K. W a d e Durhom University Durham, England
Bond Length-Bond Energy Term Correlations for Bonds in A11X6 Compounds
A
familiar feature of covalent aluminum compounds AIXI is their tendency, when in solution in nondonor solvents, in the gas phase, and in some cases in the crystal, to adopt dimeric structures AI,X6 (I), in which each aluminum atom is surrounded by a distorted tetrahedron of two terminal and two bridging atoms or groups X (X = C1, Br, I, Me, or H) ( I , 2). Indeed, aluminum compounds AlzXe are commonly used as model species for the discussion of bridged compounds in general. What is less commonly recognized, however, is the extent to which the bridging A1-X bonds differ in length and strength from the terminal AI-X bonds, and the manner in m-hich this difference depends on X. Here, published thermochemical data are used to calculate bond energy terms E(A1-X), and E(A1X), for the bridging and terminal AI-X bonds, respectively, of some representative compounds AlzXe (X = Cl, Br, I, Me, or H). These bond energy terms correlate well with the known lengths of the bonds in question, and allow an appreciation of bridging and terminal bond orders.
solid by X-ray crystallography. Interatomic distances for ALHB have not been determined directly: the bridging AI.. . H distance shown in Table 1 is that found by X-ray and neutron diffraction (6) for crystalline (AlHa),, in which all the hydrogens are bridging, and the aluminum atoms are six-coordinate. The terminal Al-H distance listed is that found by X-ray crystallography for LiAIHp(7). The data in Table 1 show that the bridging A1-X bonds are invariably lonuel than the terminal AI-X bonds, irrespective of whether the bridging bonds may formally be regarded as two center electron-pair bonds, as when X = halogen, or two center one electron bonds, as when X = H or Me. For example, the difference between the bridging and terminal bond distances, r(A1-X), - r(A1-X), for the chloride (X = C1) is little different from that for trimethylaluminum dimer (X = Me), although this difference decreases in the seTable 1 .
lnterotomic Distances
(4in Dimers AllX6
Bond Lengths
Interatomic distances for the compounds AI2X6are listed in Table 1. Data for X = Cl or I were determined for the vapor by electron diffraction (S), whereas for X = Br (4) or Me (5) they were determined for the
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References: C1(3), Br(4), I@),H(6,7), Me(5)
quence C1> Br > I, so that for Al& the terminal Al-I bonds are only slightly shorter than the bridging Al-I bonds. However, since the data for AlzCIKand AlzIK were obtained by an early electron-diffraction study (S), and may be less accurate than the other data, the variation from one halide to another may not be significant. Bond Energy Terms
The consistency of these bond distances with published thermochemical data can be demonstrated as follows. The halides Al& (I) contain four bridging AI-X bonds and four terminal Al-X bonds. Bond energy terms E(A1-X), and E(A1-X) can be assigned to each of these such that the enthalpy of atomization of (I), M.(A12XK)(.), is the sum of these terms The energy relationships used in salculoting EfAI-Xlt and EfAi-Xi, With the exception of the energy level reloting to (2AI 6x1 in their standard stales, all energy levels relote to gor-phase species.
+
Since M,(Al&)(,) can be calculated from the known standard enthalpies of formation, AH;, of gaseous A1&, A1 and X (8) (see Table 2) the following equation in E(A1-X), and E(A1-X) is obtained
+
( a ) 4E(AI-XIr 4EfAI-Xi, lcl ~AHI'(AI) ~AHJ'IXI 14 -2AH1'1plonar AIXd Is) 2AHrsordAIXs)
(bl 6E(AI-XIr Id) -2AHlolpyramidal AIXsl If1 - A H I " ( A I ~ X ~ Ihl AHdiaao..(AI2X6+ 2 planar AlXd
The extent to which (p p ) s Al 2 X bonding in the planar monomer (111) exceeds that in the pyramidal monomer (11) [the p-orbitds of X can overlap the vacant metal p-orbitd of (111) better than the vacant metal sp3-orbital of (11)) Differences in the A1-X c-bond energy as the hybridization of aluminum changes from spato spS +
A second equation in E(A1-X), is obtained by considering a hypothetical species, a pyramidal molecule AlX, (11) formally derived from the dimer by separating the two halves in a manner which preserves unchanged the original terminal bonds, and replaces by two similar terminal bonds the original four bridging bonds
A third factor, the increase in internuclear and interelectronic repulsion forces that accompanies the change from planar to pyramidal geometry, mill also contribute to the reorganization energy, but to an extent that may be ignored in an approximate treatment. Though neither the reorganization energies themselves nor these individual factors that contribute to them can be measured directly, the values given in Table 2 have been calculated for the aluminum halides Table 2.
The enthalpy of atomization of such a pyramidal monomer, AH. (pyramidal AIX1)(.), will equal the sum of its bond energy terms, 3E(A1-X),
Thermodynamic Data (kcol/mole) f o ~ Goreour Compounds (AIX,),
This equation can be solved for E(AI-X)t only if AH," (pyramidal AIXs)(p)is known. The pyramidal monomer (11) will be a higher energy species than that into which the dimer (I) actually dissociates, the planar monomer (111)
e n t h d w of formation of the gaseous compound from the el&ents in their standard states at 29R°K. = enthalpy of atomization of the gaseous compound at AH. 298'K, calculated from AHl" by use of the following heat,sof &xniziltion of theelements: Al. 78.0: Cl, 29.08; ~ r 26.74; , I, 25.54; H, 52.095; C, 171.29 kcal/gatam. AHl' (AIH,)i,l. and AHlo(Al2Hsjlg1 for gaseous samples are unknown; figures m this column are consistent with the known heat of formation of solid AIHZ(-I1 keal/mole) and yiith the known heats of dissociation of dialkylaluminum hydndes (11. AIH)a (-17.5 kcal/mole per AlHAl bridge). Calculated assumingE (C-H) = 99.4 keal/mole. A H P =
The energy relationships between (I), (11), and (111) are illustrated in the figure. The enthalpy of formation of (11) exceeds that of (111) by an amount usually referred to as the reorganization energy, AH,.,,.. (AIXI)(.). This is effectively composed of two main factors
~
~~
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(9). Subtracting these from -AH; (planar A&)(d gives -AHf (pyramidal AIXs)(pl,and hence E(A1X ) t and E(A1-X),, as listed in Table 2. The method may be illustrated by considering aluminum chloride as an example. The sum of the bond energy terms for the dimer Al2Cl6is equal to its enthalpy of atomization 4E(AI-CI)*
+ 4E(AtCI),
=
639.0 kcd/mo:e
Similarly, the entbalpy of atomization of the pyramidal monomer AlC13 is equal to the enthalpy of atomization of the planar molecule [-AH;(planar A~C~X)(~I AH(A1) 3AHf0(Cl)w] minus the energy of reorganization [ A H ( A 1 C l 3 ) ] (see the figure), and equals 3 E(A1-C1) I
+
+
3E(AI-Cl)r
:.
=
1139.4
+ 78.0 + 3 X 29.081 -31.6
E(AI--CI)l = 91.0 and E(AI-CI),
=
=
273.0
68.8 kcal/mole
The A1-Br and A1-I bond energy terms in Table 2 were calculated in the same way. I n calculating the A1-C bond energy terms for A12Mes,the reorganization energy of AIMea was taken as zero, since the A1-C bond length for planar AIMea (10) is the same as the terminal A1--C bond length in the dimer AlzMee (6),and the C-H bond energy term, E(C-H), was taken as 99.4 kcal/mole, the value for methane. For the hydrides A12Heand AIHa, entbalpies of formation are unknown. The bond energy terms E(A1H), and E(A1-H), given in Table 2 were calculated by assuming that the enthalpy of atomization of solid (AIHa). (for which -AHfo = 11 kcal/mole (8)) was equal to 6 E(A1-H),, since the polymeric solid contains six Al.. . H bridging bonds per AIHs unit. It was also assumed that a reasonable value for the enthalpy of dissociation of AlpHbinto 2A1H3 (equated to 4 E(A1-H), - 2E(A1-H)t, since four bridging A1-H bonds are broken and two terminal A1-H bonds are formed) was 35 kcal/mole, a figure consistent with the known heat of dissociation of AlHA1 bridges (-17.5 kcal/mol per bridge) in organoaluminum hydrides (RAlH)%(11). Conclusions
Because of the various assumptions made in deriving the bond energy terms in Table 2, and to a lesser extent because of possible errors in the data used, the values obtained can at best be regarded as rough guides to the strengths of these bridging and terminal A1-X bonds. That they are nevertheless realistic guides becomes apparent if one examines the variation with X for either E(A1-X), or E(A1-X), or if one compares E(A1-X), with E(A1-X), for particular species X. This last exercise is effectively carried out in the last two rows of Table 2, which list E(A1-X), - E
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(Al-X),, and E(AI-X),/E(A1-X)t, and in which the entries correlate quite well with those in the corresponding two rows in Table 1. The values of E(A1-X)t in Table 2 show the expected variation with X : a stepwise decrease in the sequence X = C1 > Br > I; a value for X = H rather larger than that for X = I; and a value for X = Me similar to that for X = I. These features are in line with the bond energy terms listed by Johnson (12) for various M-X bonds formed by elements M to the right of aluminum in the periodic table. The decrease in E(A1-X), in the sequence X = C1> Br > I > H > Me is consistent with the known relative bridging capacities of these species, and underlines the fact that bridging by two-center two-electron bonds is stronger than bridging by two-center one-electron bonds. This point is brought out most markedly by the figures in the last row of Table 2, from which i t is seen that, whereas the electron-deficient bridge bonds formed by hydrogen atoms or methyl groups are about three-fifths the strength of their terminal counterparts, halogen bridges are about three-fourths the strength of terminal aluminum-halogen bonds. This difference between electron-deficient and other bridges is much less marked when one compares bond lengths, but nevertheless appears significant (see the last row of Table 1). I n conclusion, the bond energy terms in Table 2 appear to be consistent with the following generalizations. For all bridged species, internuclersr and interelectronic repulsion terms will be greater for bridging bonds than for terminal bonds, and so the farmer will appear to he weaker even in oases where formally both bridging and terminal bonds are of the same order. The difference between bridging and terminal bonds will be heightened if a. higher bond order is possible for terminal ss opposed to bridging bonds. For species containing electrondeficient bridges, the difference is between terminal bands formally of order 1.0 and bridging honds formally of order 0.5. For halides, where ( p d ) dative irbonding from hdogen to metal is possible, the difference is between terminal bonds of order greater than unity and effectivelysingle bridging bonds. -+
Literature Cited (1) Wbos. K., Chcm. BTit.. 4,503 (1968). (2) BIGELOW. M. I. J., CREW. EDDC., 16,495(1969). (31 P*LMEB, K. J., A N D ELLIOTT. N., 3. Amer. Chcm. Soc., 60, 1852 (1938). (4) RENEB,P. A. ~ n M*cGimAva~, d C. H., Rec. Tmv. Chim., PaysBos. 64,275, (1945). (5) H o ~ ~ ~ nJ.r C., r . AND STREIB,w. E.. Chem. Commun.. 911 (1971). (6) Tnnner, J. W.. A N D RINN. H. W.. Inom. Chcm.. 8, 18 (1969). (7) SXGAR, N . . A N D POST. B..ImWg. Chem.. 6,669 (1967). (8) W A a x m , D. D., EVANS, W. H.. PABKER. V. B., HALOW. I.. BAILDY. 6. M., AND S C ~ O M R. M . M . "Seleoted Values oi Chemical Thermodynamic Propertie.." U.S.N.B.S.Technical Note 270-3. Jsn. 1968. (9) COTTON, F. AA . ND LETO,J. R., J . Chem. Phys.. 30,993 (19591. (10) ALMENNIN~BN. A,. HALYORBEN. S.. A N D HUGAND.A,. Chem. Commun.. 644 (1969). (11) CoA~m8.0. E.. A N D WIDE. K.. "Org~nomet~llic Compounds" (3rd. Ed.), Methuen. London, 1967, Vol. I, "The Main Group Elements,"
p. 340.
(12) JORNBON. D. A,, "Some Thermodynamic Aapeots of Inorganic Chemistry;' Univelsity Press, Cambridge, England, 1968. p. 158.
