New synthetic and structural aspects in the chemistry of alkylaluminum fluorides. The mutual influence of hard and soft ligands and the hybridization as rigorous structural criterion

Article abstract of DOI:10.1021/ic010131g

A general synthetic strategy starting from metal alkyls is reported based on the hydrogen difluoride anion as a suitable reagent for obtaining organometallic fluorides. The newly prepared compounds are [Me₄N][(i-Bu)₂AlF₂] (1), [Ph₄P][(i-Bu)₂AlF₂] (2), and [Ph₄P][AlF₄] (3), containing the tetrahedral anions [(i-Bu)₂AlF₂]^- and [AlF₄]^-. The actual structures are prototypes that allowed a comparison of inorganic and organometallic fluorides in the frame of the hard and soft acid and base principle, by means of ab initio calculations. A new theoretical model is designed to put in equation form the qualitative statements of the Bent rule. The model allows the rationalization of the tendencies of bond angle variation in [R₂MX₂] systems containing a main group metal (M), in terms of hybridization of the central atom and the reciprocal influence of hard and soft ligands.

Full text of DOI:10.1021/ic010131g

Inorg. Chem. 2001, 40, 4947-4955
4947
New Synthetic and Structural Aspects in the Chemistry of Alkylaluminum Fluorides.
The Mutual Influence of Hard and Soft Ligands and the Hybridization as Rigorous
Structural Criterion#
Marilena Ferbinteanu,†,‡ Herbert W. Roesky,*,† Fanica Cimpoesu,§ Mihail Atanasov,|,
Sinje Ko1pke,† and Regine Herbst-Irmer†
Institut fu¨r Anorganische Chemie der Universita¨t Go¨ttingen, Tammannstrasse 4,
D-37077 Go¨ttingen, Germany, Institute of Physical Chemistry, Splaiul Independentei 202,
77208 Bucharest, Romania, and Institut fu¨r Theoretische Chemie der Heinrich-Heine Universita¨t,
Universita¨tsstrasse 1, D-40225 Du¨sseldorf, Germany
ReceiVed January 31, 2001
A general synthetic strategy starting from metal alkyls is reported based on the hydrogen difluoride anion as a
suitable reagent for obtaining organometallic fluorides. The newly prepared compounds are [Me4N][(i-Bu)2AlF2]
(1), [Ph4P][(i-Bu)2AlF2] (2), and [Ph4P][AlF4] (3), containing the tetrahedral anions [(i-Bu)2AlF2]- and [AlF4]-.
The actual structures are prototypes that allowed a comparison of inorganic and organometallic fluorides in the
frame of the hard and soft acid and base principle, by means of ab initio calculations. A new theoretical model
is designed to put in equation form the qualitative statements of the Bent rule. The model allows the rationalization
of the tendencies of bond angle variation in [R2MX2] systems containing a main group metal (M), in terms of
hybridization of the central atom and the reciprocal influence of hard and soft ligands.
Introduction
and 2 are not in agreement with the HSAB principle, but this
does not preclude their formation. Moreover, the properties of
Following our general interest in organometallic fluorides,1,2
the compounds reported herein are prototypes for the correlation
of inner structural features with the idea of hybridization and
including the hard and soft acid and base principle (HSAB).3
This work compares the organometallic fluorides [Me4N][(i-
Bu)2AlF2] (1) and [Ph4P][(i-Bu)2AlF2] (2) with the inorganic
anion of [Ph4P][AlF4] (3) as a model.
Compound 3 is in line with the HSAB principle, containing
aluminum as a hard acid and fluorine as a hard base. The
chemical hardness,4 a quantitative measure of Lewis basicity
or acidity, approximately parallels the electronegativity,5 and
in this view, fluorine and alkyl groups as ligands appear to be
rather different. Consequently, the organometallic fluorides 1
hard (F) and soft (R) ligands in [R2AlF2]- are averaged at the
expense of each other (see mutual influence).
The interest in organoaluminum fluorides stems from the
potential importance6 of these compounds as models for certain
catalytic reactions. Thus, organoaluminum fluorides can be
found among the pioneering work of Ziegler.7 The well-known
MAO (methylalumoxane) cocatalyst8 seems to have, analo-
gously to organometallic fluorides, a structure based on methyl
and oxygen ligands with different HSAB characteristics.
Inorganic fluorides and oxo-fluorides prepared from [AlF4]-
sources function also as catalysts.9,10
Therefore we are interested in understanding the bonding of
the [R2AlF2]- and [AlF4]- anions in terms of HSAB factors as
a useful addition to the known correlations between HSAB
parameters and catalytic activity.11
# Dedicated to Professor Hans Bu¨rger on the occasion of his 65th
birthday.
A general strategy for the synthesis of compounds with hard
and soft ligands is the use of reagents containing the hydrogen
† Institut fu¨r Anorganische Chemie der Universita¨t Go¨ttingen.
‡ Permanent address: University of Bucharest, Faculty of Chemistry,
Inorganic Chemistry Department, Dumbrava Rosie 23, Bucharest 70254,
Romania. E-mail: mcimpoesu@yahoo.com.
(6) Atwood, D. A.; Yaerwood, B. C. J. Organomet. Chem. 2000, 600,
186-197.
§ Institute of Physical Chemistry, Bucharest.
| Institut fu¨r Theoretische Chemie der Heinrich-Heine Universita¨t.
On leave of absence from the Institute of General and Inorganic
Chemistry, Bulgarian Academy of Science, Sofia, Bulgaria.
(1) (a) Witt, M.; Roesky, H. W. Prog. Inorg. Chem. 1992, 40, 353-444.
(b) Liu, F.-Q.; Uso´n, I.; Roesky, H. W. J. Chem. Soc. 1995, 2453-
2458. (c) Murphy, E. F.; Lu¨bben, T.; Herzog, A.; Roesky, H. W.;
Demsar, A.; Noltemeyer, M.; Schmidt, H.-G. Inorg. Chem. 1996, 35,
23-29. (d) Roesky, H. W.; Herzog, A.; Liu, F.-Q. J. Fluorine Chem.
1995, 71, 161-161. (e) Roesky, H. W. Inorg. Chem. 1999, 38, 5934-
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(7) Ziegler, K.; Ko¨ster, R. Liebigs Ann. Chem. 1957, 608, 1-7.
(8) Fink, G., Mu¨lhaupt, R., Brintzinger, H. H., Eds. Ziegler Catalysts:
Recent Scientific InnoVations and Technological ImproVements;
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DeCanio, E. C.: Bruno, J. W.; Nero V. P.; Edwards, J. C. J. Catal.
1993, 140, 84-89. (d) Bentrup, U. Eur. J. Solid State Inorg. Chem.
1992, 29, 51-54.
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J. Am. Chem. Soc. 1999, 121, 5687-5699.
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(b) Mortier, S. K.; Ghoshi, S.; Shankar, S. J. Am. Chem. Soc. 1986,
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10.1021/ic010131g CCC: $20.00 © 2001 American Chemical Society
Published on Web 08/07/2001

4948 Inorganic Chemistry, Vol. 40, No. 19, 2001
Ferbinteanu et al.
difluoride anion [FHF]- and its reaction with metal alkyls. The
[FHF]- anion is a species with remarkable properties12-14 and
can be regarded as the simplest coordination compound contain-
ing the smallest positive ion (proton). The reaction of [FHF]-
with MRn leads to the organometallic fluoride (MRn-xFx) under
evolution of alkane (RH). This process is not of HSAB type.
Indeed, the hardest acid (H+) approaches the weakest Lewis
base of the system (R-), and vice-versa, the hardest base (F-)
leaves its hard partner. The proton from [FHF]- helps to
override15 the usual HSAB direction of a reaction, leading to
organometallic fluorides by a rational route.
CH2CH(CH3)2), 30.1 (Al-CH2CH(CH3)2) (analogously to data reported
in ref 22), 55.1 ((CH3)4N+). 19F NMR (188 MHz, C6D6, C6F6, ppm):
δ 12.60 (∆ν1/2 ) 180 Hz). IR (cm-1): 663 (s) (ν Al-F) (comparable
with data from ref 23), 695 (m), 724 (m) (ν Al-F) (comparable with
data from ref 36), 803 (s), 863 (m), 911 (m), 949 (m), 1036 (s), 1096
(s), 1262 (s), 1602 (m), 1626 (m), 1725 (w). MS (EI): m/z (%): 74
(100, Me4N+), 57 (10, (C4H9)+). Negative ion FAB-MS (3-NBA
matrix):24 m/z 179 ([(i-Bu)2AlF2]). Anal. Calcd for C12H30AlF2N (Mr
253.35): C, 56.91; H, 11.85; Al, 10.67. Found: C, 56.8; H, 10.4; Al,
10.5.
Synthesis of [Ph4P][(i-Bu)2AlF2] (2). A solution of Al(i -Bu)3 (1.05
g, 5.3 mmol) in toluene was added dropwise to a suspension of [Ph4P]-
HF2 (2 g, 5.3 mmol) in toluene (40 mL). The synthesis conditions for
2 are similar to those for 1. A colorless powder was isolated after 2
days (2.7 g, 89.8%) and decomposes slowly > 140 °C. 1H NMR (200
MHz, CD3CN, ppm): δ -0.4 (d, 4H, 3J(HH) ) 5.2 Hz, Al-CH2CH-
(CH3)2), 0.89 (d, 12H, Al-CH2CH(CH3)2), 1.6 (m, 2H, Al-
CH2CH(CH3)2), 7.64, 7.87 (m, 20H, [(C6H5)4P]+). 13C NMR (126 MHz,
CD3CN, TMS, ppm): δ 28.5 (Al-CH2CH(CH3)2), 29.2 (Al-CH2CH-
(CH3)2), 30.1 (Al-CH2CH(CH3)2),22 118.5, 119.3, 131.2, 135.7, 136.4
[(C6H5)4P]+). 19F NMR (188 MHz, C6D6, C6F6, ppm): δ 10.3. IR
(cm-1): 527 (s), 650 (m) (ν Al-F),23 690 (s), 723(m) (ν Al-F),36 753-
(s), 787 (s), 853 (w), 996 (m), 1108 (s), 1169, 1187 (w), 1315 (m),
1585 (m). MS (EI): m/z (%): 339 (100, [(C6H5)4P]+). Negative ion
FAB-MS (3-NBA matrix):24 m/z 179 ([(i-Bu)2AlF2]-). Anal. Calcd for
C32H38AlF2P (Mr 518.57): C, 74.13; H, 7.33; Al, 5.21; P, 5.98. Found:
C, 73.8; H, 7.3; Al, 5.3; P, 6.1.
The [FHF]- formed in situ can be found as a bridging block
between two metal centers.16-18 The number of such compounds
can be increased when the anion is directly introduced as an
ammonium salt.
Experimental Section
General Procedures. All experiments were performed using stan-
dard Schlenk techniques under a dry nitrogen atmosphere due to the
extreme sensitivity of the reactants toward air and moisture. A Braun
Labmaster 130 drybox was used to store the compounds and to prepare
the samples for spectroscopic characterizations. Purification and drying
of the solvents were done by standard methods.19 Triisobutylaluminum
(Witco) was used as received; [Me4N]HF2 and [Ph4P]HF2 were prepared
1
as described in the literature.20,21 The H, 13C, and 19F NMR spectra
were recorded on Bruker AM 200 and Bruker AM 250 spectrometers.
Synthesis of [Ph4P][AlF4] (3). A solution of [Ph4P]HF2 (0.45 g,
1.2 mmol, excess) in THF (10 mL) was added slowly to a suspension
of [Ph4P][(i-Bu)2AlF2] (0.31 g, 0.6 mmol) in toluene (30 mL). The
mixture was stirred for 2 h at 80 °C, and after cooling, the resulting
solution was filtered, and the filtrate kept at room temperature. Colorless
crystals of 3 were isolated after 3 days (2.3 g, 87%). Mp: 348 °C. 1H
1
The standards were TMS (external; H, 13C) and C6F6 (external; 19F)
using the δ scale. FAB mass spectra were obtained on Finnigan MAT
8230 or Varian MAT CH 5 instruments, and FT-IR spectra were
measured on a Bio-Rad FTS-7 as Nujol mulls between KBr plates in
the range 4000-400 cm-1 (abbreviations used: vs, very strong; s,
strong; m, medium; w, weak). Elemental analyses were performed by
the Analytisches Labor des Instituts fu¨r Anorganische Chemie der
Universita¨t Go¨ttingen. Melting points were measured with a HWS-SG
3000 apparatus in sealed capillaries under nitrogen (values not
corrected).
3
NMR (500 MHz, CD3CN, ppm): δ 7.67, 7.72, 7.90 (m, 20H, J(HH)
) 5.2 Hz, [(C6H5)4P]+). 13C NMR (126 MHz, CD3CN, TMS, ppm): δ
118.5, 119.3, 131.2, 135.7, 136.4 [(C6H5)4P]+). 19F NMR (188 MHz,
1
CD3CN, C6F6, ppm): δ -30.04 (sextet, I(27Al) ) 5/2, JF-Al ) 37.5
Hz). The sextet of approximately equal intensities is a characteristic
of isolated [AlF4]- tetrahedra in solution.25 IR (cm-1): 303 (s), 447
(w), 527 (s), 616 (w), 630 (s), 724, 752 (m), 783 (s), 853 (w), 996 (m),
1026 (w), 1108 (s), 1163 (w), 1316 (w), 1436 (s), 1483 (m), 1586 (m),
1683 (w). The IR band at 783 is characteristic of the [AlF4]- anion in
Synthesis of [Me4N][(i-Bu)2AlF2] (1). A solution of Al(i-Bu)3 (0.4
g, 2.03 mmol) in toluene was added dropwise to a suspension of [Me4N]-
HF2 (0.23 g, 2.03 mmol) in toluene (30 mL), and the mixture was stirred
for 2 h at -30 °C. After heating slowly, the resulting solution was
filtered, and the filtrate was kept at room temperature. Colorless crystals
1
of 1 could be isolated (0.47 g, 93%) after 2 weeks. Mp: 81 °C. H
(22) Kopp, M. R.; Kra¨uter, T.; Werner, B.; Neumu¨ller, B. Z. Anorg. Allg.
Chem. 1998, 624, 881-886.
(23) Neumu¨ller, B. Coord. Chem. ReV. 1997, 158, 69-101.
(24) Compounds 1-3 produce some of the expected signals in the FAB
(negative-ion) mass spectrum next to the signals for the matrix (3-
nitrobenzyl alcohol, 3-NBA).
3
NMR (200 MHz, C6D6, ppm): δ -0.42 (d, 4H, J(HH) ) 6.5 Hz,
Al-CH2CH(CH3)2), 0.86 (d, 12H, 3J(HH) ) 6.5 Hz, Al-CH2CH-
(CH3)2), 1.6 (m, 2H, Al-CH2CH(CH3)2), 2.42 (s, 12H, CH3). 13C NMR
(126 MHz, C6D6, TMS, ppm): δ 28.5 (Al-CH2CH(CH3)2), 29.2 (Al-
(25) Herron, N.; Thorn, D. L.; Harlow, R. L.; Davidson, F. J. J. Am. Chem.
Soc. 1993, 115, 3028-3029.
(12) Tuck, D. G. Prog. Inorg. Chem. 1968, 9, 161-194.
(13) (a) Harmon, K. M.; Alderman, S. D.; Benker, K. E.; Diestler, D. J.;
Gebauer, P. A. J. Am. Chem. Soc. 1965, 87, 1700-1706. (b) Gennick,
I.; Harmon, K. M.; Potvin, M. Inorg. Chem. 1977, 16, 2033-2040.
(14) (a) Silva, M. R.; Paixao, J. A.; Beja, A. M. Acta Crystallogr. C 2000,
56, 104-106. (b) Kruh, R.; Fuwa, K.; McEver, T. E. J. Am. Chem.
Soc. 1956, 78, 4256-4258.
(15) HSAB principles concern general stability rules for electronic
structures, but the proton possesses no electron and can be considered
out of the proper model. At the same time, while the HSAB affinities
are confined with rather weak interactions, the strong polarization
exerted by the proton is at a higher energy compared to the normal
range of the HSAB scheme.
(16) (a) Roesky, H. W.; Sotoodeh, M.; Xu, Y. M.; Schrumpf, F.;
Noltemeyer, M. Z. Anorg. Allg. Chem. 1990, 580, 131-138. (b)
Bentrup, U.; Harms, K.; Massa, W.; Pebler, J. Solid State Sci. 2000,
2, 373-376.
(17) (a) Jasim, N. A.; Perutz, R. N. J. Am. Chem. Soc. 2000, 122, 8685-
8693. (b) Richmond, T. G. Coord. Chem. ReV. 1990, 105, 221-250.
(18) Roesky, H. W.; Haiduc, I. J. Chem. Soc., Dalton Trans. 1999, 2249-
2264.
(26) Herron, N.; Harlow, R. L.; Thorn, D. L. Inorg. Chem. 1993, 32, 2985-
2986.
(27) Kottke, T.; Stalke, D. J. Appl. Crystallogr. 1993, 26, 615-619.
(28) Sheldrick, G. M. Acta Crystallogr., Sect. A. 1990, 46, 467-473.
(29) Sheldrick, G. M. SHELX97; University of Go¨ttingen, 1997.
(30) The two imaginary values of frequency are obtained, for example,
with 3-21G* or SV(P) bases in the RHF calculations. Other basis and
methods may give real and low values for the same modes, supporting
also the physical picture of a floppy skeleton.
(31) Batten, S. R.; Harris, A. R.; Murray, K. S. Acta Crystallogr. 2000,
C56, 1394-1395.
(32) (a) Murphy, V. J.; Hascall, T.; Chen, J. Y.; Parkin, G. J. Am. Chem.
Soc. 1996, 118, 7428-7429. (b) Whittlesey, M. K.; Perutz, R. N.;
Greener, B.; Moore, M. H. Chem. Commun. 1997, 187-188.
(33) (a) Bosch, P.; Camps, F.; Chamorro, E.; Gasol, V.; Guerero, A.
Tetrahedron Lett. 1987, 28, 4733-4736. (b) Clark, J. H. Chem. ReV.
1980, 80, 429-452.
(34) Cousseau, J.; Albert P. J. Chem. Soc., Chem. Commun. 1985, 14, 961-
962.
(35) Landini, D.; Molinari, H.; Penso, M.; Rampoldi, A. Synthesis 1988,
12, 953-955.
(36) Roesky, H. W.; Stasch, A.; Hatop, H.; Rennekamp, C.; Hamilton, D.
H.; Noltemeyer, M.; Schmidt, H. G. Angew. Chem., Int. Ed. 2000,
39, 171-173; Angew. Chem. 2000, 112, 177-179.
(19) Perrin, D. D.; Armarego, W. L. F.; Perrin, D. R. Purification of
Laboratory Chemicals, 2nd ed.; Pergamon Press: Oxford, 1980.
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(21) Brown, S. J.; Clark, J. H. J. Fluorine Chem. 1985, 30, 251-258.

Chemistry of Alkylaluminum Fluorides
Inorganic Chemistry, Vol. 40, No. 19, 2001 4949
Table 1. Summary of X-ray Diffraction Data
[Me4N][(i -Bu)2AlF2] (1)
C12H30AlF2N
[Ph4P][AlF4] (3)
empirical formula
fw
C24H20AlF4P
442.35
253.35
cryst size (mm)
0.4 × 0.3 × 0.2/0.4 ×
0.3 × 0.2
orthorhombic
Pnma
19.208(4)
8.783(2)
9.720(2)
1639.8(6)
4
0.4 × 0.1 × 0.1/0.2
× 0.1 × 0.1
tetragonal
I4h
17.220(2)
17.220(2)
14.000(3)
4151(1)
cryst syst
space group
a (Å)
b (Å)
c (Å)
Figure 1. Molecular structure of [Me4N][(i -Bu)2AlF2] (1).
cell vol V (Å3)
Z
8
Fc (g mm-3
)
1.026
0.124
560
1.416
0.218
1824
µ (mm-1
F(000)
)
2θ range (deg)
4.7 to 55.3
3.3 to 55.3
60925, 4819
[R(int) ) 0.0525]
133(2)
0.0397, 0.0894
0.0551, 0.0972
1.023
data measd, unique 68853, 2033
[R(int) ) 0.0364]
133(2)
R,a wR2b (I > 2σ(I)) 0.0696, 0.1816
temp (K)
R, wR2 (all data)
goodness of fit, Sc
no. of refined
params
0.0744, 0.1860
1.147
109
331
no. of restraints
62
149
largest diff peak and +0.615/-0.388
+0.173/-0.285
hole (e Å-3
)
absolute structure
param
-0.02(9)
b
2
a R ) ∑||Fo| - |Fc||/∑|Fo|. wR2 ) [∑w(Fo2 - Fc2)2]/[∑w(Fo )2]1/2
.
c S ) [∑w(Fo - Fc2)2]/[∑(n - p)]1/2
.
2
Figure 2. Molecular structure of [Ph4P][AlF4] (3). Selected bonds
lengths (Å) and angles (deg): Al(1)-F(1) 1.647(2), P(1)-C(10) 1.799-
(2), P(1)-C(20) 1.797(2), P(1)-C(30) 1.796(2), P(1)-C(40) 1.792-
(2); F(1)-Al(1)-F(1A) 109.9(1), F(1)-Al(1)-F(1B) 108.6(2), F(4)-
Al(1)-F(4A) 110.28(8), F(4)-Al(1)-F(4B) 107.9(2), C(20)-P(1)-
C(10) 110.9(1), C(30)-P(1)-C(10) 107.4(1).
normal coordinates having the representations A2 and B1.30 These modes
are figuring the directions in which the disordering takes places. An
equal superposition of A2 + B1 modes will result in a movement of
only one alkyl group, while the other remains fixed. The finding that
the experimental disorder is more pronounced at one alkyl group
suggests that both of the instability coordinates are followed in the
crystal structure.
solid state.26 MS (EI): m/z 339 ([(C6H5)4P]+). Anal. Calcd for
C24H20AlF4P (Mr 442.35): C, 65.22; H, 4.53; Al, 6.11. Found: C, 64.6;
H, 5.0; Al, 6.3.
In 3 two of the four [AlF4]- ions are disordered. A second data
collection was carried out, but did not show any improvement. The
merged data set was used for the final refinement. The disordered parts
in both structures were refined with distance restraints and restraints
for the anisotropic displacement parameters. The nondisordered [AlF4]-
anions have Al-F bond lengths of 1.647 Å. A certain differentiation
of the F-Al-F bond angles appears as a consequence of the
environment. The crystal structure of 3 is quite similar (space group,
unit cell parameters, disordering pattern) to a recently detected phase
of [Ph4P][ClO4].31 The crystal analogy is understandable by comparing
the symmetry and volume of the perchlorate and the tetrafluoroalumi-
nate anion.
X-ray Structure Determination of 1 and 3. The crystals were
mounted on a glass fiber with perfluoropolyether and flash-cooled to
133(2) K in a stream of nitrogen gas.27 Diffraction data were collected
on a Stoe-Siemens-Huber four-circle diffractometer coupled to a
Siemens CCD area detector with graphite-monochromated Mo KR
radiation (λ ) 0.71073 Å) performing æ- and ω-scans. The structure
was solved by direct methods using SHELXS-9728 and refined using
F2 on all data by full-matrix least squares with SHELXL-97.29 All non-
hydrogen atoms were refined anisotropically. Hydrogen atoms were
included on calculated positions and refined using a riding model.
Crystal Structures of 1 and 3. The structures are mononuclear
complexes of aluminum with a distorted tetrahedron in the case of 1
(Figure 1) and an almost regular tetrahedron for 3 (Figure 2). The cell
parameters and summary of crystallographic data are compiled in Table
1. Structure 1 shows substantial disorder. Both ions of 1 lie on mirror
planes, but in the anion only the [C2AlF2] part fulfills this symmetry,
while the remaining carbon atoms are disordered. Lowering the
symmetry does not lead to a fully ordered structure. Additionally
to this disorder there is a relatively high residual electron density,
which could be interpreted as a second position of the whole structure
(anion and cation) with an occupancy under 10%. Due to the poor
quality of the data, a second crystal was measured, giving the same
features. For the final refinement we used a merged data set of both
crystals.
Results and Discussion
The application of hydrogen difluoride for the preparation
of new organometallic fluorides starting from metal alkyls stems
from the fact that the moderately acidic proton of [FHF]- is
able to eliminate an alkane from the metal-bonded alkyl groups,
while the remaining empty coordination site can be occupied
by a fluoride ion. The excess of [FHF]- leads to the formation
of fluorides as the final and stable compounds (Scheme 1).
The [FHF]- anion is the most abundant species in the aqueous
solution of HF, and obviously this is the effective agent when
HF is used in fluorination reactions.32 The ammonium salts
[R4N][HF2] are soluble in nonpolar solvents,33-35 a feature that
favors their use in organometallic chemistry.
The disorder of the [(i-Bu)2AlF2]- anion in compound 1 can be
understood by means of ab initio calculation, as a consequence of the
floppy molecular backbone. The tendency for disorder is probed by
the finding of computed imaginary or very low frequencies for two
Orbital Features of Organometallic and Inorganic Fluo-
rides. A first insight into the electronic structure of organome-
tallic fluorides is given with the help of molecular orbital

4950 Inorganic Chemistry, Vol. 40, No. 19, 2001
Scheme 1. Synthesis of Compounds 1-3
Ferbinteanu et al.
central AOs. There exists a number of unoccupied orbitals, due
to the nonbonding parts on the organic skeleton, intercalated
between the a1+b2 (HOMO) and a1+b1 (post-LUMO) pairs. The
shapes of the frontier orbitals suggest that the AlR2+ fragment
has partial covalent character and forms ionic interactions with
the two fluoride ions.
Hybrid-Orbital Model for the Stereochemistry of C2W-Type
Tetrahedral Units of Main Group Metals. A valuable simple
perspective of the electronic structure of tetrahedral complexes
of main group elements can be established using the hybridiza-
tion language. The clue consists of the observation that for a
series of previously reported [Me2MF2]- anions (M ) Al, Ga,
In)36 all the experimental bond angles at the metal center can
be fitted very well if they are defined as angles between the
hybrid orbitals.
pictures, considering the Kohn-Sham functions from B3LYP
calculations with the SV(P) basis set (Figure 3). We confine
our report here only to a visual inspection of frontier orbitals.
The [AlF4]- anion shows the orbital pattern of a ligand-field
regime, with the highest occupied orbitals preponderantly of
ligand-type, while the empty frontier orbitals (a1 and t2) are
originating from the s+3p valence shell of the Al(III) ion.
More specifically, under C2V symmetry of the tetrahedral units,
the hybrid orbitals in the (xz) plane can be written
The organometallic fluorides [Me2AlF2]- and [(i-Bu)2AlF2]-
show features similar to each other and qualitatively different
from [AlF4]-. The highest two occupied MOs of the organo-
metallic systems can be qualitatively regarded as a combination
in-phase (a1) and out-of-phase (b2) of the hybrid orbitals located
on the metal center and oriented toward the alkyl groups. These
functions include combinations of s, pz, and py orbitals of Al
and AOs of the coordinated C atoms (Al-C bonds are located
in the yz plane) and are the MOs with the maximal contribution
to the Mulliken population on Al.
1
1
2
x
|h1(
)
(r|s + 1 - r |pz ) (
|px
(1.a)
x
2
x
2
and regarded as oriented toward the fluorine atoms. The hybrids
toward the alkyl groups in the (yz) plane are
1
1
2
x
|h2(
)
( 1 - r |s - r|pz ) (
|py
(1.b)
x
2
x
2
The search for the other two metal-type functions, spanning
the a1+b1 representations (in order to complete a set assigned
to a s+3p valence shell on Al), results in a corresponding pair
among the empty orbitals, having shapes based on px and pz
The angles between the components of h1( and h2( pairs and
those between each h1 component relative to each h2, respec-
tively, can be assimilated with the F-M-F, C-M-C, and
Figure 3. Kohn-Sham frontier orbitals in [AlF4]-, [Me2AlF2]-, and [(i-Bu)2AlF2]- anions (from B3LYP calculations with SV(P) basis). The
orbitals can be qualitatively regarded as having parentage in the s+3p valence shell of aluminum. This set has fully LUMO character in [AlF4]-
and is distributed between HOMO and post-LUMO in the organometallic ions.

Chemistry of Alkylaluminum Fluorides
Inorganic Chemistry, Vol. 40, No. 19, 2001 4951
Table 2. Experimental and Computed Geometry Parameters for
[R2AlF2]- (R ) i-Bu, Me)a
Table 3. Experimental and Computed Geometry Parameters for
[Me2MF2]- (M ) Ga, In)a
Al-F Al-C F-Al-F C-Al-C
R
(deg)
M-F M-C F-M-F C-M-C
R
(deg)
[R2AlF2]-
(Å)
(Å)
(deg)
(deg)
r
[Me2MF2]-
(Å)
(Å)
(deg)
(deg)
r
M ) Ga
R ) i-Bu (1)
experimental
1.839 1.969
98.74
98.94
125.10 0.15 0.5187
125.17
116.12 0.41 0.6274
115.79
114.97 0.01 0.6373
114.98
116.21 0.33 0.6255
115.95
experimental
1.711 1.99
101.6
105.28
111.5
114.29
114.74 1.31 0.6544
113.60
118.19 3.05 0.6284
115.71
112.12 0.25 0.6759
111.89
112.48 0.40 0.6731
112.11
3.29 0.6458
RHF,SV(P)
1.809 2.029 104.66
104.19
1.817 2.023 104.75
104.76
1.837 2.032 104.46
104.08
RHF,SV(P)
1.711 2.002 107.26
105.81
1.725 1.993 107.77
104.24
1.732 2.023 107.48
107.22
RHF+MP2,SV(P)
DFT(B-P),SV(P)
RHF+MP2,SV(P)
DFT(B-P),SV(P)
DFT(B3LYP),SV(P) 1.827 2.029 104.59
116.50 0.52 0.6239
116.08
DFT(B3LYP),SV(P) 1.721 2.016 107.45
103.98
107.03
M ) In
experimental
R ) Me
experimental
2.043 2.150
95.68
96.22
132.09 0.41 0.4423
132.28
115.70 0.46 0.6241
116.07
115.37 0.67 0.6260
115.91
114.69 0.99 0.6310
115.50
1.712 1.969 103.23
103.27
1.710 2.007 107.23
107.01
1.724 1.998 107.25
107.68
1.733 2.023 107.23
107.74
117.13 0.03 0.6110
117.15
112.32 0.20 0.6728
112.13
110.98 0.41 0.6826
111.36
110.85 0.48 0.6834
111.30
RHF,SV(P)
1.938 2.186 103.46
103.99
1.957 2.193 103.32
104.10
1.965 2.200 103.26
104.39
RHF,SV(P)
RHF+MP2,SV(P)
DFT(B-P),SV(P)
RHF+MP2,SV(P)
DFT(B-P),SV(P)
DFT(B3LYP),SV(P) 1.953 2.189 103.42
104.37
114.85 0.82 0.6306
115.53
DFT(B3LYP),SV(P) 1.722 2.016 107.18
107.47
111.36 0.27 0.6795
111.61
a The structure and notations are similar to those in Table 2.
a The second angles noted at each full line are results of the fit
by the hybrid model. The last column gives the r hybridization
One may note that the hybrids oriented toward the carbon
atoms carry a more pronounced s character, at the expense of
those oriented toward fluorine. The tendency can be qualitatively
understood by the Bent rule.38,39 According to this rule, the more
pronounced s character of the hybrids is concentrated on the
side of the electropositive ligands, while the electronegative ones
remain as hybrids with a higher p contribution. This is a first
explanation for the experimentally observed tendency that the
F-M-F angle is decreasing while the C-M-C angle is
increasing in the order of Al, Ga, In. Indeed, with the progressive
lowering of the s-part, the hybrid angle varies in the direction
of the 90° limit, as is seen from the experimental data in Tables
2 and 3, and this is also revealed in the given composition of
h1( hybrids.
A general validity of the hybridization pattern of bond angles
may be applied for the [(i-Bu)2AlF2]- anion as a rough
approximation of the geometry (static limit) using the angles
available from the disordered structure. In this context the [(i-
Bu)2AlF2]- and [Me2AlF2]- species should be qualitatively
similar, as is also probed by the calculated results (Table 2).
The results of geometry optimization for the [Me2MF2]-
complexes (M ) Al, Ga, In) follow the tendency of experimental
bond lengths and angles (Tables 2 and 3). However, the bond
angle variation is better accounted in the Al, Ga sequence than
in the Ga, In congeners. The anions were computed in a vacuum,
and the results were not improved after including the Madelung
field as point charges from a few surrounding cells. Furthermore,
the considered units were taken from isomorphous crystals
([Bu4N][Me2MF2]) with highly similar cell parameters and
intermolecular distances. Therefore, the Madelung field is
similar in all the complexes and plays no decisive role in
establishing the tendency of bond angle variation. As the
calculations for the free anions show, this is an intrinsic feature
of the complexes themselves.
parameter, and
R measures the accuracy of the fit. R )
1/2((RFMF-Rhybrid)2+(RCMC-Rhybrid 2
CMC ) ). The angle C-M-F is, in C2V
x
FMF
symmetry, not independent and can be deduced from F-M-F and
C-M-C ones, RCMF ) arccos(- cos(RFMF)cos(RCMC)).
x
F-M-C parameters, having the following expressions:
r2
(F-M-F, C-M-C, F-M-C) ) arccos -
,
(
)
2 - r2
(
2
1 - r2
1 + r2
r 1 - r
x
arccos -
, arccos -
(2)
(
)
(
))
(1 + r2)(2 - r2)
x
We observed the remarkable regularity that only one param-
eter (r) reproduces all coordination angles in the considered
[Me2MF2]- anions with very good accuracy. This can be
generalized to the useful working principle that all the mono-
nuclear [R2MF2]- species of Al, Ga, and In are obeying this
correlation (and possibly other MA2B2 systems,37 except cases
with very bulky and chelating ligands).
As a function of the mixing parameter r (extracted from
geometry), the hybrids can be presented in the following form:
h1( ≡ s2r2p4-2r2, h2( ≡ s2-r2p2+r2. When r ) 1/ 2, one
x
obtains the equivalency of h1( and h2(, at the sp3 functions.
For the actual convention of denoting the hybrids, the sum of
their superscripts must give 4, that is, the number of handled
orbitals. In other words, the average of h1( and h2( formally
yields sp3.
The hybrids revealed in the considered series are Al{h1(
)
)
s0.747p3.253, h2() s1.253p2.747}, Ga{h1() s0.538p3.462, h2(
s1.462p2.538}, and In{h1() s0.392p3.608, h2() s1.608p2.392}. The
corresponding mixing parameter r can be found in the rows
corresponding to the experimental entries in Tables 2 and 3.
The fitted angles are presented below the experimental ones in
the first entry of each compound in Tables 2 and 3.
Hybrid-Type Angles as Experimental Criterion for Con-
sideration of ab Initio Calculations. Hybrid patterns of bond
(38) Bent, H. A. Chem. ReV. 1961, 61, 275-311.
(39) Fro¨hlich, N.; Frenking, G. In Solid State Organometallic Chemistry:
Methods and Applications; Gielen, M., Willem R., Wrackmeyer, B.,
Eds.; John Wiley & Sons: New York, 1999; pp 173-226.
(37) Atwood, D. A. Coord. Chem. ReV. 1998, 176, 407-430.

4952 Inorganic Chemistry, Vol. 40, No. 19, 2001
Ferbinteanu et al.
angles are remarkably adequate as real geometry; therefore the
capacity of electronic structure calculations to reproduce this
regularity will be proposed as a key to judge the results of ab
initio calculations.40 A first measure is given by the value of
the fitted mixing parameter (r) in comparison with the experi-
mental data (Tables 2 and 3). All the methods have the tendency
to overestimate the value of r, especially with an increased
deviation for the heavy metals. The accurate description of heavy
elements on one side and of the anionic molecules on the other
is a notoriously difficult task, and the observed hybrid-type
regularities can be taken as a new, chemically meaningful, test
of the method.
versatile tool for obtaining absolute values46 for electronega-
tivities and hardness.47
For the neutral ligands the following ligand electronegativities
are estimated: øF 11.93, øMe 5.45, and øi-Bu 4.29 eV. The
hardness parameters are a measure of Lewis basicity of the
ligands (ηF 8.10, ηMe 4.79, ηi-Bu 3.82 eV).48 Obviously, the
fluorine is revealed as the most electronegative and hardest in
this series. For the isobutyl group the lower electronegativity
and hardness can be related with an inductive effect.
The neutral aluminum has the estimated parameters øAl 4.64
eV and ηAl 2.98 eV, while the organometallic fragment taken
as the neutral AlMe2 species has the values øAlMe2 2.77 eV,
Another measure of the ab initio results can be considered
in the quality of a hybrid fit with respect to the computed angles,
presented as mean square deviation in column R of Tables 2
and 3. This criterion is practically not related to the capability
of the method in reproducing the experimental bond angles.
Each calculation contains small deviations from the hybrid angle
pattern. Moreover, we checked a few other basis sets (ranging
from sto3g to cc-pvtz) and noted a similar decline.
η
AlMe2 2.62 eV. The latter is less hard (weaker acid) compared
to the aluminum atom. At the same time the lower electrone-
gativity suggests that AlMe2 is more electropositive compared
to Al. This will result in a higher electronegativity difference
of AlMe2 than that of Al with respect to fluorine. Therefore
the Al-F bonds are predicted to be more ionic in organometallic
fluorides than in the homoleptic inorganic fluorides.
However, a certain underestimation appears in the calculated
hardness of aluminum. The apparent failure of calculation to
detect more clearly the expected HSAB affinity between
aluminum and fluoride is probably a matter of not including in
the calculation the effects of interatomic interactions between
the acidic and basic partners. A future task of theoretical work
devoted to HSAB principle is to design a method to be able to
provide electronegativity and hardness corresponding to atoms
in molecules. In fact, one may suggest that HSAB is better kept
in terms of electronegativity and hardness calculated for
atoms in molecules than using quantities estimated for isolated
atoms. Despite the huge literature devoted to the formalism and
computation of electronegativity and hardness in relation to DFT
schemes, the systematization of the structural chemistry in terms
of a quantitative HSAB frame is still incomplete. A partial
improvement is given here, using the concept of the mutual
influence of ligands.
The present analysis demonstrates that the hybridization is
a valuable tool even in the age of advanced computer applica-
tion in quantum chemistry.41,42 According to the natural bond
orbital concepts,43 the hybrids are appropriate objects for
accounting for the so-called localized character of the correlation
effects.44
The relatively large radius of the central atom and the small
radius of the bonded ones make the validity of the hybridization
scheme in the [Me2MF2]- complexes (M ) Al, Ga, In) free
from strains due to sterical hindrance. A short comparison of
the goodness of fit (with formula from Table 2) for other
systems, like SiH2F2 (R ) 0.44), CH2F2 (R ) 0.97), and CH2-
Cl2 (R ) 2.28), shows that light central atoms and heavy ligands
enforce a deviation of the geometry from the hybrid pattern.
The broad investigation of MA2B2-type molecules by the given
model is left as a matter of other studies. The role of d orbitals
in the generalized hybridization schemes and in connection with
the practical basis sets of electron structure calculation remains
also a subject of further investigation.
An important result of the actual analysis was the detection
of a mutual influence of the hard and soft ligands, revealed on
the [Me2AlF2]- study case. A comparison of this anion with
the [AlF4] and [AlMe4]- ones was carried out by means of
DFT calculations, considering the ionic vs covalent bonding in
the Al-F and Al-Me bonds. For this purpose we applied the
so-called transition-state method by Ziegler et al.49 as imple-
mented in ADF code.45 Using optimized geometries (Td for
[AlF4]- and [AlMe4]- and C2V for [Me2AlF2]-), we calculated
Mutual Influence of Hard and Soft Ligands in Organo-
metallic Fluorides. Compounds 1 and 2 on one side and 3 on
the other (according to HSAB predictions) show certain mutual
differences in the electronic structure. This problem will be
addressed using the DFT calculations with ADF code45 as a
-
(40) This series of calculations was made with the GAMESS package:
Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon,
M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su,
S. J.; Windus, T. L. J. Comput. Chem. 1993, 14, 1347-1363. The
DFT optimizations were repeated in TURBOMOLE: Ahlrichs, R.;
Ba¨r, M.; Ha¨ser, M.; Horn, H.; Ko¨lmel C. Chem. Phys. Lett. 1989,
162, 165.
(46) The chemical hardness was computed from numerical derivatives of
total energies, η ) 1/2∂2E/∂n2, obtained after slight variations of the
corresponding total charge and populations. The systems were taken
in spin nonpolarized averaged states. The variation of charge was
distributed over the frontier orbitals in such a way that allows the
assignment related to hybrid orbitals. For instance, for aluminum, the
s0.75(x, p2.25-3x, small variations simulate an sp3 state of the atom. For
the neutral AlMe2 fragment, the direct calculation yields a singly
occupied a1 HOMO orbital and a b1 LUMO, which can represent the
pair of hybrids able to bind the fluorine. Therefore, we considered
(41) (a) Root, D. M.; Landis, C. R.; Cleveland, T. J. Am. Chem. Soc. 1993,
115, 4201-4209. (b) Landis, C. R.; Cleveland, T.; Firman, T. K. J.
Am. Chem. Soc. 1995, 117, 1959-1860. (c) Barbier, C.; Berthier, G.
AdV. Quantum Chem. 2000, 36, 1-24.
(42) (a) Nicolaides, C. A.; Komninos, Y. Int. J. Quantum Chem. 1998, 67,
321-328. (b) Komninos, Y.; Nicolaides, C. A. Int. J. Quantum Chem.
1999, 71, 25-34.
0.5(x
the smearing-out of the electrons over these functions into a10.5(xb1
configuration.
(43) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. ReV. 1988, 88, 899-
(47) Parr, R. G.; Yang, W. Density Functional Theory in Atoms and
Molecules; Oxford University Press: NewYork, 1989.
(48) For the neutral fluorine and alkyls, the computed electronegativity
and hardness were based on the variation in the population of the
HOMO orbital, with 0.5 ( x for both R and â fractions of the spin
nonpolarized DFT calculation.
(49) (a) Ziegler, T.; Rauk, A. Theor. Chim. Acta 1977, 46, 1-10. (b)
Ziegler, T.; Rauk, A. Inorg. Chem. 1979, 18, 1558-1565. (c) Ziegler,
T.; Rauk, A. Inorg. Chem. 1979, 18, 1755-1759.
926.
(44) (a) Saebo, S.; Pulay, P. Annu. ReV. Phys. Chem. 1993, 44, 213-236.
(b) Schutz, M.; Hetzer, G.; Werner, H. J. J. Chem. Phys. 1999, 111,
5691-5705.
(45) (a) Amsterdam Density Functional (ADF) package: te Velde, G.;
Baerends, E. J. J. Comput. Phys. 1992, 99, 84-98. (b) In present
calculations we employed the implemented basis sets of triple-ú type
and the PW91 density functional set.

Chemistry of Alkylaluminum Fluorides
Inorganic Chemistry, Vol. 40, No. 19, 2001 4953
Table 4. Partition of the Total Energy (Et ) EP + Eel + Eorb) of
of the negative charges (which originate from the lone pairs of
the methyl groups directed to aluminum) are located close to
each other. This results in the strong repulsion between electron
densities of different Al-C bonds.
On the contrary, in bonded fluoride, due to its intrinsic
hardness, the negative charge is less deformed compared to the
spherical anion, yielding a more relaxed repulsion between
ligands. The tendency for a bigger C-Al-C angle compared
to the F-Al-F one can be understood as driven by the higher
content of repulsion terms in Al-C bonds.
Phenomenological Model for the Energy of a Hybridized
Atom (Equating the Bent Rules). Previously it was shown
that the variation of bond angles in the [R2MF2]- series is in
line with the Bent rules. The energy factors determining the
preference of electronegative ligands for almost unhybridized
orbitals are qualitatively related to the easier ionization of the
metal when electrons are taken from its p orbitals. We target
here a simple function able to model this factor, starting from
the data offered by appropriate quantum evaluation of the
Bond Formation, as Results from the Transition State Methoda
bond formation
Et
EP
Eel
Eorb
AlF3 + F- fAlF4
-6.17 3.57 -7.44 -2.31
-4.45 5.50 -7.01 -2.93
-5.26 5.77 -8.03 -3.00
-4.93 4.07 -6.31 -2.69
-
AlMe3 + Me- f AlMe4
-
AlF2Me + Me- f AlF2Me2
-
AlFMe2 + F- f AlF2Me2
-
a See the text for definition of column entries. All quantities are in
eV.
the total energy of interaction (Et) between the corresponding
fragments (Table 4).
The result that the Al-F in [AlF4]- is stronger than the Al-
Me bond in [AlMe4]- (comparing Et in Table 4) is in line with
the HSAB concept. The covalency of the Al-Me bonds
(measured by Eorb) is invariably higher compared to the Al-F.
Consequently the reciprocal affinity between aluminum and
fluorine seems to have a noticeable ionic character.
Examining the charges from Mulliken population analysis,
one may consider [AlF4]- definitely more ionic (qAl 2.116, qF
-0.779) than [AlMe4]- (qAl 1.282, qMe -0.571). Moreover, in
[Me2AlF2]- the fluorine is more ionic (qF -0.805) than in the
tetrafluoroaluminate.
A drastic change of bonding energies appears in [Me2AlF2]-,
where Al-F becomes weaker than Al-Me. The weakening of
the Al-F bond in the organometallic structures (compared to
the inorganic anion) is clearly seen in the experimental Al-F
bond lengths ([Me2AlF2]-, [(i-Bu)2AlF2]- ∼1.71 Å, [AlF4]-
∼1.65 Å).
energies of various atomic states. The energy (WM(n1,n2)[r]) of
n2
the atom in a general (h1+)n1(h1-)n1(h2+)n2(h2-
)
configuration
was conceived as a continuous function of hybrid populations
(n1 and n2) and mixing parameter, r. The continuity of the
function ensures the availability of orbital electronegativities
(ø) and hardness (η), as derivatives of the total electronic
energy,46 with respect to the electron number.
According to Gyftopoulos theorem,51 a system with fraction-
ally occupied states can be conceived as a result of weighted
superposition of the energies for various integer-populated
configurations. Therefore the WM energy for a general population
at the hybrids can be obtained through an adequate interpolation
over energies of certain reference configurations. They are
available at integer values of the hybrid occupation numbers.
The energies of integer-populated configurations can be cor-
respondingly converted from hybrids to occupations of s and p
shells, which can be computed from the configuration interaction
on the Al atom. The details of construction are shown in the
Appendix.
Thus, a distinguished reciprocal influence of ligands occurs
in the mixed ligand complex. Namely, the former stronger
bonding partner strengthens the initially weaker one, while the
latter exerts an opposite influence on the first. This phenomenon
can be understood in such a way that the mixed hardness allows
the polarization of the central ion. This corresponds to the
mixing of odd and even atomic orbitals, which is symmetry
forbidden in tetrahedral moieties ([AlMe4]- and [AlF4]-). The
observations from the previous section show that the polarization
effects can be surprisingly accurate confined to the model of
hybridized s and p orbitals. The polarization allows the
deformation of the aluminum center in two halves differentiated
by the HSAB factors. One face, toward the alkyl groups, behaves
as a weak acid, while the other, toward the fluorine ligands,
appears as a hard acid. At the same time, the lower hardness
corresponds to more diffuse AOs, allowing a better overlapping
in the Al-C bonds.
The WM function allows (as a heuristic model) the estimation
of hybridization degrees, which yield the minimum energy for
a complete area of varying the hybrid orbital populations. Thus,
the energy of the central atom-in-molecule is proposed as the
phenomenological key for the mutual relationship of hybridiza-
tion degree versus population balance. The surface from Figure
4 contains such dependence for the population (range n1 ⊂ (0,
2), n2 ⊂ (0, 2), restricted with n1 + n2 < 4).
Other useful insights into the bonding situation are gained
by the dichotomy of the total energy, when the repulsive Pauli
exchange (EP), cohesive electrostatic energy (Eel), and the orbital
term (Eorb) are considered as components.52 Examining the EP
term (both in absolute value and relative to Et), the most
significant repulsion effects are encountered for the alkyl group.
The EP (quantum repulsion of closed shells) and the Eel
(classical electrostatic interactions) terms are quantities revealed
when the formation of the bonding between the fragments is
prevented by enforced restriction of the orbital mixing between
the wave functions located on the defined subsystems. The
relaxation from hypothetical fragments to the final bond is
possible after the allowance of orbital mixing (Eorb stabilization).
The sum EP + Eel (the so-called steric term) shows the
interesting feature of comparable values for Al-F and Al-Me
bonds. This suggests that the optimum geometry can be
interpreted as a balance of interligand repulsion. The high
repulsion terms found in Al-Me bonds shows that the centroids
Figure 4 shows that the hybridization degree decreases to a
small value (e.g., 0.2) when the population balance is n1 < n2
and approaches the plateau of r ) 1 when n1 > n2. Fixing the
subscript 1 for fluorine and 2 for alkyl ([R2AlF2]-), it is possible
to see that the case n1 < n2 corresponds to the ionic nature of
the hybrids oriented toward the fluorine face. Such a situation
results naturally as a consequence of the electronegativity
equalization principle.52 According to equation 2, this corre-
sponds to smaller angles for the moiety containing electrone-
gative ligands. The map from Figure 4 offers a semiquantitative
modeling of the empirical Bent rules.
(50) Diefenbach, A.; Bickelhaupt, F. M.; Frenking, G. J. Am. Chem. Soc.
2000, 122, 6449-6458.
(51) (a) Gyftopoulos, E. P.; Hastopoulos, G. N. Proc. Natl. Acad. Sci. U.S.A.
1965, 60, 786-793. (b) Perdew, J. P.; Parr, R. G.; Levy, M.; Balduz,
J. L., Jr. Phys. ReV. Lett. 1982, 49, 1691-1694. (c) Zhang, Y.; Yang,
W. Theor. Chem. Acc. 1999, 103, 346-348.
(52) Sanderson, R. T. Science 1951, 114, 670-672.

4954 Inorganic Chemistry, Vol. 40, No. 19, 2001
Ferbinteanu et al.
fore, a bridged [Me2AlF2]- moiety will have a more pronounced
n1 < n2 balance compared to the free one. This corresponds to
moving to lower values of r on the surface (Figure 4), which is
correlated to smaller F-Al-F angles. Indeed, in the compounds
[Cp2Ti(µ-F)2AlEt2]2, cis-{[Cp*ZrMe(µ-F)][(µ-F)2AlMe2]}2, and
cis-{[Cp*HfMe(µ-F)][(µ-F)2AlMe2]}2, the F-Al-F angles are
(100.18°, 96.85°, and 96.10°) smaller than that of the free
[Me2AlF2]- (Table 2). The dependence of the F-Al-F angle
on the nature of the transition metal bonded to fluorine can be
understood by considering the degree of the covalency increas-
ing from Ti to Hf. The fluorine will be more neutral due to
forming the bond with the heavier transition atom and therefore
more electronegative.
Another compound containing the [R2MF2]- anion is Cs-
[Me2GaF2],59 with a polymeric structure, where each fluorine
atom has close contacts with two cesium atoms. In this
compound the F-Ga-F angle is slightly smaller (96.7(3)°),
while the C-Ga-C angle is increased (127.8(6)°), compared
with [Me2GaF2]- (Table 3). This can be interpreted by a
decrease of the hybridization parameter to r ) 0.46 for the unit
embedded in the polymeric structure. The effect can be assigned
to the polarization exerted from cesium to fluorine, thus causing
further GafF charge transfer (lowering of n1).
A similar bridge is found in [Cs(THF)0.5(Me2GaF2)],60 where
the bond angles are closer to the free moiety (F-Ga-F 97.1-
(2)°) and C-Ga-C 129.8(4)°). Here the Cs atoms are com-
plexed with THF and exert a smaller perturbation to the adjacent
fluorine atoms.
Figure 4. Hybridization degree (r), giving the minimum energy of
the central atom as a function of the populations n1 and n2, describing
a general valence state of C2V symmetry. The surface is generated with
the WM function constructed for aluminum, but the pattern is general
for main group metals.
The given model is qualitatively valid for explaining the
angular tendencies in a general [MA2B2] complex (M ) Al,
Ga, In, or even throughout all main group metal elements). The
reason for expected generality is that the relative ordering of
the averaged energies of the spectral terms (which determine
the pattern of WM) is similar for the different main group atoms
(e.g., E(s2pn-2) < E(spn-1) < E(pn), simply due to the s < p
orbital energy ordering).
The bond angle variation in the [Me2MF2]- series can be
explained by accepting that the electronegativity is in the order
Al > Ga > In. The real order can be a matter of dispute and
further investigation (different sources indicating different
values53,54). However, the actual modeling is consistent with
the Al > Ga > In order and therefore appears to be effectively
valid. Thus, the electronegativity difference between the central
atom and fluorine will increase in the same order. This results
in the enhanced MfF charge transfer, which leads to a smaller
n1-population in the orbitals oriented toward fluorine. The Al,
Ga, In series is arranged in the order of the more pronounced
n1 < n2 tendency. Figuring this order on the given surface
(Figure 4), it is seen that it corresponds to the decreasing
hybridization parameter r. The more pronounced n1 < n2
separation from Al to In is revealed also by the population
analysis in the ab initio calculations.
The qualitative utility of the above model can be extended
further. One may predict, for example, the geometry changes
when [R2AlF2]- appears as a bridge in polynuclear systems.
Examples of this type are [Cp2Ti(µ-F)2AlEt2]2,55 cis-{[Cp*ZrMe-
(µ-F)][(µ-F)2AlMe2]}2,56 and cis-{[Cp*HfMe(µ-F)][(µ-F)2-
AlMe2]}2.57 The formation of a bridge reduces the negative
charge on fluorine, but enhances its electronegativity.58 There-
A qualitatively different situation is encountered in Cs-
[(PhCH2)2GaF2],61 which shows an extended structure with Cs-
F-Ga bridges. Here, the F-Ga-F and C-Ga-C angles cannot
be fitted with a unique parameter r. The deviation is caused by
the strain of packing forces, the crystal structure revealing an
η6-like interaction between phenyl groups and cesium atoms.
In summary, the designed WM function of the central atom
allowed the establishment of a connection between the dif-
ferentiated orbital hybridization and the electron populations
on the metal complexes. The model can be used to rationalize
the stereochemistry, assuming that the dependence on hybridiza-
tion effects on the central atom is the leading term in molecular
energy.42 According to preliminary verifications, the model
works for various MA2B2 systems (M ) C, Si, Ge, Sn; A,B )
R, F, Cl) where the π bonding and d orbitals are supposed to
play no significant role. The ionic nature and weak covalency
of the analyzed [R2MF2]- systems satisfy with particular
accuracy the outlined premises. The present model should not
be used for molecules such as SO2Cl2 or TiMe2Cl2, although
further similar modeling is in principle possible.
Conclusions
The synthesis of organometallic fluorides is one of the
challenging topics of modern chemistry, while it can be
conceived as working against the HSAB rules of affinity. The
use of [FHF]- as a reagent provides the interplay of chemical
rules that govern the protonic definition and reactivity of acids
and bases. The use of [FHF]- can be emphasized as a general
route to the systematic synthesis of organometallic fluorides.
(53) (a) Robles, J.; Bartolotti, L. J. J. Am. Chem. Soc. 1984, 106, 3723-
3727. (b) Bartolotti, L. J. Struct. Bond. 1987, 66, 27-40. (c) Pearson,
R. G. Inorg. Chem. 1988, 27, 734-740.
(54) (a) Bo¨hm, M. C.; Schmidt P. C. Ber. Bunsen-Ges. Phys. Chem. 1986,
90, 913-919. (b) Sen, K. D.; Bo¨hm, M. C.; Schmidt, P. C. Struct.
Bond. 1987, 66, 99-123.
(55) Yu, P.; Montero, M. L.; Barnes, C. E.; Roesky, H. W.; Uso´n, I. Inorg.
Chem. 1998, 37, 2595-2597.
(56) Herzog, A.; Roesky, H. W.; Zak, Z.; Noltemeyer, M. Angew. Chem.,
Int. Ed. Engl. 1994, 33, 964-966; Angew. Chem. 1994, 106, 1035-
1037.
(57) Herzog, A.; Roesky, H. W.; Ja¨ger, F.; Steiner, A.; Noltemeyer, M.
Organometallics 1996, 15, 909-917.
(58) This is a general tendency in the electronegativity (ø) vs charge (q)
dependence and is related with the positive hardness, η ) dø/dq.
(59) Kopp, M. R.; Neumu¨ller, B. Z. Anorg. Allg. Chem. 1998, 624, 1393-
1394.
(60) Kopp, M. R.; Kra¨uter, T.; Werner, B.; Neumu¨ller, B. Z. Anorg. Allg.
Chem. 1998, 624, 881-886.
(61) Neumu¨ller, B.; Gahlman, F. Chem. Ber. 1993, 126, 1579-1585.

Chemistry of Alkylaluminum Fluorides
Inorganic Chemistry, Vol. 40, No. 19, 2001 4955
The actual approach targeted the fluorinated compounds of
aluminum and brought into discussion the detailed aspects that
relate the electronic structure with the HSAB concept. The given
analysis elaborated a phenomenological model able to rationalize
the factors determining the bond angle in [R2MF2]-, which
offers a more quantitative basis to the Bent rules. The model
assumes a hybridization-driven bond-angle pattern and con-
structs the energy of the central atom as a function of hybrid
populations. The condition of minimum energy gives a map of
preferred hybridization degree, as a function of orbital popula-
tion balance. This can be used as a tool to understand the bond
angle variation in the stereochemistry of various members of
[R2MF2]- complexes (free or bridged units). The systematic
HSAB approach for structural problems, by means of electronic
structure calculations and phenomenological models, opens new
views on the principle and methods of chemical synthesis.
calculations of the central atom with various charges (we used
for this purpose a pVTZ basis set for aluminum). The elements
with the same orbital population but different spin coupling were
averaged, to get the spin unpolarized meaning, as is appropriate
for the diamagnetic compounds w(s1pz1px ) ) (w(s(R)pz(R)px )
2
2
2
+ w(s(R)pz(â)px ))/2. The orbital basis for estimating such
matrix elements was prepared under the generalized valence
bond (GVB) method, where in the case of degenerate ground
terms the coupling elements of the Fock matrix were imposed
in a way that corresponds to the spherically averaged ground
states.
Apparently a problem arises when (i + j)/2 is a half-integer.
This case can be empirically solved taking an interpolation on
integer populations with (i + j ( 1)/2, (i + j ( 3)/2. Aside
from the handling of matrix elements from configuration
interactions (computed with GAMESS) the wij energies can be
directly computed imposing the given orbital occupancies in
ADF code. Both versions give a similar pattern of the final WM
energy function. To establish different populations at s, px, py,
and pz orbitals, the calculation of the atom under D2 symmetry
is a convenient procedure.
Acknowledgment. M.F. is grateful to the Alexander von
Humboldt Foundation for the research fellowship. The financial
support of the Deutsche Forschungsgemeinschaft is acknowl-
edged. We are very thankful to one of the referees for his
valuable comments.
The coefficients cij(n1,n2) from eq A.1 can be proposed in a
polynomial form where, for each of them, the powers k and l
Appendix
k
l
in the n1 n2 monomial terms are running with the same values
as for the (i,j) couples of indices denominating the available
integer occupation numbers:
The key for obtaining the energy of the central atom,
WM(n1,n2)[r], as a continuous function of hybrid populations,
n1, n2, and hybridization degree, r, is to consider it as a weighted
superposition of energies taken at all possible integer-populated
configurations denoted wij.
k
l
c (n ,n ) ) Akln n
(A.5)
∑
ij
1
2
ij
1
2
k,l
The condition of eq A.2 results in the full determination of the
W (n ,n )[r] ) c (n ,n )w (r)
(A.1)
kl
∑
M
1
2
ij
1
2
ij
A
elements from various sets of linear equations (one equa-
ij
i,j
tion system per ij couple):
The i and j indices are paralleling the couples of integer
occupation numbers possible for h1 and h2 hybrids, respectively.
The defining condition is that the weighting coefficients should
recover the energy of reference configurations when n1 and n2
are taken as corresponding integers (i, j ) 0, 1, or 2):
Aklikjl ) δ δ
(A.6)
∑
ij
ik jl
k,l
The solving of eq A.6 (for the cases running with i, j, k, l ) 0,
1, 2) leads to the finding of coefficients (eq A.5) (then, replaced
in eq A.1):
WM(i,j)[r] ) wij(r) ≡ cij(k,l) ) δikδjl
(A.2)
1
4
WM(n1,n2)[r] ) (n1 - 2)(n1 - 1)(n2 - 2)(n2 - 1)w00(r) +
The (k,l) pairs are running over the same set of values as the
(i,j) ones.
The general relations between population on hybrids versus
s and p shells are
1
2
1
4
(n1 - 2)(n1 + 1)(n2 - 2)n2w01(r) + (n1 - 2)(n1 - 1)
1
2
(n2 - 1)n2w02(r) + (n1 - 2)n1(n2 - 2)(n2 - 1)w10(r) +
ns ) n1r2 + n2(1 - r2); nz) n1(1 - r2) + n2 r2;
nx ) n1; ny ) n2 (A.3)
1
2
(n1 - 2)n1(n2 - 2)n2w11(r) + (n1 - 2)n1(n2 - 1)n2w12(r)
1
4
1
2
+ (n1 - 1)n1(n2 - 2)(n2 - 1)w20(r) + (n1 - 1)n1(n2 -
The form of wij(r) can be taken as quadratic interpolation over
1
4
the distinguished values given below:
2)n2w21(r) + (n1 - 1)n1(n2 - 1)n2w22(r) (A.7)
wij(r ) 1) ) wji(r ) 0) ) w(sipzjpxipyj), wij(r ) 0) )
The above formula is continuous and differentiable in all the
parameters, n1, n2, and r, and combines the valence bond and
DFT-like approach in the model based on the hybridization
concept.
j
i
i
j
x
x
wji(r ) 1) ) w(s pz px py ), wij(r ) 1/ 2) ) wji(r ) 1/ 2) )
w(si+j/2pzi+j/2pxipyj) (A.4)
2
Example: w20(r ) 1) ) w(s2pz2), w20(r ) 0) ) w(pz2px ), and
Supporting Information Available: Tables listing detailed crystal-
lographic data, atomic positional parameters, and bond lengths and
angles. This material is available free of charge via the Internet at
http://pubs.acs.org.
1
1
2
x
w20(r ) 1/ 2) ) w(s pz px ).
The energies of various orbital configurations over s and p
valence shells are obtained by selecting corresponding diagonal
matrix elements from the output of the configuration interaction
IC010131G