The Journal of Physical Chemistry, Vol. 83, No. 7, 1979 865
Torsional Potential of Conjugated Dicarbonyl Compounds
Intramolecular Torsional Potential of Conjugated Dicarbonyl Compounds Giles L. Henderson Department of Chemistry, Eastern Illinois University, Charleston, Illinois 6 1920 (Received October 12, 1978)
A modified Buckingham “6-exp” function was employed to estimate the torsional potential of some low molecular weight conjugated dicarbonyl compounds. Ethanedial was examined first as a test case in which the torsional potential has been previously characterized by spectroscopic methods. The model was then applied to 2,3butanedione and was found to give a potential consistent with the temperature depehdence of the dipole moment, the expectation value of the torsional angle as determined from electron diffraction and the torsional oscillation frequency as observed in the IR and far-IR spectra. The study suggests that although there is appreciable T bonding interactions contributing to the torsional forces in 2,3-butanedione, there is no significant barrier to rotation from the cis conformation and hence the cis conformer is unstable. In contrast, when steric and dispersion forces are negligible and the torsional potential is dominated by Coulombic and K bonding interactions as in the case of ethanedial, a significant barrier to rotation from the cis conformation is predicted and indeed this conformer has been found to be metastable.
Introduction Intramolecular torsional potentials have been traditionally characterized by fitting experimental data with a Fourier expansioin of the form V(4) = ‘/ZcV,(l - cos n4)
(1)
where in the case of conjugated dicarbonyl compounds, 4 is the dihedral angle defined in Figure 1. Although this function is particularly convenient to employ, it will be shown in this paper that physical interpretation of the Fourier parameters may lead to erroneous conclusions. P bonding due to partial p orbital overlap between adjacent carbonyl carbon atoms is expected to stabilize both the cis and trans conformers. Moreover, it has been shown1 that P bonding interactions are reproduced remarkably well by the simple formula VP = 1/2Vz(l- cos 24). Since conjugation energies are expected to be on the order of 3-4 kcal mol-l, a Fourier expansion with a Vzterm of this magnitude would in general result in a significant barrier to rotation from the cis conformation. However, a stable cis conformation has only been experimentally observed in the case of ethanedial (glyoxal), HC(=O)C(=O)H.213 Numerous experimental investigations have failed to document the stability of cis-2,3-butanedione ( b i a ~ e t y l ) . ~A - ~previous analysis7 of the temperature dependence of the dipole moment of biacetyl in which the torsional potential was represented by a Fourier series gave optimized potential parameters of Vl = 7.60 f 0.09 and V2= 0.0 kcal mol-’ suggesting that, in contrast to glyoxal, the cis conformer of biacetyl is unstable. Although this is in agreement with infrared415and electron diffraction6 data it is hard to rationalize Vz = 0.0 in view of the expected magnitude of the T bonding interaction. In this paper we will employ nonbonding force laws to obtain a more realistilc description of the torsional potential and show that it is indeed likely that although there is appreciable T bonding interactions contributing to the torsional forces in biacetyl, there is no significant barrier to rotation from the cis conformation and hence the cis conformer is unstable.
Method In this study the torsional potential is assumed to consist of a combination of T bonding interactions and several nonbonding interactions:
V(4) = l/ZV,(l - cos 24) +
C[AiJexp(-BijriJ) - Cij/rijG + Dij/rij - Eij/ri;] (2)
where V2 is the barrier to rotation due to T bonding. The van der Waals interactions are described by the Buckingham “6-exp” potential and the last two terms in the summation correspond to Coulombic and inductive interactions, respectively. The Buckingham “6-exp” function has been sucessfully used in a number of previous studied8-11to describe the contributions of intramolecular nonbonding forces to molecular conformation. However, in this calculation, electrostatic contributions must also be included since the carbonyl groups exhibit extremely large dipole moments. This has been accommodated by assuming a simple Coulombic force law between charge densities centered on the carbonyl oxygens. It should be noted that the usual intermolecular dipole-dipole equations12are inappropriate to this in$ramolecular case since the dipole-dipole separations are small compared to the length of the dipole, r(C=O). Moreover, during a torsional rotation about the C-C cr bond, only one of the four Coulombic terms varies with the dihedral angle (see Figure 2). A preliminary investigation revealed that, in general, rotational barriers are overestimated if inductive effects are not included along with Coulombic interactions. This does not seem surprising, particularly in dicarbonyl compounds where, in addition to the very strong dipole moment, the carbonyl group is highly polarizable. In this model electrostatic and inductive effects are only considered for the 0-0 interactions and are neglected between other atomic pairs. Inductive contributions vary with l / r 4 (see eq 1.3-18in ref 12) and are described by the last term in eq 2. To calculate the nonbonding part of the torsional potential, all of the interatomic distance (rlJ were first calculated as a function of 4 with the aid of a Fortran computer program13assuming rigid bond angles and bond lengths. These interatomic distances were then used along to calculate the with appropriate parameters ( Alj...EiJ) nonbonding energies (the summation in eq 2). This calculation was performed first for glyoxal to test the method and the quality of the potential parameters discussed below by comparing the shape and the nonbonding torsional barrier height with the experimental value reported by Currie and Ramsay.2 This method was then
0022-3654/79/2083-0865$01.00/00 1979 American Chemical Society
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The Journal of Physical Chemistry, Vol. 83, No. 7, 1979
G. L. Henderson
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TABLE 111: Coulombic and Inductive Parameters (M(C=Q))= 2.5 f 0.3 D‘ glyoxal qo = 2.09E - 10 esu
p(C=O) = 2.83 Db
biacetyl
qo = 2.33E - 10 esu
D o 0 = 78.2 E o 0 = 90.7 a The carbonyl dipole averaged for formaldehyde P(C=Q) = 2.34)22and acetaldehyde (p(C=O) = 2.70 D).22 Reference 7.
R Flgure 1. Note the torsional angle q5 is zero for the trans conformation.
Figure 2. Although the Coulombic potential is dependent on four interatomic distances and interactions, only one of these (rlJ varies with a change in the torslonai angle of the rigid model. Therefore the angular dependence of the Coulombic potential may be considered as a single term, Dm/f1,,.
TABLE I: Structural Parameters glyoxalu
‘cc, A ’cop ‘4 ‘cH(ald), A ‘C-CH3, a ‘CH(Me), LCCO, deg LCCC, deg LCCH(Me), deg LHCO, deg References 1 4 and 15.
c. .c *
0 . . .O(SP’)
0.230 0.700 21.0 34.0
1.507 1.214 1.527 1.114 120.3 116.3 108.1
121.2
Reference 6.
49.2 325.0 370.0 600.0
ref 10,11 10,11 9 thisstudy
applied to biacetyl to calculate the nonbonding interactions and optimize V , to fit experimental dipole data.
Structure and Potential Parameters The necessary bond lengths and bond angles required in this calculation were obtained from recent electron diffraction studies on glyoxa114J5and biacety16 and are summarized in Table I. The van der Waals force constants used to describe homonuclear interactions have been optimized in previous conformation studies9-11 and are cited in Table 11. However, Scott and Scheraga’sgvalue for Coo is based on a polarizability16 for carbonyl oxygen of a(C=O) = 0.84E - 24 cm3. Since the resulting nonbonding rotational barrier appears to be too large, we have elected to recalculate Coo by means of the Slater-Kirkwood equation17using a(C=O) = 1.16E - 24 cm3 cited by Hirschfelder et al.:la Cij
0
?r
‘../‘
,
2 4
where e and m are the electronic charge and mass, respectively, and N&O) = 7.03.*317 In order to maintain a set of self-consistent force constants, Aoo was also recalculated to ensure the minimum of the Buckingham “6-exp” function corresponds to twice the van der Waals radius (3.0 A) for a carbonyl oxygen atom.19 The force constants for heteronuclear interactions were estimated from the usual combination rules:20
126.6
3.60 3.20 4.59 4.59
\
Figure 3. (a) Nonbonding torsional potential for glyoxal. The lower, middle, and upper dashed curves correspond to the steric, dispersion, and electrostatic (Coulombic and inductive) components, respectively. The solid curve gives the total nonbonding potential. Note all of the potential components have been adjusted to zero at the trans conformation ($ = 0). (b) A comparison of the nonbonding potential described by the modified Buckingham function (solid curve) with the first term of a Fourier expansion (dashed curve).
biacetylb
TABLE 11: van der Walls Force Constants A;; x 10-4 B,; cj; H* . .H
‘
L,‘
Pl
1.526 1.212 1.132
I,
‘.
= (3e hai2)/4[mai/Neff(i)]1 / 2
(3)
The residual charge (qo) on the carbonyl oxygens was estimated by dividing the appropriate carbonyl dipole moment by its bond length. This charge was then used to calculate the Coulomb force constant Doo and, along with the carbonyl polarizability cited above, to calculate the inductive parameter Eoo where the mutual inductive potential is given byz1
Vipd = --Eij/r4
(5)
where E,, = qO2a(C=0). The dipole data and corresponding electrostatic force constant are presented in Table 111. All the potential parameters give energy in kcal/mol with rij in A.
Results and Discussion The various components of the nonbonding interactions for glyoxal are shown in Figure 3a. In this molecule the
Torsional Potential of Conjugated Dicarbonyl Compounds
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The Journal of Physical Chemistty, Vol. 83, No. 7, 1979 807
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Flgure 4. (a) The calculated torsional potential of glyoxal (solid curve) and its nonbonding (upper dashed curve) and a bonding (lower dashed curve) components. (b) The calculated torsional potential of glyoxal (solid curve) compared to a Fourier potential reported by Durig and co-workers3 (dashed curve).
attractive and repulsive van der Waals forces are small and nearly cancel. The nonbonding potential is clearly dominated by the electrostatic potential (Coulombic and inductive). It can be seen from Figure 3b that in this case, where steric factors are negligible, the shape of the nonbonding potential 1s qualitatively described by the first term of a Fourier expansion, 1/zV2(l- cos $1. The a interaction can be calculated from the dependence of the molecular orbital matrix elements on the dihedral angle. It has been shown1 that such calculations are remarkably well reproduced by the second term of a Fourier expansion, 1/2V2(1- cos 24). Figure 4a shows the nonbonding and 7r bonding components of the total torsional potential calculated from eq 2 where V2 was taken as3 2.66 kcal mol-l. Our potential is then compared with a Fourier function previously characterized from spectroscopic intensity measurement^.^ Since both potential functions in Figure 4b describe a bonding interactions by the same second-order Fourier component, their differences can be attributed entirely to the difference in the nonbonding components, i.e., the modified Buckingham function described in eq 2 vs. the first term of a Fourier expansion. Our nonbonding barrier height of 3.5 f 0.9 kcal mol-l reflects the uncertainty in the electrostatic force constants and agrees with the experimental value2 of 3.2 f 0.3 kcal mol-l. Since the model and the force constants employed gave a satisfactory result in this test case, the calculation was then extended to biacetyl. The nonbonding barrier height is particularly sensitive to the orientation of the methyl radicals. Figure 5 illustrates three characteristic cases. The corresponding nonbonding torsional potentials are shown in Figure 6. Appreciable steric forces are noted in case A where the methyl hydrogens are at their closest approach in the cis conformation. This strain is greatly reduced in cases B and C where one or both of the methyl radicals have been rotated 60”, respectively. It is of some interest to compare these potentials with that of a “pseudoatom” model in which the methyl group is considered to have a constant van der Waals radius describing the average methyl interaction as determined by analogy with the potential energy between two methane molecules.s This potential was calculated using force constants cited by Mason and Rice% and is shown as a dashed curve in Figure 6. It appears that this simplified model overestimates the effective or average methyl-methyl interaction and approximates our case A. In order to calculate experimentally observable properties of biacetyl it is convenient
Figure 5. Three representative methyl orientations in biacetyl.
d Figure 6. Nonbonding torsional interactions for biacetyl. The dashed curve corresponds to the “pseudoatom” model, see Results and Discussion. The upper, middle, and lower solid curves give the nonbonding potentials corresponding to case A, B, and C methyl orientations, respectively (see Figure 5).
to describe the torsional potential in terms of an effective average potential. We obtain the best fit of dipole moment data using the intermediate case B as the effective nonbonding potential. Alternatively, an effective potential was calculated by averaging the three torsional potentials corresponding to cases A, B, and C over all values of $ where each case was weighted by its appropriate degeneracy (9, 18, and 9 for A, B, and C, respectively) and Boltzmann factor. Although this latter method is theoretically more pleasing, it does not give as good of fit of the experimental dipole data. The total effective potential depicted in Figure 7 was obtained by adding the nonbonding terms in eq 2 for case B to the P bonding term and V2was optimized by a least-squares fit of the dipole moment data. The temperature dependent rms dipole moment was calculated from the classical expectation value of the torsional angle by the method of Beach and Steven~on:~,~~,~~ pz
=A
-
B(COS4 )
(6)
where A = B = 11.91 D2 are molecular constants7 and (cos
868
The Journal of Physical Chemistry, Vol. 83, No. 7, 1979
G. L. Henderson T A B L E IV: Eigenvalues for t h e L o w e r Torsional Levels of Biacetyl
-
$ s
UT
E T , cm-'
0 1 2 3
23.32 69.84 116.11 162.13
J
Y
0 IO 20
21
30
0 Flgure 7. The effective torsional potential of biacetyl (solid curve) and its nonbonding(upper dashed curve) and T bonding (lower dashed curve) components. The nonbonding components correspond to the intermediate case B methyl conformation (see Figure 5).
# 40
1900
WAVENUMBERS CM-1 I800 1700
1600
;ii
B
f
50
z a
E
60
1.26 70
w
80
1.18 v
90
W
g
1.10
100
Figure 9. The antisymmetric C=O stretch infrared band of biacetyl vapor. The intense P and R branches exhibit weak torsional satellites at (up uR)/2f 47.5 cm-I. (Spectrum measured at room temperature in a 10-cm KBr cell with a Perkin-Elmer 137 spectrometer.)
+
1.02
400
300
500
T( K O ) Figure 8. The temperature dependence of the dipole moment of biacetyl: (0)Henderson and Meyer's7 dielectric vapor phase measurements; (A) Bloom and Sutton's'' dielectric vapor phase measurements; the line through the experimental points gives the theoretical dipole moment calculated from eq 6 and 7 for the torsional potential given in Figure 7.
4) represents the expectation value of the cos 4 averaged over the torsional potential V(4): &rcos
4 e x p ( - W ) / h T ) d4
(cos 4) =
(7) Lrexp(-V(4)/kT) d 4
The T bonding potential parameter, V2 in eq 2, that best fits the temperature dependence of the dipole moment was found by a numerical least-squares fit of eq 6 and 7 to the experimental observations. These calculated dipoles are compared with experimental value^^^^^ in Figure 8. The optimum V2 = 3.60 kcal molt1 is in reasonable comparison with glyoxal2 (V2= 3.2 kcal mol-l) and butadiene (V2= 3.98 kcal m ~ l - l , ~or' 5.91 kcal Equation 7 can be used to calculate a classical expectation value of the torsional angle for a given potential at any desired temperature. We calculate ( 4 ) = 30' for the intermediate potential given in Figure 7 at T = 501 K which is in close agreement with the upper limit reported by Hagen and Hedberg6 from the analysis of electron diffraction data of biacetyl at this temperature. They report a rms torsional angle of 24 f 6'. This potential was also used to estimate the far-IR torsional potential. Torsion about the conjugated carbon atoms is not strictly a normal mode since the center of
mass is not fixed on the internuclear axis during a rotation about the c-c axis. However, this motion clearly approximates the normal mode for small amplitude displacements from the equilibrium trans conformation and was used to calculate the lower lying torsional quantum levels. The variational method was employed in which the torsional eigenfunctions were written as a linear combination of Hermite polynomials. The basis set was restricted to orders of zero to fifteen to calculate the first four eigenvalues. The torsional potential in Figure 7 was expanded in a Taylor series around the minimum or trans conformation. The resulting coefficients of the fourthorder polynomial were then used to calculate the matrix elements of the secular determinant by the method of Somorjai and H ~ r n i g The . ~ ~ structural parameters cited in Table I were used to calculate the reduced moment of inertia of the trans conformer as I , = 4.010 X g cm2. The diagonalization was carried out utilizing a standard computer program30and the eigenvalues for the lower lying torsional levels are given in Table IV. This calculation gives a transition frequency for the 1 0 fundamental of ut = 46.5 cm-' which is in excellent agreement with observed spectra: Fateley et al.31report the acetyl torsion at ut = 48 cm;l; Durig and co-workers4 report two lowfrequency features at 47 and 56 cm-' which they assign to acetyl torsion. In addition, the antisymmetric C=O stretch exhibits satellites at 1680 and 1775 cm-l. If these features (see Figure 9) are assumed to be combination and difference bands of the acetyl torsional mode, then the approximate torsional frequency is given by 1/2(1775 1680) = 47.5 cm-'. In conclusion the modified Buckingham "6-exp" function used in this study yields a torsional potential which satisfactorily reproduces a number of experimentally
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Transference Numbeir Measurements
The Journal of Physical Chemistry, Vof. 83, No. 7, 1979 869
observed properties of biacetyl. These include the temperature dependence of the dipole moment, the expectation value of the torsional angle as determined from electron diffraction studies, and the torsional oscillation frequency observed in the IR and far-IR spectra. The nonbonding barrier height, V(cis) - V(trans) = 7.9 kcal mol-’, is in good agreement with the previous Fourier analysis7of the dipole moments (Vl = 7.6 f 0.1 kcal mol-l). However, it should be emphasized that the shape of the torsional potential is not reproduced by a low order Fourier expansion. Moreover, the optimized Fourier description results in V 2= 0.0 which might incorrectly suggest there is no significant P conjugation in this molecule. In contrast, this study gives a realistic optimized V, = 3.60 kcal mol-I. These results suggest that physical interpretations of Fourier parameters are probably not meaningful except in special cmes such as glyoxal where van der Waals and steric factors are negligible.
W. G. Fateiey, R. K. Harris, F. A. Miiier, and R. E. Witkowski, Spectrochim. Acta, 21, 231 (1965). K. Hagen and K. Hedberg, J. Am. Chem. Soc,, 95, 8266 (1973). G. L.Henderson and G. H. Meyer, J. Phys. Chem., 80, 2422 (1976). E. A. Mason and M. M. Kreevoy, J. Am. Chem. SOC.,77, 5808 (1955). R. A. Scott and H. A. Scheraga, J . Chem. Phys., 42, 2209 (1965). J. B. Hendrickson, J. Am. Chem. SOC.,89, 7036 (1967). R. J, Abraham and K. Parry, J. Chem. SOC. 6 ,539 (1970). For example see equation 12.1-45, J. 0. Hirschfeider, C. F. Curtis, and R. B. Bird, “Molecular Theory of Gases and Liquids”, Wiiey, New York, 1964, p 849. M. J. S. Dewar and N. C. Baird, COORD, QCPE No. 136, Indiana University, Bioomington, IN. K. Kuchitsu, T. Fukuyama, and Y. Morino, J. Mol. Struct., 1, 463 (1968). K. Kuchitsu, T. Fukuyama, and Y. Morino, J. Mol. Sbvct.,4,41 (1969). J. Keteiaar, “Chemical Constitution”, Eisevier, Amsterdam, 1953, p 91. K. S. Pitzer, Adv. Chem. Phys., 2, 59 (1959). 01 = (1/3)(aii 2a,), see p 949, ref 12. A. Bondi, J . Phys. Chem., 68, 44 (1964). E. A. Mason and W. E. Rice, J . Chem. Phys., 22, 522 (1954). See eq 1.3-18 in ref 12. A. L. McCielian, “Tables of Experimental Dipole Moments”, W. H. Freeman, San Francisco, 1963. E. A. Mason and W. E. Rice, J. Chem. Phys., 22, 843 (1954). J. Y. Beach and D. P. Stevenson, J . Chem. Phys., 6, 635 (1938). Beach and Stevenson give p* = A 6 (cos 4 ) and express the torsional potential as V(4) = 1/2C,Vn(1 cos @). However, we have chosen to write the potential in the more conventional form V(4) = ’/2cnVn(1-cos I @ ) which requires that p* = A - COS 4 ). G. I. M. Bloom and L. E. Sutton, J . Chem. SOC,727 (1941). N. L. Ailinger and J. T. Sprague, J. Am. Chem. Soc., 95,3893 (1973). L. A. Carreira, J. Chem. Phys., 62, 3851 (1975). R. L. Somorjai and D. F. Hanig, J. Chem. Phys., 36, 1980 (1961). W. G. Rothschild, POT, QCPE No. 74, Indiana University, Bioomington, IN. W. G. Fateley, R. K. Harris, F. A. Miller, and R. E. Witkowski, Spectrochim. Acta, 21, 231 (1965).
Acknowledgment. The author expresses his gratitude t o the Eastern Illinois University Council of Faculty Research for financial support of this study, to his students, Mark; Anfenson and Bill Schinzer, for their assistance with the computations, and to the Institute of Paper Chemistry, Appleton, WI for the use of their Calcomp program PAIMOLEused to prepare Figure 5. References and Notes (1) (2) (3) (4)
Fischer-Hjaimars, Tetrahedron, 19, 1805 (1963). G. N. Currie and D. A. Ramsay, Can. J. Phys., 49, 317 (1971). J. R. Durig, C. C. Tong, and Y. S.Li, J. Chem. Phys., 57,4425 (1972). J. R. Durig, S. E. Hannum, and C. S.Brown, J . Phys. Chem., 75, 1946 (1971).
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+
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Determination of the Nature of the Ionic Species in a Low Dielectric Constant Solvent from Transference Number Measurements A. Reger, E. Peled, and E. Gileadi” Institute of Chemistry, Tel-Aviv University, Tel-Aviv, Israel (Received July 3 1, 1978)
An electrolyte consisting of KBr or LiBr and AlzBrBdissolved in toluene was studied. This is representative of a class of electrolytes consisting of an ionic bromide or iodide and aluminum bromide dissolved in an aromatic hydrocarbon or mixture of aromatic hydrocarbons, which can serve as a practical bath for the electroplating of aluminum on an industrial scale. The system is unique in that it combines a reasonably high electrolytic conductivity with a very low value of the dielectric constant of the solvent. The transference numbers were determined by two independent methods in an attempt to identify the predominant ionic species. Results based on measurements by the Hittorf method indicate that A1,Brf is the basic ionic unit containing aluminum. All combinations containing A1Br4- lead to an unreasonable value for the sum of the transference numbers of the anion and the cation. Combining this with transference numbers determined by the emf method leads to the conclusion that the predominant ionic species in this system are [K2(A1,Br7)]+and [K(AlzBr7)2]-,This conclusion is consistent with the well-known properties of the system, namely, that aluminum bromide exists as a dimer in solution in aromatic hydrocarbons, that the solubility of KBr (or LiBr) in the pure solvent is vanishingly small and its solubility in the present system is proportional to the concentration of AlzBr6,and that the conductivity of this electrolyte is unexpectedly high in view of the nonpolar nature of the solvent.
Introduction The system consisting of aluminum bromide and an alkali bromide dissolved in toluene or a mixture of aromatic hydrocarbons can serve as a practical plating bath for the electrodeposition of aluminum.1~2This system is unique in that it possesses a fairly high electrolytic conductivity (up to ca. 6 mmho cm-’ in concentrated solutions) 0022-3654/79/2083-0869$0 1.OO/O
in spite of the low dielectric constant of the solvent. This and similar system were studied by Plotnikov and coworkers about 40 years ago. A detailed literature survey of earlier work was given in a previous p ~ b l i c a t i o n . ~ Recently, this system has been studied in our laboratory both from the applied’J and the fundamental points of view.34 In spite of the extensive amount of work done on 0 1979 American Chemical Society
