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Effect of conjugation beyond multiple bonds
Journal of Molecular Structure (Theochem), 136 (1986) 57-63 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
EFFECT
OF CONJUCATION
BEYOND MULTIPLE
Part III. The nature of carbon-carbon
BONDS
bond length
CHEN ZHIXING Chemistry Department,
Zhongshan University, Guangzhou (China)
(Received 20 May 1985)
ABSTRACT The effect of the change in the form of a carbon atom (tetrahedral, trigonal or linear) on the carbon-carbon bond length is studied by a statistical method. The interference of conjugative effects on bond length is eliminated by regression with the n-resonance integral contribution to energy. The charge or inductive effect is found to be insignificant in the regression. The shortening of the C-C bond length in the change from a tetrahedral to a trigonal carbon atom is found to be 0.007 A, while the change from a trigonal form to a linear form shortens the C-C bond by 0.0396 A. It is thus concluded that the change in form of the carbon atoms is not a major factor in shortening the middle C-C bond of butadiene, as compared with that of ethane. INTRODUCTION
There have long been controversial ideas about the shortening of the middle CC bond of butadiene by ca. 0.07 A compared with that of ethane. According to the correlation of bond length with bond order presented by Coulson [l] , the shortening in bond length is attributed to conjugation. Dewar and Schmeising [2] suggested a different view, that the origin of the shortening is a change in hybrid state. Mulliken [3] recognized the importance of the change in the hybrid state, but denied that conjugation is insignificant. Bartell [4] presented a view of strong nonbonded repulsion between bonded atoms, and claimed that this shortening results from the decrease of the nonbonded repulsion due to the change from tetrahedral to trigonal carbons. Skaarup et al. [5] calculated the change, due to twisting the middle bond of butadiene by 90”, to be a lengthening of 0.02 W which is only a small part of the difference of 0.07 8. They regarded the lengthen ing to be due to the destroying of the conjugated system, thus concluding that conjugation is not the main influence on bond length. However, Daudey et al. [ 61 disagreed with this view. They asserted that hyperconjugation does not vanish after the twist, so the change of the bond length cannot be explained as the vanishing of conjugation. They verified that conjugation is the main factor of the shortening by using an approach of direct analysis. 0166-1280/86/$03.50
0 1986 Elsevier Science Publishers B.V.
58
To solve this problem the magnitude of the shortening due solely to the change from a tetrahedral to a trigonal carbon atom must be known. Such information can be obtained by the statistical method described here. METHODOLOGY
In principle, quantum chemical calculation can give information about the nature of the change in bond lengths. However, the available quantum chemical methods cannot give quantitative results in an absolute sense. They can make comparisons in a set of similar entities, but not between factors far different in nature. Conjugation and the form of a carbon atom are quite different in nature, so comparison between their effects on bond lengths cannot be reliably made by quantum chemical calculations alone. Statistics is suitable for discriminating between the effects of various factors, provided that a large number of accurate data are available and that the factors are represented by suitable variables. In this problem, the interference of con jugation effects in the statistics of bond lengths vs. the carbon atom form can be eliminated by regression with arguments representing n-bonding and the form of the carbon atom. The variable representing the change from a trigonal to a tetrahedral carbon is taken as the number of tetrahedral carbon atoms nc4 of a given CC bond. Similarly, the number of linear carbon atoms nc, is taken to represent the change from a trigonal to a linear carbon. Suitable quantum chemical quantities can be chosen as a measure of conjugation in a relative sense. HMO bond order may be acceptable but it is not the most suitable. For molecules with a symmetry plane, the n-MOs provided by any MO method can be separated out and the n-bond order can be calculated and serves as a measure of n-bonding. However, n-bond order is not the most suitable measure of a-bonding. For styrene, the n-bond order between the pam-carbon and the remote side-chain carbon has a considerable value (0.144 in CND0/2, 0.114 in MNDO), but the overlap is too small to give rise to bonding. The n-resonance integral contribution to energy EnR calculated by Semiempirical SCF methods is a good measure of n -bonding [ 71:
(1) where 5” is the r-bond order between atomic orbitals cc and Z.Jbelonging to atoms A and B respectively, and HP, is the corresponding resonance integral. In this work, CNDO/B and MNDO data of EnR were adopted as the variable representing the n-bonding in conjugated systems. Powers up to the eighth together with nc4 and ncz are taken as arguments (factors) in regard to the non-linearity of the correlation of bond length with E nR, and the significant factors are automatically selected by stepwise regression by using the variance ratio F as a measure of significance:
59 F = (N
-
m
-
1) (Q(m
- 1) -
Q(m))/Q(W,
(2)
where N is the total number of datum points, m is the number of introduced factors, Q(m) is the sum of squares of (residual) deviations and Q(m - 1) is the Q value after deleting a specified factor. As the experimental bond lengths are defined differently and of different accuracy, those to be used should be chosen carefully. It is best to use equilibrium bond lengths, r,, i.e., those corresponding to the minimum total energy of a molecule. However, most experimental data are of average bond lengths and are greater than re. A great part of the early data relate to ro, and are often of poor precision. A greater part of the modem data pertains to the rs proposed by Costain [S] , who pointed out that the difference between rs and re does not, in general, exceed 0.003 A. Therefore, the rs and re data were chosen as the main experimental bond lengths. There is also much rg data; these are obviously greater than rs. Table 1 lists the values of r,,, rs, and rg cited in [9] , from which linear regression gives rs = 0.02846 + 0.9752 rg
(3)
with a root-mean-square deviation (RMSD) of 0.0032 a and a correlation coefficient of 0.9993. The rg data were converted into r, and the results, together with the experimental re and r8 values, were adopted as a set of experimental bond lengths, designated by R, for the regression. The r. of benzene was also adopted owing to its high precision [9]. It is necessary to know whether or not the charge or inductive effect will interfere in the correlation. Ionic species are suitable for such a check as their charge effect is strong. Experimental bond lengths of ions are seldom available and so geometry optimizations by suitable MO methods must be performed for them The optimized geometries often contain systematic errors, which can be greatly diminished by regression with known experimental data. The corresponding data for the regression are listed in Table 1. Stepwise regression results in the following function of CNDO/B bond length
R = 0.8245 + 0.2189 R;,,, the RMSD being 0.012 A, and the correlation Similarly
R = 0.7105 + 0.3466 RLNDo
(4) coefficient
being 0.9928. (5)
the RMSD being 0.015 8, and the correlation coefficient being 0.9892. These results show the superiority of CNDO/B over MNDO, in the relative sense as discussed in a previous paper [7]. RESULTS
AND DISCUSSION
For the neutral molecules in Table 1, both MNDO and CNDO/B data give the in the stepwise regression with F > 2 selected factor of nc4, ncZ, EnR and (EnR)"
60 TABLE 1 Experimental CC bond lengths and data of MNDO and CNDO/B
Ethane Propane Ethylene Propylene
rS
MNDO
CND0/2
MNDO
1.521 1.530 1.335 1.340 1.496 1.465 1.344 1.520 1.362 1.478 1.407 1.194 1.565 1.467 1.196 1.192 1.350 1.367 1.422 1.404 1.406 1.539 1.517 1.439 1.197 1.342 1.488 1.423 1.344 1.452
1.467 1.466 1.310 1.321 1.449 1.440 1.323 1.466 1.347 1.445 1.384 1.197 1.481 1.444 1.209 1.197 1.317 1.323 1.388 1.384 1.385 1.464 1.442 1.416 1.208 1.323 1.436 1.412 1.321 1.422
1.336 1.501
Benzene Acetylene tert-Butylacetylene
Fluoroacetylene Fluoroethylene cio-Difluoroethylene Fluorobenzene
Ethanol Acetaldehyde Propynal Acrolein Acrylonitrile
+
EnR
1.526
Cyclopentadiene
R = a0
WC. bond length
-
Butadiene
Acetonitrile
Experimental bond length
1.509 1.342 1.469 1.3964a 1.2031b 1.531 1.500 1.209 1.198 1.329 1.324 1.383 1.395 1.397 1.5115 1.4446 1.2089 1.345 1.470 1.4256 1.3389 1.4584
‘g
1.5326 1.532 1.337 1.3417 1.5063 1.465 1.345 1.399 1.333 1.331 1.515 1.4527 1.211 1.345 1.484 1.438 1.343 1.468
u1n,-.4 + a2nc2 + a3EnR + u~(E~R)~
CNDO/P
-0.0091 -0.0087 -0.1269 -0.1240 -0.0142 -0.0247 -0.1206 -0.0139 -0.1139 -0.0279 -0.0737
-0.0713 -0.0678 -0.4374 -0.4154 -0.0875 -0.1072 -0.4080 -0.0885 -0.3719 -0.1244 -0.2580
-0.0068 -0.0134
-0.0510 -0.0658
-0.1195 -0.1119 -0.0691 -0.0746 -0.0734 -0.0083 -0.0129 -0.0224
-0.4225 -0.4102 -0.2506 -0.2595 -0.2572 -0.0702 -0.0981 -0.1140
-0.1216 -9.0206 -0.0234 -0.1213 -0.0147
-0.4044 -0.1161 -0.1110 -0.4096 -0.0914
(6)
The constants and the variance ratios corresponding to the selected factors are listed in Table 2. The total correlation coefficient r is employed as a measure of the effectiveness of regression ,. = (1 _ Q(m)/Q(o))ll2 (7) where Q(O)is the sum of squares of deviations without any factor introduced. The total correlation coefficient is 0.9938 for MNDO and 0.9931 for CNDO/2, showing excellent regressions. The RMSD is 0.0078 A for MNDO and 0.0083 R for CNDO/B, appearing to be satisfactory. The plots of bond length vs. IFR for MNDO and CNDO/S are shown in
61 TABLE 2 Results of stepwise regression of experimental bond length with respect to carbon atom forms i
Factor
MNDO F
0
1 2 3 4
“C.
ncz E-
(ERR)’
-
3.6 42.1 66.7 10.4
CNDO/P 9
1.5249 0.0076 -0.0393 2.3168 6.2235
F
2.2 37.6 51.6 11.7
9
1.6653 0.0064 -0.0397 0.3754 0.7696
Fig. 1. Bond length (A) vs. MNDO EmR (hartree).
Figs. 1 and 2, respectively. The curves represent the values calculated by Eqn. 6 without the terms no4 and n,,. The circles represent the experimental bond lengths of neutral molecules. The corrections for nc4 and nc2 are shown by arrows. The set of molecules in the regression included those with strongly electron-withdrawing groups such as F, CO, and CN. The corresponding points in Figs. 1 and 2 do not systematically deviate from the curves to one side, showing no significant interference of the inductive effect. Some ionic species were used to check the correlations. The bond lengths of ions were calculated by Eqns. 2 and 3 using the MNDO and CNDO/B bond lengths listed in Table 3; they are also shown in Figs. 1 and 2, in which the dots represent anions and the circles with a central dot represent cations. It can be seen that the points corresponding to ions where the correction for the carbon atom form has been used close to the curves. Thus, the charge
62
1.3'
I
-0.4
I
-0.3
-0.2
-0.1
'
E
7rR
Fig. 2. Bond length (A) vs. CNDO/Z EnR (hartree). TABLE 3 MNDO and CNDO/Z data of ions MNDO
E"R Ethyl cation Ethyl anion Ally1 cation Ally1 anion Cyclopentadienyl anion Protonated acetaldehyde Deprotonated acetaldehyde Protonated acetonitrile Detwotonated acetonitrile
-0.0392 -0.0446 -0.0799 -0.0820 -0.0699 -0.0219 -0.0843 -0.0179 -0.0703
CNDO/B
R
R(regr.)
1.469 1.428 1.391 1.379 1.418 1.603 1.381 1.466 1.368
1.448 1.417 1.381 1.370 1.407 1.493 1.372 1.446 1.360
E -0.2294 -0.1838 -0.2841 -0.2794 -0.2443 -0.1688 -0.3349 -0.1181 -0.2719
R
R (regr. )
1.376 1.406 1.362 1.366 1.399 1.411 1.346 1.400 1.363
1.396 1.433 1.378 1.382 1.424 1.439 1.368 1.426 1.367
or inductive effect does not interfere significantly even in the cases of ions, and the success of the regression is further confirmed. Triple bonds are not included in the regressions, as E” represents only one of the two R-systems. The CC bond of the vinyl anion has some triple bond character and the corresponding point lies on the right far of the curves, owing to disregarding one n-system. For the ethyl cation and anion, only the eclipsed conformations I and II are included. For the staggered species III and IV (in which III has no equilibrium CNDO/B structure), the disregarded n-bond lying in the symmetry plane is strong, thus these points also deviate to the right in the figures (not shown for clarity). Since the correlation is excellent, the aim of eliminating the interference of conjugation is achieved, and the effect of the form of carbon atoms can
63
II
I
III
be quantitatively estimated with good reliability. The coefficients a, and a2 reflect the effect of the carbon atom form The excellent of itc4 and nc, correlation leads to good coincidences of both al and a2 between the regressions with CNDO/B EnR and MNDO EnR, no matter how the values of EnR differ between CNDO/B and MNDO. The average value amounts to a1
=
0.007 A, a2 = -0.0395
A.
(3)
i.e., lengthening of 0.007 A will be caused by changing from a trigonal to a tetrahedral carbon, and shortening of 0.0395 A by changing to a linear carbon. Obviously, the latter is much more significant than the former. The shortening of the bond due to the change of two tetrahedral carbon atoms to trigonal forms is 0.007 X 2 = 0.014 8, which is only a minor part of the difference of 0.07 W between the bond of butadiene and that of ethane. Therefore, neither the change of hybrid state nor the change of nonbonded repulsion has a major effect on the bond length. This conclusion is in agreement with the view of Daudey et al. [6 1. REFERENCES 1 2 3 4 5 6 7 8 9
C. A. Coulson, Proc. R. Sot. London, Ser. A, 169 (1939) 413. M. J. S. Dewar and H. N. Schmeising, Tetrahedron, 6 (1959) 166. R. S. Mulliken, Tetrahedron, 6 (1959) 68. L. S. Bartell, J. Chem. Phys., 32 (1960) 827; Tetrahedron, 17 (1962) 177; 34 (1978) 2891; J. Chem. Educ., 45 (1968) 754. S. Skaarup, J. E. Boggs and P. N. Skancke, Tetrahedron, 32 (1976) 1179. J. P. Daudey, G. Trinquier, J. C. Barthelat and J. P. Malvieu, Tetrahedron, 36 (1980) 3399. Chem Zhixing, J. Mol. Struct. (Theochem), 105 (1983) 281. C. C. Costain, J. Chem. Phys., 29 (1958) 864. K.-H. Hellwage, Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology, New Series, Group II, Vol. 7, Springer Verlag, Berlin, 1976.
EFFECT
OF CONJUCATION
BEYOND MULTIPLE
Part III. The nature of carbon-carbon
BONDS
bond length
CHEN ZHIXING Chemistry Department,
Zhongshan University, Guangzhou (China)
(Received 20 May 1985)
ABSTRACT The effect of the change in the form of a carbon atom (tetrahedral, trigonal or linear) on the carbon-carbon bond length is studied by a statistical method. The interference of conjugative effects on bond length is eliminated by regression with the n-resonance integral contribution to energy. The charge or inductive effect is found to be insignificant in the regression. The shortening of the C-C bond length in the change from a tetrahedral to a trigonal carbon atom is found to be 0.007 A, while the change from a trigonal form to a linear form shortens the C-C bond by 0.0396 A. It is thus concluded that the change in form of the carbon atoms is not a major factor in shortening the middle C-C bond of butadiene, as compared with that of ethane. INTRODUCTION
There have long been controversial ideas about the shortening of the middle CC bond of butadiene by ca. 0.07 A compared with that of ethane. According to the correlation of bond length with bond order presented by Coulson [l] , the shortening in bond length is attributed to conjugation. Dewar and Schmeising [2] suggested a different view, that the origin of the shortening is a change in hybrid state. Mulliken [3] recognized the importance of the change in the hybrid state, but denied that conjugation is insignificant. Bartell [4] presented a view of strong nonbonded repulsion between bonded atoms, and claimed that this shortening results from the decrease of the nonbonded repulsion due to the change from tetrahedral to trigonal carbons. Skaarup et al. [5] calculated the change, due to twisting the middle bond of butadiene by 90”, to be a lengthening of 0.02 W which is only a small part of the difference of 0.07 8. They regarded the lengthen ing to be due to the destroying of the conjugated system, thus concluding that conjugation is not the main influence on bond length. However, Daudey et al. [ 61 disagreed with this view. They asserted that hyperconjugation does not vanish after the twist, so the change of the bond length cannot be explained as the vanishing of conjugation. They verified that conjugation is the main factor of the shortening by using an approach of direct analysis. 0166-1280/86/$03.50
0 1986 Elsevier Science Publishers B.V.
58
To solve this problem the magnitude of the shortening due solely to the change from a tetrahedral to a trigonal carbon atom must be known. Such information can be obtained by the statistical method described here. METHODOLOGY
In principle, quantum chemical calculation can give information about the nature of the change in bond lengths. However, the available quantum chemical methods cannot give quantitative results in an absolute sense. They can make comparisons in a set of similar entities, but not between factors far different in nature. Conjugation and the form of a carbon atom are quite different in nature, so comparison between their effects on bond lengths cannot be reliably made by quantum chemical calculations alone. Statistics is suitable for discriminating between the effects of various factors, provided that a large number of accurate data are available and that the factors are represented by suitable variables. In this problem, the interference of con jugation effects in the statistics of bond lengths vs. the carbon atom form can be eliminated by regression with arguments representing n-bonding and the form of the carbon atom. The variable representing the change from a trigonal to a tetrahedral carbon is taken as the number of tetrahedral carbon atoms nc4 of a given CC bond. Similarly, the number of linear carbon atoms nc, is taken to represent the change from a trigonal to a linear carbon. Suitable quantum chemical quantities can be chosen as a measure of conjugation in a relative sense. HMO bond order may be acceptable but it is not the most suitable. For molecules with a symmetry plane, the n-MOs provided by any MO method can be separated out and the n-bond order can be calculated and serves as a measure of n-bonding. However, n-bond order is not the most suitable measure of a-bonding. For styrene, the n-bond order between the pam-carbon and the remote side-chain carbon has a considerable value (0.144 in CND0/2, 0.114 in MNDO), but the overlap is too small to give rise to bonding. The n-resonance integral contribution to energy EnR calculated by Semiempirical SCF methods is a good measure of n -bonding [ 71:
(1) where 5” is the r-bond order between atomic orbitals cc and Z.Jbelonging to atoms A and B respectively, and HP, is the corresponding resonance integral. In this work, CNDO/B and MNDO data of EnR were adopted as the variable representing the n-bonding in conjugated systems. Powers up to the eighth together with nc4 and ncz are taken as arguments (factors) in regard to the non-linearity of the correlation of bond length with E nR, and the significant factors are automatically selected by stepwise regression by using the variance ratio F as a measure of significance:
59 F = (N
-
m
-
1) (Q(m
- 1) -
Q(m))/Q(W,
(2)
where N is the total number of datum points, m is the number of introduced factors, Q(m) is the sum of squares of (residual) deviations and Q(m - 1) is the Q value after deleting a specified factor. As the experimental bond lengths are defined differently and of different accuracy, those to be used should be chosen carefully. It is best to use equilibrium bond lengths, r,, i.e., those corresponding to the minimum total energy of a molecule. However, most experimental data are of average bond lengths and are greater than re. A great part of the early data relate to ro, and are often of poor precision. A greater part of the modem data pertains to the rs proposed by Costain [S] , who pointed out that the difference between rs and re does not, in general, exceed 0.003 A. Therefore, the rs and re data were chosen as the main experimental bond lengths. There is also much rg data; these are obviously greater than rs. Table 1 lists the values of r,,, rs, and rg cited in [9] , from which linear regression gives rs = 0.02846 + 0.9752 rg
(3)
with a root-mean-square deviation (RMSD) of 0.0032 a and a correlation coefficient of 0.9993. The rg data were converted into r, and the results, together with the experimental re and r8 values, were adopted as a set of experimental bond lengths, designated by R, for the regression. The r. of benzene was also adopted owing to its high precision [9]. It is necessary to know whether or not the charge or inductive effect will interfere in the correlation. Ionic species are suitable for such a check as their charge effect is strong. Experimental bond lengths of ions are seldom available and so geometry optimizations by suitable MO methods must be performed for them The optimized geometries often contain systematic errors, which can be greatly diminished by regression with known experimental data. The corresponding data for the regression are listed in Table 1. Stepwise regression results in the following function of CNDO/B bond length
R = 0.8245 + 0.2189 R;,,, the RMSD being 0.012 A, and the correlation Similarly
R = 0.7105 + 0.3466 RLNDo
(4) coefficient
being 0.9928. (5)
the RMSD being 0.015 8, and the correlation coefficient being 0.9892. These results show the superiority of CNDO/B over MNDO, in the relative sense as discussed in a previous paper [7]. RESULTS
AND DISCUSSION
For the neutral molecules in Table 1, both MNDO and CNDO/B data give the in the stepwise regression with F > 2 selected factor of nc4, ncZ, EnR and (EnR)"
60 TABLE 1 Experimental CC bond lengths and data of MNDO and CNDO/B
Ethane Propane Ethylene Propylene
rS
MNDO
CND0/2
MNDO
1.521 1.530 1.335 1.340 1.496 1.465 1.344 1.520 1.362 1.478 1.407 1.194 1.565 1.467 1.196 1.192 1.350 1.367 1.422 1.404 1.406 1.539 1.517 1.439 1.197 1.342 1.488 1.423 1.344 1.452
1.467 1.466 1.310 1.321 1.449 1.440 1.323 1.466 1.347 1.445 1.384 1.197 1.481 1.444 1.209 1.197 1.317 1.323 1.388 1.384 1.385 1.464 1.442 1.416 1.208 1.323 1.436 1.412 1.321 1.422
1.336 1.501
Benzene Acetylene tert-Butylacetylene
Fluoroacetylene Fluoroethylene cio-Difluoroethylene Fluorobenzene
Ethanol Acetaldehyde Propynal Acrolein Acrylonitrile
+
EnR
1.526
Cyclopentadiene
R = a0
WC. bond length
-
Butadiene
Acetonitrile
Experimental bond length
1.509 1.342 1.469 1.3964a 1.2031b 1.531 1.500 1.209 1.198 1.329 1.324 1.383 1.395 1.397 1.5115 1.4446 1.2089 1.345 1.470 1.4256 1.3389 1.4584
‘g
1.5326 1.532 1.337 1.3417 1.5063 1.465 1.345 1.399 1.333 1.331 1.515 1.4527 1.211 1.345 1.484 1.438 1.343 1.468
u1n,-.4 + a2nc2 + a3EnR + u~(E~R)~
CNDO/P
-0.0091 -0.0087 -0.1269 -0.1240 -0.0142 -0.0247 -0.1206 -0.0139 -0.1139 -0.0279 -0.0737
-0.0713 -0.0678 -0.4374 -0.4154 -0.0875 -0.1072 -0.4080 -0.0885 -0.3719 -0.1244 -0.2580
-0.0068 -0.0134
-0.0510 -0.0658
-0.1195 -0.1119 -0.0691 -0.0746 -0.0734 -0.0083 -0.0129 -0.0224
-0.4225 -0.4102 -0.2506 -0.2595 -0.2572 -0.0702 -0.0981 -0.1140
-0.1216 -9.0206 -0.0234 -0.1213 -0.0147
-0.4044 -0.1161 -0.1110 -0.4096 -0.0914
(6)
The constants and the variance ratios corresponding to the selected factors are listed in Table 2. The total correlation coefficient r is employed as a measure of the effectiveness of regression ,. = (1 _ Q(m)/Q(o))ll2 (7) where Q(O)is the sum of squares of deviations without any factor introduced. The total correlation coefficient is 0.9938 for MNDO and 0.9931 for CNDO/2, showing excellent regressions. The RMSD is 0.0078 A for MNDO and 0.0083 R for CNDO/B, appearing to be satisfactory. The plots of bond length vs. IFR for MNDO and CNDO/S are shown in
61 TABLE 2 Results of stepwise regression of experimental bond length with respect to carbon atom forms i
Factor
MNDO F
0
1 2 3 4
“C.
ncz E-
(ERR)’
-
3.6 42.1 66.7 10.4
CNDO/P 9
1.5249 0.0076 -0.0393 2.3168 6.2235
F
2.2 37.6 51.6 11.7
9
1.6653 0.0064 -0.0397 0.3754 0.7696
Fig. 1. Bond length (A) vs. MNDO EmR (hartree).
Figs. 1 and 2, respectively. The curves represent the values calculated by Eqn. 6 without the terms no4 and n,,. The circles represent the experimental bond lengths of neutral molecules. The corrections for nc4 and nc2 are shown by arrows. The set of molecules in the regression included those with strongly electron-withdrawing groups such as F, CO, and CN. The corresponding points in Figs. 1 and 2 do not systematically deviate from the curves to one side, showing no significant interference of the inductive effect. Some ionic species were used to check the correlations. The bond lengths of ions were calculated by Eqns. 2 and 3 using the MNDO and CNDO/B bond lengths listed in Table 3; they are also shown in Figs. 1 and 2, in which the dots represent anions and the circles with a central dot represent cations. It can be seen that the points corresponding to ions where the correction for the carbon atom form has been used close to the curves. Thus, the charge
62
1.3'
I
-0.4
I
-0.3
-0.2
-0.1
'
E
7rR
Fig. 2. Bond length (A) vs. CNDO/Z EnR (hartree). TABLE 3 MNDO and CNDO/Z data of ions MNDO
E"R Ethyl cation Ethyl anion Ally1 cation Ally1 anion Cyclopentadienyl anion Protonated acetaldehyde Deprotonated acetaldehyde Protonated acetonitrile Detwotonated acetonitrile
-0.0392 -0.0446 -0.0799 -0.0820 -0.0699 -0.0219 -0.0843 -0.0179 -0.0703
CNDO/B
R
R(regr.)
1.469 1.428 1.391 1.379 1.418 1.603 1.381 1.466 1.368
1.448 1.417 1.381 1.370 1.407 1.493 1.372 1.446 1.360
E -0.2294 -0.1838 -0.2841 -0.2794 -0.2443 -0.1688 -0.3349 -0.1181 -0.2719
R
R (regr. )
1.376 1.406 1.362 1.366 1.399 1.411 1.346 1.400 1.363
1.396 1.433 1.378 1.382 1.424 1.439 1.368 1.426 1.367
or inductive effect does not interfere significantly even in the cases of ions, and the success of the regression is further confirmed. Triple bonds are not included in the regressions, as E” represents only one of the two R-systems. The CC bond of the vinyl anion has some triple bond character and the corresponding point lies on the right far of the curves, owing to disregarding one n-system. For the ethyl cation and anion, only the eclipsed conformations I and II are included. For the staggered species III and IV (in which III has no equilibrium CNDO/B structure), the disregarded n-bond lying in the symmetry plane is strong, thus these points also deviate to the right in the figures (not shown for clarity). Since the correlation is excellent, the aim of eliminating the interference of conjugation is achieved, and the effect of the form of carbon atoms can
63
II
I
III
be quantitatively estimated with good reliability. The coefficients a, and a2 reflect the effect of the carbon atom form The excellent of itc4 and nc, correlation leads to good coincidences of both al and a2 between the regressions with CNDO/B EnR and MNDO EnR, no matter how the values of EnR differ between CNDO/B and MNDO. The average value amounts to a1
=
0.007 A, a2 = -0.0395
A.
(3)
i.e., lengthening of 0.007 A will be caused by changing from a trigonal to a tetrahedral carbon, and shortening of 0.0395 A by changing to a linear carbon. Obviously, the latter is much more significant than the former. The shortening of the bond due to the change of two tetrahedral carbon atoms to trigonal forms is 0.007 X 2 = 0.014 8, which is only a minor part of the difference of 0.07 W between the bond of butadiene and that of ethane. Therefore, neither the change of hybrid state nor the change of nonbonded repulsion has a major effect on the bond length. This conclusion is in agreement with the view of Daudey et al. [6 1. REFERENCES 1 2 3 4 5 6 7 8 9
C. A. Coulson, Proc. R. Sot. London, Ser. A, 169 (1939) 413. M. J. S. Dewar and H. N. Schmeising, Tetrahedron, 6 (1959) 166. R. S. Mulliken, Tetrahedron, 6 (1959) 68. L. S. Bartell, J. Chem. Phys., 32 (1960) 827; Tetrahedron, 17 (1962) 177; 34 (1978) 2891; J. Chem. Educ., 45 (1968) 754. S. Skaarup, J. E. Boggs and P. N. Skancke, Tetrahedron, 32 (1976) 1179. J. P. Daudey, G. Trinquier, J. C. Barthelat and J. P. Malvieu, Tetrahedron, 36 (1980) 3399. Chem Zhixing, J. Mol. Struct. (Theochem), 105 (1983) 281. C. C. Costain, J. Chem. Phys., 29 (1958) 864. K.-H. Hellwage, Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology, New Series, Group II, Vol. 7, Springer Verlag, Berlin, 1976.