Application of Ab initio MO calculations to methods for predicting reactivity in free radical copolymerization

Eur. Polym. J. Vol. 29, No. 10, pp. 1311-1317, 1993 Printed in Great Britain. All rights reserved

0014-3057/93 $6.00 + 0.00 Copyright © 1993 Pergamon Press Ltd

APPLICATION OF AB INITIO MO CALCULATIONS TO METHODS FOR PREDICTING REACTIVITY IN FREE RADICAL COPOLYMERIZATION T. P. DAVISl and S. C. ROGERS2 ~Department of Chemical Engineering and Industrial Chemistry, University of New South Wales, P.O. Box 1, Kensington, Sydney, Australia 2033 2ICI C&P, Runcorn Technical Centre, P.O. Box 8, The Heath, Runcorn, Cheshire, England (Received 4 December 1992) Abstract--Ab initio MO calculations have been performed utilizing several different basis sets, viz.

STO-3G, SV3-21G and TZV. The output from these calculations included the electronegativity of a set of vinyl monomers and their corresponding radicals formed by the addition of a hydrogen atom or a methyl radical. These electronegativities were correlated with the Patterns of Reactivity ~t parameters and the Ito-Matsuda 1-I parameters. The energy of formation (Ey) of a radical from the monomer was also calculated and correlated with the Patterns fl parameter and the Ito Matsuda log k values. The polarity-electronegativity plots displayed a strong correlation. However, the correlation of E v with fl was very poor and deteriorated with higher basis sets. We determined to improve matters by rescaling the Patterns scheme using styrene as the standard monomer. This attempt was unsuccessful as there were considerable problems with the Patterns scheme itself. They were attributed to the kinetic database on which it is based, both reactivity ratios and the Hammett ap parameters which are crucial to the successful application of the scheme. Correlations with the Ito-Matsuda parameters showed more promise but were limited by the amount of experimental data available.

INTRODUCTION

There have been some attempts to relate parameters derived using M O procedures with the Q - e scheme [1-3]. The Alfrey-Price e parameter can be adequately correlated with the calculated electronegativity of the monomer, whereas attempts at correlating the Q parameter with a general reactivity of the m o n o m e r have been less successful. This general m o n o m e r reactivity has been represented by the calculated energy of formation (Ev) of a monomeric radial on addition of either a hydrogen atom [1, 3] or a methyl radical [1]. It is clear from this previous work that there is a polar influence on the relationship between E v and Q, and the magnitude of this influence is determined to some extent by the arbitrary selection of reference values for styrene. An alternative methodology for predicting reactivity was described by Bamford et al. [4-6] and was termed the Patterns scheme. This procedure has the advantage over the Q--e scheme that it is not dependent on an arbitrary reference point. The aim of the authors was to propose a scheme whereby the polar and general reactivity features of the radical addition reaction were completely separated. The basis of the scheme was the use of one type of

reaction, viz. the abstraction of a hydrogen from toluene by a monomeric radical. The rate constant, k3,T, for this reaction was said to represent the general reactivity of the radical. If hydrocarbon substrates other than toluene were used then the new rate constants ks were found to be related to k3.T for the radicals studied. In fact what emerges is one of two characteristic patterns when k~ is plotted against k3.T, dependent on the type of substrate. The nature of these patterns is dictated by polar effects in the transition state. Bamford et al. introduced a polarity parameter, PR. given by: PR- = log k s - log k3,x

they also showed that PR- was linearly related to the H a m m e t t %ara constant for the substituents on the ~t carbon atom in the radical (when there is more than one substituent, the values are summed): PR. = gtr + fl

(2)

where ct and fl are characteristic of the substrate. Combination of equations (1) and (2) leads to: l o g k s = l o g k3, T q'- cto" ~- fl

CH 3 k3,T Ro

(1)

•v

+

60"C

1311

RH

(3)

1312

T . P . DAVIS and S. C. ROGERS kl X,,,

S"

+

X

CH2~CH

I

Y

F o r a single m o n o m e r ~ (for the m o n o m e r ) a n d a (for the radical) are f o u n d to be linearly correlated: = -p2o

(4)

where/~2 = 5.3. This scheme can be applied to copolymerization, a n d the reactivity ratios are given by: log rl = al (gl -- g2) + fll "[- f12 log

r 2 ~-- - - 6 2 ( 0 ( 1 - - ~ 2 ) - - ( i l l - - f12)

(5) (6)

a n d therefore log r I r 2 = -- (1//~ 2) (~q _ ot2)2.

&

SCH/CHY"

k.1

(7)

The utility o f the scheme is easily extended to chain transfer reactions. A n o t h e r m e t h o d o l o g y has recently been published by Ito a n d M a t s u d a [7]. As with the Q - e scheme, it is a dual p a r a m e t e r model a n d it uses as its basis the reversible addition reactions of p - s u b s t i t u t e d phenylthiyl radicals to vinyl m o n o m e r s . The absolute rate c o n s t a n t s a n d the relative equilibrium constants for these reactions were determined. A polarity p a r a m e t e r (termed P in the original scheme b u t labelled H here so as to avoid confusion with the P p a r a m e t e r in the Q - e scheme) was determined from plots of the H a m m e t t c o n s t a n t for s u b s t i t u e n t - X vs k~. These H values were scaled so t h a t styrene = 1.00 a n d acrylonitrile = - 1.00. The resonance stabilization terms o f the p r o p a g a t i n g radicals were evaluated from the equilibrium c o n s t a n t s (K). This K - H scheme can be used to predict the reactivities o f p r i m a r y radicals a n d also reactivity ratios. As with the p a t t e r n s scheme, the a u t h o r s claim t h a t the separation o f the resonance term from the polar term is complete a n d also t h a t steric factors are n o t included in the polar term. In o u r previous work [1] we correlated M O calculated p a r a m e t e r s with the Q a n d e factors for the Price-Alfrey scheme [8]. A logical extension to this work is a n investigation of alternative reactivity schemes, t h a t have distinct advantages over the Q - e scheme; the P a t t e r n s scheme is not scaled arbitrarily a n d the K - H scheme does not rely o n the reactivity ratio d a t a base. The purpose of the work reported here was to investigate w h e t h e r a better correlation exists between c o m p u t e d a n d experimental data which would allow us to predict m o n o m e r reactivity w i t h o u t recourse to experimentation.

starting structures representing different conformers were used to find the lowest energy structure. The optimized STO-3G structures were then refined at SV 3-21G and finally TZV level [I0, 11], except where difficulties with convergence or where the system was too large for our computational resources. The fully optimized structures are available from the authors (in Z-matrix format). Calculations were performed on each monomer and the corresponding radicals formed by addition of a hydrogen atom or a methyl radical to the alpha carbon. We were restricted to these model calculations because the calculation time scales with n 4 where n is the number of electrons in the system. The output includes the optimized geometry, molecular orbital energies (eigenvalues) and total electronic energy as well as orbital population. This output is tabulated elsewhere [12]. All calculations were performed on UNIX workstations made by Sun, Silicon Graphics and IBM. Typical calculation times were of the order of I-3 days of cpu per species at the TZV level. Calculated parameters The polarity term. The output obtained from our calculations allows us to calculate the Mulliken charge on both the fl and ~ carbon of the monomer (and radical). In addition we can estimate the electronegativity of both the monomer and radical using the following approximate procedure: The electronegativity, Z, is calculated after Mulliken [13], by: Z = 1/2(1 + A) (8) where I is the ionization potential and A the electron affinity. Assuming Koopman's theorem: X....... = - (E, + E, + t )/2

where E, is the energy of the highest occupied molecular orbital (HOMO) and E,+~ is the energy of the lowest unoccupied molecular orbital (LUMO). For the radical the electron affinity equals the ionization potential and: Zradical =

- - En

PROCEDURES

The calculations reported in this paper were all made at the Hartree--Fock level using the GAMESS program [9] which provides a state of the art package for ab initio calculations. The procedural process for the calculation was as follows. The geometry of the monomer was optimized (the molecular orbital energy as a function of bond lengths, bond angles and torsion angles was minimized) at STO-3G level from an initial guess. Where it was relevant, several

(1

O)

where e. is the energy of the singly occupied molecular

orbital (SOMO). We can define an average electronegativity, as suggested by Hoyland [14]. Z,v = (X. . . . . . . + Z~a~)/2

(11)

The general reactivity term. Initially, we followed the model of Colthup [3] whereby the polymer radical is represented by a monomer unit to which a hydrogen has been added. Colthup related the Alfrey-Price Q parameter to the energy of formation of this H-monomer radical: H" + CH2~-----------CXY~

CH3---CXY"

ECH2CXV- E H We cannot propose a more suitable (practical) model at present. However, we are aware from some of our other work that the energetics of reactions involving bare hydrogen atoms are poorly reproduced at even high ab inith~/Hartree-Fock level because of electron correlation. We therefore sought to overcome this known problem by replacing the H atom with a methyl radical: AEH.re.actio n = E c n ~ c x Y - -

EXPERIMENTAL

(9)

CH~ + CH~------CXY~

CH3CH 2 - CXY"

AEcH3.REAC-rlON = ECH3CH2CX Y - - ECH2CXY - - ECH ~

Application of MO calculations for predicting reactivity

(A) I

1

0

I

&,t.~

be that Bamford et al. [6] were realistic about the limitations in their interpolation procedure to derive alpha and rounded the values to one decimal place, so that several monomers share identical ~t values. It is probably this factor that limits the degree of correlation with the computed electronegativity values. There is a slight improvement on adopting the average electronegativity parameter. The beta parameter. In an analogous m a n n e r to our previous work, we fitted the Ev data for hydrogen and methyl addition to the following model:

t

• II

11,.

1

"A

•

•

2

¢.O.

"41

• •

3

e=qo • "..

•

1313

4 el•

5 6

t

0.08

0.1

t

0.12

t

0.14

fl = q)o + q)lEv q- q~2Xm'+ qgl2Ev.Zm.

I

0.16

0.2

0.18

Monomer electronegativity

B) 9

0

• •

=

t

-1

m r-" O.

~

"= • "",tl

-2

p "-.O

•'ql,

-3

•

e~.

•

"-~

-4

" = = ° ••

-5

(12)

If there are no polar effects on either the beta parameter or on our model reaction of methyl or hydrogen addition to a monomer, then the latter two terms will be insignificant. However, we have shown [1] that there is a small polar effect on these model reactions. In addition, when we applied this model to the Alfrey-Price Q value, there did appear to be some polar contribution to Q. The extent of this polar contribution was dictated to some extent by the arbitrary scaling of the Q - e scheme. Table 2 shows the results of these correlations for the Patterns scheme. The R2dj coefficient gives an indication of the fit to the model equation, whilst compensating for the additional degrees of freedom in the model conferred by the adoption of additional parameters (the closer

•

-6

0.2

1

t

t

I

t

0.22

0.24

0.26

0.28

0.3

(A)

0.32

2

Average electronegativity

1

Fig. 1. Linear least squares fits to plots of (A) a vs monomer

0

electronegativity and (B) ~t vs average electronegativity. Electronegativity calculated using the STO-3G basis set. In our previous paper, we found a better correlation between the energy of methyl addition and the Q parameter. A justification for the use of this type of reaction to define general reactivity is evident from plots in the paper of Ito and Matsuda [7]. They plotted methyl affinities obtained by Szwarc against their polarity factor •-•, and found that methyl affinity was independent of H. As they state, this is good evidence that the addition of methyl radical is a virtually "electric-neutral reaction". However, our previous work [12] has shown that there is a small polar influence on this reaction, that needs to be accounted for.

6~.

-1 c¢3. 0~

• "-4

-2

o• "'.to•

-3

iB 3"-..0 • "'.

-4

-5 I -6 -0.04-0.02

I

L

0

0.02

0.04

0.06

0.1

0.08

Monomer electronegativity

B) ]

1

RESULTS AND DISCUSSION

0

of reactivity scheme

The alpha parameter. The correlations of alpha with both m o n o m e r and average electronegativities for the three basis sets are shown in Figs I, 2 and 3. The correlation coefficients for a linear least squares fit are given in Table 1. These alpha values were obtained via an interpolation procedure using tabulated reactivity ratio data [6]. The correlations at the STO-3G level are poor. In contrast, the extended basis sets SV3-21G and TZV show an improved correlation, although these are poorer than the equivalent correlations obtained earlier for the Alfrey-Price e parameter (which were predictive). The main reason for this result may well

°''t

•

I

Patterns

m

°.

I

[

I

I

I

to.

•

•

• "~-...~

-1

"'-.•o

-2

"-

• -4

~'~o • o• •

-3

''",•

•

-5 -6

• I

I

L

,

]

I

i

0.08 0.1 0 . 1 2 0 . 1 4 0 . 1 6 0 . 1 8 0.2 0.22 L24 Average electronegativity Fig. 2. Linear least squares fits of plots o f ( A ) c¢vs monomer

electronegativity and (B) ~t vs average electronegativity. Electronegativity calculated using the SV321-G basis set.

T.P. DAVISand S. C. ROGERS

1314

Table 2. Comparisonof modelsfor fittingthe calculateddata to the patterns ,8 data using equation (18)

A) 1

i

0

e'.

i I

i

i

i

Coefficient o f determination

•

Model

-1 •

"4 L

",It

-2

r= o. m t~

• •

"L • •

-3

•

-4

~°0, ~a only ¢0, qh, ¢2, ~ o ] 2

H addition

tp0, tp I only tP0, ~n, ~2 only tP0, ~n, tP2, qh2

0.25 0.47 0.47

0.19 0.38 0.32

CH 3 addition

~00, tp I only ~Po, ~n, q:'2 only ¢Po, ¢Pl, ¢P2, ~°~2

0.47 0.69 0.69

0.43 0.61 0.58

H addition

~Po, ~Pl only % , tp I , ~02 only {P0, ~1, ~o2, ~0i2

0.40 0.50 0.51

0.37 0.45 0.42

CH 3 addition

tp0, tp~ only ¢P0, tp~, tp 2 only ~P0, tp~, tp2 , ¢P,2

0.52 0.75 0.76

0.49 0.71 0.70

H addition

tp0, tp~ only tP0, qh, tP2 only ¢0, tPn, ~2, ~n2

0.55 0.57 0.58

0.53 0.53 0.53

TZV

=4te I=.o

•

IQo Q°

-5 SV3-21G

-6 0.08

I

I

I

~

I

0.1

0.12

0.14

0.16

0.18

0.2

Monomer electronegativity

B)

STO-3G i

0

i

•

~

i

i

•

-1

•

•l !

"'.p

Q.

•

• "(ll•

"~ - 3

Ollq.

-4

..

-5

•

•

0.2

Insufficient d a t a Insufficient d a t a

".p

-2

-8

R ~dj )

R2

CH 3 addition

I

I

I

I

[

0.22

0.24

0.28

0.28

0.3

0.32

Average electronegativity Fig. 3. Linear least squaresfits to plots of(A) = vs monomer electronegativity and (B) = vs average electronegativity. Electronegativity calculated using the TZV basis set.

R 2 is to one, the better the correlation). The first point to note is that, as we improve the level of computer calculation, the fit actually worsens. This finding would indicate a fundamental flaw in either the procedure or with the fl values. The surprising factor is that these calculations with this model equation provided a reasonable fit for Alfrey-Price Q values. Previously [6] Bamford et al. showed that fl values correlate with Q. Therefore, it is surprising that we did not obtain a better correlation with larger basis sets as we found for Q and Ey. It is also noteworthy that methyl addition provides a significant improvement over the hydrogen addition data. Also for the methyl addition data, the correlations indicate that the electronegativity of the m o n o m e r needs to be accounted for in this 1. Correlationcoefficientsfor the linearleast squaresfit to the relationship betweencalculatedmonomerelcctronegativityor average electronegativityand the experimental ,, parameter Correlation coefficient Data Level R Table

Xm

STO-3G SV3-21G TZV

0.64 0.84 0.84

(Xm + Z,)/2

STO-3G SV3-21G TZV

0.75 0.86 0.86

supposedly non-polar term. However, the interaction (fourth) term can be ignored. The plot of observed vs predicted values for the best correlation (STO-3G, methyl addition) are given in Fig. 4. Following this slightly disappointing result, we returned to the original papers on the Patterns scheme. One drawback with the scheme is that in order to extend its utility, the authors employed reactivity ratio data from the literature. One of the strengths of the original Patterns scheme was that it was based only on the abstraction reaction with toluene. By utilizing the polymerization kinetic data base, the system is weakened in the same way that the much criticized Q - e scheme has been weakened. In fact, the Q - e scheme is very useful and predictive when the values are determined using a statistically rigorous process, as shown by Laurier et al. [15]. In addition, the Patterns scheme is dependent on the Hammett ap parameter. The tabulated parameters used by us were taken from Bamford et al. [6]. As all the ap values were not available, Bamford et aL used the relationship between • and trp [equation (4)] to interpolate a values. However, as we shall discuss 8

7 mgO Dm

"10 (l)

>

In .o

0

6

..#.~IP"

5

DI

mg

t

4

Oo..-'" o

3 2

I

I

I

[

I

I

r

8.5

4

4.5

5

5.5

6

6.5

Predicted 13

Fig. 4. Plot of observed vs predicted fl, using a multiple regression fit to equation [12] and data calculated from the STO-3G basis set.

Application of MO calculations for predicting reactivity i

A)

q)

1

1315

0.15

I •

h_

0.5 L..

"• • . .

O i¢q

0

:

~.~ 0 . 1 4

•3

•=== •

".g 0 . 1 3

"-.. I°=

LO

I • m•

0.12 -0.5

4e'"5

• .6 • 711 I).. ".

'-

0.11

"~

0.1

I

I

1

i

I

I

0

0.1

0.2

0.3

0.4

0.5

-1 -0 1

tO

..

¢J oJ

E

Fig. 5. Plot to derive ct and t~ parameters for the Patterns of Reactivity scheme, using reactivity ratio data from Ref. [15]. 1, 1,3-Butadiene;2, vinyl acetate; 3, vinyl chloride; 4, methyl methacrylate; 5, vinylidene chloride; 6, n-butyl acrylate; 7, methyl acrylate.

0 tO

later, some of these values are considerably different from actual Hammett tr values. As a major drawback of the Patterns scheme appears to be the kinetic data on which it is based (but not necessarily the scheme itself), we decided to investigate the modified Patterns scheme suggested by Jenkins [16]. This scheme adopts styrene as the non-polar standard. Early work indicated that there is a proportionality between a velocity constant for radical addition to styrene and that for transfer of the same radical to toluene, leading to a relation of the type (13)

the replacement of fl by t$ is simply to indicate the change of standard. Our intention was to use the reactivity ratios given by Laurier et al. [15] which we successfully utilized previously. These Laurier values are based on a statistical analysis of existing data using as many of the reactivity ratio citations in the literature as possible. We used this data in conjunction with the relationship (13) above to derive values for ~t2 and 62 would be unchanged from the original patterns scheme. Figure 5 shows a plot for several radicals reacting with acryionitrile as the substrate. There is a large degree of scatter to the plot and values for ~t and 6 taken from this plot could not be used with confidence. The Hammett trp values used for this plot were those given in the original paper [6]. In fact these Table 3. Hammett % parameters for several monomers taken from two different sources Monomer

Styrene Methyl acrylate Acrylonitrile Methyl methacrylate Methacrylonitrile Acrylic acid Vinyl acetate Vinylidene chloride Butyl acrylate Vinyl chloride 1,3-Butadiene

ap (Ref. [6])

ap

0 0.57 0.57 0.28 0.47 0.57 0 0.38 0.47 0.28 0

*There was considerable v a r i a t i o n for this m o n o m e r

(Ref. [17])

0 0.44 0.70 0.30 0.56 0.44 0.08* 0.48 0.44 0.24 0

0.09 -0.2

I

0

I

I

I

0.2

0.4

0.6

0.8

ap u)

E "r-

- - ~2

m• •

II

0.6

Gp

log r]2 = log rlsty - - 0t20"l

.b

B) 0.4

i

i •

•

o=

.e."7, •

0.35

•••;

c:

0,)

.tO "0

tr

0.3 -0.2

I

0

0.2

0.4

L

0.6

0.8

Op

Fig. 6. Linear least squares fits to plots of (A) monomer electronegativity and (B) radical electronegativity vs Hammett % constants.

values differ from actual Hammett ap values as indicated in Table 3. We therefore utilized Hammett values from the organic chemistry literature [17] and replotted the data. There was little improvement and we do not show the result here (although it should be noted that ~t2 and 62 values derived from this plot would be considerably different). We attempted several other recalculations using reactivity ratio data and found equally disappointing results. As a consequence, we did not attempt any further correlations between ct, fl and our MO computed values. However, we plotted the Hammett ap values taken from Exner [17] against both calculated monomer and radical electronegativity (calculated using the SV3-21G basis set) for the monomers listed in Table 3. These plots are shown as Fig. 6. There is a better linear fit with monomer electronegativity (R = 0.92) than with the radical electronegativity (R = 0.83). This result is interesting as Bamford et al. likened the Patterns scheme to Wall's Q - e - e * scheme [18], with ap corresponding to the e* term. The e* term represents the polar characteristics of the radical. During this work, it became evident that the Patterns scheme suffers from the choice of kinetic data on which it is based. The selection of Hammett % value is also critical as it can greatly affect the

T. P. DAvis and S. C. ROGERS

1316

(A) prediction of reactivity ratios using this scheme. To illustrate this point, we use the example of acrylo4 .A . n n n ~ I nitrile (AN) and methacrylonitrile (MAN) given 3 1~.o.. • by Jenkins [16]. The adoption of his Hammett parameters for A N (trp = 0.66) and M A N (ap = 0.49) 2 '''".. led to values of r]2 = 0.34 and r2] = 2.47. If we use alternative values from the organic chemistry v 1 e ' " " Omml literature [17] ( M A N ~rp = 0.56, A N ap = 0.70), then oo~ we get r]2 = 0.42 and r2~ = 4.01. ..a We do not know which are 'the best' Hammett 0 ..I O values but use this case as an example of the -I sensitivity of the scheme to their selection. It should be remembered that a, fl (or 6) values are also J k I I -2 dependent on ap. -0.18 -0.17 -0.16 -0.15 -0.14 -0.13 -0.12 The K - H scheme. The reason for relating our Ey for H addition (Hartrees) computed parameters to the scheme of Ito and Matsuda is that their resonance and polarity terms were derived from a set of internally consistent B) experiments. Unfortunately there are only a few 4 1 monomers with which we can correlate. Figure 7 8. • shows the relation between H parameter and 3 electronegativity, calculated at the STO-3G level. The correlation coefficient, R, is 0.90 for both plots. 2 Similarly, Fig. 8 shows plots of log K vs Ey for both ,,, 1 H and C H 3 addition at the STO-3G level. Again we obtained a strong correlation (R = 0.95) for b o t h . . a ° 0 Because of the diminishing n u m b e r of data points, we did not extend these correlations to higher basis sets. -1 Q

2.5

(A) :.

~O

~

~

'

T

1.5 iO

"" ".. **

1

I

-0.12

I

-0.11

I

-0.1

-0.09

Fig. 8. Linear least squares fits to plots of (A) log K vs Ey for H addition and (B) log K vs Ev for CH3 addition. Ev calculated using the STO-3G basis set.

•o,.

E

''

0.5

•

It should be noted that K and H parameters do not directly relate to monomer reactivity ratios though they are correlated.

0 -0.5 -I

•

-I .5

i

n

J

J

i

CONCLUSIONS

i

-0.04-0.02 0 0.02 0.04 0.06 0.08 Monomer electronegativity

0.1

B) 2.5

,

,

,

,

1.5

•

,

$•.. ;..

o.5

t~

~

"e. •

1

n

,

"',

2

E

I

-0.13

Ey for CH 3 addition (Hartrees)

"'.

2

a. =

-2 -0.14

0

• •

I::: - 0 . 5 -I

•

-1,5 0.08

L

1

0.1

0.12

Average

i

i

0.140.180.18

L

i 0.2

l 0.22

0.24

elactronagativity

Fig. 7. Linear least squares fits to plots of (A) H vs monomer electronegativity and (B) 17 vs average electronegativity. Electronegativity calculated using the STO-3G basis set.

As with our previous work on the Q - e scheme, we find strong correlations between calculated monomer electronegativity and polarity factors in both the Patterns and I t o - M a t s u d a schemes. Similarly there is a correlation between the general reactivity parameters and our E v. However, we were less successful in approaching a predictive relationship for the Patterns scheme. There may be a number of reasons for this lack of success. Previously we showed that the nature of the kinetic data base on which the Q - e scheme is based is one of its primary weaknesses. The Patterns scheme is also deficient in this respect. When we tried to rescale the scheme using styrene as a standard (as suggested by Jenkins [16]) in conjunction with reliable data, we still had a problem with scatter in the plots used to derive • and fl and therefore they could not be determined with confidence. We also note that the choice of Hammett ap in the patterns scheme is crucial to its predictive ability. These ap values are themselves subject to experimental error in their determination and values for the same substituent can vary widely depending

Application of MO calculations for predicting reactivity o n the literature source. O u r correlations with the p a r a m e t e r s o f Ito a n d M a t s u d a [7] were m o r e p r o m ising, reinforcing o u r belief t h a t one o f the primary limitations to predicting experimental rate c o n s t a n t s by M O calculations is the paucity of experimental d a t a b o t h in q u a n t i t y a n d especially quality.

Acknowledgements--We thank ICI C&P for allowing us to publish the results of our work. Also we wish to express our gratitude to Professors Bamford and Jenkins for supplying us with references on the Patterns scheme. REFERENCES

I. S.C. Rogers, W. C. Mackrodt and T. P. Davis. Polymer (in press). 2. N. Kawabata, T. Tsuruta and J. Furukawa. Makromolek. Chem. 51, 70 (1962). 3. N. B. Colthup../. Polym. Sci.; Polym. Chem. Edn 20, 3167 (1972). 4. C. H. Bamford, A. D. Jenkins and R. Johnston. Trans. Faraday Soc. 55, 418 (1959).

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5. C. H. Bamford and A. D. Jenkins. J. Polym. Sci. 53, 149 (1961). 6. C. H. Bamford and A. D. Jenkins. Trans. Faraday Soc. 59, 530 (1963). 7. O. Ito and M. Matsuda. J. Polym. Sci.: Part A: Polym. Chem. 28, 1947 (1990). 8. T. Alfrey and C. C. Price. J. Polym. Sci. 2, 101 0947). 9. M. F. Guest. GAMESS Manual. Daresbury Laboratory Daresbury, U.K. (1991). 10. T. H. Dunning. J. Chem. Phys. 55, 716 (1971). I I. A. D. McLean and G. S. Chandler. J. Chem. Phys. 72, 5639 (1980). 12. S. C. Rogers and T. P. Davis. J. Comput. Chem. (in preparation). 13. R. S. Mulliken. J. Chem. Phys. 2, 782 (1934). 14. J. R. Hoyland. J. Polym. Sci. A-I 8, 885 (1970). 15. G. C. Laurier, K. F. O'Driscoll and P. M. Reilly. J. Polym. Sci. Polym. Symp. 72, 17 (1985). 16. A. D. Jenkins. Eur. Polym. J. 25, 721 0989). 17. O. Exner. In Correlation Analysis in Chemistry--Recent Advances (edited by N. B. Chapman and J. Shorter). Plenum Press, New York (1978). 18. L. A. Wall. J. Polym. Sci. 2, 5 (1947).