8 g, 12.0 mmol) was 75% of that based on
quantitative conversion of the ZrCl4 taken. After the purity of the
sample had been checked by reference to its IR spectrum,4,5,27 the
material was stored until needed in evacuated Pyrex glass ampules
each equipped with a break seal.
Uranium tetrakis(tetrahydroborate), U(BH4)4 was prepared in a
novel manner by solid-state metathesis between UCl4 (ex BNFL)
and a 2- to 10-fold excess of freshly recrystallized LiBH4 (ex
Aldrich). The finely ground solids, together with some glass beads,
were introduced into a Pyrex glass reaction vessel closed by a
greaseless (Young’s) valve and connected to an all-glass train of
U-traps. Mixing of the powders in the evacuated apparatus (P <
10-4 Torr) was achieved by the slow stirring action of a glass-
coated magnetic flea. The mixture was allowed to react for up to
2 weeks at room temperature, the volatile products being fraction-
ated in vacuo. The purity of the sample was checked by reference
to the IR spectrum of an annealed solid film at 77 K.13
Spectroscopic Measurements. The IR spectra of Zr(BH4)4 and
U(BH4)4 in the solid and matrix-isolated states were measured in
the region 400-4000 cm-1 with a Mattson “Galaxy” or a Nicolet
“Magna” 560 FT-IR spectrometer. Solid Ar or N2 matrixes doped
with these molecules, typically at dilutions estimated to be ca. 1:200,
were prepared by continuous deposition of the tetrahydroborate
vapor with an excess of the matrix gas on a CsI window cooled to
ca. 12 K by means of a Displex closed-cycle refrigerator (Air
Products Model CS 202). Solid films of the tetrahydroborates were
analyzed by causing the vapor to condense on a CsI window
contained in an evacuated shroud and maintained at 77 K.
Gas Electron Diffraction. The gas electron diffraction data for
Zr(BH4)4 and U(BH4)4 were recorded on the Baltzers KDG2 unit
at the University of Oslo28 with a metal inlet system at 22 ( 2 (Zr)
or 62-65 °C (U) and nozzle-to-plate distances of approximately
50 and 25 cm. The scattering pattern of Zr(BH4)4 was recorded on
Fuji Imaging Plates BAS-III (three plates for each nozzle-to-plate
distance) and scanned on a Fujifilm BAS 1800 II imaging plate
reader. The relative intensity data were processed using a program
written by S. Samdal, D. J. Shorokhov, and T. G. Strand.29 The
scattering pattern of U(BH4)4 was recorded on Kodak Electron
Image Plates; six plates from each distance were scanned on an
Agfa Arcus II scanner and the data processed as described
elsewhere.30 Atomic scattering factors were taken from ref 31.
Backgrounds were drawn as least-squares adjusted polynomials to
the difference between the total experimental and calculated
such study of U(BH4)4. The calculations indicate that the
equilibrium conformations of Zr(BH4)4 and Hf(BH4)4 have
T rather than Td symmetry, a conclusion confirmed by the
GED structure refinement. By contrast, calculations and
experiment favor Td symmetry for U(BH4)4.
Density Functional Theory Calculations
The DFT calculations on M(BH4)4, M ) Ti, Zr, Hf, or U,
were carried out using the ADF program system developed
by Baerends et al.20,21 Orbitals were described by Slater type
orbital (STO) basis sets. The frozen core approximation was
used for all atoms except H. For B the 1s orbital was kept
frozen in its atomic shape. For Ti the orbitals were frozen
up to and including 2p, for Zr up to and including 3d, for
Hf up to and including 4f, and for U up to and including 5d.
The number of unfrozen basis functions, in order of
increasing angular momentum, was (2,1) for H, (2,2,1) for
B, (5,3,3) for Ti, (5,4,3) for Zr, (5,4,3,1) for Hf, and (4,3,3,3)
for U, thus yielding basis sets of TZV quality for the metal
atoms and of DZVP quality for B and H. Slater exchange
and the Vosko-Wilk-Nusair parametrization of the LDA
correlation energy,22 with the gradient correction of Becke23
for exchange and of Perdew24 for correlation, were used for
the exchange-correlation energies. Most calculations were
carried out with the accuracy of numerical integrations set
to 10-6.5 for each integral.21 This is believed to give a
numerical noise less than 0.5 kJ mol-1 in the final energies.
Calculation of the force field of the Td model of U(BH4)4
and the search for possible Jahn-Teller distorted structures
were, however, carried out with an accuracy of 10-9.5
.
Exploratory structure optimizations were carried out with
an earlier version of the ADF program (Release 2.3.0) and
relativistic effects taken into account through the quasi-
relativistic Pauli formalism.25 The final results quoted in this
article were, however, all obtained with the 2000.02 Release
and the zero-order regular approximation (ZORA).
Force constants were calculated numerically from analyti-
cal gradients. Vibrational frequencies, root-mean-square
amplitudes of vibration, l, and vibrational correction terms,
D ) ra - rR¢, were calculated by the program ASYM40.26
Experimental Section
Syntheses. Zirconium tetrakis(tetrahydroborate), Zr(BH4)4, was
prepared by the reaction between LiBH4 and ZrCl4 in the absence
of a solvent, broadly in accordance with the procedure described
(20) ADF Program System, Release 2000.02, Scientific Computing and
Modeling NV, Vrije Universiteit; Theoretical Chemistry, De Boelelaan
1083, 1081 HV Amsterdam, The Netherlands. A description of the
program system is found in the following publications: Baerends, E.
J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41. Versluis, L.; Ziegler,
T. J. Chem. Phys. 1988, 88, 322. Fonseca Guerra, C.; Snijders, J. G.;
te Velde, G.; Baerends, E. J. Theor. Chem. Acc. 1998, 99, 391.
(21) te Velde, G.; Baerends, E. J. J. Comput. Phys. 1992, 99, 84.
(22) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200.
(23) (a) Becke, A. D. Phys. ReV. 1986, A33, 2786. (b) Becke, A. D. ACS
Symp. Ser. 1989, 394, 165. (c) Becke, A. D. Int. J. Quantum Chem.
1989, Symp. No. 23, 599. (d) Becke, A. D. Phys. ReV. 1988, A38,
3098.
(27) Davies, N.; Saunders: D.; Wallbridge, M. G. H. J. Chem. Soc. A 1970,
2915.
(28) Zeil, W.; Haase, J.; Wegmann, L. Z. Instrumentenkd. 1966, 74, 84.
(29) Gundersen, S.; Samdal, S.; Shorokhov, D. J.; Strand, T. G.; Volden,
H. V. The Norwegian Electron Diffraction Group, Annual Report
2000, Oslo/Trondheim, 2001.
(30) Gundersen, S.; Strand, T. G. J. Appl. Crystallogr. 1996, 29, 638.
(31) Ross, A. W.; Fink, M.; Hilderbrandt, R. In International Tables for
Crystallography; Wilson, A. J. C., Ed.; Kluwer Academic Publish-
ers: Dordrecht, The Netherlands, 1992; Vol. C, p 245.
(24) (a) Perdew, J. P. Phys. ReV. 1986, B33, 8822. (b) Perdew, J. P. Phys.
ReV. 1986, B34, 7406.
(25) Ziegler, T.; Tschinke, V.; Baerends, E. J.; Snijders, J. G.; Ravenek,
W. J. Phys. Chem. 1989, 93, 3050.
(26) Hedberg, L.; Mills, I. M. J. Mol. Spectrosc. 1993, 160, 117.
6648 Inorganic Chemistry, Vol. 41, No. 25, 2002

Molecular Structures of Zr(BH4)4 and U(BH4)4
Figure 1. Left: Ball-and-stick molecular model of Zr(BH4)4, symmetry
T. Right: Space-filling model showing the Zr and twelve bridging H atoms.
Program Pluton.33
Figure 3. Experimental (dots) and calculated (line) radial distribution
curves for Zr(BH4)4. The vertical scale is arbitrary. Major interatomic
distances are indicated by bars of height approximately proportional to the
area under the corresponding peak. Artificial damping constant k ) 0.12
pm2.
Figure 2. Above: Experimental (dots) and calculated (line) modified
molecular intensity curves for Zr(BH4)4. The vertical scale is arbitrary.
Below: Difference curves.
Figure 4. Above: Experimental (dots) and calculated (line) modified
molecular intensity curves for U(BH4)4. The vertical scale is arbitrary.
Below: Difference curves.
molecular intensities. Structure refinements by least-squares cal-
culations on the molecular intensities were carried out using the
program KCED 26 written by G. Gundersen, S. Samdal, H. M.
Seip, and T. G. Strand. The calculated intensity contained terms
for all interatomic distances including nonbonded H‚‚‚H distances.
Since the refinements had been carried out with diagonal weight
matrixes, the estimated standard deviations listed in Tables 1 and
2 have been multiplied by a factor of 2.5 to include uncertainty
due to data correlation32 and expanded to include a scale uncertainty
of 0.1%.
Structure refinements of Zr(BH4)4 were based on a molecular
model of T symmetry (see Figure 1) characterized by five
independent structure parameters, viz. the M-B bond distances,
the terminal and bridging B-H distances, B-Ht and B-Hb, the
valence angle HtBHb, and the torsional angle τ(BMBHb). The
five independent structure parameters were refined along with the
six root-mean-square vibrational amplitudes indicated in Table 1.
The final structure refinements of U(BH4)4 were based on a model
of Td symmetry. Four structure parameters were refined along with
the six root mean square vibrational amplitudes indicated in Table
4.
Figure 5. Experimental (dots) and calculated (line) radial distribution
curves for U(BH4)4. The vertical scale is arbitrary. Major interatomic
distances are indicated by bars of height approximately proportional to the
area under the corresponding peak. Artificial damping constant k ) 0.12
pm2.
Calculated and observed intensity curves and radial distribution
curves are compared in Figures 2-5. We consider the agreement
satisfactory.
Results and Discussion
Zirconium Tetrakis(tetrahydroborate). The ADF pro-
gram allows structure optimization under Td but not under
T symmetry. Structure optimization of Zr(BH4)4 without
imposition of symmetry, however, converged to a model of
T symmetry with the structure parameters listed in Table 1.
Calculation of the molecular force field followed by normal
(32) Seip, H. M.; Strand, T. G.; Stølevik, R. Chem. Phys. Lett. 1969, 3,
617.
(33) Spek, A. L. The Euclid Package. In Computational Crystallography;
Sayre, D., Ed.; Clarendon Press: Oxford, U.K., 1982. The hydrogen
atoms have been drawn with van der Waals radii of 120 pm; the radius
of Zr has been reduced to 200 pm for clarity.
Inorganic Chemistry, Vol. 41, No. 25, 2002 6649

Haaland et al.
Table 1. Interatomic Distances (r), Root Mean Square Vibrational
Amplitudes (l), Valence Angles, and Torsional Angles in Zr(BH4)4
Obtained by Density Functional Theory (ADF-ZORA) Calculations or
Gas Electron Diffraction (GED)a
The barrier to concerted rotation of the four BH4 groups
into a staggered orientation was estimated by optimizing a
Td(stag) model. The barrier thus obtained was V(60°) ) 1.0
kJ mol-1. The energy difference is so small that intermo-
lecular forces well may lead to a Td molecular structure in
the crystalline phase.
ADF-ZORA
GED
symmetry
T
T
Bond Distances
The energy required to rotate one BH4 group into an
eclipsed orientation was estimated by optimizing a molecular
model with three staggered and one eclipsed BH4 group and
overall C3V symmetry. The rotational barrier thus obtained
was 13.9 kJ mol-1. Optimization of a Td (ecl) model yielded
a barrier to concerted rotation of the four BH4 groups into
eclipsed orientations of V(0°) ) 123 kJ mol-1, more than
eight times larger than the barrier to rotation of one group.
What is the origin of these barriers? In Figure 1 we present
a space-filling model of Zr and the twelve bridging H atoms.
It is seen that each bridging H atom is in van der Waals
contact with two bridging H atoms in neighboring BH4
groups. The distance between them is Hb‚‚‚Hb ) 235 pm,
slightly shorter than the sum of their van der Waals radii,
240 pm,35 thus indicating a slightly repulsive interaction. The
total number of such short Hb‚‚‚Hb contacts in the molecule
is twelve. Concerted internal rotation of the BH4 groups by
12° to bring them into a perfectly staggered Td orientation
reduces these twelve distances to 231 pm, while the energy
of the molecule increases by 1.0 kJ mol-1. We suggest,
therefore, that the barrier to concerted rotation is due to a
slightly increased van der Waals repulsion between bridging
H atoms.
Rotation of one BH4 group into an eclipsed orientation
yields a C3V structure also characterized by twelve short Hb‚
‚‚Hb contacts. Nine of these distances are indistinguishable
from those of the Td (stag) model, while three have been
reduced by about 7 pm to 225 pm. The reduction of these
distances is hardly sufficient to explain an energy increase
of 13.9 kJ mol-1. We suggest that the energy increase is
due to an inherent, electronic barrier to internal rotation of
the BH4 group. Concerted rotation of the four tetrahydrobo-
rate groups into eclipsed orientations yields a model char-
acterized by six very short Hb‚‚‚Hb contacts at 178 pm, and
the energy rises to 123 kJ mol-1 above the equilibrium
conformation. We suggest that half of this energy barrier,
4 × 13.9 kJ mol-1 or about 56 kJ mol-1, is due to the inherent
barriers to internal rotation of the four BH4 groups, while
the remainder is due to increased repulsion between bridging
hydrogen atoms.
re
l
ra
l
Zr-B
Zr-Hb
B-Hb
B-Ht
232.2
214.8
125.3
119.4
5.8
14.0
9.1
8.3
232.4(5)
214.4(6)
127.8(8)
7.1(4)
14.8(13)
[9.1]
118.8(17)
[8.3]
Nonbonded Distances
re
l
ra
l
Z‚‚‚Ht
B‚‚‚B
B‚‚‚Hb
B‚‚‚Hb
B‚‚‚Hb
B‚‚‚Ht
351.6
379.1
307.8
335.3
421.1
481.5
9.6
11.7
20.3
21.0
14.8
16.8
350(2)
379(1)
303(2)
339(2)
420(1)
479(2)
15(3)
11.3(12)
[20.3]
[21.0]
12(2)
18(3)
Valence Angles
e
R
<ZrBHb
<HbBHb
<HbBHt
66.2
104.8
113.8
65.6(3)
104.2(4)
114.4(3)
Torsional Angle
τe
48.2
τR
45(2)
0.036
τ(BZrBHb)
R-factorb
a Interatomic distances and vibrational amplitudes in picometers, angles
in degrees. Estimated standard deviations in parentheses in units of the last
digit. Nonrefined amplitudes in square brackets. b R ) x[Sw(Iobs - Icalc)2/
Sw(Iobs)2].
coordinate analysis yielded only real vibrational frequencies,
thus confirming that this structure corresponds to a minimum
on the potential energy hypersurface. The smallest torsional
angle of type τ(BZrBHb) is calculated to be 48°. If this angle
is 60°, each tetrahydroborate group is oriented in such a way
that the three B-Hb bonds are staggered with respect to the
opposing ZrB3 fragment, and the molecular symmetry is Td.
In the following we shall refer to this conformation as Td
(stag). If the torsional angle is 0°, the three B-Hb bonds of
each tetrahydroborate group are eclipsing the opposing Zr-B
bonds, and the symmetry will again be Td. We shall refer to
this conformation as Td (ecl). The calculations thus yield an
equilibrium conformation of Zr(BH4)4, which is closer to
staggered than eclipsed. The lowest vibrational mode (183
cm-1) involves concerted internal libration of the (µ-H3BH)
groups about the Zr-B bond axes under retention of
molecular T symmetry.
Least-squares structure refinement of a model of T
symmetry to the gas electron diffraction data yielded structure
parameters in very good agreement with the calculated ones
(see Table 1). In particular the torsional angle, which has
been corrected for thermal motion, was found to be 45(2)°,
i.e. significantly smaller than 60°. When structure refinements
were carried out on a staggered Td model, the R-factor
increased from 3.6 to 4.5% corresponding to an R-factor ratio
of R ) 1.25. The use of Hamilton’s R-factor ratio test34
confirmed that the Td model may be rejected at the 99.5%
confidence level. Thus both calculation and experiment
indicate that the equilibrium structure has T rather than Td
symmetry.
If this suggestion is correct, the rotational barriers at the
Td staggered and eclipsed conformations should increase if
the Zr atom is replaced by a smaller atom like Ti. We
decided, therefore to carry out similar ADF calculations on
the model compound Ti(BH4)4.36,37 The results are sum-
marized in Table 2; the equilibrium conformation of Ti(BH4)4
(34) Hamilton, W. C. Statistics in Physical Science; The Ronald Press
Co.: New York, 1964; pp 157-162 and 216-222. The number of
observed intensity values is 174. These values are correlated, and we
assumed them to be equivalent to 174/2.5 ) 70 independent observa-
tions.32 The number of refined parameters (including two scale factors)
was 15, and the dimension of the hypothesis one.
(35) Bondi, A. J. Phys. Chem. 1964, 68, 441.
6650 Inorganic Chemistry, Vol. 41, No. 25, 2002

Molecular Structures of Zr(BH4)4 and U(BH4)4
Table 2. Molecular Conformations of M[(µ-H)3BH]4, M ) Ti, Zr, or Hf; Dihedral Angles (deg), Relative Energies (kJ mol-1), and M-B Bond and
Shortest Distances (pm) between Bridging H Atoms in Different Tetrahydroborate Groups Obtained by DFT Calculations
M
symmetry(conformn)
τ(BMBHb)
47
∆E
M-B
Hb‚‚‚Hb
Ti
Ti
Ti
Ti
Zr
Zr
Zr
Zr
Hf
Hf
Hf
Hf
T
0
217
217
12 × 212
12 × 206
Td (stag)
C3V
Td (ecl)
T
Td (stag)
C3V
Td (ecl)
T
60
2.7
24.6
195
0
1.0
13.9
123
0
2.7
15.5
129
3 × 60; 1 × 0
3 × 218; 1 × 218
6 × 209; 3 × 203; 3 × 206
6 × 162; 24 × 312
12 × 235
0
224
232
232
48
60
12 × 231
3 × 60; 1 × 0
3 × 232; 1 × 233
6 × 231; 3 × 225; 3 × 232
6 × 178; 24 × 326
12 × 237
0
236
231
232
47
Td (stag)
C3V
Td (ecl)
60
3 × 60; 1 × 0
0
12 × 231
3 × 232, 1 × 232
6 × 231; 3 × 226; 3 × 232
6 × 178; 24 × 327
236
Table 3. Bond Distances (pm) and Valence and Torsional Angles (deg)
in Hf(BH4)4 Obtained by Density Functional Theory (ADF-ZORA)
Calculations or Single Crystal Neutron Diffraction at 110 K
differ by less than 1 pm and valence angles by less than a
degree. The dihedral angles τ(BMBHb) also differ by less
than 1°, as is to be expected if the orientation is determined
by repulsion between bridging hydrogen atoms. The calcu-
lated barriers to concerted rotation of four BH4 groups into
staggered orientations differ by about 2 kJ mol-1 and the
barriers to rotation into eclipsed orientations by 6 kJ mol-1,
the barriers of the hafnium compound being the larger in
both cases (see Table 2).
ADF-ZORAa
neutron diffractionb
symmetry
T
Td
Bond Distances
231.5
Hf-B
Hf-Hb
B-Hb
B-Ht
228.1(8)
213.0(9)
123.5(10)
115.0(19)
215.5
125.2
119.2
Valence Angles
66.8
The agreement between calculated bond distances and
valence angles and those obtained by neutron diffraction at
110 K7 is as close as is to be expected considering that the
latter have not been corrected for thermal motion (see Table
3). However, while the calculations indicate that the equi-
librium symmetry is T, the neutron diffraction study indicates
the molecular structure in the solid state to be Td. Since the
calculations indicate that rotation of the BH4 groups into
staggered orientations requires no more than about 3 kJ
mol-1, the orientations adopted in the crystalline phase may
well be determined by intermolecular forces.
HfBHb
HbBHb
HbBHt
67.1(5)
105.8(6)
112.9(10)
105.5
113.2
Torsional Angle
47.4
τ(BHfBHb)
60.0c
a This work. b Reference 2. Uncorrected for thermal motion. c Determined
by the space group.
is calculated to be very similar to that of Zr(BH4)4, in
particular with torsional angle τ(BTiBHb) ) 47°. The M-B
bond distance is, however, about 15 pm shorter than in the
Zr compound, and the distances between H atoms in
neighboring BH4 groups are consequently reduced by about
20 pm to 212 pm. The barrier to concerted rotation of four
tetrahydroborate groups into staggered orientations is in-
creased from 1.0 to 2.7 kJ mol-1, and the barrier to concerted
rotation into eclipsed orientations from 123 to 195 kJ mol-1.
Hafnium Tetrakis(tetrahydroborate). Structure optimi-
zation of Hf(BH4)4 converged to a model of T symmetry
and the structure parameters listed in Table 3. Comparison
of bond distances in the tetrahalides MX4, M ) Zr or Hf;
X ) F, Cl, Br or I, suggests that, as a result of the well-
known lanthanide contraction38 and relativistic effects,39 the
bonding radius of Hf is marginally (between 0 and 2 pm)
smaller than that of Zr,40 and Hf-B distances are indeed
calculated to be marginally shorter than the Zr-B distances
in Zr(BH4)4. The structures of the tetrahydroborate groups
in the two compounds are also very similar; bond distances
Uranium Tetrakis(tetrahydroborate). While Zr(BH4)4
and Hf(BH4)4 are closed shell molecules, U(BH4)4 contains
two nonbonding electrons in 5f atomic orbitals on the metal
atom. These electrons are expected to enter different f-orbitals
with parallel spins to yield a triplet electronic ground state.
Density functional theory calculations without spin-orbit
coupling were therefore carried out on triplet states, with a
set of separate Kohn-Sham orbitals for each spin.
Exploratory structure optimizations were carried out with
a start model with two bidentate and two tridentate tetrahy-
droborate groups, i.e. on U[(µ-H)2BH2]2[(µ-H)3BH]2, as well
as on a start model with one bidentate and three tridentate
groups; i.e. on U[(µ-H)2BH2][(µ-H)3BH]3. When structure
optimizations were carried out without symmetry restrictions,
the bidentate BH4 groups rotated into tridentate bonding
modes. The IR spectra of the matrix isolated molecule (see
below) confirm that the equilibrium structure of the molecule
indeed is characterized by four tridentate tetrahydroborate
groups.
(36) To the best of our knowledge, Ti(BH4)4 has never been prepared and
may not exist under normal conditions. Thus the reaction of TiBr4
with LiBH4 gives Ti(BH4)3 rather than Ti(BH4)4.37
(37) Dain, C. J.; Downs, A. J.; Goode, M. J.; Evans, D. G.; Nicholls, K.
T.; Rankin, D. W. H.; Robertson, H. E. J. Chem. Soc., Dalton Trans.
1991, 967.
(38) Kaltsoyannis, N.; Scott, P. The f Elements; Oxford University Press:
Oxford, U.K., 1999.
(39) Pyykko¨, P.; Snijders, J. G.; Baerends, E. J. Chem. Phys. Lett. 1981,
83, 432.
When structure optimization was continued with four
tridentate tetrahydroborate groups, the structure approached
Td symmetry, but did not converge. A molecular field of Td
symmetry splits the 5f manifold into one nondegenerate
orbital of a1 and two triply degenerate sets of t1 and t2
(40) Hargittai, M. Chem. ReV. 2000, 100, 2233.
Inorganic Chemistry, Vol. 41, No. 25, 2002 6651

Haaland et al.
Table 4. Interatomic Distances (r), Root Mean Square Vibrational
Amplitudes (l), Valence Angles, and Torsional Angles in U(BH4)4
Obtained by Density Functional Theory (ADF-ZORA) Calculations or
Gas Electron Diffraction (GED)a
even for the Td(stag) conformation; there is no need for
distortion of this conformation in order to reduce van der
Waals repulsion.
Structure optimizations under Td symmetry were also
carried out for the singly excited states with the 5f-electron
ADF-ZORA
Td
GED
symmetry
Td
2
1
1
1 1
configurations t2 , a1 t1 , or t2 t1 . Calculations with t1 or t2
electrons distributed equally over the three degenerate orbitals
yielded energies 39, 55, and 102 kJ mol-1, respectively,
Bond Distances
re
l
ra
l
U-B
U-Hb
B-Hb
B-Ht
248.8
227.7
126.0
119.5
6.2
13.6
9.2
8.4
251.2(4)
231.5(6)
131.6(5)
117.8(11)
7.0(3)
17.3(10)
[9.2]
1
1
above that of the a1 t2 configuration. See Table 5. Even
though spin-orbit coupling reduced the relative energy of
the t22 configuration to 21 kJ mol-1, we believe these energies
to be too high for molecules in excited electronic states to
be present in detectable quantities at the temperature of our
GED experiment (about 340 K).
[8.4]
Nonbonded Distances
re
l
ra
l
U‚‚‚Ht
B‚‚‚B
B‚‚‚Hb
B‚‚‚Hb
B‚‚‚Ht
368.4
406.4
345.7
447.5
508.7
9.9
18.5
42.1
16.3
24.3
368(1)
409(1)
347(5)
445(1)
507(1)
8.9(14)
15.9(17)
[42.1]
14(3)
Finally we explored possible Jahn-Teller (J-T) distor-
1
tions of the Td structure with the ground state a1 t21 electron
24(4)
Valence Angles
configuration.41 Distortion along an e vibrational mode yields
an elongated or compressed tetrahedral structure of D2d
symmetry. At the same time the t2 f-orbitals are split into a
nondegenerate orbital of b2 and two degenerate orbitals of e
symmetry. Structure optimization converged to a slightly
compressed tetrahedral structure with the electron configu-
ration a1 b2 . The energy was 12.8 kJ mol-1 below that
calculated for the Td structure.43 Examination of the optimal
D2d structure showed that the deformations from Td symmetry
were very small: two BUB valence angles were increased
by less than 1°, while the remaining four were decreased by
less than 0.5°. UBHb and HBH valence angles were all
changed by less than 1°. Such distortions are surely too small
to be detected by GED.
e
R
UBHb
HbBHb
HbBHt
65.6
104.1
114.4
63.1(3)
101.1(4)
116.9(3)
Torsional Angle
τe
60
τR
τ(BUBHb)
R-factor
[60]b
1
1 42
0.034
a Interatomic distances and vibrational amplitudes in picometers, angles
in degrees. Estimated standard deviations in parentheses in units of the last
digit. Nonrefined parameters in square brackets. b See comment in text.c R
) V[Sw(Iobs - Icalc)2/Sw (Iobs)2].
symmetry. One nonbonding electron was found to occupy
the 5f a1 orbital, the other flitted from one 5f t2 orbital to
another.
The Jahn-Teller Td to D2d distortion energy obtained at
the DFT computational level is so small that we decided to
investigate the effect of spin-orbit coupling. Combination
of the a1 f-orbital of the Td structure with the appropriate
spin functions (R or â) gives a pair of degenerate spin-
orbitals of e1/2 symmetry, while spin-orbit coupling splits
the 6-fold degenerate spin-orbitals based on the t2 f-orbitals
into a quadruply degenerate u3/2 and a doubly degenerate
e5/2 orbital. Single point calculations on the optimized Td
model indicated that the most stable electron configuration
U(BH4)4 with Td symmetry and the f-electron configuration
1
1
a1 t2 is orbitally degenerate and may be subject to Jahn-
Teller distortion. We shall return to this question below. For
the moment we solved the convergence problem by continu-
ing the calculations under Td symmetry and the t2 electron
distributed equally between the three degenerate orbitals.
(Population analysis of the optimized wave function indicates
that the t2 orbitals have 96% U f-character, while the a1
orbital has 90% U f- and 6% U s-character). The optimized
structure parameters are listed in Table 4. Calculation of the
molecular force field and normal coordinate analysis yielded
no imaginary frequencies and thus confirmed that the Td
structure represents a minimum on the potential energy
hypersurface (at this computational level). The lowest
vibrational mode (46 cm-1) is of a2 symmetry and involves
concerted internal rotation of the tetrahydroborate groups.
The barrier to concerted internal rotation of the four BH4
groups into eclipsed orientations is calculated to be 49 kJ
mol-1, less than one-half of the corresponding barrier in the
Zr analogue.
1
is e1/2 u3/21, while a single point calculation on the optimized
D2d structures indicated that the most stable electron con-
1
1
figuration is e1/2 e3/2 (where e1/2 and e3/2 refer to the
irreducible representations of the group D2d*). The calcula-
tions including spin-orbit coupling indicate that the energy
of the D2d structure is 4.5 kJ mol-1 higher than that of the
Td structure. See Table 5.
Distortion of the Td structure along a t2 vibrational mode
yields a trigonal pyramidal structure of C3V symmetry. At
the same time the t2 f-orbitals are split into a nondegenerate
orbital of a1 and two degenerate orbitals of e symmetry.
Structure optimization without spin-orbit coupling con-
Comparison of the bond distances in ZrCl4 and UCl4
indicates that the bonding radius of U is about 18 pm larger
than that of Zr,40 and the U-B distance is indeed calculated
to be 17 pm longer than the Zr-B distance. As a conse-
quence the shortest distances between bridging H atoms in
different tetrahydroborate groups in U(BH4)4 (255 pm) are
longer than the sum of their van der Waals radii (240 pm);
(41) Jotham, R. W.; Kettle, S. F. A. Inorg. Chim. Acta 1971, 5, 183.
(42) A D2d structure with the electron configuration a1 e1 would be orbitally
1
degenerate and thus subject to further J-T distortion to D2 or C2V
symmetry.41 These possibilities were not explored.
(43) Calculation of the molecular force field for the D2d structure with the
1
1
a1 b2 electron configuration was thwarted by SCF convergence
problems for distorted geometries.
6652 Inorganic Chemistry, Vol. 41, No. 25, 2002

Molecular Structures of Zr(BH4)4 and U(BH4)4
Table 5. Molecular Symmetry and Conformations of U(BH4)4, Electron Configurations, Binding (E) or Relative Energies (DE) (kJ mol-1) and Number
of Imaginary Frequencies (nimag) Obtained by Calculations at the ADF-ZORA and ADF-ZORA + Spin-Orbit (SO) Coupling Computational Levels
ADF-ZORA
config
ADF-ZORA + SO
symmetry (conformn)
E/∆E
nimag
config
E/∆E
1
1
1
1
Td (stag)
a1 t2
E ) -8825.0
(∆E ) 0)
0
e1/2 u3/2
E ) -8907.0
(∆E ) 0)
∆E ) +46.8
∆E ) +0.7
∆E ) +4.5
∆E ) +20.9
1
1
1
1
1
1
2
Td (ecl)
a1 t2
∆E ) +48.6
∆E ) -4.2
∆E ) -12.8
∆E ) +38.8
∆E ) +80.2
∆E ) +102.1
1
e1/2 u3/2
1
1
1
1
C3V (stag)
a1 e1
e1/2 a3/2
1
1
D2d (stag)
a1 b2
e1/2 e3/2
2
Td (stag)
Td (stag)
Td (stag)
t2
u3/2
1
1
a1 t1
t21 t1
1
verged to a slightly elongated pyramidal structure with the
equilibrium structure of each molecule is characterized by
four tridentate tetrahydroborate groups. Hence we note that
both display the pattern characteristic of tridentate BH4
groups with but a single absorption at 2560-2600 cm-1
corresponding to a ν(B-Ht) fundamental, a prominent
doublet at 2155-2185/2090-2117 cm-1 corresponding to
ν(B-Ht) fundamentals, and a single strong absorption near
1230 cm-1 associated with a M(µ-H)3B deformation mode.4,47
The case for tridentate binding is reinforced, moreover, by
the resemblance, in both wavenumbers and intensities, that
the spectra bear to those of such structurally authenticated
tetrahydroborates as Hf(BH4)4 and Ti(BH4)3.7,37,48 The ab-
sence of features characteristic of bidentate binding, as
exhibited for instance by Al(BH4)3,49 gives us good grounds
for concluding that all the tetrahydroborate groups are indeed
triply bridging, as indicated by the DFT calculations.
The high symmetry of the M(BH4)4 molecules gives rise
to many degenerate normal modes; whether the molecular
symmetry is T or Td, the 57 vibrational degrees of freedom
form only 24 distinct vibrational fundamentals. These span
the following representations:
1
electron configuration a1 e1.44 The energy was 4.2 kJ mol-1
below that calculated for the Td structure and 8.6 kJ mol-1
above that for the D2d structure. Examination of the optimal
C3V structure showed that the deformations from Td symmetry
were even smaller than those of the D2d model described
above: no valence angle changed by more than 0.2°. Single
point calculations including spin-orbit coupling on the
optimized C3V structure indicated that the most stable electron
1
1
configuration is e1/2 a3/2 (where e1/2 and a3/2 refer to the
irreducible representations of the group C3V*) and that the
energy of the C3V structure is 0.7 kJ mol-1 above that of the
Td structure. The present calculations are hardly conclusive,
but taken together the results summarized in Table 5 indicate
that that Jahn-Teller distortion of the Td model is either
quenched by spin-orbit coupling or very small. In this
context it may be pertinent to recall that recent, careful
investigations of UCl4 and UF4 by gas electron diffraction
failed to reveal any evidence for Jahn-Teller distortion.45,46
When the molecular structure of U(BH4)4 was refined to
the GED data under T symmetry, the dihedral angle
τ(BUBHb) oscillated around 60°, while the refinements failed
to converge. Refinements under Td symmetry (i.e. with
τ(BUBHb) fixed at 60°) proceeded without difficulty and
yielded the parameter values listed in Table 4. A series of
refinements with τ(BUBHb) fixed at values ranging from 60
to 26° in steps of 2° showed that the best fit is indeed
obtained with τ(BUBHb) ) 60° and that the R-factor
increases slowly, but monotonically, with increasing devia-
tion from the Td model. Only when τ(BUBHb) had been
reduced to 42°, however, had the R-factor increased suf-
ficiently to allow the model to be rejected at the 99.5%
confidence level.34 The GED data are clearly not good
enough to allow the precise determination of H atom
positions in the presence of the strongly scattering U atom.
Vibrational Spectroscopy. The IR spectra of matrix-
isolated Zr(BH4)4 and U(BH4)4 are shown in Figure 6. Where
comparisons can be made, they are consistent with the results
of previous studies.9,10,15,16,18 The spectra confirm that the
Td symmetry,4a1 (Raman) + 1a2 (inactive) + 5e(Raman)
+ 5t1 (inactive) + 9t2 (Raman, IR);
T symmetry, 5a(Raman) + 5e(Raman) + 14t(Raman,IR).
Whereas Td symmetry requires only nine IR-active fun-
damentals in all, T symmetry requires fourteen, the previously
silent t1 modes becoming IR-active under the lower sym-
metry. The structural difference is, however, a small one,
and the new t modes are unlikely to absorb very strongly;
indeed the intensities calculated for the T equilibrium
structure of Zr(BH4)4 indicate that the intensities of the
former t1 modes are less than 1% of those of the analogous
former t2 modes. Since the former t1 and t2 versions of a
particular motion occur at very similar wavenumbers, there
is ample opportunity for the former to be masked by the
latter.
Even if the spectrum should prove to contain more lines
than predicted for the Td model, these cannot be taken as a
proof of symmetry lowering since they might equally well
be due to 10B/11B isotopic splitting or to splitting by matrix
site effects.50,51 Additional absorptions may also be due to
1
(44) A C3V structure with the electron configuration a1 e1 is also orbitally
degenerate and might suffer further J-T distortion to Cs or C1,41 but
these distortions were not explored.
(45) Haaland, A.; Martinsen, K.-G.; Swang, O.; Volden, H. V.; Booij, A.
S.; Konings, R. J. M. J. Chem. Soc., Dalton Trans. 1995, 185. See
also: Haaland, A.; Martinsen, K.-G.; Konings, R. J. M. J. Chem. Soc.,
Dalton Trans. 1997, 2473.
(46) Konings, R. J. M.; Booij, A. S.; Kovacs, A.; Girichev, G. V.; Giricheva,
N. I.; Krasnova, O. G. J. Mol. Struct. 1996, 378, 121.
(47) Marks, T. J.; Kennelly, W. J.; Kolb, J. R.; Shimp, L. A. Inorg. Chem.
1972, 11, 2540.
(48) Keiderling, T. A.; Wozniak, W. T.; Gay, R. S.; Jurkowitz, D.;
Bernstein, E. R.; Lippard, S. J.; Spiro, T. G. Inorg. Chem. 1975, 14,
576.
(49) Coe, D. A.; Nibler, J. W. Spectrochim. Acta, Part A 1973, 29, 1789.
Inorganic Chemistry, Vol. 41, No. 25, 2002 6653

Haaland et al.
Figure 6. IR spectrum in the region 400-3000 cm-1 of U(BH4)4 (above) and Zr(BH4)4 (below) each isolated in an N2 matrix at 14 K.
overtone or combination bands, particularly in the critical
regions associated with the ν(B-H) (2000-2600 cm-1) and
the δ(BH2) and ν(M-Hb) modes (1000-1300 cm-1). For
example, weak bands at 2504 and 2442 cm-1 in the spectrum
of matrix-isolated Zr(BH4)4 must be associated not with
ν(B-H) fundamentals, but with a combination and overtone,
respectively, of the δ(BH2) fundamentals occurring near 1200
cm-1. By intensifying features such as these, Fermi resonance
with neighboring fundamentals spanning the same irreducible
representation may tend to blur the distinction between
primary and binary transitions. Finally, possible dynamic or
static Jahn-Teller distortions of U(BH4)4 represent another
source of uncertainty52,53 and spin-orbit coupling may lead
to composite rather than simple vibrational wave functions.
If J-T distortions and spin-orbit coupling are of comparable
importance, the so-called Ham effect53 will be operative, with
significant, but largely incalculable, implications for intensity
mixing of spectroscopic transitions.
other strong absorption characterizing the matrix-isolated
U(BH4)4 molecule, which occurs near 481 cm-1, is readily
ascribed to the t2 ν(U-B) mode. Of the nine IR-active
fundamentals of the U(BH4)4 molecule with Td symmetry
seven have thus been located more or less certainly; a
U(µ-H)3B deformation mode expected near 650 cm-1 was
evidently too weak to be observed, and a skeletal deformation
mode would fall at wavenumbers below the observed range.
The spectrum is thus consistent with, but does not by itself
prove, Td symmetry for the equilibrium structure of U(BH4)4.
Conclusions
Our studies of metal tetrakis(tetrahydroborate) molecules,
M(BH4)4, by DFT calculations, gas electron diffraction, and
matrix-isolation IR spectroscopy lead to the following
conclusions.
1. Both DFT calculations and GED structure refinements
indicate that the equilibrium conformation of Zr(BH4)4 has
T symmetry with the triply bridging BH4 groups twisted
about 15° away from staggered orientations. It is suggested
that the small potential energy maximum at the staggered
Td conformation is due to repulsion between bridging H
atoms in different tetrahydroborate groups, while the much
higher barrier at the eclipsed Td conformation is due to both
inherent electronic effects and repulsion between bridging
H atoms.
2. DFT calculations on Hf(BH4)4 indicate that the equi-
librium structure is very similar to that of the Zr analogue.
It is suggested that the Td molecular structure found in the
solid phase is induced by intermolecular forces.
3. DFT calculations on U(BH4)4 indicate that all tetrahy-
droborate groups are bonded to the metal atom through triple
H bridges and that the UB4 coordination geometry is
tetrahedral. The tridentate binding mode of the BH4 groups
is confirmed by matrix-isolation IR spectroscopy. Structure
optimization with one of the two nonbonding 5f electrons
occupying an a1 and the other distributed equally over the
In conclusion, even though other investigators have found
evidence for T rather than Td symmetry in the IR and Raman
spectra of Zr(BH4)4,10 we do not believe it possible to make
a distinction on the basis of vibrational spectroscopy alone.
The spectra of U(BH4)4 can be satisfactorily interpreted
on the basis of a Td model. Thus there are just three
absorptions in the region 2000-2600 cm-1 associated with
ν(B-Ht) and ν(B-Hb) modes. The region 1000-1300 cm-1,
where δ(BH2) and ν(M-Hb) modes occur, is made difficult
to interpret by matrix and/or 10B/11B splittings, as well as
problems of Fermi resonance. With the help of the spectrum
calculated for the Td model, however, three features (near
1240, 1150, and 1070 cm-1) can be identified with the t2
fundamentals expected to absorb in this region. The only
(50) Almond, M. J.; Downs, A. J. AdV. Spectrosc. 1989, 17, 1.
(51) Dunkin, I. R. Matrix-Isolation Techniques; A Practical Approach;
Oxford University Press: Oxford, U.K., 1998.
(52) Bersuker, I. B. The Jahn-Teller Effect and Vibronic Interactions in
Modern Chemistry; Plenum Press: New York and London, 1984.
(53) Ham, F. S. J. Lumin. 2000, 85, 193.
6654 Inorganic Chemistry, Vol. 41, No. 25, 2002

Molecular Structures of Zr(BH4)4 and U(BH4)4
three t2 orbitals indicates that the equilibrium conformation
has staggered BH4 groups and Td symmetry. Calculations
on models distorted from Td to D2d or C3V symmetry indicate
that Jahn-Teller distortions are either very small or quenched
by spin-orbit coupling. GED structure refinements give bond
distances and valence angles in reasonable agreement with
those calculated. The GED data are not good enough to allow
the precise determination of H atom positions in the presence
of the heavy metal atom, but the best fit between observed
and calculated GED data is indeed obtained with a molecular
model of Td symmetry, as indicated by the calculations.
Acknowledgment. We are grateful to the Norwegian
Research Council for a generous grant of computer time
through the NOTUR project (Account No. NN2147K) and
to the EPSRC for financial support of the Oxford group.
IC020357Z
Inorganic Chemistry, Vol. 41, No. 25, 2002 6655