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Effect of conjugation beyond multiple bonds
Journal of Molecular Structure (Theochem), 109 (1984) 271-275 Elsevier Science Publishers B.V., Amsterdam -Printed in The Netherlands
EFFECT OF CONJUGATION BEYOND MULTIPLE BONDS Part II. On the relative stability of various conformations ions*
of cadmium
CHEN ZHIXING Chemistry
Department,
Zhongshan
University,
Guangzhou
(People’s Republic
of China)
CA1 WENZHENG Chemistry Department, South China Normal (People’s Republic of China)
University,
Guangzhou
(Received 16 January 1984)
ABSTRACT MNDO geometry optimization indicates that the coplanar forms of the allylcarbinyl cation are more stable than the corresponding perpendicular forms. An explanation is given from the viewpoint of hyperconjugation. It can then be concluded that for cations of the type XCH,CHi the adjacent double bond in X will strengthen the hyperconjugation in the coplanar conformation, thus lowering the energy to a greater extent. INTRODUCTION
The electronic structure of carbonium ions is of theoretical importance to the research of nucleophilic reactions. Hoffmann and co-workers [l] studied the conformation of o-substituted ethyl ions, XCH,CH:, by using the MO method and showed that the cations prefer the coplanar form I if the substituent X is more electronegative than hydrogen, whereas they prefer the perpendicular form II if X is less electronegative. When X has a double bond in the nearer terminal, no illustration was afforded in the paper [l] . Murthy and Ranganathan [2] performed calculations on two conformations of the allylcsrbinyl cation by using the EHMO method, indicating that the coplanar form III is lower in energy than the perpendicular form IV, but they gave no interpretation. They also performed calculations on the same species by using CND0/2, but no total energies were reported. CALCULATIONS
Our CNDO/B results with the standard geometrical models [3] show the opposite to EHMO: IV is lower in energy than III. We also performed calcu*The previous paper in this series appeared in J. Mol. Struct., Theochem, 0166-1280/84/$03.00
0 1984 Elsevier Science Publishers B.V.
105 (1983)
281.
272
lations on the cisoids, V and VI, which show a similar trend: the perpendicular form VI is lower in energy than the coplanar form V. Considering that the standard geometry may be inadequate, we performed a full geometry optimization with C, symmetry. However, IV changed into a three-membered ring and VI into a four-membered ring, so that comparisons could not be made. To clarify the problem, we used the MNDO method to perform the calculations. As is well known, the MNDO method gives fairly good relative energies. For example, Dewar and Thiel [4] reported barriers to rotation in ethane, methylamine, methanol, and hydrogen peroxide with an average error of only 0.9 kcal mol-‘; the error of the energy of torsion by 90” in ethylene is also small, amounting to 2.5 kcal mol-‘. We believe that MNDO is suitable for predicting the relative stability of various conformations.
RESULTS
AND DISCUSSION
The results are listed in Table 1. For both cisoid and transoid, the energies of the perpendicular form are lower than those of the coplanar form in the standard geometrical model, the trends being similar to those given by CND0/2. However, geometry optimization gives the opposite trends. The main feature is the deviation of the bond angles in the standard geometrical models from the true. As is well known, the angle between a C=C bond and a C-H bond is generally greater than 120”. The standard bond
213 TABLE 1 MNDO heats of formation (in kcal mol-’ ) of allylcarbinyl cations
Standard geometries Geometry optimization
III
IV
V
VI
241.2 235.4
239.9 236.7
256.4 231.4
246.4 238.1
of 120” is too small. The terminal hydrogen atoms, H-l and H-4, of the co-planar cisoid V will repel each other, resulting in an elevation of the total energy. As the four angles from H-l to H-4 in the standard geometrical model are too small, the distance between H-l and H-4 become too short, causing the energy to elevate abnormally. It goes so far as to exceed the energy of the corresponding perpendicular form VI by 10.0 kcal mol-‘. Geometry optimization, as expected, gives greater bond angles (Table 2). The distance between H-l and H-4 is thus not so short as to elevate the energy very much. As a result, the true feature that the coplanar cisoid is lower in energy than the perpendicular one is revealed. The transoids present a similar feature. As geometry optimization was not employed by Hoffmann and coworkers [ 11, detailed comparison between coplanar and perpendicular forms of the species such as allylcarbinyl cations could not be made, although they succeeded in the cases of substitution by groups with extremely electronegative and electropositive atoms, fluorine and boron, respectively. The stability of the coplanar form relative to the corresponding perpendicular form can be accounted for by hyperconjugation. The essence of hyperconjugation in this case is the energy decrease due to delocalization of electrons from the u bonding orbitals around C-2 to the vacant p orbital on C-l. The effect manifests itself as the shortening of the C-l-C-2 bond. The results given by geometry optimization (Table 3) do show shorter bond
angle
TABLE 2 Optimized MNDO bond angles (in degrees) of the aIIylcarbiny1 cation
c!’ cw c?c3c4 C’C’H’ H’C’H” C3CaH2 HaC’H” CX”H” C3C’H4’ C’C4H4
III
IV
V
VI
Standard geometry
117.4 124.9 123.6 115.9 110.8 103.3 115.9 121.8 124.4
111.4 123.6 121.8 116.4 108.8 107.9 116.1 121.4 124.7
121.9 130.3 124.4 115.5 108.8 102.8 111.1 121.6 125.2
116.0 129.6 121.8 116.3 106.8 107.9 110.1 121.3 125.6
120 120 120 120 109.47 109.47 120 120 120
274 TABLE
3
Optimized MNDO
C’c? cw cv C’H’ C’H” CzHZ C”H” C?H”’ C4H4
bond lengths (in A) of the allylcarbinyl cation
III
IV
V
VI
Standard geometry
1.464 1.500 1.345 1.095 1.095 1.130 1.094 1.091 1.090
1.469 1.523 1.343 1.095
1.460 1.499 1.342 1.096 1.093 1.132 1.098 1.091 1.089
1.466 1.522 1.340 1.095
1.52 1.52 1.34 1.08 1.08 1.09 1.08 1.08 1.08
lengths between C-l orbital on C-l of the carbon plane, should tals while that of the with those symmetrical
1.119 1.092 1.092 1.090
and C-2 than coplanar form hyperconjugate perpendicular to the carbon
1.121 1.096 1.092 1.089
those between C-2 and C-3. The vacant VII (=III), being antisymmetrical to the with the antisymmetrical group orbiform VIII (=IV) should hyperconjugate plane thus
The presence of the double bond lengthens the conjugated system, thus strengthening the hyperconjugation and further lowering the energy. The evidence of the strengthening due to hyperconjugation can be shown by making a comparison between the optimized bond lengths. As shown in Table 3, the C-l-C-2 bonds of the coplanar forms are shorter than those of the perpendicular forms for both the cisoid and the transoid, showing that the hyperconjugation is stronger in the former. The C-3-C-4 bonds of the coplanar forms are slightly longer than those of the perpendicular forms, showing that the double bonds are weakened by donating electrons onto the positive centre of the cation through hyperconjugation. CONCLUSIONS
The rule of conformation of XCH,CH2+ should be complimented as follows. If X is more electronegative than hydrogen, the coplanar form will be more stable; if X is less electronegative than hydrogen, the perpendicular form will be more stable; the presence of an adjacent double bond in X will stabilize the coplanar form.
275
The rule of conformation of XCH&H; shows an opposite order to the cations, as shown by Hoffmann and co-workers [ 11. However, the influential factors seem comparatively complicated in the case of anions and remain to be studied further. REFERENCES 1 R. Hoffmann, L. Radom, J. A. Pople, P. v. R. Schleyer, W. J. Hehre and L. Salem, J. Am. Chem. Sot., 94 (1972) 6221. 2 A. S. N. Murthy and S. Ranganathan, Int. J. Quantum Chem., 18 (1980) 1479. 3 J. A. Pople and M. S. Gordon, J. Am. Chem. Sot., 89 (1967) 4253. 4 M. J. S. Dewar and W. Thiel, J. Am. Chem. Sot., 99 (1977) 4907.
EFFECT OF CONJUGATION BEYOND MULTIPLE BONDS Part II. On the relative stability of various conformations ions*
of cadmium
CHEN ZHIXING Chemistry
Department,
Zhongshan
University,
Guangzhou
(People’s Republic
of China)
CA1 WENZHENG Chemistry Department, South China Normal (People’s Republic of China)
University,
Guangzhou
(Received 16 January 1984)
ABSTRACT MNDO geometry optimization indicates that the coplanar forms of the allylcarbinyl cation are more stable than the corresponding perpendicular forms. An explanation is given from the viewpoint of hyperconjugation. It can then be concluded that for cations of the type XCH,CHi the adjacent double bond in X will strengthen the hyperconjugation in the coplanar conformation, thus lowering the energy to a greater extent. INTRODUCTION
The electronic structure of carbonium ions is of theoretical importance to the research of nucleophilic reactions. Hoffmann and co-workers [l] studied the conformation of o-substituted ethyl ions, XCH,CH:, by using the MO method and showed that the cations prefer the coplanar form I if the substituent X is more electronegative than hydrogen, whereas they prefer the perpendicular form II if X is less electronegative. When X has a double bond in the nearer terminal, no illustration was afforded in the paper [l] . Murthy and Ranganathan [2] performed calculations on two conformations of the allylcsrbinyl cation by using the EHMO method, indicating that the coplanar form III is lower in energy than the perpendicular form IV, but they gave no interpretation. They also performed calculations on the same species by using CND0/2, but no total energies were reported. CALCULATIONS
Our CNDO/B results with the standard geometrical models [3] show the opposite to EHMO: IV is lower in energy than III. We also performed calcu*The previous paper in this series appeared in J. Mol. Struct., Theochem, 0166-1280/84/$03.00
0 1984 Elsevier Science Publishers B.V.
105 (1983)
281.
272
lations on the cisoids, V and VI, which show a similar trend: the perpendicular form VI is lower in energy than the coplanar form V. Considering that the standard geometry may be inadequate, we performed a full geometry optimization with C, symmetry. However, IV changed into a three-membered ring and VI into a four-membered ring, so that comparisons could not be made. To clarify the problem, we used the MNDO method to perform the calculations. As is well known, the MNDO method gives fairly good relative energies. For example, Dewar and Thiel [4] reported barriers to rotation in ethane, methylamine, methanol, and hydrogen peroxide with an average error of only 0.9 kcal mol-‘; the error of the energy of torsion by 90” in ethylene is also small, amounting to 2.5 kcal mol-‘. We believe that MNDO is suitable for predicting the relative stability of various conformations.
RESULTS
AND DISCUSSION
The results are listed in Table 1. For both cisoid and transoid, the energies of the perpendicular form are lower than those of the coplanar form in the standard geometrical model, the trends being similar to those given by CND0/2. However, geometry optimization gives the opposite trends. The main feature is the deviation of the bond angles in the standard geometrical models from the true. As is well known, the angle between a C=C bond and a C-H bond is generally greater than 120”. The standard bond
213 TABLE 1 MNDO heats of formation (in kcal mol-’ ) of allylcarbinyl cations
Standard geometries Geometry optimization
III
IV
V
VI
241.2 235.4
239.9 236.7
256.4 231.4
246.4 238.1
of 120” is too small. The terminal hydrogen atoms, H-l and H-4, of the co-planar cisoid V will repel each other, resulting in an elevation of the total energy. As the four angles from H-l to H-4 in the standard geometrical model are too small, the distance between H-l and H-4 become too short, causing the energy to elevate abnormally. It goes so far as to exceed the energy of the corresponding perpendicular form VI by 10.0 kcal mol-‘. Geometry optimization, as expected, gives greater bond angles (Table 2). The distance between H-l and H-4 is thus not so short as to elevate the energy very much. As a result, the true feature that the coplanar cisoid is lower in energy than the perpendicular one is revealed. The transoids present a similar feature. As geometry optimization was not employed by Hoffmann and coworkers [ 11, detailed comparison between coplanar and perpendicular forms of the species such as allylcarbinyl cations could not be made, although they succeeded in the cases of substitution by groups with extremely electronegative and electropositive atoms, fluorine and boron, respectively. The stability of the coplanar form relative to the corresponding perpendicular form can be accounted for by hyperconjugation. The essence of hyperconjugation in this case is the energy decrease due to delocalization of electrons from the u bonding orbitals around C-2 to the vacant p orbital on C-l. The effect manifests itself as the shortening of the C-l-C-2 bond. The results given by geometry optimization (Table 3) do show shorter bond
angle
TABLE 2 Optimized MNDO bond angles (in degrees) of the aIIylcarbiny1 cation
c!’ cw c?c3c4 C’C’H’ H’C’H” C3CaH2 HaC’H” CX”H” C3C’H4’ C’C4H4
III
IV
V
VI
Standard geometry
117.4 124.9 123.6 115.9 110.8 103.3 115.9 121.8 124.4
111.4 123.6 121.8 116.4 108.8 107.9 116.1 121.4 124.7
121.9 130.3 124.4 115.5 108.8 102.8 111.1 121.6 125.2
116.0 129.6 121.8 116.3 106.8 107.9 110.1 121.3 125.6
120 120 120 120 109.47 109.47 120 120 120
274 TABLE
3
Optimized MNDO
C’c? cw cv C’H’ C’H” CzHZ C”H” C?H”’ C4H4
bond lengths (in A) of the allylcarbinyl cation
III
IV
V
VI
Standard geometry
1.464 1.500 1.345 1.095 1.095 1.130 1.094 1.091 1.090
1.469 1.523 1.343 1.095
1.460 1.499 1.342 1.096 1.093 1.132 1.098 1.091 1.089
1.466 1.522 1.340 1.095
1.52 1.52 1.34 1.08 1.08 1.09 1.08 1.08 1.08
lengths between C-l orbital on C-l of the carbon plane, should tals while that of the with those symmetrical
1.119 1.092 1.092 1.090
and C-2 than coplanar form hyperconjugate perpendicular to the carbon
1.121 1.096 1.092 1.089
those between C-2 and C-3. The vacant VII (=III), being antisymmetrical to the with the antisymmetrical group orbiform VIII (=IV) should hyperconjugate plane thus
The presence of the double bond lengthens the conjugated system, thus strengthening the hyperconjugation and further lowering the energy. The evidence of the strengthening due to hyperconjugation can be shown by making a comparison between the optimized bond lengths. As shown in Table 3, the C-l-C-2 bonds of the coplanar forms are shorter than those of the perpendicular forms for both the cisoid and the transoid, showing that the hyperconjugation is stronger in the former. The C-3-C-4 bonds of the coplanar forms are slightly longer than those of the perpendicular forms, showing that the double bonds are weakened by donating electrons onto the positive centre of the cation through hyperconjugation. CONCLUSIONS
The rule of conformation of XCH,CH2+ should be complimented as follows. If X is more electronegative than hydrogen, the coplanar form will be more stable; if X is less electronegative than hydrogen, the perpendicular form will be more stable; the presence of an adjacent double bond in X will stabilize the coplanar form.
275
The rule of conformation of XCH&H; shows an opposite order to the cations, as shown by Hoffmann and co-workers [ 11. However, the influential factors seem comparatively complicated in the case of anions and remain to be studied further. REFERENCES 1 R. Hoffmann, L. Radom, J. A. Pople, P. v. R. Schleyer, W. J. Hehre and L. Salem, J. Am. Chem. Sot., 94 (1972) 6221. 2 A. S. N. Murthy and S. Ranganathan, Int. J. Quantum Chem., 18 (1980) 1479. 3 J. A. Pople and M. S. Gordon, J. Am. Chem. Sot., 89 (1967) 4253. 4 M. J. S. Dewar and W. Thiel, J. Am. Chem. Sot., 99 (1977) 4907.