Polymorphism in the crystal structures of the group 13 trimethyls

Article abstract of DOI:10.1021/om0300272

Crystal structure have been determined for trimethylboron, BMe₃, and for a new polymorph of trimethylgallium, GaMe₃; in addition, the crystal structure of trimethylthallium, TlMe₃, has been redetermined. The BMe₃ crystal structure represents a new structural type for the group 13 trimethyl derivatives in the solid state. In contrast to its heavier analogues, it consists of layer containing only very weakly interacting BMe₃ molecules. GaMe₃ forms a ladder-like pseudo-polymer via long gallium-to-methyl intermolecular interactions with Ga...C distances in the range 3.096(3)-3.226(4) A. This is compared with a recently reported crystal structure of a polymorph, which, like InMe₃ and TlMe₃, is characterized by the formation of pseudo-tetramers. The effects of crystallization and secondary interactions have been analyzed by comparison with related crystallographic, gas-phase electron diffraction, and spectroscopic studies of these and other trimethyl derivatives of the group 13 elements. The energetic differences between polymorphs of BMe₃, GaMe₃, and InMe₃ have been explored by plane wave DFT calculations. The energy differences between the BMe₃-like layered structure and the InMe₃-like pseudo-tetrameric structure are calculated to be -1.7, +3.6, and +10.4 kJ mol^-1 for BMe₃, GaMe₃, and InMe₃, respectively.

Full text of DOI:10.1021/om0300272

2450
Organometallics 2003, 22, 2450-2457
P olym or p h ism in th e Cr ysta l Str u ctu r es of th e Gr ou p 13
Tr im eth yls
Roland Boese,† Anthony J . Downs,‡ Timothy M. Greene,§ Alexander W. Hall,‡
Carole A. Morrison,| and Simon Parsons*,|
Institut fu¨r Anorganische Chemie, Universita¨t Essen, Universita¨tsstrasse 3-5,
45117 Essen, Germany; Inorganic Chemistry Laboratory, University of Oxford, South Parks
Road, Oxford, England OX1 3QR; School of Chemistry, University of Exeter, Chemistry
Building, Stocker Road, Exeter, England EX4 4QD; and School of Chemistry, The University
of Edinburgh, King’s Buildings, West Mains Road, Edinburgh, Scotland EH9 3J J
Received J anuary 14, 2003
Crystal structures have been determined for trimethylboron, BMe3, and for a new
polymorph of trimethylgallium, GaMe3; in addition, the crystal structure of trimethylthallium,
TlMe3, has been redetermined. The BMe3 crystal structure represents a new structural type
for the group 13 trimethyl derivatives in the solid state. In contrast to its heavier analogues,
it consists of layers containing only very weakly interacting BMe3 molecules. GaMe3 forms
a ladder-like pseudo-polymer via long gallium-to-methyl intermolecular interactions with
Ga‚‚‚C distances in the range 3.096(3)-3.226(4) Å. This is compared with a recently reported
crystal structure of a polymorph, which, like InMe3 and TlMe3, is characterized by the
formation of pseudo-tetramers. The effects of crystallization and secondary interactions have
been analyzed by comparison with related crystallographic, gas-phase electron diffraction,
and spectroscopic studies of these and other trimethyl derivatives of the group 13 elements.
The energetic differences between polymorphs of BMe3, GaMe3, and InMe3 have been explored
by plane wave DFT calculations. The energy differences between the BMe3-like layered
structure and the InMe3-like pseudo-tetrameric structure are calculated to be -1.7, +3.6,
and +10.4 kJ mol-1 for BMe3, GaMe3, and InMe3, respectively.
In tr od u ction
or possibly electrostatic, interactions. The longstanding
debate over the nature and geometry of the bridging
methyl groups in Al2Me6 has recently been resolved in
a neutron powder diffraction study at 4.5 K,6 and in this
paper we limit our attention to the second and third
structural types.
There are three different structures that are observed
for the group 13 trimethyl derivatives in the crystalline
state. One is the dimeric form observed for trimethyla-
luminum,1 in which methyl groups participate in strong
metal-metal bridges, with C-Al interaction distances
commensurate with those of terminal Al-C bonds.
Methyl bridging is also observed in a second structural
type featured by the derivatives with Ga, In, and Tl,
but the interaction distances are substantially longer
than the primary metal-carbon bonds. Prior to this
study, crystal structures had been determined for
GaMe3,2 InMe3,3,4 and TlMe3;5 here we describe crystal
structure determinations of a new polymorph of GaMe3
and a redetermination of the structure of TlMe3. The
third structural type is represented by BMe3. As we
show below, this crystal structure consists of layers in
which the molecules interact by weak van der Waals,
We have also investigated theoretically the energetic
differences between polymorphs of BMe3, GaMe3, and
InMe3 in which the molecules form layers (as in the
observed structure of BMe3) or weak methyl bridges (as
in InMe3). Polymorphism has been described as the
supramolecular equivalent of molecular isomerism.7
Traditional ab initio modeling procedures (notably
GAUSSIAN) simulate isolated molecules, but while this
style of calculation is suitable for studying gaseous
isomers, it is not so readily applicable to solids. Plane
wave density functional theory (DFT) can simulate the
periodic wave function characteristics of a repeating
unit such as a crystallographic unit cell. The lattice
parameters and atomic positions can all be varied to
minimize the crystal lattice energy, atomic forces, and
unit cell stress, and we therefore use these methods to
draw energetic comparisons between trimethyl poly-
morphs.
* To whom correspondence should be addressed. Tel: +44 131 650
5804. Fax: +44 131 650 4743. E-mail: S.Parsons@ed.ac.uk.
† Universita¨t Essen.
‡ University of Oxford.
§ University of Exeter.
| The University of Edinburgh.
(1) Vranka, R. G.; Amma, E. L. J . Am. Chem. Soc. 1967, 89, 3121.
Byram, S. K.; Fawcett, J . K.; Nyberg, S. C.; O’Brien, R. J . J . Chem.
Soc. D 1970, 16. Huffman, J . C.; Streib, W. E. J . J . Chem. Soc. D 1971,
911.
Our results complete the series of crystal structures
for the group 13 trimethyls. The trimesityls (mesityl )
(2) Mitzel, N. W.; Lustig, C.; Berger, R. J . F.; Runeberg, N. Angew.
Chem., Int. Ed. 2002, 41, 2519.
(3) Amma, E. L.; Rundle, R. E. J . Am. Chem. Soc. 1958, 80, 4141.
(4) Blake, A. J .; Cradock, S. J . Chem. Soc., Dalton Trans. 1990, 2393.
(5) Sheldrick, G. M.; Sheldrick, W. S. J . Chem. Soc. A 1970, 28.
(6) McGrady, G. S.; Turner, J . F. C.; Ibberson, R. M.; Prager, M.
Organometallics 2000, 19, 4398.
(7) Bernstein, J . Polymorphism in Molecular Crystals; Clarendon
Press: Oxford, U.K., 2002.
10.1021/om0300272 CCC: $25.00 © 2003 American Chemical Society
Publication on Web 05/14/2003

Polymorphism in Group 13 Trimethyls
Organometallics, Vol. 22, No. 12, 2003 2451
Ta ble 1. Cr ysta llogr a p h ic Da ta Collection a n d
Refin em en t P a r a m eter s
2,4,6-trimethylphenyl) are the only other group 13
organometallics for which a complete series of crystal
structures has been determined.
BMe3
GaMe3
TlMe3
formula
Mr
cryst syst
space group
a/Å
C3H9B
55.91
monoclinic
C2/c
6.3473(9)
C3H9Ga
114.82
monoclinic
C2/c
18.409(3)
C9H9Tl
249.47
tetragonal
P42/n
13.3049(7)
13.3049(7)
6.2891(5)
90
Exp er im en ta l Section
Syn t h esis of Com p ou n d s. (i) Tr im et h ylb or on was
prepared by direct metathesis between trimethylaluminum
(obtained from Aldrich and purified by fractional condensation
in vacuo) and tri-n-butyl borate (also obtained from Aldrich)
as neat liquids.8 To moderate the exothermic reaction, the
b/Å
c/Å
10.9284(16) 6.2652(9)
14.224(2)
91.099(3)
986.5(2)
95
18.268(3)
91.361(2)
2106.4(5)
120
â/deg
V/Å3
1113.30(12)
150
mixture was held in
a Pyrex glass vessel fitted with a
T/K
greaseless (Young’s) valve at temperatures <233 K. Trimeth-
ylboron was the only volatile product. It was purified by
fractional condensation in vacuo with traps held at 162, 144,
and 77 K. The fraction collected at 144 K was identified as
essentially pure trimethylboron on the evidence of the IR
spectrum of the vapor.9
(ii) Tr im eth ylga lliu m was prepared similarly by ligand
redistribution between trimethylaluminum and gallium(III)
chloride (obtained from Aldrich).10 Warming the mixture to
room temperature caused a vigorous reaction to occur. After
the mixture was stirred for 90 min to ensure completion of
the reaction, the volatile products were vaporized in vacuo and
fractionated via traps held at 222, 178, and 77 K. Trimethyl-
gallium was collected at 178 K and was authenticated by the
IR spectrum of the vapor.11
Z
8
16
1.448
5.044
0.071-0.272
8
Dc/Mg m-3
µ/mm-1
range of
transmissn
0.753
0.038
0.396-1
2.977
28.844
0.233-1
cryst dimens/mm 0.5 × 0.5 × 1 0.26 × 0.26 × 1 0.4 × 0.2 × 0.2
cryst habit
max/deg
colorless
cylinder
25.00
12 095/1804 8030/2168
colorless
cylinder
26.49
colorless
block
29.00
θ
no. of rflns:
8902/1413
total/unique
no. of data with
F > 4σ(F)
1487
1789
1143
Rint
0.0328
300
102
0.0456
0.1344
0.001
0.0346
0
85
0.0294
0.0753
0.002
0.067
0
41
0.0351
0.0890
0.002
+1.75, -1.69
no. of restraints
no. of params
R (F>4σ(F))
Rw (F2, all data)
max shift/su
final diff map
extremes/e Å-3
(iii) Tr im eth ylth a lliu m was synthesized rather differ-
ently, namely in accordance with eq 1 by the addition of an
excess of methyllithium in ether solution (1.4 M) to thallium-
(I) iodide in the presence of iodomethane (all reagents being
used as supplied by Aldrich).12 After the mixture had been
+0.11, -0.13 +0.81, -0.50
.
KR radiation (λ ) 0.710 73 Å); collection parameters are listed
in Table 1 or in the Supporting Information.
2MeLi + TlI + MeI f TlMe3 + 2LiI
(1)
Cr ysta l Str u ctu r e Deter m in a tion of BMe3. Diffraction
data were collected for a sample at 95 K. Complete indexing
of the diffraction pattern of the sample of BMe3 described above
required two orientation matrices.16 The relationship between
the component orientations could be described with the matrix
stirred for 1 h at room temperature, the ether solution was
siphoned off into a clean, preconditioned Schlenk tube. The
solvent was evaporated under reduced pressure and the
trimethylthallium isolated as a crystalline solid by fraction-
ation in vacuo, being retained by a trap held at 242 K. The
purity of the product was checked by reference to the IR
spectrum of its vapor at ambient temperatures.13
Cr ysta l Gr ow th . Samples of BMe3, GaMe3, and TlMe3 were
loaded into Pyrex capillaries and mounted on a Bruker Smart
Apex CCD diffractometer equipped with an Oxford Cryosys-
tems low-temperature device.14 The boron and gallium com-
pounds (the former being a gas and the latter a liquid under
ambient conditions) were respectively frozen at 100 and 213
K, and crystals were grown in situ by means of Boese’s zone
refinement method using an OHCD infrared laser-assisted
crystallization device.15 The sample of TlMe3 was treated
similarly, but since this tended to sublime rather than melt
under laser irradiation, a suitable crystal was obtained by
careful sublimation inside the capillary at 273 K. Data
collections were carried out using graphite-monochromated Mo
-1.00 -0.03
0.00
0.04 ,
-0.09
1.00
0.06 -1.00
(
)
0.01
which approximates to a 180° rotation about [010]. Since this
is a symmetry operation of a monoclinic lattice, the result
implies that the sample consisted of two slightly misaligned
crystals. Such “twinning” conditions may give rise to refine-
ment difficulties because reflections from different domains
partially overlap, but such problems were avoided by simul-
taneous integration of both components, which ensures that
fully and partially overlapping reflections are treated cor-
rectly.17 An absorption correction was applied using the
recently written program TWINABS,18 which is based on the
multiscan procedure of Blessing19 and designed to treat
twinned data. Data from both components were used in
refinement, the final residuals being only some 0.2% higher
than if pure single-component data were used.
(8) Ko¨ster, R. J ustus Liebigs Ann. Chem. 1958, 618, 31.
(9) Woodward, L. A.; Hall, J . R.; Dixon, R. N.; Sheppard, N.
Spectrochim. Acta 1959, 15, 249.
(10) Gaines, D. F.; Borlin, J .; Fody, E. P. Inorg. Synth. 1974, 15,
203.
(11) McKean, D. C.; McQuillan, G. P.; Duncan, J . L.; Shephard, N.;
Munro, B.; Fawcett, V.; Edwards, H. G. M. Spectrochim. Acta 1987,
43A, 1405.
The structure was solved by direct methods and refined by
2
full-matrix least squares against |F| using all data (SHELX-
TL),20 with anisotropic displacement parameters modeled for
the B and C atoms. It was clear from electron density
difference maps that the methyl groups were disordered by a
(12) Gilman, H.; J ones, R. G. J . Am. Chem. Soc. 1946, 68, 517.
(13) Schwerdtfeger, P.; Bowmaker, G. A.; Boyd, P. D. W.; Ware, D.
C.; Brothers, P. J .; Nielson, A. J . Organometallics 1990, 9, 504.
J ohnson, E. M. D.Phil. Thesis, University of Oxford, 1971.
(14) Cosier, J .; Glazer, A. M. J . Appl. Crystallogr. 1986, 19, 105.
(15) Boese, R.; Nussbaumer, M. In Correlations, Transformations,
and Interactions in Organic Crystal Chemistry; J ones, D. W., Katru-
siak, A., Eds.; IUCr Crystallographic Symposia 7; Oxford University
Press: Oxford, U.K., 1994; p 20.
(16) Sparks, R. A. GEMINI: Program for Indexing X-ray Diffraction
Patterns Derived from Multiple or Twinned Crystals; Bruker-AXS,
Madison, WI, 2000.
(17) SAINT, version 6.33; Bruker-Nonius, Madison, WI, 2002.
(18) Sheldrick, G. M. TWINABS: Program for Performing Absorp-
tion Corrections to X-ray Diffraction Patterns Collected from Non-
Merohedrally Twinned and Multiple Crystals; University of Go¨ttingen,
Go¨ttingen, Germany, 2002.
(19) Blessing, R. H. Acta Crystallogr. 1995, A51, 33.

2452 Organometallics, Vol. 22, No. 12, 2003
Ta ble 2. Obser ved Bon d a n d Con ta ct Dista n ces (Å) a n d An gles (d eg) in MMe3 (M ) B, Ga , Tl)a
BMe3 (obsd, C2/c) GaMe3 (obsd, C2/c) GaMe3 (obsd, P42/n) TlMe3 (obsd, P42/n)
Boese et al.
B1-C1
B1-C2
B1-C3
1.5548(11)
1.5565(11)
1.5541(12)
Ga1-C1
1.956(3)
1.958(3)
1.968(3)
3.096(3)
3.512(4)
1.964(3)
1.970(3)
1.956(3)
Ga1-C1
1.952(3)
1.962(2)
1.958(2)
3.149(3)
3.647(3)
Tl1-C1
2.196(8)
2.206(8)
2.216(7)
3.243(8)
3.364(7)
Ga1-C2
Ga1-C2
Ga1-C3
Ga1‚‚‚C2f
Ga1‚‚‚C3g
Tl1-C2
Tl1-C3
Tl1‚‚‚C2h
Tl1‚‚‚C3i
Ga1-C3
Ga1‚‚‚C5b
Ga1‚‚‚C6c
Ga2-C4
Ga2-C5
Ga2-C6
Ga2‚‚‚C2d
3.226(3)
3.204(3)
Ga2‚‚‚C3e
C1-B1-C2
C1-B1-C3
C2-B1-C3
120.06(7)
120.09(7)
119.86(7)
C1-Ga1-C2
C1-Ga1-C3
C2-Ga1-C3
Ga1‚‚‚C5b-Ga2b
Ga1‚‚‚C6c-Ga2c
C4-Ga2-C5
C4-Ga2-C6
C5-Ga2-C6
Ga2‚‚‚C2d-Ga1d
Ga2‚‚‚C3e-Ga1e
122.02(16)
119.46(16)
118.27(16)
171.09(18)
120.02(17)
120.45(17)
120.16(18)
119.39(17)
162.14(18)
168.71(17)
C1-Ga1-C2
C1-Ga1-C3
C2-Ga1-C3
Ga1‚‚‚C2f-Ga1f
Ga1‚‚‚C3g-Ga1g
119.72(14)
121.29(14)
118.85(13)
167.22(12)
164.67(13)
C1-Tl1-C2
C1-Tl1-C3
C2-Tl1-C3
Tl1‚‚‚C2h-Tl1h
Tl1‚‚‚C3i-Tl1i
120.7(3)
124.1(3)
115.1(3)
167.8(4)
167.5(4)
a
Dimensions for the tetragonal phase of GaMe3 were calculated from the data in ref 2 (data taken from CCDC 163477). All standard
b
1
c 1
uncertainties were calculated with a full variance-covariance matrix, with the exception of those given in italics. -x, y + 1, /2 - z.
- x,
/
2
1
1
d
1
3
1
g
h
3
1
i
/
+ y,
/
- z. x, y - 1, z. e x, -y,
/
+ z. f y,
/
- x,
/
- z. y - 1/2, 1 - x, z - 1/2.
/ - y, x, /
- z. 1 - y, x - 1/2, z - 1/2.
2 2
2
2
2
2
2
180° rotation about their B-C axes. The relative occupancies
were initially refined independently, but later these were
modeled with one variable for all three methyl groups after
they had converged to common values. The occupancy of the
major component (labeled H1A-H1C etc. in the Supporting
Information) was 0.577(6).
The orientation of the methyl groups was such that one
C-H bond lay in the molecular BC3 plane, and some distortion
from ideal, local C3v symmetry was anticipated (see below).
The H atom positions were refined subject to the restraint that
all in-plane BCH angles were similar. Similarity restraints
were also applied to the out-of-plane BCH angles and all 1,2-
C-H and 1,3-H‚‚‚H distances. “Opposite” H atoms attached
to the same carbon atom but in different disorder components
were constrained to have equal isotropic displacement param-
eters.
www.ccdc.cam.ac.uk/conts/retrieving.html (or from the Cam-
bridge Crystallographic Data Centre, 12 Union Road, Cam-
bridge CB2 1EZ, U.K.; fax +44 1223 336033; e-mail deposit@
ccdc.cam.ac.uk).
Th eor etica l Meth od s. Total energy plane-wave DFT cal-
culations were performed using the CASTEP 4.2 simulation
code24 for the compounds BMe3, GaMe3, and InMe3 in ordered
layered monoclinic (C2/c) and tetragonal (P42/n) polymorphic
forms. Periodic boundary conditions allow the valence elec-
tronic wave function to be expanded in terms of a discrete
plane-wave basis set (set at 540 eV for BMe3 and 500 eV for
GaMe3 and InMe3), while the core wave function is described
by standard ultrasoft pseudopotentials available with the
software package. The symmetry-reduced set of k points used
to sample the reciprocal space were generated using Monk-
hurst-Pack grids25 (dimensions 2 × 1 × 1 and 1 × 1 × 2 for
the monoclinic and tetragonal lattices, respectively, both
generating one k point in the symmetry-reduced first Brillouin
zones). The generalized gradient approximation (GGA) func-
tional PW9126 was used to model electronic correlation and
exchange. Simultaneous optimization of lattice vectors and
atomic positions was performed until the convergence criteria
were met (maximum energy change per atom 2 × 10-5 eV,
maximum RMS displacement 1.0 × 10-3 Å, maximum RMS
force 0.05 eV Å-1, and maximum RMS stress 0.1 Gpa). The
starting geometries used for the optimizations of the mono-
clinic lattice polymorphs were taken from the experimental
structure determination of BMe3 reported in this paper, with
the boron atoms simply replaced by gallium or indium to
generate input coordinates for the other two structures. The
tetragonal lattice atomic coordinates and cell vectors for the
BMe3 and InMe3 structures originated from Blake’s InMe3
X-ray structure determination;4 calculations on GaMe3 used
Mitzel’s data2 on the tetragonal polymorph as the starting
Cr ystal Str u ctu r e Deter m in ation s of GaMe3 an d TlMe3.
Diffraction data were collected for crystals held at 120 K
(GaMe3) and 150 K (TlMe3), and absorption corrections were
applied using the program SADABS.21 The structures were
solved by direct methods and refined by full-matrix least
2
squares against |F| using all data (SHELXTL), with aniso-
tropic displacement parameters modeled for the metal and C
atoms. The methyl groups were treated as freely rotating rigid
groups. Four out of the six independent methyl groups in
GaMe3 were found to be disordered in a fashion similar to that
described above for BMe3. The relative occupancies were fixed
at 0.5:0.5. No attempt was made to model a deviation of the
methyl groups from local C3v symmetry; the improvement to
refinement statistics on introduction of a more flexible model
was marginal for BMe3 and would have been negligible for this
compound, where H atom scattering contributes relatively
much less to the diffraction pattern.
Refinement and geometric data for all compounds are
collected in Tables 1 and 2, respectively. Structural analyses
used the program PLATON,22 and figures were drawn using
SHELXTL or CAMERON.23 The file CCDC 209601-209603
contains the supplementary crystallographic data for this
paper. These data can be obtained free of charge via
(22) Spek, A. L. PLATON: A Multipurpose Crystallographic Tool;
Utrecht University, Utrecht, The Netherlands, 2002. PC version:
Farrugia, L. J . J . Appl. Crystallogr. 1999, 32, 837.
(23) Watkin, D. J .; Pearce, L.; Prout, C. K. CAMERON-A Molecular
Graphics Package; Chemical Crystallography Laboratory, University
of Oxford, Oxford, U.K., 1993.
(24) Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; J oannopo-
ulos, J . D. Rev. Mod. Phys. 1992, 64, 1045. CASTEP 4.2 Academic
version, licensed under the UKCP-MSI agreement, 1999.
(25) Monkhurst, H. J .; Pack, J . D. Phys. Rev. B 1976, 13, 5188.
(26) Perdew, J . P.; Chevary, J . A.; Vosko, S. H.; J ackson, K. A.;
Pederson, M. R.; Singh, D. J .; Fiolhais, C. Phys. Rev. B 1992, 46, 5571.
(20) Sheldrick, G. M. SHELXTL: Suite of Programs for Crystal
Structure Analysis, Incorporating Structure Solution (XS), Least-
Squares Refinement (XL), and Graphics (XP); University of Go¨ttingen,
Go¨ttingen, Germany, 2001.
(21) Sheldrick, G. M. SADABS: Program for Performing Absorption
Corrections to Single-Crystal X-ray Diffraction Patterns; University
of Go¨ttingen, Go¨ttingen, Germany, 2002.

Polymorphism in Group 13 Trimethyls
Organometallics, Vol. 22, No. 12, 2003 2453
point (as this structure is the most directly comparable with
the others in our series).
The Supporting Information contains tables of crystal-
lographic data for BMe3, GaMe3, and TlMe3 (also deposited
with the CCDC, as described above) and tables of optimized
theoretical coordinates for polymorphs of BMe3, GaMe3, and
InMe3.
Resu lts a n d Discu ssion
Under ambient conditions, the trimethyl derivatives
of the group 13 elements range from a gas (BMe3),
through a liquid (AlMe3 and GaMe3), to a low-melting
solid (InMe3 and TlMe3).27 On the evidence of mass and
vibrational spectroscopic and electron diffraction mea-
surements, the vapors of all but the aluminum com-
pound consist of monomeric MMe3 molecules (M ) B,
Ga, In, Tl), each with a trigonal-planar MC3 skeleton
and more or less freely rotating methyl groups.9,11,13,28-31
In contrast, the analogous aluminum species, AlMe3, is
found in appreciable concentrations only at elevated
temperatures and/or low pressures;32,33 otherwise, the
dimer Me2Al(µ-Me)2AlMe2 prevails throughout the con-
densed and vapor states.6 Increasing the atomic number
of the group 13 element results in an overall rise in
melting and boiling points consistent with the expected
strengthening of van der Waals interactions. That the
pattern is far from regular, however, is evidenced by
the following melting points (in K):27 BMe3, 112; AlMe3,
288; GaMe3, 257; InMe3, 362; TlMe3, 312. To what
extent the implied cohesive energies of the crystal reflect
differences of structure and/or variations in the type or
degree of the intermolecular interactionsspossibly in-
cluding so-called “agostic” interactions34sis not possible
to judge on the evidence available to date. Previous
studies involving X-ray crystallography,1-5 gas electron
diffraction,28-30 and vibrational spectroscopy4,11,13 argue
that perturbation of the MMe3 units in the crystal is
quite modest, with the sole exception of M ) Al, for
which the dimer Me2Al(µ-Me)2AlMe2 holds sway (but is
itself subject to relatively little change with the transi-
tion from the vapor to the crystalline state6). One or two
of these studies have also alluded to the possibility of
polymorphism, for example in the case of InMe3.3,4 The
aims of the present study have been to enlarge on
knowledge of the crystal structures of these compounds
and of the secondary interactions they reveal and to
explore the possibilities of polymorphism, partly by
experiment (in the case of GaMe3) but, more widely, by
plane wave DFT analysis.
F igu r e 1. Crystal structure of BMe3 viewed along the
crystallographic c direction. The molecules are related
either by lattice translations or C-centering operations. The
minor disorder component has been omitted for clarity.
Displacement ellipsoids enclose 50% probability surfaces.
adopts the expected D3h symmetry (Figure 1). The most
closely related crystal structure in the literature is that
of triethylboron, BEt3; the B-C distances in that
compound lie around 1.573(1) Å.35 The corresponding
distance in BMe3 is 1.555(1) Å, but a riding analysis36
suggests that this difference is probably owed to the
relatively high librational motion of the methyl groups
at the temperature used for data collection (95 K), which
is only 17 K below the melting point. In this context, it
is perhaps significant that the B-C distance in the
gaseous BMe3 molecule (determined by electron diffrac-
tion) is reported to be 1.5783(11) Å.28
The BCC angle in BEt3 would be expected, on the
basis of simple predictions using VSEPR theory, for
example, to be close to 109.5°, and the most remarkable
feature of the structure of this compound is the rather
large BCC angle, reported to be 118.9(2)°. A similar
effect has recently been observed in GaEt3.2 The reason
for this deviation has been ascribed to hyperconjugation
between the out-of-plane CH2 bonds and the vacant p
orbital on the central group 13 atom. The methyl groups
in BMe3 are disordered by a 180° rotation about the
B-C vector, each component containing one CH bond
in the BC3 plane. The ab initio optimized crystal
structure of an ordered model of BMe3 (see below)
revealed that the average in-plane BCH angle was 115°,
whereas the average out-of-plane BCH angle was 110°.
Scattering from the H atoms in BMe3 contributes some
28% to F(000), giving them a significant influence on
data fitting, and it seemed possible that a deviation from
ideal tetrahedral geometry about the carbon atoms in
BMe3 might be detectable, despite the disorder. Re-
strained refinement of a model in which the BCH angles
Tr im eth ylbor on . The boron-to-carbon distances in
BMe3 are equal within error, and the BC3 framework
(27) Starowieyski, K. In Chemistry of Aluminium, Gallium, Indium
and Thallium; Downs, A. J ., Ed.; Blackie Academic and Professional:
Glasgow, U.K., 1993; p 339. Macintyre, J . E., Ed. Dictionary of
Organometallic Compounds, 2nd ed.; Chapman and Hall: London,
U.K.; 1995.
(28) Bartell, L. S.; Carroll, B. L. J . Chem. Phys. 1965, 42, 3076.
(29) Beagley, B.; Schmidling, D. G.; Steer, I. A. J . Mol. Struct. 1974,
21, 437.
(30) Fjeldberg, T.; Haaland, A.; Seip, R.; Shen, Q.; Weidlein, J . Acta
Chem. Scand., Ser. A 1982, 36, 495.
(31) Hall, J . R.; Woodward, L. A.; Ebsworth, E. A. V. Spectrochim.
Acta 1964, 20, 1249.
(32) Almenningen, A.; Halvorsen, S.; Haaland, A. Acta Chem. Scand.
1971, 25, 1937.
(33) Atiya, G. A.; Grady, A. S.; Russell, D. K.; Claxton, T. A.
Spectrochim. Acta 1991, 47A, 467. Kvisle, S.; Rytter, E. Spectrochim.
Acta 1984, 40A, 939.
(34) Brookhart, M.; Green, M. L. H.; Wong, L.-L. Prog. Inorg. Chem.
1988, 36, 1. Scherer, W.; McGrady, G. S. Submitted for publication in
Angew. Chem., Int. Ed.
(35) Boese, R.; Bla¨ser, D.; Niederpru¨m, N.; Nu¨sse, M.; Brett, W. A.;
Schleyer, P. v. R.; Bu¨hl, M.; van Eikema Hommes, N. J . R. Angew.
Chem., Int. Ed. Engl. 1992, 31, 314.
(36) J ohnson, C. K. In Crystallographic Computing, Proceedings of
the International Summer School; Munksgaard: Copenhagen, Den-
mark, 1970; pp 220-226.

2454 Organometallics, Vol. 22, No. 12, 2003
Boese et al.
F igu r e 3. Structure of TlMe3 projected onto (001), showing
methyl bridge formation. Hydrogen atoms have been
omitted for clarity. Ellipsoids enclose 50% probability
surfaces.
F igu r e 2. Formation of layers in the crystal structure of
BMe3 (view along the crystallographic b direction). Packing
within the layers is illustrated in Figure 1.
Trimethylindium has the highest melting point of the
trimethyl derivatives formed by the three heaviest
group 13 metals, and it might be inferred from this that
it exhibits the strongest degree of association in the solid
state. Its crystal structure, first investigated by Amma
and Rundle in 19583 and then again by Blake and
Cradock in 1990,4 is characterized by the formation of
pseudo-tetramers (Rundle’s term) which consist of four
InMe3 molecules connected via long In‚‚‚methyl bridges
(In‚‚‚C ) 3.083(12) Å). These are disposed about a
crystallographic 4h site, forming a flattened tetrahedron.
Longer In‚‚‚methyl bridges (In‚‚‚C ) 3.558(15) Å) con-
nect the tetramers. Projections of this structure along
[001] (Figure 3 shows the isostructural Tl derivative in
this projection) can beguile one into thinking that this
structure is a two-dimensional network. In fact, it is
three-dimensional, consisting of two mutually exclusive
networks which are interlaced by means of a 4-fold
screw axis.3
An atoms-in-molecules analysis39 on the related gal-
lium system has shown that the critical point in the
metal‚‚‚methyl bridge region occurs along the Ga‚‚‚C
vector, implying that this is not an agostic interaction.2
In the following sections we discuss intermolecular
interactions in terms of metal-to-carbon distances partly
for this reason, but also because H atom positions have
not been determined very precisely and because they
are consistent with the contemporary literature in this
area.
were allowed to vary revealed a trend rather similar to
that observed in the BCC angles in BEt3, with the in-
plane BCH angles averaging 116°, compared with 109°
for the out-of-plane BCH angles, in very good agreement
with the theoretical results. The standard uncertainties
of these quantities (excluding the effects of restraints)
fall in the range 1.1-1.8°. This places the difference on
the limit of statistical significance. A refinement model
in which the methyl groups were constrained to adopt
perfect C3v symmetry yielded a conventional R factor
of 5.2% (48 parameters), compared with 4.5% for the
model described here (102 parameters). For what it is
worth, the Hamilton test37 using weighted residuals
implies that the improvement is significant.
In the crystal structure of BMe3 the molecules pack
in layers which stack along the c direction (Figure 2).
The boron and hydrogen atoms respectively carry small
positive and negative charges, and the boron atoms lie
between methyl groups in neighboring layers. The
shortest intermolecular B‚‚‚H contact is 3.04 Å, which
is well beyond the sum of the van der Waals radii of B
and H (2.83 Å),38 a finding consistent no doubt with the
high volatility of trimethylboron. The arrangement of
the molecules within the layers (Figure 1) resembles a
close-packed array.
Tr im eth ylga lliu m a n d Tr im eth ylth a lliu m . Tri-
methylboron is unique among the group 13 trimethyls
in showing no significant association in the solid state.
Trimethylaluminum exists as a methyl-bridged dimer
both in the solid state and in the gas phase. Although
such behavior is not observed for Ga, In, and Tl, it has
long been clear that these trimethyls are also associated
via secondary metal‚‚‚methyl contacts in the solid state.
The melting points of GaMe3 (257 K), InMe3 (362 K),
and TlMe3 (312 K) alternate along the series, and are
all significantly higher than that of BMe3 (112 K), partly
as a result of these interactions.
The crystal structure of TlMe3 was investigated using
photographic methods by Sheldrick and Sheldrick in
1970.5 Our data set establishes the structural param-
eters to greater precision than was possible in that
study, although the conclusions are unchanged. TlMe3
adopts the InMe3 structure (Figure 3), but there is a
much smaller difference between the lengths of the
short and long secondary metal to methyl contacts: the
Tl‚‚‚C distances are 3.243(8) and 3.364(7) Å within and
(37) Hamilton, W. C. Acta Crystallogr. 1965, 18, 502.
(38) Bondi, A. J . Phys. Chem. 1964, 68, 441.
(39) Bader, R. F. W. Atoms in Molecules: A Quantum Theory;
Clarendon Press: Oxford, U.K., 1994.

Polymorphism in Group 13 Trimethyls
Organometallics, Vol. 22, No. 12, 2003 2455
F igu r e 4. Pseudo-polymer formed in the crystal structure
of the monoclinic polymorph of GaMe3. The heavy dotted
lines are short contacts of 3.096(3) Å; the light dotted lines
are longer contacts of 3.204(3) and 3.226(3) Å. The el-
lipsoids enclose 50% probability surfaces; H atoms have
been omitted for clarity.
between the tetramers, respectively. The primary Tl-C
bond distances, averaging 2.206(8) Å, are identical with
those in the gaseous molecule (2.206(3) Å), as gauged
by electron diffraction.30
Very recently Mitzel et al. reported a crystal structure
of GaMe3 which is isostructural with that of InMe3.2 In
this tetragonal phase both the Ga‚‚‚methyl contacts
which form the tetramers and those between the tet-
ramers are slightly longer than in InMe3 (3.134 and
3.647 Å, respectively). This phase was obtained by
cooling a sample of GaMe3 through its melting point,
but crystal growth by laser-assisted zone refinement
yielded a new polymorph of GaMe3, which is C-centered
monoclinic. The structure contains two crystallographi-
cally independent molecules, both of which adopt the
expected trigonal-planar geometry in the primary co-
ordination sphere.
F igu r e 5. Structure of monoclinic GaMe3 projected onto
(001). The polymers shown in Figure 5 pass into the page,
and different polymers have been shown in different colors.
Domains of short (between 3.0 and 3.3 Å) and long (3.512
Å) Ga‚‚‚C contacts are indicated by the letters S and L,
respectively.
The length of the b axis of the unit cell of the
monoclinic phase is similar to that of the c axis of the
tetragonal phase, and when projected along these direc-
tions the structures bear a close resemblance to each
other. However, the tetramers which characterize the
tetragonal phase of GaMe3 are replaced in the mono-
clinic phase by a polymer. The two crystallographically
independent molecules alternate along chains with
methyl‚‚‚Ga contacts of 3.226(3) and 3.204(3) Å formed
above and below the planes of the molecules containing
Ga2. Shorter contacts of 3.096(3) Å made to Ga1 serve
to link the chains together into a ladderlike array
(Figure 4). Long contacts measuring 3.512(4) Å are
formed between the ladders, completing the trigonal-
bipyramidal coordination about Ga1. In the tetragonal
forms of MMe3 (M ) Ga, In, Tl) the angles subtended
at bridging carbon atoms fall in the range 160-170°.
This trend is also followed in the structure of monoclinic
GaMe3, except in the case of the long interconnecting
methyl bridge (C6), where the angle is 120.02(17)°.
Figure 5 shows a projection of the monoclinic struc-
ture along the c direction; it should be compared with
Figure 6, which shows the structure of TlMe3 (which
can be taken to be representative of all the tetragonal
MMe3 phases) projected perpendicular to the (110)
plane. These rather similar packing arrangements are
related by a shift in the relative positions of layers
containing the short contacts. The pattern of contacts
in the two phases is represented schematically in Figure
7, which is intended to illustrate the transition from a
structure consisting of two independent three-dimen-
F igu r e 6. Structure of TlMe3 projected onto (110). The
two different three-dimensional networks are shown in blue
and red. Domains of shorter (3.243 Å) and longer (3.364
Å) Tl‚‚‚C contacts are indicated by the letters S and L,
respectively. Isostructural tetragonal polymorphs are known
for GaMe3 (in which the short and long contacts are 3.149-
(3) and 3.647(3) Å, respectively) and InMe3 (contact dis-
tances 3.083(12) and 3.558(15) Å).
sional networks in the tetragonal phases of MMe3 (M
) Ga, In, Tl) to a single three-dimensional network in
the monoclinic phase of GaMe3.
Ab In itio Ca lcu la tion s of P olym or p h s of Gr ou p
13 Tr im eth yls. There is some evidence in the literature
that InMe3 may exist in at least two different polymor-

2456 Organometallics, Vol. 22, No. 12, 2003
Boese et al.
very successful and useful tool to investigate (a) poly-
morphic transitions which occur in small organic sys-
tems under the application of high pressure,40,41 (b) the
properties of hydrogen bonds,42 and (c) crystal disorder
in PbCp2.43 Our calculations on GaMe3 used Mitzel’s
coordinates for the tetragonal polymorph, as this is most
directly comparable with InMe3.
The results of the calculations are shown in Table 3.
Bond and contact distances tend to be overestimated
at this level of theory, an effect which carries through
to the unit cell dimensions, which are also overesti-
mated. Of course, the C-H bond lengths are all ca. 0.1
Å longer than those obtained experimentally, but most
of this disagreement arises from the systematic short-
ening of these parameters when derived from X-ray
data. Nevertheless, both the present results and those
of our previous work in this area show that structural
trends (for example, in a set of bond lengths within a
structure) are reliably reproduced. So too are relative
energies. In all three cases, the lower energy structure
corresponds to the experimentally observed polymorph.
The calculated tetragonal polymorph of BMe3 has a very
long B‚‚‚C “contact” of 3.715 Å, exceeding even the
related distances in either GaMe3 or InMe3. Modeling
suggests that shortening this contact to a more reason-
able distance between 3.0 and 3.3 Å begins to incur
repulsive H‚‚‚H interactions between methyl groups of
less than twice the van der Waals radius of H (2.4 Å).
This does not occur in the heavy-atom derivatives
because of their longer metal-to-carbon bonds. Con-
versely, the short B-C bond enables the electron
deficiency of the boron to be relieved by hyperconjuga-
tion between the empty 2p orbital on the boron and the
out-of-plane C-H bonds of the methyl groups, a cir-
cumstance supported both experimentally and by the
results of these calculations (see above). Presumably the
reverse of this argument explains the preference for the
methyl-bridged structures by the heavier group 13
trimethyls. As the experimental structure of GaEt3
shows, hyperconjugation is also possible in these sys-
tems, although it is notable that the shortest calculated
interplanar M‚‚‚C distances in the C2/c polymorphs
become shorter along the series B > Ga > In. There is
also a tendency along this series for the methyl groups
to rotate about the C-metal bond away from the
conformation described above for BMe3.
F igu r e 7. Schematic representations of Figure 5 (top,
monoclinic GaMe3) and Figure 6 (bottom, TlMe3) showing
the formation of two independent networks following
displacement of layers. In the top part of the figure, the
ellipses represent polymers passing into the plane of the
paper. In the bottom part of the figure, they represent
columns of tetramers.
phic forms. Blake and Cradock4 refer to an alternative
form of InMe3, which they describe as being less volatile,
and more stable, than the tetragonal form. However, a
careful variable-temperature X-ray diffraction study
between 273 and 113 K did not reveal any new phases.
In their study of the same compound, Amma and
Rundle3 noted that, in addition to the tetragonal phase,
a less common, less stable, pseudo-hexagonal (more
likely triclinic) form was found to exist. This conclusion
was based on crystal morphology, and no diffraction
data have ever been collected on this form of InMe3.
However, the reduced cell dimensions of BMe3 are
pseudohexagonal, with a ) b ) 6.319 Å, c ) 14.224 Å,
R ) â ) 90.55°, and γ ) 119.70°, and it is possible that
the less stable phase is closely related to the structure
of BMe3 described here. The ab plane of this pseudo-
hexagonal lattice is evident in Figure 1, perhaps most
clearly by treating each B atom as a lattice point, though
this would not be the conventional choice of origin.
Polymorphism is a very common phenomenon, and it
seems perfectly reasonable that the group 13 trimethyls
should be as susceptible to it as any other class of
compound. Indeed, as described above, we have ob-
served it for GaMe3. However, our new polymorph falls
into the same structural category, being characterized
by long methyl bridges, as the known tetragonal struc-
tures; whereas the latter are pseudo-tetrameric, the new
polymorph is pseudo-polymeric, and the energy differ-
ence between the two forms is presumably small. The
observations by previous workers concerning trimeth-
ylindium suggest that it may be possible to observe
transitions between structural types by varying the
conditions of temperature and/or pressure. With this in
mind, we have investigated the energetic differences
between layered and pseudo-tetrameric polymorphs of
BMe3, GaMe3, and InMe3 using plane wave density
functional theory (DFT). Previous work in our research
groups has shown plane wave DFT calculations to be a
Mitzel et al. performed calculations at the MP2/TZVP
level on an isolated pair of GaMe3 molecules in which a
Ga‚‚‚C bridging interaction measuring 3.206 Å was
found to have an energy of 11.4 kJ mol-1. Of this, only
3.4 kJ mol-1 was ascribable to electrostatic forces; the
remainder arose from a dispersion interaction (7.5 kJ
mol-1), an ionic correlation contribution (4.2 kJ mol-1
,
from a reduction in intramolecular correlation on ap-
proach of two molecules), and a negative repulsive term
(-3.8 kJ mol-1).2 The total interaction energy is rather
similar to that of a weak hydrogen bond. The energy
differences between polymorphs are of the same order
of magnitude as the terms given above. The two
(40) Allan, D. R.; Clark, S. J .; Ibberson, R. M.; Parsons, S.; Pulham,
C. R.; Sawyer, L. Chem. Commun. 1999, 751.
(41) Allan, D. R.; Clark, S. J .; Dawson, A.; McGregor, P. A.; Parsons,
S. Acta Crystallogr. 2002, B58, 1018.
(42) (a) Morrison, C. A.; Siddick, M. M. Chem. Eur. J ., in press. (b)
Wilson, C. C.; Morrison, C. A. Chem. Phys. Lett. 2002, 362, 85.
(43) Morrison, C. A.; Wright, D. S.; Layfield, R. A. J . Am. Chem.
Soc. 2002, 124, 6775.

Polymorphism in Group 13 Trimethyls
Organometallics, Vol. 22, No. 12, 2003 2457
optimized structures of BMe3 both consist of very weakly
interacting molecules, and not surprisingly, the energy
difference between them is small. The corresponding
energy difference between the polymorphs of InMe3 is
greater than for GaMe3, consistent with the shorter
bridges formed in InMe3. Enthalpy differences between
real polymorphs usually fall in the range 0-10 kJ mol-1
and probably do not exceed 25 kJ mol-1.7 Therefore, the
results of these calculations show it to be quite possible
that the unstable phase of InMe3 observed by Amma
and Rundle had the BMe3 structure.
Distor tion s Ca u sed by Meth yl Br id gin g. When an
atom forms a strong contact, any other bonds that it
forms are generally weakened as a result. In our
structure of GaMe3 the primary Ga-C distances span
the range 1.956(3)-1.970(3) Å; the average distance in
the gaseous molecule, deduced by electron diffraction,29
is 1.967(2) Å. The carbon atom involved in the shortest
intermolecular contact (C5‚‚‚Ga1 ) 3.096(3) Å) also
makes the longest primary C-Ga bond, but there is no
discernible relationship between the other bond and
contact lengths in the structure. The calculations on
tetragonal InMe3 show that the In-C bond length
involving the carbon atom making the stronger second-
ary contact is 0.03 Å longer than the bond involving the
carbon atom, which is not involved in bridging. The
relative lengthening of the In-C bond involving the
carbon that makes the longer contact is much less, viz.
0.009 Å.44 The corresponding figures for tetragonal
GaMe3 are 0.012 and 0.004 Å, in excellent agreement
with the experimental values. The relative lengthening
of the bond involving the more strongly bridging methyl
group which has been discussed by several authors2-5
thus appears to be a genuine effect, even though the
differences observed crystallographically tend to teeter
on the brink of statistical insignificance.
Bond angles are somewhat “softer” interactions than
bond lengths, and all structures exhibit C-M-C angles
which differ from 120°. Where a significant deviation
occurs, the largest bond angle is invariably the one not
involving the carbon atom making the stronger inter-
molecular contact. There is no deviation from planarity
in the molecular MC3 unit in any of the crystal struc-
tures. In contrast, the very strong bridging contacts
established in monomeric aluminum derivatives con-
45
taining bulky groups, such as Al(CH2Ph)3 and Al-t-
Bu3,46 have been observed to lift the Al atom out of the
plane formed by the three directly bound carbon atoms
by up to 0.4 Å.
Ack n ow led gm en t. We thank the EPSRC for re-
search funding and for an Advanced Fellowship to
T.M.G. and the Royal Society for a University Research
Fellowship to C.A.M.
Su p p or tin g In for m a tion Ava ila ble: Tables giving crys-
tallographic data for BMe3, GaMe3, and TlMe3 and optimized
theoretical coordinates for polymorphs of BMe3, GaMe3, and
InMe3. This material is available free of charge via the Internet
at http://pubs.acs.org.
OM0300272
(44) The experimentally observed differences for these In-C bond
lengths are 0.041(18) and -0.015(19) Å, respectively; neither of these
is statistically significant.
(45) Rahman, A. F. M. M.; Siddiqui, K. F.; Oliver, J . P. Organome-
tallics 1982, 1, 881.
(46) Downs, A. J .; Greene, T. M.; Parsons, S.; Taylor, R. A.
Unpublished results.