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The Geometry of the Methyloxocarbonium Ion Trimer: A CNDOIBW Study
JAMES DOUGLAS PULFER' AND MICHAEL ANTHONY WHITEHEAD^ The Chemistry Department, McGill University, P.O. Box 6070, Montreal 101, Quebec
Received November 15, 1972
Within the Boyd-Whitehead CNDO theory three consistent methods were developed to calculate the carbon-oxygen infrared frequency of several oxocarbonium ions. The first method, type I, showed that the parameters of the CNDOIBW theory are not useful for predicting bond angles. Type I1 established a correlation between the C(a j C bond length and the carbon-oxygen frequency. Type I11 predicted the correct trend for the homologous series of alkyloxocarbonium ions; however, the calculated frequency was consistently higher than experiment by 2&50 cm-I. Conjugation effects were estimated by applying the above methods to the phenyloxocarbonium ion.
Variations on two possible configurations of the methyloxocarbonium ion trimer were studied. The pro- tonated, planardiacetylmethenyloxocarbonium ion, AczHCCO+, was shown to be the most stable. A type I1 calculation estimated the C(a j C bond to be about 1.37 A. A type 111 calculation showed the possibility of the existence of the methyloxocarbonium ion dimer.
A I'intCrieur de la thCorie CNDO de Boyd-Whitehead, trois mCthodes cohCrentes furent dCveloppCes pour calculer la frkquence d'absorption en infra-rouge du groupe carbone-oxygkne pour plusieurs ions oxocarboniums. La premikre mCthode, type I, a montrC que les paramktres de la theorie CNDOIBW ne sont pas utiles lors de la prCdiction des angles de liaison. Le type I1 a permis d'ttablir une corrClation entre la longueur du lien C(a j C et la frkquence du lien carbonwxygkne. Le type 111 a permis d e prCdire la tendance correcte pour une sCrie homologue d'ions alcoyloxocarboniums; cependant, la frkquence calculCe a CtC constamment plus ClevCe que les valeurs expCrimentales par 20 1 5 0 cm-I. Les effets de conjugaison ont pu &tre estimCs en appliquant les mCthodes ci-haut mentionnkes 1 I'ion phCnyl oxocarbonium.
Les changements dans les deux conformations possibles du trimere de I'ion mCthyloxo carbonium ont Cte CtudiCs. La forme protonee et planaire de l'ion diacCtylmCthknyloxocarbonium, Ac2HCCOC, est la plus stable, comme il est dCmontrC. Un calcul selon le type I1 a permis d'estimer que la longueur d e la liaison C(a j C est d'environ 1.37 A. Un calcul du type 111 nous a permis de montrer la possibilite d'existence du dimkre de I'ion mCthyloxocarbonium. [Traduit par le journal]
Can. J . Chem.. 51. 2220 (1973)
Introduction There continues to be considerable scientific
interest in the geometries and charge distributions of the alkyl-, acyl-, and aryloxocarbonium ions. These ions have been shown to be the active electrophillic reagents in Friedel-Crafts reac- tions. When See1 (1) first reported the presence of the stable, crystalline methyloxocarbonium tetrafluoroborate (CH3COf)(BF,-) salt it was thought (2, 3) that the principle acylating agent in Friedel-Crafts reactions was the linear methyloxocarboniurn ion; however, no clear statement could be made on this problem for a number of reasons: Wuhrmann and Susz (4) were the first to report the presence of a weakly absorbing infrared frequency in the CH3- COCl-AlC1, complex at 2200cm-l, in addition to
the strongly absorbing frequency at 2300 cm-l. Cook (5) showed that the 2200 cm-' band was almost nonexistent in the freshly prepared com- plex, yet in a solution of nitrobenzene the 2300 cm-l band was almost completely replaced by the one at 2200cm-l. Cassimatis et al. (6) have also reported that during attempts to recrys- tallize the methyloxocarboniurn tetrachloro- aluminate salt from liquid sulfur dioxide, the crystalline complex converted partly to an amor- phous, less structured mass, and the presence of both frequencies was detectable from this material.
For the above reasons, further investigation into the chemistry of the methyloxocarbonium ion has beennecessary. Germain et a1.(7) have iso- lated two chemically distinct salts from a mixture of acetvl chloride and aluminium trichloride: the familiar methyloxocarbonium tetrachloroalumi-
'Holder of an NRCC Bursary, 1971-1972. 'Author to whom all correspondence should be nate (1) and the trimer salt. They postulated that
addressed. Holder of an NRCC Travel Fellowship, the trimer is the ~rotonated, planar diacet~l- 1971-1973. methenyloxocarbonium ion, Ac,HCCOf ; how-
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PULFER AND WHITEHEAD: A CNDOIBW STUDY
ever, they did not discount the possibility that it might be the diacetylmethyloxocarbonium ion, Ac,CHCO + .
The skeleton structure and electron charge distribution of the cation in 1 is thought to be known (8, 9); the same cannot be said of the trimer. LeCarpentier and Weiss (9) are in the process of elucidating the crystal structure of the recrystallized tetrachloroaluminate salt of the trimer by X-ray techniques. One of the purposes of the present paper is to theoretically investigate the relative stability of the two most likely con- formations of the trimer by means of the Boyd- Whitehead (10, 11) bond length dependent CNDO theory. The two principle structures of the trimer considered have been shown in Figs. 1,2, and 3.
discuss the possible the FIG. 2. Coordinates for the diacetylmethyloxocar- trimer, it was necessary to study the stereo- bonium ion. The O6C4C5 plane is rotated 60" to the x-z chemistry and charge structures of some related plane; hydrogen atoms 11 and 12 are staggered with oxocarbonium ions and to try to correlate the respect to the C4-06 bond. The atoms c,, c,, c,, and
C4 are in the x-z plane. The C7-Cs bond bisects angle geometry of these structures to the observed C,-C,-H,,, infrared frequency in a theoretical manner. The phenyloxocarbonium ion and the homologous G. series of alkyloxocarbonium ions, starting with the methyloxocarbonium ion, were particularly useful. Two major attempts have been put v5 ;/Oq forward to elucidate the structure and electron configuration of the methyloxocarbonium ion. \... Boer (12) did an X-ray study of the crystal struc-
06
.Hl 6 8 60 g , ture of the methyloxocarbonium hexafluoro- 0 6 A16
antimonate salt. Based on the results of that H ~ I
work, the NEMO method (13) was used to try to obtain the electron configuration of the ion. In this calculation it was assumed that the hydro-
'r2 gen atoms were in the tetrahedral positions. An interesting result was obtained. Carbon atom C,, in Fig. 4, had a formal positive charge of c 3
H 1,
FIG. 3. The sterographic choice of angles used to generate the coordinate system of the diacetylmethyloxo- carbonium ion.
1.18 electrons on it. Boer's X-ray work showed
z that the C,-C, bond length was 1.385 A.
Veillard and co-workers (8) performed a series 'YI of a6 inilio calculations on the methyloxocar-
bonium ion where the geometry of the C,-C, bond was o~timized. After a reasonable value
I was obtainei for this bond, the positions of the FIG. 1 . Coordinates for the protonated planar three methyl hydrogens were optimized. ~~~h
acetyl- and diacetylmethenyloxocarbonium ions. In the former case, the C7 atom is replaced by a hydrogen atom. optimizations were carried out with respect the All atoms except the hydrogens, are in the x-y plane. total energy of the ion. These calculations showed
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CAN. J . CHEM.
FIG. 4. The coordinates of the alkyloxocarbonium ions: R4 = R, = R6 = Hydrogen, CH3CO+; R4 = CH3, R5 = R6 = H, C2H5CO+; Rq = R5 = CH3, R, = H, i-C3H7CO+; R4 = R5 = R6 = CH3, t-C4H9CO+.
that the C,-C, bond was longer than that reported by Boer, around 1.452 A. Le Carpentier and Weiss (9) have recently verified this value by X-ray analysis. The ab initio charge distribution showed that carbon atom C, had a net positive charge of 0.605 electrons. This appears to be a much better estimate, the rest of the formal positive charge being delocalized onto the three equivalent hydrogen atoms in the molecule-ion. The optimum position of the hydrogen atom was found to be the tetrahedral position.
The structures and electron configurations of the other cations in the homologous series are generally less well known. Le Carpentier and Weiss (14) have published some refined results of X-ray studies done on the structure of the ethyl- and isopropyloxocarbonium ions. The structure of the latter ion does not differ signi- ficantly from their earlier results (15). The ab initio charge distribution of the isopropyloxocar- bonium ion has been calculated using a con- tracted set of gaussian s and p type orbitals (8). The charge on the carbon atom, C,, was found to be $0.733, and the C,-C, bond was 1.46 A. There is no X-ray analysis of the tert-butyloxo- carbonium hexafluoroantimonate salt.
Veillard and co-workers (8) have pointed out that the molecular structure of methyl cyanide is very similar to the corresponding isoelectronic methyloxocarbonium ion. Corresponding struc- tural data is not available for isobutyronitrile; however, the average length of the C,-C, bond
VOL. 51, 1973
I in nitriles of the type -C,-C,=N is around
I 1.464 A (16) which is 0.014 A longer than the length of the corresponding bond in the isopro- pyloxocarbonium ion (14). The difference is not large and can be partly explained by the higher positive charge located on carbon atom C, of the oxocarbonium ion. As a result, the C2-C, bond of the tertbutyloxocarbonium ion was assigned a length of 1.46 A, which is the same as the com- parable bond in tert-butyl cyanide (17).
In addition to these ions, the phenyloxocar- bonium ion was studied, in order t o estimate how well the various types of calculations might pre- dict the geometry and infrared stretching fre- quency of a highly conjugated system. The X-ray structure of the phenyloxocarbonium hexafluoroantimonate salt has not been done although the X-ray structure of the covalent complex C1,Sb-O=C-C,H, has (18). In this
I C1
complex, the corresponding C,-C, bond was found to be 1.51 A, an elongated n bond. A much shorter bond would be expected for the ionic salt; consequently, this bond had to be estimated from available data for the isoelectronic phenyl cyanide molecule. Two independent microwave studies of this molecule (19, 20) have shown C2-C3 values of 1.4509 A and 1.419 A. The shorter length was chosen for these calculations because of the shortening effect of the positive charge at C, (Fig. 5).
The infrared spectra are known for all the oxocarbonium ions, including the trimer. The possible existence of the methyloxocarbonium ion dimer was also investigated. N o infrared data are available to prove the existence of this ion in solution; however, there is the possibility that the stretching frequency of it might be masked by the stretching frequency of the trimer.
The Calculation The molecular orbitals and the total energy of
each of the organic oxocarbonium ion conforma- tions was evaluated within the LCAO-MO- CNDO-BW approximation (10, 11). The core resonance integral was evaluated as an "overlap ionization potential" between two atomic orbitals k and I o n atoms A and B, i.e.
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PULFER AND WHITEHEAD: A CNDOIBW STUDY
z
t
Frc. 5 . Coordinatesfor the aryloxocarboniurn ion C6H5CO+. LC4C3C8 = 120°, LC3CsH9 = 120°, L C3CzOl = 180".
[1 1 H k l = PAB{J~ + I I ) S ~ I In the current calculations the CNDOIBW
Here Ik is the Hinze-Jaff6 valence state ionization potential of the kth atomic orbital and Sk, is the overlap between the two Slatar type atomic orbitals k and 1.
In these calculations, the nuclear-nuclear core repulsion terms between two atoms A and B, NAB, was evaluated as a weighed average between the point charge nuclear repulsion term and the appropriate electron charge interaction between atoms A and B
Here LAB was defined as
The electron-electron repulsion integral yAB, in eq. 2, is an average electron repulsion integral between two atoms A and B. It was evaluated by Ohno's method (21), and modified by Sichel and Whitehead (22) to take into account the relative proportions of y,,, y,,, y,,, and y,,,, required to yield a homopolar bond within the CNDO approximation.
In Boyd's thesis (23) it is shown that if eqs. 1 and 2 are used to calculate the core resonance integrals and the nuclear-nuclear core repulsion integrals then slightly better and more consistent force constants were obtained than by other methods of calculating HkI and NAB. The param- eters, a,, and PA, were determined from diatomic molecules where the internuclear distance was accurately known. The a,, and PA, used in the present calculations were evaluated in the manner outlined above. This set of characteristic con- stants have been designated parameter set I by Boyd and Whitehead.
computer program was fitted with a subprogram for efficiently calculating the optimum geometry of the molecule. This subprogram makes use of a method first developed by Fletcher and Powell (24). A gradient vector for any initially selected geometry was computed for several molecular geometry parameters. From this gradient vector, the subprogram determines the direction of the steepest descent and steps in that direction. The stepsize of each parameter is determined by the size of the partial derivatives of each of the vari- ables. At the new position, another gradient vector and a second total energy were calculated. If the program has stepped too far then a quadratic fit of the points available is made and a new position of the minimum energy found. The process is repeated until the total minimum energy agreed to a specified tolerance, 1 x lo-'. The method has quadratic convergence and has proven to be superior t o other existing methods (24).
Once the optimum geometry was calculated by this method, the several variables employed in the calculation were frozen and the bond length of the carbon oxygen bond was set at two posi- tions bracketing the lowest energy position. A useful stepsize was 0.02 A. At this stepsize, the anharmonic nature of the potential well of the carbon-oxygen bond was minimized. This made it possible to calculate the force constant using only three points. If the shape of the potential energy curve was badly skewed, i.e. one of the terminal points on the interval of interest had a much higher energy than the other, then more points were calculated and a higher order polynomial was used t o approximate the total energy function.
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2224 C A N . J. CHEM. VOL. 51, 1973
The interpolating polynomial was the Newton forward difference polynomial (25). The total energy of the molecule was expressed as a func- tion of the carbon-oxygen bond length.
A is the forward difference operator defined as
In general, En, is the total energy of the ion corre- sponding to a carbon-oxygen bond length x,,, where
[ 6 ] x,, = x, + {(n + 1 - 2rn)/2}h, n odd
The equilibrium bond length, x,, was usually the value calculated by the Fletcher-Powell mini- mization procedure, n is the total number of points in the interpolating polynomial and h is the stepsize between various consecutive points. The variables, in eq. 4, is a simple function of the bond length x where
Equation 4 yields a simple relationship for the second derivative of the energy with respect to the carbon-oxygen bond length if three inter- polating points were used.
If the bond has a large degree of anharmonic character to it, then further points must be included in the interpolating polynomial and an equilibrium bond length must be calculated in order to evaluate the second derivative. For most cases, eq. 8 was sufficient to numerically evaluate the second derivative.
Let kc, be the force constant of the carbon- oxygen bond. The second derivative was identi. fied with the force constant.
Here K is a conversion factor, from ev/A2 to ergs/cm2. This force constant was used to cal- culate the infrared stretching frequency.
The constant c is the speed of light and pcO the reduced mass of the carbon-oxygen bond; h is the stepsize mentioned previously.
Results In order to calculate a consistent carbon-
oxygen infrared stretching frequency for a wide range of organic oxocarbonium ions a systematic approach had to be developed. The methyl-, ethyl-, isopropyl-, tert-butyl-, and phenyloxocar- bonium ions were used as a basis for testing the three different methods of calculating this particular frequency. In the first method, desig- nated type I, all nearest neighbor geometries that might have an influence on the electron charge structure of the linear chain 0,-C2-C,, seen in Fig. 4, were simultaneously varied so as to achieve the most stable geometry. Consequently, all bond lengths shown in Fig. 4 were varied, with the exception of the carbon-hydrogen bonds in the methyl radicals (R,, R,, and R,). These were fixed at 1.09 A. The bond angles M, P, and y were also varied at the same time. The resulting geometries for the first three ions mentioned in this series have been presented in Table 1 along with the total energy minimum.
The carbon-oxygen bonds for the methyl- and ethyloxocarbonium ions have been found to be slightly longer (-0.018 A) than those in the literature; and for the isopropyloxocarbonium ion the calculated carbon-oxygen bond has been shown to be insignificantly longer (-0.008 A). In general, the slightly longer carbon-oxygen bond lengths are mainly the result of an overesti- mation of the core nuclear-nuclear repulsion energy terms in the Boyd-Whitehead CNDO theory. In Boyd's thesis (23) there was a discus- sion of this problem for the carbon monoxide molecule, and the singly ionized carbon monoxide ion. The core nuclear-nuclear repulsion energy terms for carbon monoxide were calculated using eq. 2, and were compared to the Morse potential curve. The calculated values were shown to be consistently too large for all but the equilibrium internuclear distance (1.128 A). As a conse- quence, cataris parebus, any overestimation of the core repulsion terms will result in an over- estimation of the subsequently calculated bond length. Boyd's thesis also shows that parameter set I overestimates the correct bond length for the ionized carbon monoxide molecule by 0.012 A. These results imply that, within the limitations
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PULFER AND WHITEHEAD: A CNDOIBW STUDY 2225
TABLE 1. A summary of the bond lengths and angles of the alkyloxocarbonium ions yielding a minimum total energy
Type of calculation Molecular
RCO + geometries A I* 11 t 111s Experimental Reference
CH3CO+ R(Cz-01) 1.124 1.125 1.124 1.108 9 R(C3-C2) 1.471 1.452 1.471 1.452 9 R(C3-H) 1.101 1.098 1.101 1.09 8 a = B = y 1O9"3Of 109"30' 10Y28' E T / ~ V - 640.3052 -640.3121 - 640.3052
CzH,CO+ R(Cz-01) 1.118 1.130 1.123 1.099 14 R(C3-Cz) 1 .500 1.420 1.488 1.435 14 R(C3-H5) 1.110 1.110 1.096 1.09 8 R(C3-CH.4 1.572 1.572 1.572 1.550 14 a 100°36' 100°36' 10Y28' B 109"59' 10Y59' 1OY28' 109.3"8 26 Y 111°14' 111°14' 10g028' 110.5" 26 E T / ~ V - 803.4625 - 803.3632 - 803.4126
i-C3H7C0 + R(C2-01) 1.124 1.131 1.125 1.116 14 R(C3-Cz) 1.515 1.440 1.506 1.450 14 R(C3-Hs) 1.121 1.121 1.113 1.107/) 29 R(C3-CH3) 1.570 1.570 1.580 1.551 14 a 87"12' 87"12' 1OY28' 108.3" 14 I3 105"38' 10Y38' 10Y28' Y 112"12' 112"12' 10Y28' 108.3" 14 E T / ~ V -966.3353 -966.2589 -966.1159
t-C4H9CO+ R(C2-0,) 1.129 1.1608 17 R(C3-Cz) 1.460 1 .460 17 R(C3-CH3) 1.570 1.540 17 a = B = y 1OY28' 109.5" 17 E T / ~ V - 1112.7322
'A11 important geometries were varied. both bond lengths and angles. tThe bond angles found in the type I calculation were frozen; the C2-C3 bond length taken from experiment; and all other important
geometries were varied. $The bond angles were fixed at ideal angles: 0 1 - C 2 - C 3 = 180'; C1-C3-R4 = 109'28' where R4 is H- or CH3-; and the important bond
lengths were varied to find a global energy minimum. §These resulb are for the isoelectronic nitrile. llCyclopropyl cyanide.
of the theory, the carbon-oxygen bond lengths calculated for the alkyloxocarbonium ions are in reasonably good agreement with experiment.
The carbon-carbon bond lengths presented .in Table 1 are also consistently overestimated when compared to experiment. This is primarily due to an overestimation of the core repulsion terms as well. For the two oxocarbonium ions with methyl groups substituted for hydrogens at the C, position, the average overestimation for the carbon-carbon C,-C, bond is 0.08 A. The observation implies that in chemically similar systems, it may be possible to apply this overesti- mation as a correction to any carbon-carbon bond length computed by the Boyd-Whitehead CNDO theory.
The computed angles of the three ions studied by type I calculations were interesting. The angles of the methyloxocarbonium ion were found to
be very close to the ideal. This is the same result as was found by Veillard and co-workers (8). In the case of the ethyloxocarbonium ion the angles are close to those found for the isoelectronic ethyl cyanide molecule (26). There is a slight widening of the H-C-H angle, probably due to the increase in the angle y, which is the result of the increase in the non-neighbors electron- electron repulsion terms between the methyl group and the linear carbon~arbon-oxygen skeleton chain C,-C,-0,. The angles found for the isopropyloxocarbonium ion show that the single hydrogen attached to the C , carbon atom has floated to a position that allows it to bond with maximum overlap to the carbon p, atomic orbital. This calculated result arises because the Boyd-Whitehead theory was not parameterized to take non-neighbor interactions explicitly into account (10, 11, 23). As a result,
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2226 C A N . J . CHEM. VOL. 31, 1973
there is a general tendency to overestimate non- neighbor repulsive forces. In the case of the hydrogen atom this has lead to the anomalous result where the angle a is 87".
The two methyl groups experience roughly the same electron-electron repulsions from the linear carbon-carbon-oxygen C3-C,-0, sys- tems as did the methyl group in the ethyloxocar- bonium ion, as a result the movement of the hydrogen atom to the energetically more stable position has allowed the angle y to widen further than in the case of the ethyloxocarbonium ion. The angle P has decreased, when compared to the ethyloxocarbonium ion. This was possible because of the significant lengthening of the carbon-hydrogen bond.
Type I calculations do not reproduce a con- sistent trend in the observed carbon-oxygen infrared frequency of the methyl-, ethyl-, and isopropyloxocarbonium ions. Figure 6 shows that the curve plotted from the calculated infrared frequencies does not consistently reproduce the shape of the experimental curve. Both the ethyl- and the isopropyloxocarbonium ions gave fre- quencies larger than necessary to reproduce a smooth, consistent approximation to the experi- mental curve. Consequently, as a method of
0 experimental o type I
A, type 11
/ '. otype 111
i \. \
i \
2 2 5 0 -1 . > 4 3 5 7 7 1 8 5
ATOMIC MASS OF THE RCO+ IONS (amu)
FIG. 6. The frequency of the carbon-oxygen bond as a function of the atomic mass of the alkyloxocarbonium ions where R = CH,, C2H,, i-C3H,, t-C4H,.
calculating the frequency of the carbon-oxygen bond, the type I calculation proved to be generally unacceptable. The shape of the total energy sur- face of the carbon-oxygen bond is not well reproduced by type I calculations, even though this type of calculation generally gives the lowest possible energy. As was previously pointed out, the inconsistency of this type of calculation may be partly the result of parameterization. The CNDOIBW theory has been parameterized for bond length dependence and not for non-neigh- bor dependence. A new, greatly expanded set of parameters would have to be developed, to take into account the non-neighbor effects.
A second method, type 11, was developed. The length of the carbon-carbon bond adjacent to the carbon-oxygen bond has a critical effect on the shape of the total energy surface of the ions in the region of the carbon-oxygen bond. This has been described by many authors (6, 7). The extent of the conjugation along the carbon-car- bon-oxygen (C3-C,-0,) chain directly affects the frequency of the carbon-oxygen bond. The smaller the conjugation effects, the higher the frequency. For example, the frequency of the methyloxocarbonium ion bond is around 2300 cm-' (3,7,27) whereas the phenyloxocarbonium ion carbon-oxygen frequency has been measured to be 2212 cm-'.
Those observations can be rationalized by looking at the gross charge structure of the carbon-carbon-oxygen system. The bulk of the positive charge resides on the carbon atom bonding with oxygen. Typical results have been presented in Table 2. The calculated value for the methyloxocarboniurn ion, + 0.73 compares favor- ably with the ab initio result obtained by Veillard and co-workers (8) which was +0.605. This high positive charge is thought to be responsible for the high carbon-oxygen frequency observed for the methyloxocarbonium ion. The observed frequency is about 160 cm-' higher than that of the carbon monoxide molecule. The major dif- ference between these two stretching frequencies is the difference in the positive charge on the carbon atom. Any change in this high positive charge causes a corresponding change in the net negative charge on the oxygen atom. In Table 2 it can be seen that the total differential charge density on the oxygen atom increases regularly as the positive charge on the carbon atom C, decreases. In the limiting case, carbon monoxide
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PULFER AND WHITEHEAD: A CNDOIBW STUDY 2227
TABLE 2. Charge distributions from type I11 CNDO/BW calculations on a homologous series of alkyloxocarbonium ions (RCO+) where R is CH3-, C2HS-, i-C3H7-, and t-C4H9-
Atomic basis Symmetry
'Charge on methyl carbon. tHydrogen towards carbon-oxygen bond (staggered). $Hydrogen away from carbon-oxygen bond. §Bond order.
would be expected to have the largest total differential charge on the oxygen atom. In pre- liminary calculations this was the case. The presence of the positive charge has the effect of equalizing the electronegativities of the oxygen and carbon atoms. The result is a higher carbon- oxygen bond order in the oxocarbonium ions than in carbon monoxide. This implies a larger force constant and a higher frequency; all observed frequencies of the oxocarbonium ions are higher than carbon monoxide.
Conjugation of the skeleton chain delocalizes the positive charge on the carbon atom and, as a consequence, lowers the stretch frequency towards that of the free carbon monoxide fre- quency. A comparison of the results for the planar protonated diacetylmethenyloxocarbonium ion, Ac2HCCO+, with those for the tetrahedral case, shown in Table 3, supports the above arguments. The conjugated species has a larger negative charge on the oxygen atom and a smaller total bond order for the carbon-oxygen bond. The calculated infrared stretching frequencies, in Table 4, show that the conjugated ion has a much lower stretching frequency than the tetrahedral case.
For the above reasons, type I1 calculations
were devised as an improvement on the type I calculations and as a method for correlating the C,-C3 bond length to the observed frequency. The extent of the conjugation of the carbon- carbon-oxygen (C3-C2-0,) skeleton chain is governed, in large part, by the length of the carbon-carbon bond, and as was previously pointed out, the bond length dependent theory overestimates the carbon-carbon bond lengths. Consequently, in type I1 calculations, the experi- mental bond length, when available, o r a reason- able estimate of it, based on microwave studies of the isoelectronic alkyl- or phenyl cyanides was substituted. The experimental bond lengths ought to increase the degree of conjugation of the chain; and lower the calculated frequency of the carbon-oxygen bond provided all other aspects of the calculation remain the same. In the type I1 calculations, no attempt was made to vary the bond angles, those found in type I calculation were used without change. The carbon-oxygen and carbon-radical bonds, i.e. C,-R,, C3-R,, and C3-R,, were simultaneously varied to find a new energy minimum. The calculated infrared frequencies were placed in Table 4. I n general, the frequencies have been lowered to values very close to experimental; however, Fig. 6 shows that
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2228 CAN. J. CHEM. VOL. 51, 1973
TABLE 3. The results of CNDO/BW calculations on a number of conjugated acyl and phenyloxocarbonium ions (RCO+) where R is acetylmethenyl-,
diacetylmethenyl-, diacetylmethyl-, and the phenyl- radicals p~
AczHCCO+ Atomic AcHCHCO + AczCHCO+ C6H,CO+
basis Symmetry Type 111 Type 112 Type 111 Type 111 Type 112
0 1
c z
c3
c4 c s 0 6 (or c6) H (planar)
HI^ +
cz-01 t
c3-cz
'The tetrahedral hydrogen atom. ?Bond order.
TABLE 4. Three different methods of calculating the carbon-oxygen infrared vibrational frequency of several oxocarbonium ions are compared with experiment
I I1 111 Experimental
RCO+ G(cm-') Reference Type Ill* Type IIzt C3Tetrahedral C3Planar
CH3C0 + 2300 7 2319 23 14 C2H5CO+ 2290 3 2364 2283 i-C3H7CO+ 2270 3 2325 2273 t-C4H9C0 + 2260 3 C6HSCOC 2212 3 2277 AcHCHCO+ AczHCCO+ 2200 7 AczCHCO+
*The C2--C3 bond length from experimental data, except the phenyloxocarbonium ion. ?The C2--C3 bond length estimated.
the correct trends are not predicted by this method. It does show that if the correct carbon- carbon bond length is substituted then reasonable values, close to the observed infrared frequency, could be calculated.
A third method, type 111, was devised. The CNDOIBW theory was parameterized for bond length dependence. This parameterization took
no account of angular correlation between non- neighbor groups. This implied that angular variation in CNDOIBW calculations might have little meaning. As a consequence, idealized chem- ical bond angles might be just as reasonable as those obtained by an explicit calculation. The concept of an ideal chemical bond is a simple one. If a chemically related system has nearly tetra-
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PULFER AND WHITEHEAD: A CNDOIBW STUDY 2229
hedral bond angles, then type I11 calculations would be set up to fix the bond angles in an ideal tetrahedral position. For example, the nearly tetrahedral bond angles of the isoelectronic ethyl cyanide molecule would be a good indication of the ideal angles for the ethyloxocarbonium ion. They would be tetrahedral. In type I11 calcula- tions, the bond lengths of the carbon-oxygen C2-O,, carbon-carbon C,-C,, and carbon- radical C,-R,, C,-R,, and C,-R, bonds were simultaneously varied to find a global energy minimum. The resulting frequencies are uniformly higher than the experimental ones, as can be seen in Fig. 6; however, the trend in the experimental frequencies was reproduced. Of the three methods considered, type I11 calcula- tions have shown the most consistent results for reproducing the experimental trend of the ob- served infrared frequencies. The results of the type 111 CNDOIBW calculations are presented in Tables 1,2, and 4. If the methyloxocarbonium ion is omitted as a special case, then type I11 calculations consistently yield frequencies that are about 35 cm-' higher than experiment.
A further calculation could be devised whereby the carbon-carbon C,-C, bond length could be fixed at a chemically reasonable value and the other bond lengths varied along the same idealized angles as were used in type I11 calcula- tions. This method was used on the phenyloxocar- bonium ion and the trimer. It is, in fact, a modification of the type I1 method. The drawback with this calculation is a lack of generality; how- ever, for specific ions, it can aid in pinpointing the correct C,-C, bond lengths.
Type I11 calculations have been outlined, in the preceding paragraphs, for the consistent calculation of the infrared stretching frequency of the carbon-oxygen bond in the homologous series of alkyloxocarbonium ions; however, this general scheme was not comprehensive enough. In addition to the aliphatic oxocarbonium ions, it was necessary to ascertain the reliability of the type I11 calculations for a highly conjugated ion like the phenyloxocarbonium ion. This cal- culation predicted a rather long carbon-carbon C2-C, bond length, 1.51 A. The isoelectronic phenyl cyanide molecule has a carbon-carbon length between 1.4509 A (19) and 1.419 A (20), the average of these two values being 0.075 A smaller than the result given by the Boyd- Whitehead calculation. Consequently, the bond length is probably overestimated by at least that
length. This analysis has important implications for applying the modified type I1 calculations to the phenyloxocarbonium ion.
The type I11 calculation showed a frequency 93 cm-' higher than the experimental value of 2212 cm-' for the phenyloxocarbonium ion. This implied that in cases of high conjugation, the infrared frequency calculated by this method may be overestimated by as much as 90-100 cm-'. In absolute terms this is not very satisfac- tory. A comparison of the results in Table 4 shows that the calculated infrared frequencies of the phenyloxocarbonium ion are of the same order of magnitude as those for the aliphatic series; however, as has been pointed out previously, type I11 calculations are only valuable for being able to consistently predict a trend within a series of chemically similar molecule-ions. I t is this property that makes them useful. As a conse- quence of this, caution must be exercised when analyzing the absolute values that result from a type 111 calculation. This type can point out certain possibilities and trends, but more detailed calculations must follow.
Two modified type I1 calculations have been carried out on this system in order to try to isolate the major factor that contributes to this rather large error in the frequency. In the first case, type II,, the carbon-carbon bond was estimated to be the same as the isoelectronic phenyl cyanide molecule (20). The bond angles at O,, C,, and C, were fixed at ideal values: 120" at C, and 180" at C,. The benzene ring was slightly distorted. The C,-C, type bonds were made a bit longer, 1.402 A ; the others were fixed at 1.394 A. This was in keeping with the findings of Casado et al. (19). The carbon-oxygen bond was the only variable. This calculation gave a frequency of 2277 cm-', 65 cm-' too high. The frequency and bond lengths are presented in Tables 4 and 5. The C,-C, bond used was about 0.09 A smaller than the type I11 value. By shortening this bond there has been a 30 cm-' improvement in the fre- quency. As in the case of the aliphatic ions, there appears to be a direct correlation between the C2-C, bond length and the calculated frequency.
In the second, modified type II,, calculation the carbon-carbon bond was estimated as approximately the same as the bond length between two carbon atoms in the sp hybridized valence state. The result was a calculated fre- quency 4 cm-' above the experimental value. In this calculation the benzene ring was not
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2230 C A N . J . CHEM. VOL. 51. 1973
TABLE 5. A summary of the calculated results for the phenyloxocarbonium ion
The phenyloxocarbonium ion
Experimental values Geometry
parameters (A) Type II,* Type IIzt Type 111 C6HsCN (19) C6HsCN (20)
'The C2-CI bond is taken from microwave studies of the isoelectronic phenyl cyanide. ?The C2--C3 bond is estimated as a carbon+arbon sp-sp bond length.
distorted. The C2-C, bond was shortened 0.171 A when compared with the type I11 value. This may seem a large change, however, there is some justification for this type 11, calculation. Casado et al. (19) have shown that electrophillic substituents, like the cyanide radical, distort the shape of the benzene ring. Figure 5 shows the C,-C,-C, bond angle as 120"; however, if an electron withdrawing substituent is situated at the C, position, this angle opens up to around 122", and the carbon-carbon C3-C, bonds of the benzene ring lengthen from the normal length of 1.394 A to 1.402 A. If this bond angle widened still further, as it might for the C"-0'- sub- stituent, then the sp2 hybridization of the carbon atom C3 would undergo further reorganization towards an sp hybridized state. Carbon atom C , is already in an sp hybridized valence state. In addition, the mean average radii of the electrons in the sp valence state localized on carbon atom C2 are probably shortened as a result of the large positive charge carried by that carbon atom (+0.73). The net effect of these three factors will be to considerably shorten the C2-C, bond, possibly to 1.339 A which is the carbon-carbon bond length in acetylene.
It would appear that the type I11 calculation has overestimated the C2-C, bond in the phenyloxocarbonium ion more than when the same calculation was applied to the aliphatic series. In the homologous series of ions, the over- estimation varied, but was generally around 0.08 A. It would appear that the same bond in the phenyloxocarbonium ion has been overesti- mated by between 0.09 A and 0.17 A. This leads to the interesting observation that the type I11 bond length calculation may act as a reflection of the degree of conjugation. The higher the degree of conjugation between the C,-C2-0,
chain and the rest of the molecule, the longer the overestimation. For example, the results of type I11 calculations on the homologous series of alkyloxocarbonium ions have shown that in the cases where the overestimation of the bond length was small, the corresponding overestima- tion of the frequency was also small. In conclu- sion, the difference between the calculated and observed frequencies can be directly correlated to the overestimation of the bond length: both within the homologous series and for a highly conjugated system. It is with this conclusion in mind that one must interpret any type I11 results. Thus in the case where there is almost no possibi- lity of conjugation, as with the methyloxocar- bonium ion, the overestimation of the infrared frequency is about 20cm-I. A reasonably accurate bond length would be expected and this is what is observed. On the other end of the scale, in a highly conjugated system the frequency is in error by 40 cm-' and it is reasonable to suppose that the bond length is also quite a bit larger than the actual figure.
These observations have interesting implica- tions for the applicability of this work to the shapes and structures of the methyloxocarbonium ion dimer and trimer. Modified type I1 calcula- tions could point the way to an accurate estima- tion of the bond lengths of the C,-C2-0, skeleton shown in Fig. 1, whereas type 111 calcu- lations could indicate which, of several possible configurations, is the most stable and, because of its consistency within a given series, point the way to the possible existence of the dimer.
The geometry of the methyloxocarbonium ion trimer is not known although it is thought to be a protonated planar diacetylmethenyloxocar- bonium ion (7) as shown in Fig. 1. T o apply type I11 calculations, i t is necessary to know the
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PULFER AND WHITEHEAD: A CNDOIBW STUDY 2231
TABLE 6. A summary of the geometries calculated for the acetyl-, methenyl-, diacetylmethenyl-, and diacetyImethyloxocarbonium ions
AczHCCO+ Geometry AcHCHCO+ AczCHCO +
parameters Type I11 Type 11, Type I11 Type I11
NCz-01) 1.132 A 1.139A 1 .I36 A 1.130 A R(C3-Cz) 1.481 A 1.375 A 1.481 A 1.471 A R(C3-C4) 1.533 A 1.533 A 1.533 A 1.664 A R(C4-06) 1.228 A 1.228 A 1.228 A 1.173 A R(06-Hi 6) 1.081 8, 1.081 8, 1.081 A R(C,-O,) 1.228 A 1.205 A 1.173 A R(C3-Hid 1.084 A 1.093 A Ac rotation 0" 0" 2" 60" ET -1273.7994 eV -1905.7812 eV -1907.6460 eV -1906.8102 eV
idealized valence state of carbon atom C,; con- I sequently two cases were studied. The first I considered C, in the sp3 state. The geometry I employed for this calculation has been shown in
Figs. 2 and 3. The bond lengths were varied and the bond angles were fixed. In this case, five bond lengths were simultaneously varied, the C2-O,, C2-C,, C,-C,, C,-0, and the C,-H,, bond
~ lengths. The results of this work have been shown
I in the last column of Table 6. Two features I of note in this calculation are the lengths of the I C,-C, and C,-0, bonds. In the former, the I bond length is a long sigma bond and, in the I latter case, a shortened pi bond. Normally a I carbon-carbon sigma bond would be about I 1.54A; the calculated length was 1.664 A. This
is probably overestimated by at least 0.08 A and,
I if that correction is applied, the result is a bond length of about 1.58 A, which is an elongated carbon-carbon sigma bond. On the other hand, the normal carbon-oxygen pi bond for the acetyl chloride molecule is 1.25 A. The corresponding bond in this ion is 1.173 A which is probably overestimated by about 0.02 A. The considerable shortening of this bond can be described, in part,
, by the charge on the carbon atom C,. As is shown 1 in Table 3 this carbon atom is almost carrying
as much formal positive charge as carbon C2. One other significant feature of this calculation is the energy of the ion. The total energy of this ion is - 1906.81 eV.
1 A second study was carried out where carbon ~ atom C, was assigned an sp2 hybridized valence I
1 state. The idealized geometry of this ion is shown in Fig. 1. This is the protonated planar ion
1 favored by Germain et al. (7). The hydrogen is situated in a double well potential between the
two acetyl radical oxygen atoms. A preliminary calculation showed that the ion was most stable when the oxygen-carbon bonds of the acetyl radicals were nearly parallel and the 0,-C7-C, axis was rotated 2" counterclockwise with respect to the x-y plane, i.e. counterclockwise in the sense of looking along the C,-C7 bond from C,. Starting with this preliminary geometry, six bond lengths were simultaneously varied in this calculation; these six variables were the C2-O,, C2-C,, C,-C4, C4-O,, C7-0,, and 06-H,, bonds. The results have been shown in Table 6 as a type I11 calculation. The total minimum energy of this configuration is - 1907.64 eV. This result shows that the planar case is more stable by 19.3 kcal/mol. Tentatively one could conclude that the methyloxocarbonium ion trimer is the protonated planar diacetylmethenyl- oxocarbonium ion.
A comparison of the stretch frequencies, cal- culated for the two geometries, provides incon- clusive evidence. The tetrahedral case gave a frequency of 2278 cm-', the planar case, a fre- quency of 2234 cm- l . This would appear to favor the planar case, as the observed frequency is 2200 cm-l ; however, this is not the case. Recall that when type 111 calculations were applied to the aliphatic ions, the overestimation was around 35 cm-l. In addition, for a mod- erately conjugated system such as this one, the overestimation is probably around 70 cm-'. If these corrections are applied to the two calcula- tions then in the former case it would become around 2240 cm-' and in the latter about 2160 cm-l.
The gross structure of the ion is probably the planar protonated species. This conclusion is
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2232 C A N . J. C H E M . VOL. 51. 1973
based upon the calculated relative stabilities of the two ions. To obtain a more accurate geom- etry, a modified type 11, calculation was initiated. With this calculation it is possible to refine the calculated estimates of some of the more impor- tant bond lengths such as the C2-C, bond. The results are presented inTable6. In this calculation, the angles were fixed in idealized positions, and the carbon-carbon C2-C, bond was estimated at 1.375 A. This estimation was based upon comments made by Veillard and co-workers (8) about the unpublished results of the o-methyl- phenyloxocarbonium ion structure (28). The carbon-carbon C(ol)-C bond of this ion has been found by X-ray analysis, to be 1.387 A, considerably shorter than had been expected; consequently a similar bond length was sub- stituted for that bond in the planar trimer ion. All other bond lengths were frozen at the equi- librium distance established by the type I11 calculation, except the carbon-oxygen bond. It was varied to find the equilibrium position of this bond for this new geometry. The result was a much less stable ion; however, the infrared fre- quency, given in Table 4, was only 12 cm- ' above the experimentally found value. The stability of the ion could have been greatly improved by relaxing all other bond lengths of significance; however, this is an extremely costly calculation and, besides which, the relative stabilities of the two major cases has already been established. Also, it has already been shown that the major factor influencing the carbon-oxygen stretch frequency is the conjugation of the carbon-car- bon bond with the contiguous carbon-oxygen bond. This result, taken together with the results found for the length of the carbon-carbon bond in the phenyloxocarbonium ion tend to suggest that the C2-C, bond length for the planar trimer is between 1.374 A and 1.387 A and that the general shape of the ion is that found in Fig.1. The lengths of the other bonds are not as accu- rately known as this one. In general, those bonds reported for the type 11, calculation, in Table 3, approximate the geometry of this ion, within the limitations of the theory.
As well as the trimer, there is the interesting possibility that the dimer of the methyloxocar- bonium ion might exist. Preliminary calculations have shown that the planar acetylmethenyloxo- carbonium ion is more stable than the tetrahedral case. A modified type 111 calculation was per- formed on the planar configuration of the dimer.
N W B E R OF ACEYL GROUPS
FIG. 7. The frequency of the carbon-oxygen bond as a function of the number of planar acetyl groups substi- tuted in the methyloxocarbonium ion.
In this calculation, the bond lengths found for the planar trimer ion are substituted in all equivalent positions in the dimer except the carbon-carbon, C,-C,, and the carbon-oxygen bond C2-0,. These two were freely varied to find a global energy minimum. The results have been presented in Table 6. The calculated fre- quency has been reported in Table 4 at 2265 cm- l . If the experimental values of the methyl- oxocarbonium ion and the protonated planar diacetylmethenyloxocarbonium ions are plotted along with the type I11 calculated values of the methyl-, protonated acetylmethenyl-, and dia- cetylmethenyloxocarbonium ions, shown in Fig. 7, then it is possible to observe a trend similar to the trend found for the type I11 calculations of the alkyloxocarbonium ions. If this trend is regular, then the experimental value of the pro- tonated acetylmethenyloxocarbonium ion ought to lie at about 2225 cm-l. This value has not been recorded; however, this may be due to the masking effect of the trimer peak. The possibility of its existence shows promise for interesting future work.
The authors would like to thank Mr. Geoff Zeiss and Dr. R . J. Boyd for many thoughtful discussions. This research was supported by the National Research Council
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PULFER AND WHITEHEAD: A CNDOIBW STUDY 2233
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