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Electronic structure and geometry of the active centres in anionic polymerization of vinyl monomers
European Pol)mer Journal, Vol. 12. pp 59 to 63. Pergamon Press 1976. Printed in Great Britain.
ELECTRONIC STRUCTURE A N D GEOMETRY OF THE ACTIVE CENTRES IN ANIONIC POLYMERIZATION OF VINYL MONOMERS Yu. YE. EIZNER and B. L. ERUSSALIMSKY Institute of High Molecular Weight Compounds, Bolshoi pr. 31. Leningrad 199004, U.S.S.R. (Received 18 September 1974)
Abstrac~The charge distributions in the ions (CH3--CHR) and in the molecules CH3--CHR Li (R = N O 2 , C N , C O O C H 3 , C 6 H 5 , CH~------CH2~ H , NH: or OCH3), modelling the active centres of the two extreme types in anionic polymerization, were calculated by the CNDO/2 method. The geometry of these compounds was partly optimized. Both the geometry and the charge distribution in anions were found to exhibit no strong dependence on R. This suggests that in free ion polymerization, the equality fir 2 = 1 holds. The active centres of the polarized bond type are fairly varied. Two reasons for their reactivity may exist: the polarity of their C--Li bond and their geometry facilitating the insertion of a monomer. The electronic structure of the neutral molecules considered correlates with the low degree of association of the living chains. The active centres in anionic polymerization initiated by organometallic compounds exist in different forms. The extreme forms are polarized M6,- Mt ~+ molecules and M,, free anions with quite different reactivities. The charge distribution at the end of the growing chain might be the most important factor determining its reactivity. Hence, it is interesting to compare the electronic structures of species of both types and the role of the nature of the end group. In order to carry out these comparisons, we calculated the electronic structure of the C H a - - C H R - - L i molecules and the ( C H 3 - - C H R ) - anions, thus modelling the active centres in anionic polymerization of CHz~-------CHR monomers with R = NO2, CN, COOCH3, C6Hs, C H = C H 2 , H, NH 2 and OCHa. The first five R groups correspond to the monomers commonly known as typically "'anionic". Although this cannot be said about ethylene, R = H is also included as a reference. Macroanions with R = OCH3 and NH2 can hardly exist because the corresponding monomers are typically "cationic". These substituents are also included only for comparison. Q u a n t u m chemical calculations were carried out by the C N D O / 2 method [1-4] now the most used semiempirical method; its possibilities and limitations are quite well known [4-9]. The errors in atomic charges estimated by this method are not more than a few hundredths of the electron charge [4, 10, 11]. These errors are comparable in order of magnitude to the error introduced by the replacement of Mn with CH3 [12] and by neglect of the influence of the solvent [13. 14]. Thus, the C N D O / 2 method is quite acceptable for the calculation of atomic charges in our case.* The calculation of the electronic structure of the active centre requires a search for the most stable conformation because the corresponding experimen* The calculations were carried out to within 0.0001 of the electron charge. Only two figures after the decimal point are given in the schemes because only they are significant. 59
tal data are quite insufficient, in contrast to the case of monomers. The C N D O / 2 method is known to predict the stable geometry of molecules qualitatively well, the errors in the bond lengths being about 0.1 A and in the bond angles a few degrees [9]. Low barriers between conformations are not calculated accurately but high barriers are dealt with satisfactori l y [ l ( ~ l S ] . The stability of conformations of high connectivity is usually somewhat overestimated [19]. The initial geometry of all the molecules was constructed according to the "standard geometry" [20]. This means that the angles at the N atom in NO2 and NH2, at the C atom in carbonyl and all the angles in the vinyl and phenyl groups were put equal to 120 °, and all these groups were assumed to be planar. All the other angles were put equal to 109.47 '~. The bond lengths were: r ( C - - H ) = 1.08 ,4 in CH~---CH 2 and in C6H~; other C - - H bonds are 1.09 /~; r(N--H) = 1"01 ~ ; ~2(C--C) = 1-34 A: r ( C " C ) = 1"40 A; r [ C - - ( C - N ) ] = 145 A; r[C--(C~---O)] = r[C--(CH~-----CHE) ] = 1'52 A; other C - - C bonds are 1.54 A; r(C~------O)= 1"22 h ; r [ O - - ( C - - O ) ] = 1"36 A; other C - - O bonds are 1.43 A:r ; r ( C - N ) 1'16 A; r(C--N) = 1"47 A; r(N--O) = 1-24 A. Then the geometry was partly optimized. Only the following geometrical parameters were varied: (1) the angle 0p between any of the C--(CH3) , C - - H or C - - R bonds forming an equiangular pyramid and the prolongation of the axis of this pyramid; (2) the righthanded spherical coordinates rLi, 0L~ and q~Li of the Li atom (naturally, only for neutral molecules) with respect to the terminal C atom, to the above-mentioned prolongation of the axis and to the plane of this axis and the C - - R bond; (3) the angle q5R of rotation about the C - - R bond (if R is not C-= N or H) in the clockwise direction from the trans-contbrmation of the axis and the bond between the first and the second atoms of R (the second atom in COOCH3 is the carbonyl oxygen atom and in C H = C H 2 - the C atom of the methylene group); (4) the angle q~o of rotation about the O---(C---O) bond if R is C O O C H 3 and about O--(CHLi) bond if R
Yu. YE. ]~IZNERand B. L. ERUSSALIMSKY
60
Table 1 R
In molecules AE 0p rLi
OLi JLi
JR Jo
NO2
CN
COOCH a
C6H 5
CH=CH2
H
NH2
OCH3
37-3 110 2"05 48 - - 122 84
55'3 102 2"06 44 - 52
74.1 76 2.23 9
93.8 100 2.06 40 --51 81
85.9 90 2.07 23 -49 68
38.5 111 1.98 37
40.9 108 1.94 47 - - 177 169
82.4 11! 2.06 42 --81 30 38
2.5 101 90
1.5 104 90
7.2 110 173
3.3 112 - 27 32
-- lO0
-
In anions AE
0.6 106 90
0v
JR Jo
0.3 106
104 108 1.9 103 86
-
120
0.2 111
-13
is OCH3, in the same direction as ~bR from the t r a n s conformation of the corresponding bonds. The irritial values of these parameters were: 0p = 109.5 °, rL~ = 2'10 A, 0Li = ~bLi= 0 °, ~bR = 90 °, 4)0 = 0 °. The minim u m total energy of the molecule in the space of these coordinates (4-6 coordinates for neutral molecules and 1-3 coordinates for anions) were sought by Powell's method of conjugated gradients [21]. The minimization was continued until the difference between the values of these parameters in two successive iterations of the method became lower than 0.005 A and 0.5 °. The resulting values (in A and degrees) and the values of AE (in kcal/mole) of decrease in the total energy in the process of its minimization are given in Table 1. The atomic charges (in atomic units) in anions corresponding to their optimized geometry are shown in Figs. 1-3. Both these charges and the optimized geometry itself are shown in Figs. 4-11 for neutral molecules because this geometry changes markedly in the course of its optimization. In order to give a clear idea of the spatial perspective, the spheres corresponding to atoms of different chemical elements were put identical.
-0"07 "~0'04 -0.05
C - -
o • o6 / -
-0"36 C
I
o
-0"49
/ -O.IO
c - -
-0"12
I -0.12
-0.10 ~+ 0.06
- 0 ' 39
+0-08
-0.23/0"03
N
C
-0-06--
-
-
-
o • 09/
C
-
-
C
- 0l. 0 9
-
-
C
- 01- 0 8
\
-0.04
-o.,/
-0"08
-0"06
-o.o, -o.os---Lo.o
-0.03 -0-06 Fig. 2. Atomic charges in anions (CH3CHR)- corresponding to hydrocarbon monomers.
We can see that the negative charges at the end of the macroion are not concentrated on the terminal C atom in contrast to the formal scheme. Less than a half of the charge remains on this atom. The fraction of the charge on the terminal atom in different macroions is surprisingly constant. At any rate, the differences are too low to be discussed if account is
0 -0"47 +0.49///N%
-o.o
- 0 ' 1 2 "~,,+ 0 . 0 7 -O.lO-- c - -
-o.48
-0'10
-0.07--
+0.07 C
- o"o 9 /
-0"43 +0.10 C - - C __
-0.41 N
-0.tO "~0'04 -0.09--C
I -0"07
-0"09
-0-09
/
-0"36 -0-2<
-0"01
C--N
I
\
-O-13
- 0"01
-0.06 "~
-0-06--C
-0"08
- -
/
0.07 - -
-0-42 C - -
i -0.07
+0.38 C - -
fr 0
-0"48
-0.27 0
+0-I~ C_-----0"03
\
-0-03
Fig. 1. Atomic charges (in atomic units) in anions (CH3CHR)- corresponding to polar monomers active in anionic systems.
-0'10
,~0.03
-0-08--C
/ 08
-0.32 C
-
I - 0.13
-0'25 -
O
-
+0-14///-0"06 -
C---0"09
\
-0- O . 06 Fig. 3. Atomic charges in anions (CHaCHR)- corresponding to polar monomers passive in anionic systems.
Active centres in anionic polymerization Li -(CHR) Li -(HCR) Li-(CH 3)
61 Li - ( C H R )
2'2
2"8
Li - (HCR)
2-4
2"1
Li - ( C H 3 )
2"2 2"0
Li - ( H 3 C )
2.1 3.2
Li - ( C = O )
2-4
Li - ( O = C ) Li - ( / 0 ~ )
3.0 2.9
Li - (CH30)
2-4 2-0 2"2 3"4
2-0
2"1
Li-(H3C)
2"1
LI -N
3"2 3"t
Li-0
3"5 4'~
Li - (H3CO)
+ 0-27 Li °0"39 0.~...0.4 9 [-0"20 ~ + * : ' : : ', ")N C--C-"
-o37 /
+0"18 Li
1.oo. .oo
•o
+0"02
.oo
+0.04
Fig. 4. Model of the anionic active centre (AAC) of nitroethylene. Left--conformation. Right some interatomic distances: (XYZ)-(UVW) refers to the distance in A between the nucleus of the X atom in the XYZ group and the nucleus of the U atom in the UVW group. Below-atomic charges (in atomic units). taken of the approximations involved. This stability is supported by a comparison with the macroions of aminoethylene and of methyl vinyl ether. The situation is completely analogous to that of the oxonium ions CHr--O==CHR modelling the macrocations of vinyl ethers and cyclic acetals [12]. However, if the displacement of the charge in oxonium ions as well as the stability of this displacement can be explained by the presence of a heteroatom carrying the unshared pairs of electrons, in this case the analogous phenomena are not so easily understood. The geometry at the terminal C atom in all the anions investigated is nearly tetrahedral and the stability is also high. This stability of charge distribution in the ions and of their geometry suggests that the propagation rate in free ion polymerization is determined exclusLi-(CHR)
2"1
Li-(HCR)
3"0
L i - ( C H 3) Li-(H3C) Li -(C--N) Li -N
/C
÷0.04/
0 -0"24
C
Lo
,/:oo
C--C~-~
0.03
[ +0"08~_ 0 +0.01 -0"37
0,0 i
Fig. 6. Model of AAC of methyl acrylate (see legend to Fig. 4). ively by the nature of the monomer. The experimental manifestation of this fact would be an equality r l r 2 = 1. To our knowledge, corresponding experimental data are not available. In contrast to free ions, the active centres of the polarized molecule type are fairly varied. They differ both in the charges on the Li and terminal C atoms and in the geometry of the terminal group. It is known experimentally that differences in the reactivity of active centres of this type are also high [22]. The most striking example of this is the fact that living chains of polystyrene with lithium counter-ion initiate the polymerization of methyl methacrylate while L i - (CHR) Li - (HCR) Li-(CH~)
2'1 3"0 .~'4
3"4
Li-(H3C)
21 20
2"4
Li - (Ca)
2'2
2"0 2"2
Li - (C8)
3"4 2"2
Li-(Cy)
34 2'2 42
2"8
Li
- (C 8 )
[ .4 4-'2,.
Li - ( H C s )
L i - (HC ;..) Li-(HC s ) ÷0"18 Li -0"21
-oo,
+0"17 I-0"23 / - 0 " 0 4 C--
N~
C
15,:2 1'4.0 5-2
C~---- + 0 " 0 3
÷0"07~-0"02 ",'002
Fig. 5. Model of AAC of acrylonitrile (see legend to Fig. 4). 4).
•o 0.00--
c-oo5 C ,'-0.05~¢
+o.o5/ -0"01
\-o.o4
L_o23 j _ o o 2 C--
I o.oo
C,------+ 0"02
oo,
+0"04
Fig. 7. Model of AAC of styrene (see legend to Fig. 4).
62
Yu. YE. EIZNER and B. L. ERUSSALIMSKY L i - (CHR) L I - (HCR)
Li -(CHR) Li -{HCR) Li -(CH 3)
2"1 2"7 2"4 2 "2 L i - ( H 3C) 2"7 3"4 L i - (CHCH2) ::"2 Li -(HCCH2) 3" I Li - (CHzCH) 2 3 2 "I Li -(H2CCH) 3"2
L i - ( C H 3)
2.1 3.0 2.3
Li - 0 Li-(CH30)
2-0 2'6 3'3 2'7 ;)'4
L i - (H3CO)
2" I 2'2
Li-(HaCl
:5'5
~'O'lO Li +0"05
÷O't4 I-0"25 / - 0 - 0 2 C=C--C--C~--~
÷0"01
/-0"14
I +o.o6
+ 0-02
+O08 Li
~0"00
0"00 +0"02
Fig. 8. Model of AAC of butadiene (see legend to Fig. 4). living chains of methyl methacrylate do not polymerize styrene [23]. According to Figs. 4-11, the possible reasons for the reactivity of these molecules are also different. High reactivity of polynitroethyl lithium might be associated with the relatively high polarity of the Li-C bond. In the living chains of acrylonitrile and methyl acrylate, the polarity of this bond is not so high. Nevertheless, the substituents in these compounds attract the Li atom. Hence, these active centres are deformed in such a manner that the C - - L i bond is accessible to the attack of a monomer. Consequently, this deformation can also lead to high reactivity of the active centre. Incidentally, we can see that both these factors, the high polarity of the C - - L i bond and its convenient orientation, are absent in the hypothetical "anionic active centres" of aminoethylene and methyl vinyl ether--these centres are probably as inactive as are the corresponding monomers in anionic systems. The unexpected deformation of geometry in Figs. 4-11 should be considered only as a trend because of the well-known tendency of the CNDO/2 method Li-(CH 2 ) Li-(HzC) Li-(CH 3 )
÷0'03 O'O0-~C / +0"03
• 0'15
-0'11 / 0 . 0 0 0--C--C--+0.03 -0-20 +0"02 ~'+0"02 -0'04
Fig. 10. Model of AAC of vinyl ether (see legend to Fig. 4). to overestimate the stability of compact conformations [19]. However, there are qualitative arguments confirming this result: a large number of extensive vacant atomic orbitals does permit the lithium atom to form multiple donor-acceptor bonds [24]. This ability of the Li atom to form multiple bonds was observed experimentally taking as examples crystalline triphenylmethyllithium-tetramethylethylenediamine and living chains ~CH2CH(CN)Li [25]. The formation of these bonds can lead to a three-centered structure in ethyl lithium. It is facilitated by the presence of unshared pairs in polar substituents such as CN o r C O O C H 3 and by the conjugation in substituents such as CH-------CH2. Another corroboration of this geometry is its considerable stability as compared to the initial confor-
2.0
2-7 2" I
Li - (CHR) Li - (HCR) Li - ( C H 3)
1.9 2.1 2.3
Li - ( H 3 C )
2"8 3"2
L'-"
Li-(H3C)
2" I 3"2
+o.14 Li
I -O.24 0,00 _ 0 . 0 1 _ _ C _ _ C__/--'~+O. 03 J " 0 " 0 6 ~ + 0.03 -0"01
Fig. 9. Model of AAC of ethylene (see legend to Fig. 4).
Li - ( H 2 N )
3.7 4-1
+0'15 Li +0 " 0 7 ~ LOI2 / + 0-04 _ _ ~ 0 " 2 5 C - - C ~ - - ~ + 0.0 I .0.07 /
+0"04~_ 0.01 0"00 Fig. II. Model of AAC of aminoethylene (see legend to Fig. 4).
Active centres in anionic polymerization mation: the decrease in the total energy of the neutral molecules in the course of minimization exceeds the error in the C N D O / 2 method, in contrast to the corresponding decrease for anions. In turn, the saturation of virtual bonds of lithium atom within a molecule explains the relatively low degree of association of the living chains with the lithium counter-ion. As a rule, L i C H 3 exists in a tetrameric or a hexameric form [26] whereas the degree of association (p) of the (MnLi)p living chains in nonpolar solvents depends on the nature of M,. Thus, it is 4 for polybutadiene and 2 for polystyrene. In the case of polyisoprene, p is 4 at concentrations above 10-3 mole/1 and less than 4 at lower concentrations [27]. The monomeric form was established for hydrocarbon living chains with acrylonitrile terminal units [28, 29]. The above mentioned intramolecular saturation of the tendency of the Li atom to form multiple bonds can also explain the lower association ability of lithium aryls [30] as compared to lithium alkyls [31 ]. REFERENCES
1. J. A~ Pople, D. P. Santry and G. A. Segal, J. chem. Phys. 43, t 30S (1965). 2. J. A. Pople and G. A. Segal, J. chem. Phys. 43, 136S (1965). 3. J. A. Pople and G. A. Segal, J. chem. Phys. 44, 3289 (1966). 4. J. A. Pople and D. L. Beveridge, Approximate Molecular Orbital Theory. McGraw-Hill, New York (1970). 5. H. H. Jaff6, Accts Chem. Res. 2, 136 (1963). 6. G. Kloppman and B. O'Leary, Fortschr. chem. Forsch. 15, 447 (1970). 7. N. D. Chuvylkin and G. M. Zhidomirov, Zh. strukt. Khim. 12, 347 (1971). 8. D. A. Brown, W. J. Chambers and N. J. Fitzpatrick, lnorg. Chim. Acta Rev. 6, 7 (1972).
63
9. V. G. Dashevsky, Usp. Khim. 42, 2097 (1973). 10. D. T. Clark, W. J. Feast, D. Kilcast, D. B. Adams and W. E. Preston, J. Fluorine Chem. 2, 199 (1972). 11. W. R. Hall and H. F. Hameka, lnor 9. Chem. 12, 1878 (1973). 12. Yu. Ye. Eizner and B. L. Erussalimsky, Vysokomolek. Soedin. 12A, 1610 (1970). 13. E. Clementi, J. chem. Phys. 54, 2492 (1971). t4. D. Rinaldi and J. L. Rivail, Theor. chim. Acta 32, 57 (1973). 15. W. C. Herndon, J. Feuer and J. H. Hall, Tetrahedron Lett. 22, 2625 (1968). 16. M. S. Gordon, J. Am. chem. Soc. 91, 3122 (1969). 17. L. A. Carreira, J. chem. Phys. 55, 181 (1971). 18. G. Robinet, J.-F. Labarre and C. Leibovici, Chem. phys. Lett. 22, 356 (1973). 19. H. Imamura, K. Morio, M. Oki and T. L. Kunii, Tetrahedron Lett. 52, 4575 (1970). 20. J. A. Pople and M. Gordon, J. Am. chem. Soc. 89, 4253 (1967). 21. M. J. D. Powell, Comput. J. 7, 155 (1964). 22. G. E. Ham (editor), Copolymerization. Interscience, New York (1964). 23. M. Scwarc, Carbanions, Living Polymers and Electron Transfer Processes. Wiley-lnterscience, New York (1968). 24. Yu. Ye. Eizner, B. L. Erussalimsky and E. B. Milovskaya, Polym. J. 5, I (1973). 25. (a) J. J. Brooks and G. D. Stucky, J. Am. chem. Soc. 94, 7333 (1972); (b) Ch. Tsvetanov, I. Panayotov and B. Erussalimsky, Europ. Polym. J. 10, 557 (1974). 26. H. Lewis and T. L. Brown, J. Am. chem. Soc. 92, 4664 (1970). 27. S. Bywater, D. Worsfold and G. Hollingsworth, Macromolecules 5, 389 (1972). 28. Ch. B. Tsvetanov, V. N. Zgonnik, B. L. Erussalimsky and I. M. Panayotov, Vysokomolek. Soedin. 14B, 404 (1972). 29. Ch. B. Tsvetanov, V. N. Zgonnik, B. L. Erussalimsky and I. M. Panayotov, Liebi.q. Ann. 763, 53 (1972). 30. R. Waack and P. Rest, J. Organomet. Chem. 5, 188 (1966). 31. T. L. Brown, Adv. Oroanomet. Chem. 3, 365 (1966).
ELECTRONIC STRUCTURE A N D GEOMETRY OF THE ACTIVE CENTRES IN ANIONIC POLYMERIZATION OF VINYL MONOMERS Yu. YE. EIZNER and B. L. ERUSSALIMSKY Institute of High Molecular Weight Compounds, Bolshoi pr. 31. Leningrad 199004, U.S.S.R. (Received 18 September 1974)
Abstrac~The charge distributions in the ions (CH3--CHR) and in the molecules CH3--CHR Li (R = N O 2 , C N , C O O C H 3 , C 6 H 5 , CH~------CH2~ H , NH: or OCH3), modelling the active centres of the two extreme types in anionic polymerization, were calculated by the CNDO/2 method. The geometry of these compounds was partly optimized. Both the geometry and the charge distribution in anions were found to exhibit no strong dependence on R. This suggests that in free ion polymerization, the equality fir 2 = 1 holds. The active centres of the polarized bond type are fairly varied. Two reasons for their reactivity may exist: the polarity of their C--Li bond and their geometry facilitating the insertion of a monomer. The electronic structure of the neutral molecules considered correlates with the low degree of association of the living chains. The active centres in anionic polymerization initiated by organometallic compounds exist in different forms. The extreme forms are polarized M6,- Mt ~+ molecules and M,, free anions with quite different reactivities. The charge distribution at the end of the growing chain might be the most important factor determining its reactivity. Hence, it is interesting to compare the electronic structures of species of both types and the role of the nature of the end group. In order to carry out these comparisons, we calculated the electronic structure of the C H a - - C H R - - L i molecules and the ( C H 3 - - C H R ) - anions, thus modelling the active centres in anionic polymerization of CHz~-------CHR monomers with R = NO2, CN, COOCH3, C6Hs, C H = C H 2 , H, NH 2 and OCHa. The first five R groups correspond to the monomers commonly known as typically "'anionic". Although this cannot be said about ethylene, R = H is also included as a reference. Macroanions with R = OCH3 and NH2 can hardly exist because the corresponding monomers are typically "cationic". These substituents are also included only for comparison. Q u a n t u m chemical calculations were carried out by the C N D O / 2 method [1-4] now the most used semiempirical method; its possibilities and limitations are quite well known [4-9]. The errors in atomic charges estimated by this method are not more than a few hundredths of the electron charge [4, 10, 11]. These errors are comparable in order of magnitude to the error introduced by the replacement of Mn with CH3 [12] and by neglect of the influence of the solvent [13. 14]. Thus, the C N D O / 2 method is quite acceptable for the calculation of atomic charges in our case.* The calculation of the electronic structure of the active centre requires a search for the most stable conformation because the corresponding experimen* The calculations were carried out to within 0.0001 of the electron charge. Only two figures after the decimal point are given in the schemes because only they are significant. 59
tal data are quite insufficient, in contrast to the case of monomers. The C N D O / 2 method is known to predict the stable geometry of molecules qualitatively well, the errors in the bond lengths being about 0.1 A and in the bond angles a few degrees [9]. Low barriers between conformations are not calculated accurately but high barriers are dealt with satisfactori l y [ l ( ~ l S ] . The stability of conformations of high connectivity is usually somewhat overestimated [19]. The initial geometry of all the molecules was constructed according to the "standard geometry" [20]. This means that the angles at the N atom in NO2 and NH2, at the C atom in carbonyl and all the angles in the vinyl and phenyl groups were put equal to 120 °, and all these groups were assumed to be planar. All the other angles were put equal to 109.47 '~. The bond lengths were: r ( C - - H ) = 1.08 ,4 in CH~---CH 2 and in C6H~; other C - - H bonds are 1.09 /~; r(N--H) = 1"01 ~ ; ~2(C--C) = 1-34 A: r ( C " C ) = 1"40 A; r [ C - - ( C - N ) ] = 145 A; r[C--(C~---O)] = r[C--(CH~-----CHE) ] = 1'52 A; other C - - C bonds are 1.54 A; r(C~------O)= 1"22 h ; r [ O - - ( C - - O ) ] = 1"36 A; other C - - O bonds are 1.43 A:r ; r ( C - N ) 1'16 A; r(C--N) = 1"47 A; r(N--O) = 1-24 A. Then the geometry was partly optimized. Only the following geometrical parameters were varied: (1) the angle 0p between any of the C--(CH3) , C - - H or C - - R bonds forming an equiangular pyramid and the prolongation of the axis of this pyramid; (2) the righthanded spherical coordinates rLi, 0L~ and q~Li of the Li atom (naturally, only for neutral molecules) with respect to the terminal C atom, to the above-mentioned prolongation of the axis and to the plane of this axis and the C - - R bond; (3) the angle q5R of rotation about the C - - R bond (if R is not C-= N or H) in the clockwise direction from the trans-contbrmation of the axis and the bond between the first and the second atoms of R (the second atom in COOCH3 is the carbonyl oxygen atom and in C H = C H 2 - the C atom of the methylene group); (4) the angle q~o of rotation about the O---(C---O) bond if R is C O O C H 3 and about O--(CHLi) bond if R
Yu. YE. ]~IZNERand B. L. ERUSSALIMSKY
60
Table 1 R
In molecules AE 0p rLi
OLi JLi
JR Jo
NO2
CN
COOCH a
C6H 5
CH=CH2
H
NH2
OCH3
37-3 110 2"05 48 - - 122 84
55'3 102 2"06 44 - 52
74.1 76 2.23 9
93.8 100 2.06 40 --51 81
85.9 90 2.07 23 -49 68
38.5 111 1.98 37
40.9 108 1.94 47 - - 177 169
82.4 11! 2.06 42 --81 30 38
2.5 101 90
1.5 104 90
7.2 110 173
3.3 112 - 27 32
-- lO0
-
In anions AE
0.6 106 90
0v
JR Jo
0.3 106
104 108 1.9 103 86
-
120
0.2 111
-13
is OCH3, in the same direction as ~bR from the t r a n s conformation of the corresponding bonds. The irritial values of these parameters were: 0p = 109.5 °, rL~ = 2'10 A, 0Li = ~bLi= 0 °, ~bR = 90 °, 4)0 = 0 °. The minim u m total energy of the molecule in the space of these coordinates (4-6 coordinates for neutral molecules and 1-3 coordinates for anions) were sought by Powell's method of conjugated gradients [21]. The minimization was continued until the difference between the values of these parameters in two successive iterations of the method became lower than 0.005 A and 0.5 °. The resulting values (in A and degrees) and the values of AE (in kcal/mole) of decrease in the total energy in the process of its minimization are given in Table 1. The atomic charges (in atomic units) in anions corresponding to their optimized geometry are shown in Figs. 1-3. Both these charges and the optimized geometry itself are shown in Figs. 4-11 for neutral molecules because this geometry changes markedly in the course of its optimization. In order to give a clear idea of the spatial perspective, the spheres corresponding to atoms of different chemical elements were put identical.
-0"07 "~0'04 -0.05
C - -
o • o6 / -
-0"36 C
I
o
-0"49
/ -O.IO
c - -
-0"12
I -0.12
-0.10 ~+ 0.06
- 0 ' 39
+0-08
-0.23/0"03
N
C
-0-06--
-
-
-
o • 09/
C
-
-
C
- 0l. 0 9
-
-
C
- 01- 0 8
\
-0.04
-o.,/
-0"08
-0"06
-o.o, -o.os---Lo.o
-0.03 -0-06 Fig. 2. Atomic charges in anions (CH3CHR)- corresponding to hydrocarbon monomers.
We can see that the negative charges at the end of the macroion are not concentrated on the terminal C atom in contrast to the formal scheme. Less than a half of the charge remains on this atom. The fraction of the charge on the terminal atom in different macroions is surprisingly constant. At any rate, the differences are too low to be discussed if account is
0 -0"47 +0.49///N%
-o.o
- 0 ' 1 2 "~,,+ 0 . 0 7 -O.lO-- c - -
-o.48
-0'10
-0.07--
+0.07 C
- o"o 9 /
-0"43 +0.10 C - - C __
-0.41 N
-0.tO "~0'04 -0.09--C
I -0"07
-0"09
-0-09
/
-0"36 -0-2<
-0"01
C--N
I
\
-O-13
- 0"01
-0.06 "~
-0-06--C
-0"08
- -
/
0.07 - -
-0-42 C - -
i -0.07
+0.38 C - -
fr 0
-0"48
-0.27 0
+0-I~ C_-----0"03
\
-0-03
Fig. 1. Atomic charges (in atomic units) in anions (CH3CHR)- corresponding to polar monomers active in anionic systems.
-0'10
,~0.03
-0-08--C
/ 08
-0.32 C
-
I - 0.13
-0'25 -
O
-
+0-14///-0"06 -
C---0"09
\
-0- O . 06 Fig. 3. Atomic charges in anions (CHaCHR)- corresponding to polar monomers passive in anionic systems.
Active centres in anionic polymerization Li -(CHR) Li -(HCR) Li-(CH 3)
61 Li - ( C H R )
2'2
2"8
Li - (HCR)
2-4
2"1
Li - ( C H 3 )
2"2 2"0
Li - ( H 3 C )
2.1 3.2
Li - ( C = O )
2-4
Li - ( O = C ) Li - ( / 0 ~ )
3.0 2.9
Li - (CH30)
2-4 2-0 2"2 3"4
2-0
2"1
Li-(H3C)
2"1
LI -N
3"2 3"t
Li-0
3"5 4'~
Li - (H3CO)
+ 0-27 Li °0"39 0.~...0.4 9 [-0"20 ~ + * : ' : : ', ")N C--C-"
-o37 /
+0"18 Li
1.oo. .oo
•o
+0"02
.oo
+0.04
Fig. 4. Model of the anionic active centre (AAC) of nitroethylene. Left--conformation. Right some interatomic distances: (XYZ)-(UVW) refers to the distance in A between the nucleus of the X atom in the XYZ group and the nucleus of the U atom in the UVW group. Below-atomic charges (in atomic units). taken of the approximations involved. This stability is supported by a comparison with the macroions of aminoethylene and of methyl vinyl ether. The situation is completely analogous to that of the oxonium ions CHr--O==CHR modelling the macrocations of vinyl ethers and cyclic acetals [12]. However, if the displacement of the charge in oxonium ions as well as the stability of this displacement can be explained by the presence of a heteroatom carrying the unshared pairs of electrons, in this case the analogous phenomena are not so easily understood. The geometry at the terminal C atom in all the anions investigated is nearly tetrahedral and the stability is also high. This stability of charge distribution in the ions and of their geometry suggests that the propagation rate in free ion polymerization is determined exclusLi-(CHR)
2"1
Li-(HCR)
3"0
L i - ( C H 3) Li-(H3C) Li -(C--N) Li -N
/C
÷0.04/
0 -0"24
C
Lo
,/:oo
C--C~-~
0.03
[ +0"08~_ 0 +0.01 -0"37
0,0 i
Fig. 6. Model of AAC of methyl acrylate (see legend to Fig. 4). ively by the nature of the monomer. The experimental manifestation of this fact would be an equality r l r 2 = 1. To our knowledge, corresponding experimental data are not available. In contrast to free ions, the active centres of the polarized molecule type are fairly varied. They differ both in the charges on the Li and terminal C atoms and in the geometry of the terminal group. It is known experimentally that differences in the reactivity of active centres of this type are also high [22]. The most striking example of this is the fact that living chains of polystyrene with lithium counter-ion initiate the polymerization of methyl methacrylate while L i - (CHR) Li - (HCR) Li-(CH~)
2'1 3"0 .~'4
3"4
Li-(H3C)
21 20
2"4
Li - (Ca)
2'2
2"0 2"2
Li - (C8)
3"4 2"2
Li-(Cy)
34 2'2 42
2"8
Li
- (C 8 )
[ .4 4-'2,.
Li - ( H C s )
L i - (HC ;..) Li-(HC s ) ÷0"18 Li -0"21
-oo,
+0"17 I-0"23 / - 0 " 0 4 C--
N~
C
15,:2 1'4.0 5-2
C~---- + 0 " 0 3
÷0"07~-0"02 ",'002
Fig. 5. Model of AAC of acrylonitrile (see legend to Fig. 4). 4).
•o 0.00--
c-oo5 C ,'-0.05~¢
+o.o5/ -0"01
\-o.o4
L_o23 j _ o o 2 C--
I o.oo
C,------+ 0"02
oo,
+0"04
Fig. 7. Model of AAC of styrene (see legend to Fig. 4).
62
Yu. YE. EIZNER and B. L. ERUSSALIMSKY L i - (CHR) L I - (HCR)
Li -(CHR) Li -{HCR) Li -(CH 3)
2"1 2"7 2"4 2 "2 L i - ( H 3C) 2"7 3"4 L i - (CHCH2) ::"2 Li -(HCCH2) 3" I Li - (CHzCH) 2 3 2 "I Li -(H2CCH) 3"2
L i - ( C H 3)
2.1 3.0 2.3
Li - 0 Li-(CH30)
2-0 2'6 3'3 2'7 ;)'4
L i - (H3CO)
2" I 2'2
Li-(HaCl
:5'5
~'O'lO Li +0"05
÷O't4 I-0"25 / - 0 - 0 2 C=C--C--C~--~
÷0"01
/-0"14
I +o.o6
+ 0-02
+O08 Li
~0"00
0"00 +0"02
Fig. 8. Model of AAC of butadiene (see legend to Fig. 4). living chains of methyl methacrylate do not polymerize styrene [23]. According to Figs. 4-11, the possible reasons for the reactivity of these molecules are also different. High reactivity of polynitroethyl lithium might be associated with the relatively high polarity of the Li-C bond. In the living chains of acrylonitrile and methyl acrylate, the polarity of this bond is not so high. Nevertheless, the substituents in these compounds attract the Li atom. Hence, these active centres are deformed in such a manner that the C - - L i bond is accessible to the attack of a monomer. Consequently, this deformation can also lead to high reactivity of the active centre. Incidentally, we can see that both these factors, the high polarity of the C - - L i bond and its convenient orientation, are absent in the hypothetical "anionic active centres" of aminoethylene and methyl vinyl ether--these centres are probably as inactive as are the corresponding monomers in anionic systems. The unexpected deformation of geometry in Figs. 4-11 should be considered only as a trend because of the well-known tendency of the CNDO/2 method Li-(CH 2 ) Li-(HzC) Li-(CH 3 )
÷0'03 O'O0-~C / +0"03
• 0'15
-0'11 / 0 . 0 0 0--C--C--+0.03 -0-20 +0"02 ~'+0"02 -0'04
Fig. 10. Model of AAC of vinyl ether (see legend to Fig. 4). to overestimate the stability of compact conformations [19]. However, there are qualitative arguments confirming this result: a large number of extensive vacant atomic orbitals does permit the lithium atom to form multiple donor-acceptor bonds [24]. This ability of the Li atom to form multiple bonds was observed experimentally taking as examples crystalline triphenylmethyllithium-tetramethylethylenediamine and living chains ~CH2CH(CN)Li [25]. The formation of these bonds can lead to a three-centered structure in ethyl lithium. It is facilitated by the presence of unshared pairs in polar substituents such as CN o r C O O C H 3 and by the conjugation in substituents such as CH-------CH2. Another corroboration of this geometry is its considerable stability as compared to the initial confor-
2.0
2-7 2" I
Li - (CHR) Li - (HCR) Li - ( C H 3)
1.9 2.1 2.3
Li - ( H 3 C )
2"8 3"2
L'-"
Li-(H3C)
2" I 3"2
+o.14 Li
I -O.24 0,00 _ 0 . 0 1 _ _ C _ _ C__/--'~+O. 03 J " 0 " 0 6 ~ + 0.03 -0"01
Fig. 9. Model of AAC of ethylene (see legend to Fig. 4).
Li - ( H 2 N )
3.7 4-1
+0'15 Li +0 " 0 7 ~ LOI2 / + 0-04 _ _ ~ 0 " 2 5 C - - C ~ - - ~ + 0.0 I .0.07 /
+0"04~_ 0.01 0"00 Fig. II. Model of AAC of aminoethylene (see legend to Fig. 4).
Active centres in anionic polymerization mation: the decrease in the total energy of the neutral molecules in the course of minimization exceeds the error in the C N D O / 2 method, in contrast to the corresponding decrease for anions. In turn, the saturation of virtual bonds of lithium atom within a molecule explains the relatively low degree of association of the living chains with the lithium counter-ion. As a rule, L i C H 3 exists in a tetrameric or a hexameric form [26] whereas the degree of association (p) of the (MnLi)p living chains in nonpolar solvents depends on the nature of M,. Thus, it is 4 for polybutadiene and 2 for polystyrene. In the case of polyisoprene, p is 4 at concentrations above 10-3 mole/1 and less than 4 at lower concentrations [27]. The monomeric form was established for hydrocarbon living chains with acrylonitrile terminal units [28, 29]. The above mentioned intramolecular saturation of the tendency of the Li atom to form multiple bonds can also explain the lower association ability of lithium aryls [30] as compared to lithium alkyls [31 ]. REFERENCES
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9. V. G. Dashevsky, Usp. Khim. 42, 2097 (1973). 10. D. T. Clark, W. J. Feast, D. Kilcast, D. B. Adams and W. E. Preston, J. Fluorine Chem. 2, 199 (1972). 11. W. R. Hall and H. F. Hameka, lnor 9. Chem. 12, 1878 (1973). 12. Yu. Ye. Eizner and B. L. Erussalimsky, Vysokomolek. Soedin. 12A, 1610 (1970). 13. E. Clementi, J. chem. Phys. 54, 2492 (1971). t4. D. Rinaldi and J. L. Rivail, Theor. chim. Acta 32, 57 (1973). 15. W. C. Herndon, J. Feuer and J. H. Hall, Tetrahedron Lett. 22, 2625 (1968). 16. M. S. Gordon, J. Am. chem. Soc. 91, 3122 (1969). 17. L. A. Carreira, J. chem. Phys. 55, 181 (1971). 18. G. Robinet, J.-F. Labarre and C. Leibovici, Chem. phys. Lett. 22, 356 (1973). 19. H. Imamura, K. Morio, M. Oki and T. L. Kunii, Tetrahedron Lett. 52, 4575 (1970). 20. J. A. Pople and M. Gordon, J. Am. chem. Soc. 89, 4253 (1967). 21. M. J. D. Powell, Comput. J. 7, 155 (1964). 22. G. E. Ham (editor), Copolymerization. Interscience, New York (1964). 23. M. Scwarc, Carbanions, Living Polymers and Electron Transfer Processes. Wiley-lnterscience, New York (1968). 24. Yu. Ye. Eizner, B. L. Erussalimsky and E. B. Milovskaya, Polym. J. 5, I (1973). 25. (a) J. J. Brooks and G. D. Stucky, J. Am. chem. Soc. 94, 7333 (1972); (b) Ch. Tsvetanov, I. Panayotov and B. Erussalimsky, Europ. Polym. J. 10, 557 (1974). 26. H. Lewis and T. L. Brown, J. Am. chem. Soc. 92, 4664 (1970). 27. S. Bywater, D. Worsfold and G. Hollingsworth, Macromolecules 5, 389 (1972). 28. Ch. B. Tsvetanov, V. N. Zgonnik, B. L. Erussalimsky and I. M. Panayotov, Vysokomolek. Soedin. 14B, 404 (1972). 29. Ch. B. Tsvetanov, V. N. Zgonnik, B. L. Erussalimsky and I. M. Panayotov, Liebi.q. Ann. 763, 53 (1972). 30. R. Waack and P. Rest, J. Organomet. Chem. 5, 188 (1966). 31. T. L. Brown, Adv. Oroanomet. Chem. 3, 365 (1966).