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Applicability of the additivity relationship to ESR coupling constants
JOURNAL
OF MAGNETIC
RESONANCE
74,503-525
(1987)
Applicability of the Additivity Relationship to ESR Coupling Constants MARTING.BAKKER,RODNEYF.C.CLARIDGE,ANDCHRISTOPHERM.KIRK Chemistry Department, University of Canterbury, Christchurch, New Zealand Received February 13, 1987 The application of the additivity relationship to a number of radical anions is reported. The coupling constants calculated from the additivity relationship for deuterobenzene anions agree well with the observed coupling constants. The poor agreement for methyland cyanobenzene anion radicals is ascribed to changes in the HOMO. New assignments of coupling constants in some t-butylacenaphthene and methylbiphenyl anion radicals are suggested. Coupling constants for the asymmetric dimethylnaphthalenes, 1,3,5,7-tetra-, 1,2,3,4,5,8-hexa-, and 1,2,3,4,5,6,7,8octamethylnaphthalene are reported. The additivity relationships for both proton and methyl group coupling constants for methyl-substituted naphthalenes were determined. Changes in the assignment of coupling constants in 2,3-, 2,7-, and 1,8-dimethylnaphthalene anion radicals are proposed. o 1987 Academic press, ITIC. INTRODUCTION
Since the concept of an additivity relationship was first postulated by Fraenkel and co-workers (1) in 1959, this relationship has been applied to a wide variety of systems (2-4). The relationship has been used principally in the assignment of coupling constants, but has also been used to determine compound structure (5). We present here an account of the application of the additivity relationship to a number of series of compounds, aimed at evaluating the accuracy and applicability of the relationship. Use is made of data from the literature and of our own results for the methylnaphthalene anion radicals. The concept of an additivity relationship arises naturally from perturbation theory, where the assumption is made that only first-order perturbations are significant. An additivity relationship exists within a series of compounds if the effect of several substituent groups on the spin density at any position can be represented by the sum of the effects due to the individual substituents. This is subject to the assumption that all other factors are kept constant so that the addition of a substituent(s) is the only difference between two compounds of a series. Some factors which can cause this assumption to be violated are: (a) If the coupling constants used come from a number of different sources, there must inevitably be some differences in experimental conditions, which will result in small, but significant differences in the observed coupling constants. Such differences cannot be accounted for by the additivity relationship. (b) The coupling constants of some series are very strongly affected by the solvent chosen, so that an additivity relationship determined from coupling constants measured in a number of different solvents, may not fit the 503
0022-2364181 $3.00 Co~yi8ht 0 1987 by Academic F’res, Inc. AI1 rights of reproduction in any form reserved.
504
BAKKER,
CLARIDGE,
AND
KIRK
observed coupling constants very well. (c) Nonlinear changes in the electronic or molecular structure when substituents are added is another factor. Examples of such changes are ion-pairing effects, distortions in the molecular skeleton due to steric interaction between the substituents, and strong conjugation of substituents. METHOD
The nomenclature that will be used throughout this account is based on that of Goldberg and Peake (4) and is as follows: in the parent compound of a series (i.e., in the absence of any substituents), the coupling constants will be denoted aI, u2, . , . . . Where there are symmetry-equivalent positions, the smallest possible subscript is used. The effect on the coupling constant at position k due to a substituent at position 1 is defined as Au. Symmetry considerations are used to minimize the subscript k. For example, consider 1,2,4-trimethylnaphthalene. The proton splitting at the 5 position would be calculated as follows: Symmetry operators are used to change the position of the 5-proton to position 1; this transforms the methyl groups at the 1, 2, and 4 positions into substituents at the 5,6, and 8 positions, respectively. The proton splitting constant is then aI + A,, + Ai6 + Ai8. For all series of compounds studied in this investigation the number of parameters (the ai’s and Akl’s) is less than the number of observed coupling constants. This requires that the value of the parameters be optimized for a given set of assignments. This optimization is carried out using the method of minimization of least-squares residuals. That is, the values of the parameters are chosen to minimize the sum of the squares of the differences between the observed coupling constants and the values of the coupling constants calculated from the additivity relationship. The program used to perform this minimization was a modified form of ORGLS (6), which produces as output a listing of optimized parameters with estimated standard deviation, observed and calculated values with differences, and the R factor. The R factor is a measure of goodness of fit and is defined as
R= where 0, are the N observed coupling constants, C,, are the calculated coupling constants, and k is the number of variable parameters, The output from program ORGLS was checked against a second least-squares minimization program, program REGRES (7). The results of the two programs were in excellent agreement. If the parent compound of a series of compounds has two or more nonequivalent positions, then the sets of parameters a,, A,, , , An2, A,, 3, - * * and a,, A,,, , , Am2, - * for m # n, are independent. When this occurs, the independent sets of parameters were refined separately. RESULTS
AND
DISCUSSION
Deuterium-substituted benzene radical anions. Using the coupling constants reported by Lawler and Fraenkel(8), we determined the additivity parameters given in Table
ADDITIVITY
OF ESR COUPLING
CONSTANTS
505
TABLE 1 Deuterobenzene Anion Radicals” Part A : l.*ast squaresR*Cl”ed*&iitivity Parametem Parameter Value (G)
a
3. *oo+o.Ollb
pa
o.leo_+o.oot
b3
0.190_*0.009
Compound
Position
ECJUEltiO”
Best Least s.Juams *saignments hpt.
ca1c.
oirr.
(0)
(0)
(0)
ba!mne’
1
P
3.807
3.800
0.007
d-benzene-
*
a+&*
3.9.3,
3.990
-0.006
1 A-d-bemener 1,3-d-benzene-
1,3.3-d-banzeneStandard Deviation
3
a+A)
3.98, 3.990 -0.006
,
=+,A,
3.43,
3.,,9
2
.W2+L13
4.163
4.181
192 4.181
2
a+2A2
,.
4
WIZ+d,
3.628
192 ,.
3
a+lA3
,.
2
a*ZdZ+b,
3.836
CR)
3.639
0.005 -0.018
0.011 -0.011
180
0.012
3,830
0.006 0.013 Gauss
a Experimental coupling constants taken from Ref. (S), calculated coupling constants from the additivity relationship. b Error given is the estimated parameter standard deviation.
1. The four parameters were determined from nine coupling constants, and hence were overdetermined. The agreement between the observed coupling constants and those calculated on the basis of the additivity relationship is excellent. The largest difference between an observed and a calculated coupling constant is 20 mG. The substitution of deuterium for hydrogen is clearly a small perturbation. It should be noted, however, that the addition of deuterium results in a change of 0.35 G in the para position, which represents a substantial change in the coupling constant at this position. Methyl-substituted benzene radical anions. From the coupling constants of a number of methylbenzene radical anions reported by various authors (8-11) the additivity parameters given in Table 2 were determined. The agreement between observed and calculated coupling constants is very poor, with a difference of 1.1 G between the observed and calculated coupling constants for 1,3,5-trimethylbenzene radical anion. Discarding this coupling constant improves the fit somewhat, and reduces the largest difference between observed and calculated coupling constants to 0.6 G. This is still a very substantial difference. The observed coupling constants are drawn from four
506
BAKKER,
CLARIDGE,
AND KIRK
TABLE 2 Methylbenzene Anion Radicals” Part I : Least squares RePinsd Additivity ParaEetsr
Parameters
Value ,a,
a
3.908_*0.424b
%
1.188_+0.267
13 4
1.604~0.324 -3.633-4.39,
Part B : Obaewsd and Calculated Com9ou"d
Position
Proton Coupling Constants
Eg"atiO"
Least squares *ssignments Ifxpt.
ca1c.
(0)
(G)
DITP. (0) -0.101
benzene”
1
a
3.807
3.908
tO”le”e*
2
“‘4 =+a, E4+.A4
5.167
3.093
0.072
3.419
5.512
-0.093
0.41,
0.272
0.143
3
6.930
6.700
0.230
4 -f
1.810
1.877
-0.067
3 4 l.z-dimetbylbmene~
l.3-dimet~lbsn!mne~
2
a+2 4
6.830
6.283
0.367
4
“‘$+A4
1.460
1.460
-0.000
3
a+24
7.720
7.116
2
a+$+4
3.420
6.700
-1.280
a+2 4+ A4
2.370
2.648
-0.078
0.604
1.4-diatky1t.mene~
1.3.3~trimthy1bmzsne'g 2 Standard Deviation
CR)
0.389 Gauss
a Experimental coupling constants from indicated reference, calculated coupling constants tram the additivity relationship. b Error given is the estimated parameter standard deviation. ’ From Ref. (S), dFrom Ref. (9X ‘From Ref. (25), ‘From Ref. (IO), BFrom Ref. (II).
different sources. A variety of solvent systems were used. It would be expected that some of the differences between the calculated and observed coupling constants would result from these two factors. However, comparisons of the coupling constants reported by different groups for the same compound indicated that differences of about 0.1 G would be expected rather than the 1.1 G found. A possible explanation appears to be that the poor agreement between the additivity relationship and the observed coupling constants results from a change in the electronic structure of the molecule. The ground state of benzene differs from that of a number of methyl-substituted benzene anions.
ADDITIVITY
OF ESR COUPLING
CONSTANTS
507
In benzene the lowest unoccupied molecular orbital is doubly degenerate. One of the two orbitals is symmetric to reflection, the other is antisymmetric. The effect of adding a substituent is to remove the degeneracy of the two orbitals. The pattern of substitution appears to determine which of the two orbitals is more stable. As the spindensity distributions in the two orbitals are different it would be expected that the additivity relationship would fail to fit accurately observations taken from a group of methylbenzene anions containing compounds in both states. Cyano-substituted benzene radical anions. From the results of Rieger et al. (12) the additivity relationship given in Table 3 has been determined. The agreement between TABLE 3 Cyanobenzene Anion Radicals” Part I : Least squares Aeflned 9sMitivity ParamteP
Paran%t*rs
Value (0)
a
2.m3~o.855b 0.0939.558
5 %
-1.609~0.558 ..519*0.992
d4
Part B : Observed and Calculated comgounds
POSitiQ”
temene" cyanoteneene
1 -4
1 .l-dicyanobnza"a
1.3-dicyanobanz.ena
1.4-dicyanobeneene
Proton co”pli*
Equation
a
Constants
sxgt.
cat.
(0)
(0)
(G)
3.801
2.873
0.934
2
a*$
3.630
1.966
3
B+A3
0.300
1.165
4
'*A4
8.420
7.452
oi*r.
0.664 -0.965 0.968
r*
3
~*dl+d3
0.420
1.358
-0.938
4
B+b3+A4
4.130
5.343
-1.713
-1.619
* 2
a+tb2
1.440
3.059
4
++A4
8.290
7.545
5
C3+2tJ3
0.080
-0.344
0.4*4
a+Al+A3
1.590
I.358
0.232
&b2+2A3
1.110
-0.158
1.268
0.745
.d 2 Id
1.2.4.5-tetracyanobenzeoe 5
a Experimental coupling constants from indicated reference, calculated coupling constants from the additivity relationship. b Error given is the estimated parameter standard deviation. ’ From Ref. (8). dFrom Ref. (12).
508
BAKKER,
CLARIDGE,
AND KIRK
TABLE 4 Methyl-Substituted
Biphenyl Anion Radicals”
Part I : Least Squares Refined ldditivity Parameter
Value
Paramet*r
Paramet& Parameter
"due (Cl
(0)
(G)
0.466_+0.036 -0.22po.
43 44 45 46 42 ’ 43,
0.16320.066
*34
0.159yJ.061
635
-0.141~0.070
-0.322+0.064
'36
-0. zzz_+o. 064
632'
0.043_+0.066
&33*
-0.077~0.064
45,
-0.01*_+0.066
d3s.
'26'
-0.121~.056
%S#
&34*
Part B : Observed and Calculated Equation
d42
-O.Z%?O. 058
d43
-0.233?0.105
0.035~0.051
%4'
Posltlon
5.439~0.075
a4
051
-0.238_*0.066 0.193~0.064
"ahe
0.057~0.051 -0.126+0.089 -O.l2l~.OSl -0.091+0.070 0.039_*0.05l
Cou~lirs
Literature
44'
-0.079?0.156
45e
-0.063?0.105
'46'
-0.032*0.058
Constants *ssigments
Best Least
Squares
*ss1glments sxpt. d Ccllc. (0)
(0)
Mfr. (G)
rapt. e ca1c.
IllI-P.
(G)
(0)
(G)
0.036
bi9benyl'f 1
a2
2.660
1.734 -0,074
2.660
2.624
3
a3 a4
0.410
0.470 -0.060
0.410
0.466 -0.056
5.310
5.439 -0.129
5.310
5.4*9 -0.179
4
2-methylbi9henyl=6 2'
%+%2'
2.860
2.556
0.305
2.360
2.402 -0.042
3
83+%2
0.330
0.218
0.112
0.330
0.139
0.091
3'
a3+%2'
0.610
0.501
0.109
0.610
0.523
0.087
4
a4*642
5.300
5.136
0.164
5.300
5.197.
0.108
4'
a4+A46'
5.440
5.481 -0.041
5.440
5.456 -0.016
5
=3+'36
0.610
0.480
0.130
0.610
0.501
0.109
5'
'3+%6,
0.610
0.483
0.127
0.610
0.505
0.105
6
%+'26
2.100
2.315 -0.115
2.200
2.302 -0.102
’ Experimental coupling constants from indicated references, calculated coupling constants from the additivity relationship. b The additivity parameters given are those calculated on the basis of the best fitting assignments. ’ Errors given are the estimated parameter standard deviations. d Assignments as given in the references cited, calculated coupling constants calculated from the additivity relationsihp determined from these assignments. ’ Assignments as given in the text, calculated coupling constants calculated from the additivity relationship determined from the assignments given. ‘From Ref. (13). gFrom Ref. (14). hFrom Ref. (16). ‘From Ref. (17). ‘From Ref. (18).
ADDITIVITY
OF ESR COUPLING
509
CONSTANTS
TABLE &-Continued Part 8 : Observed PODitioll
and Calculated
Equation
Couplisg
Literature
Constants *ssignmnta
Beat
.3qu*ren
Least Assignments
Bxpt. d talc.
Ilie.
hpt.'
ca10.
(0)
(0)
(0)
(0)
(0)
2.860
2.671
0.189
2.360
2.504
Diff. (0)
biphenyl sr 6'
-0.144
*
2.790
2.689
0.101
2.790
2.787
0.003
2'
2.710
2.609
0.101
2.710
2.667
0.043
3'
0.340
0.340
0.340
0.340
4
5.220
5.224
5.220
5.255
0.000 -0.004
o.ooP -0.035
.'
5.390
5.394
-0.004
5.390
5.425
-0.035
5
0.290
0.327
-0.037
0.290
0.325
-0.035
5'
0.340
0.371
-0.037
0.340
0.375
-0.035
6
2.430
2.609
-0.179
2.430
2.387
0.043
6'
2.610
2.789
-0.179
2.610
2.607
0.003
2.830
2.889
-0.059
2.S60
2.540
0.020
2.830
2.817
0.013
2.560
2.547
0.013
0.570
0.613
-0.043
0.570
0.625
-0.055
0.290
0.330
-0.040
0.290
0.345
-0.055
5.410
5.613
-0.203
5.410
5.410
o.oG.3
2,6-dimetk,lbipba,,yl-b a2+42’+46’
2.340
2.492
-0.252
2.340
2.281
a3+dj2+%6
0.210
0.228
-0.018
0.210
0.273
-0.063
0.059
-0.081
a33*%2*+$6’
0.480
0.515
-0,035
0.480
0.561
a4+2d42
4.990
4.832
0.158
4.990
4.897
0.093
a4+2b46 I
5.580
5.525
0.057
5.530
5.424
0.156
2.2,'-dimth,Qbipher,ylTi a3+%Z+%2’
0.260
0.249
0.011
0.260
0.295
‘4+‘42+46
5.210
5.178
0.032
5.210
5.160
-0.035 0.050
‘3*46*Q6’
0.510
0.493
0.017
0.510
0.539
-0.029
a2+A26+A26’
2.270
2.252
0.018
2.270
2.181
0.089
0.001
3,3’-di&h9lbiOhsnyl?J a2*b23+A23’
2.430
2.565
2.430
2.429
a4+643*645’
5.220
5.179
-0.135 0.041
5.220
5.192
0.028
a3+A35+A35*
0.270
0.233
0.037
0.270
0.235
0.035
a2+A25+%5’
2.810
2.665
0.145
2.810
2.769
0.041
‘2+‘24*‘24’
2.730
2.695
0.035
2.730
2.740
-0.010
a3*A34+A34*
0.470
0.472
-0.002
0.470
0.504
-0.034
2.220
2.299
-0.079
2.204
-
4.4’diathylbiphe,,yl~~
2,4,6-tri~t~lbiphsnl~h a2+A22’+624’+%6*
-
510
BAKKER,
CLARIDGE,
Part B : ObJerved and Calculated Equation
KIRK
4-Continued
TABLE
Position
AND
Coupling Constanta
Literature
Aasignwnts
Beat Least Squares Assigmnts
Pmt. d ca1c. (0)
(0)
DiPf.
Bxpt.'
Calo.
(Cl
(0)
(Cl
Diff. (Cl
-
biphenyl si 3
=3+%l+A34+%6
0.000
0.371 -0.371
-
0.433
3’
*)+A32'*A$,'+$6'
0.000
0.37. -0.314
-
0.441
-
4’
*,+b,,.q6'
3.900
3.69,
-
5.346
-
0.203
2.4.6.4'-tetr~thglbiphenyl:h 7.’
a2+A24+%~+A24'+A26'
2.380
2.434 -0.074
2.380
2.397 -0.01,
3
a3'A32+A34+A36+A34'
0.300
0.230
0.070
0.300
0.311 -0.011
3’
a3+4j,+42,+4,,+s6,
0.610
0.317
0.093
0.610
0.600
0.010
a3+42+44+42'+44*
0.390
0.232
0.138
0.390
0.333
0.057
a3+A34*A36tA34'+A36*
0.610
0.,96
0.114
0.610
0.377
0.033
a2+AA4+A26+%4'+%6'
2.310
2.213
0.097
2.310
2.297
0.013
2,4,2',4'-tetraz&bylbiphenyl:h
2,6,2',6'-tetranrt~lbipbeql~h 3
a3+~2+~6+‘J2,+~6'
0.330
0.*73
0.037
0.330
0.369 -0.039
4
*,+a A,2+2 A,6'
4.660
..916
-0.236
4.660
4.332 -O.l,Z
3,3,3',3'-tetramet~lbipb~~l~f 2
a2+43+45+43'+43~
2.530
2.496
0.034
2.330
2.374 -o.o,,
4
a,+2A,,+2 43
4.900
4.919 -0.019
4.900
4.096
Standard Deviation
I
0.00,
(in Gauss)
*2 parameter
set
0.139
0.082
a3 parameter
set
0.175
0.081
a, parameter
set
0.119
0.137
calculated and observed coupling constants is clearly very poor. As, with one exception, all the coupling constants were determined by the same group under the same conditions, it is clear that either the electronic structure must change within the series, or the addition of multiple cyano substituents is not additive, that is, second-order perturbations become significant. In view of the effect of the lifting of the degeneracy discussed for methyl benzene anions, above, the poor agreement of the additivity relationship to the observed coupling constants could be attributed to the lifting of the degeneracy of the symmetric and antisymmetric molecular orbitals. Methyl-substituted biphenyl anions. By use of coupling constants from a number of sources (13-18) it has been possible to determine the additivity relationship for this series of compounds. The literature assignments and the coupling constants calculated from the additivity relationship using these assignments are given in columns 3 and 4 of Part B of Table 4. When the observed and calculated were compared, three
ADDITIVITY
OF
ESR
COUPLING
CONSTANTS
511
constants were found to give especially large differences (column 5). These were the coupling constants assigned to the 2’ position in 2-methylbiphenyl;, and the 3,5 and 3’,5’ positions in 2,4,6-trimethylbiphenyl;. The coupling constants of 2,4,6-trimethylbiphenyl; were reported by Ishizu et al. (26) in 1965, from an ESR investigation. Eliminating these results entirely from the additivity relationship results in a considerable improvement in the least-squares fit to the additivity relationship. We believe that the reported solution to the ESR spectrum is incorrect. The coupling constants used for 2-methylbiphenyl; were those determined by Christidis and Heineken (14) using ENDOR. These authors assigned the methyl coupling constant on the basis of the intensity ratios of the ENDOR peaks. However, it is now well recognized that ENDOR intensities are not determined solely by the number of resonating protons (I 9). Examination of the coupling constants predicted by the additivity relationship and those reported by Christidis and Heineken suggested the possibility of interchanging the coupling constants assigned to the methyl protons at position 2 and the protons at positions 6’ and 2’. This resulted in considerably better agreement between the observed coupling constants and the coupling constants calculated from the additivity relationship. A check on the reasonableness of this change in assignment was made by simulating the ESR spectra using the two sets of assignments and comparing the simulated spectra with the observed ESR spectra published by Ishizu (15). Neither simulated spectrum agreed well with the observed ESR spectrum. In complicated spectra with large numbers of coupling constants, minor changes in the values of coupling constants will often produce substantial changes in the simulated ESR spectrum, so that, unless the coupling constants are very close to the correct values, the simulated ESR spectra will not agree with the experimental spectra (20). The new assignments and the coupling constants calculated from the additivity relationship determined from the new assignments are given in columns 6, 7, and 8 of Part B of Table 4. The additivity parameters are given in Part A of Table 4. The changes described result in a decrease in R values from 0.189, 0.175, and 0.179 G to 0.082,0.08 1, and 0.137 G for the u2, a3, and a4 parameter sets, respectively. In view of the improvement in agreement resulting from the changes discussed above, we believe that 2-methylbiphenyl; and 2,4,6&methylbiphenyl; both warrant reinvestigation using modern ESR techniques. t-Butyl-substituted naphthalene and acenaphthene radical anions. From the results of Huffadine, Peake, and Deady (21), the additivity relationship for the t-butyl-substituted acenaphthene radical anions has been determined. As all coupling constants
FIG. 1. Nonstandard numbering system.
numberingsystemfor acenaphtheneand
derivatives;
based on substituted
naphthalene
512
BAKKER,
CLARIDGE,
AND KIRK
TABLE 5 t-Butyl-Substituted Acenaphthene Anion Radicals” Part
I
: Leant
Parameter
squares
rmrinfl.5
Value
*d*iti”ity
Parametsr
parameters Value
(0) 82
1.080
A23
0.180
A24
-0.230
A25
0.110
426
-0.230
b21
0.240
Part
0.069
83
1.430
Value (0)
0.017
a,
4.236
0.058
A42
0.069
0.013
A32
-0.440
0.020
A34
-0.330
0.021
0.080
43
0.106 0.106
A35
0.210
0.027
A45
0.080
A36
0.240
0.027
A46
0.106
A31
0.120
0.020
A447
B : Observed
Position
PalWWt*F
(0)
Equation
806
Calculated
Literature
coupling Assi6nrmnts
Fxpt.
cake
DiPP.
(0)
(0)
(0)
-0.27,
0.034 -0.127 0.139
0.073
0,095 0.073 0.073
conatanta Best fkpt. (0)
Least
Squares ca1c.
d
Assignments DiPP.
(0)
(0)
“AcenaDhthalene’” 2 3 4
*2 *3 a4
1.040
1.423
2.420
2.260
4.170
4.236
‘“a-t-butylaosnapbthalene’” 3 4 5 6 7
a3+A32 B4+A42 a4AA41 a3+A31 a2+A2l
-0.333 0.160 -0.066
1.040
1.080
-0.040
2.420
2.430
-0.010
4.170
4.236
-0.066
(3-t-butylacenaphthe~~~)’ 2.560
2.720
2.000
1.990
0.010
4.330
4.305
0.025
4.330
4.305
0.025
4.400
4.315
0.025
4.400
4.375
0.025
1.320
1.480
2.560
2.550
0.010
2.000
1.000
1.320
1.320
0.000
“3-t-butylacenaphthalene’”
-0.160
-0.160 0.000
(4-t-butylace”apbthe”e7Jp
1
=2+b23
2.670
2.288
0.332
1.300
1.260
0.040
4
a4+A43
4.000
3.959
0.041
4.000
3.953
0.041
5
%+‘46
4.150
4.109
0.041
4.150
4.109
0.041
6
a3+A36
1.300
1.300
0.000
2.670
2.670
0.000
0.890
0.508
0.382
0.390
0.850
0.040
7
e2tA26 “4-t-butylacenaphthalene’”
1 3
a2tA24 L3+A34
15-t-butylace”aphtbene’~p 1.100
1.100
0.000
0.850
0.350
0.000
0.850
0.850
0.000
2.100
2.100
0.000
5
a4+A45
4.270
4.210
0.000
4.270
4.270
0.000
6
‘)+A35
1.250
1.250
0.000
2.640
2. MO
0.000
7
a2+A25
2,640
2.640
0.000
1.250
1.250
0.000
a Experimental coupling constants from indicated references. A nonstandard numbering system is used to give compatibility with Table 6.The correct systematic names are given in parentheses. b Error given is the estimated parameter standard deviation. ’ Calculated from the additivity relationship determined from the assignments given in Ref. (21). d Calculated from the additivity relationsihp determined from the assignments discussed in the text. ’ From Ref. (28). rFrom Ref. (21). gFrom Ref. (29).
ADDITIVITY
OF
ESR
TABLE
COUPLING
513
CONSTANTS
5--Continued
PartB : Observed andCalculated couplingconstants Position
Equation
Literature
Assigameots
Best Least
Squares Assignments
Bxpt..
cahc
DUP.
Expt.
ca1c. '
DiPf.
(0)
(0)
(G)
(0)
(0)
(0)
.AC~"~phth~k"~'" (3.8di-t-butylacenaphtb~~~~)'
"2.7di-t-butylacenapbthalene:" 3
a3+A32+A37
7,. 100
1.940
0.160
2.100
2.100
-0.010
4
a,+A,2+A17
,.
4.445
-0. oz5
4.420
,. ,,5
-0.025
420
"3,6di-t-butylacenaphthaleoe:"
(4,7-di-t-b"tylaacena~hthe"e'~g
2
aZ+*23+b*6
0.990
1.373
-0.383
0.990
1.030
-0.040
4
a,+A,3*A,6
3.790
3.831
-0.041
3.790
3.831
-0.041
a2 s*t
OP parameters
0.765
a3 **t
OP paramters
0.320
0.020
0.075
0.075
a, set OP parameters
0.080
are from one source, any variability in the additivity relationship will not be a result of differences in solvent or in experimental technique. To increase clarity in the following discussion, a nonstandard numbering system will be used. Acenaphthene will be treated as a 1,8-disubstituted naphthalene, and referred to as “acenaphthalene,” and the compounds will be numbered accordingly (see Fig. 1). To indicate that the numbering used is nonstandard, compounds named using this system will be given in quotation marks, in both text and in Tables 5 and 6. Part B of Table 5 compares the observed and calculated coupling constants for the t-butyl-substituted acenaphthene radical anions. Columns 3 and 4 give the observed coupling constants and the coupling constants calculated on the basis of the additivity relationship for the assignments given by Huffadine et al. Column 5 gives the difference between columns 3 and 4. Columns 6 and 7 give, respectively, the observed coupling constants and the coupling constants calculated using the additivity relationship for the assignments which give the best fitting additivity relationship, as will be discussed below. A detailed examination of the agreement between the observed coupling constants and those predicted using the additivity relationship (column 5) suggested that some of the assignments given by Huffadine et al. may have been incorrect. These authors gave assignments for the monosubstituted compounds, based on MO calculations, such that the coupling constants at the 3, 6 positions were smaller than those at the 2, 7 positions. It was found that, by assuming the coupling constants at the 3, 6 positions were in fact larger than those at the 2, 7 positions, the agreement between the observed and calculated coupling constants could be improved dramatically. The R value for the coupling constants from the 2,7 positions (i.e., the a2 set of parameters) decreases from 0.77 G using the assignments given by Huffadine et al. to 0.080 G using the assignments given in columns 1 and 6 of Part B of Table 5. Similarly the R
BAKKER,
CLARIDGE,
AND KIRK
TABLE 6 t-Butyl-Substituted Naphthalene and Acenaphthene Anion Radicals” ml-t
B
and Calculated
: Observed
cGnpouod
Position
Coupli~
Equation
"4-t-butylacenaphthalene:"
Constants neat least
squares A.¶signmmts
Ekpt.
cam
Oil-f.
CC)
(0)
(0)
0.168
(5-t-b"tylacenaphtbene:)e
2
‘2+A41+T44
1.250
1.082
3
a2+A44+T41
2.100
2.232 -0.132
5
al+A44+T4*
4.270
4.182
0.088
6
a2+A44+T4*
2.640
2.505
0.135
7
a2+A41+T43
0.850
0.966 -0.116
'?,7di-t-butylacenaphthalene;"
(3.8di-t-butylacenapbth~~~~~*
3
aZ+A44+T43+T46
2.100
2.287 -0.187
4
a2+A44+T43+T46
4.420
4.426
'1,6di-t-butylacenaphthalane:"
-0.006
L4.7~i-t-butylaceMphth~~=~)f
2
a2+A41+T43+T46
0.990
1.054 -0.064
4
ai+A44+T42+T47
3.900
3.932
al+T4*
4.632
4.702 -0.070
a~+T%
2.035
2.155 -0.120
5.013
4.948
0.065
5.212
5.085
0.127
1.631
1.523
0.108
2.035
2.003
0.032
-0.032
2-t-butylnaphthalene= 1 3 4 5 6
‘1+T46 a,+T 46
7
a2+T47
8
al+T47
4.731
4.835 -0.104
aZ*T41+T 44
1.769
1.719
5.124
5.188 -0.064
aZ+T45+T48
1.769
1.876 -0.107
a1+T42+T46
4.846
4.861 -0.015
%.+T%3+ T627 T T al+ %3+ Al7
2.200
2.287 -0.087
4.846
4.856 -0.010
T al+ 42+
4.677
4.611
0.066
a2+Td23+T%6 T T %+ %3+ '16
1.817
1.808
0.010
5.050
5.106 -0.056
a*+T41+T43
1.957
2.037 -0.080
al+T42’T44
4.463
4.476 -0.013
5.180
5.162
0.018
1.957
1.852
0.105
1.637
1.680 -0.042
5.060
5.020
0.040
2.100
1.887
0.213
1.4-di-t-butylnaphthalene'g 2 5 6
al+T43+T48
0.051
2,6-di-t-butylnaphthalem~ 1 3 4 2.7-di-t-butylmphthaUTg 1 3 4
T
%7
2,3-di-t-butylnaphthalene~ 2 4 5 6
al+T43+T47 a2+T43+Tb27
7
a2+T46+T48
8
a1+T46+T48
1,3.5-tri-t-butylnaphthal~~e~~ 2
“z+T41+T43+T45
ADDITIVITY
OF ESR COUPLING
CONSTANTS
TABLE 6-Continued Part
II
: I,*a?t
PaIWWter
Squares
Rerinad
dddltivity
hl"B
eammetsrr
P*l-amFtW
"Pl"*
(0) *1
(0)
4.927~0.03lb
**14
-0.680_*0.033
TA12
-0.224~0.035
TAl3
0.021~0.036
Y4
1.307~0.093
*2 **21 *A 24 =*u
-0.227~.046
-0.733~.090 0.419_+0.086 -0.117+0.091 0.2*4~0.072
TA*3 TA24
-0.033~O.llS
TA15
0.321~0.049
=*25
-0.151_*0.092
TA16
0.13*_*0.034
Tb26
-0.347$l.0,3
%7
-0.09*~0.039
-0.065_*0.039 L Part B : Observed and Calculated compound
PoSitioll
naptltmene*
acenaphthene -d
0.133_+0.090
x7
0.136~0.099 TAz8 Coupling Constants
Eq"*tion
oe*t Least &y*re*
*asignments
mpt.
ca1c.
(0)
(0)
OiPf. (0)
4.940
4.921
0.013
1
81
2
*1
1.323
1.870 -0.045
2
*z+ AA21
1.040
1.117 -0.077
3
==2+I Aa4
2.420
2.349
4
*1+ AA14
4.170
4.243 -0.07*
"2-t-butylacenaphthalene'"
0.071
(3-t-butylaceMphthene')e
3
*2+ A A24+TA23
2.560
2.634 -0.074
4
al+ AA14+T A13
4.330
4.263
0.062
5
%+ A '14+ T'16
4.400
4.406 -0.006
6
%+ A '24+ T'26
2.000
7..002 -0.002
7
*1+ AA14+T A27
1.320
1.149
"3-t-butylacenaphthelene'" 2
0.071
(4-t-butylacenaphthe~~~)=
4.000
4.023 -0.023
3
*a+A 41* T%3 A T *1+ %4+ 42 *1+A 44+ TAl7
4.150
4.156 -0.006
6
a*+A%4+T47
2.670
2.482
0.1**
7
a2+A41tT46
0.890
0.770
0.120
4
1.300
1.401 -0.101
a Experimental coupling constants from indicated reference, calculated coupling constants were calculated from the additivity relationship. Additivity parameters superscripted “T” are those for the t-butyl group, those superscripted “A” are for the alkyl bridge in the acenaphthenes. A nonstandard numbering system is used for the t-hutylacenaphthenes to assist in comparison with the t-butylnaphthalenes. the standard compound names are given in parentheses. b Error given is the estimated parameter standard deviation. ’ From Ref. (8). dFrom Ref. (28). “From Ref. (21). fFrom Ref. (29). gFrom Ref. (4).
515
516
BAKKER,
CLARIDGE, TABLE
PaeB
: Observed
COWGWld
and
Caloulated
Positlo.
AND
KIRK
6-Continued Coupling Constants
Equation
Best
Least apt.
Squares Ca.10.
Asslgnmants DifP.
(G)
(0)
(G)
4.411
0.021
4
a1+T42+i44+T4*
4.432
6
aZ+T41+T45+T4,
1.426
1.135
7
aZ+T44*T46+T46
1.426
1.643 -0.219
8
a1+T44+T46+T46
4.764
4.793 -0.029
-0.309
1.3,6-tri-t-butylnaphthalene'B 2
aZ+T41+T43+T46
1.134
1.690
4
“I+T4*+T44+T4,
4.406
4.383
0.021
5
VT
42+T46+T 47 aZ+T 43+T46+T 48
4.984
4.936
0.046
2.196
1.964
0.232
a1+T43+T46+T46
4.984
5.040 -0.036
7 8 Standard Deviation for
0.044
(in Gauss)
a1 parameter
set
0.067
Par a* parameter
set
0.163
value for the coupling constants from the 3, 6 positions (i.e., the a3 set of parameters) decreases from 0.320 to 0.020 G. The assignments made by Huffadine et al. are based on MO calculations made for individual compounds, whereas the assignments made on the basis of the additivity relationship are made using data from a set of compounds. The use of a set of data would tend to average out measurement errors in the individual coupling constants. The assignments of some coupling constants are still ambiguous. The additivity relationship fits equally well when the following pairs of coupling constants were exchanged; positions 4 and 5, and positions 3 and 6 in “3-t-butylacenaphthalene;,” positions 2 and 7, and positions 4 and 5 in “4-t-butylacenaphthalene T,” and positions 2 and 7, and positions 3 and 6 in “5-t-butylacenaphthalene;.” Some indication of the correct assignment of these pairs of coupling constants can be found by considering the additivity relationship that can be derived by including the coupling constants of the series of t-butyl-substituted naphthalene radical anions reported by Goldberg and Peake (4). If the assumption is made that the presence of the saturated alkyl bridge in acenaphthalene is a small perturbation, then an additivity relationship can be determined for both t-butyl-naphthalene and “t-butyl-acenaphthalene” radical anion series simultaneously. This is done by treating the saturated alkyl bridge as a substituent added to naphthalene. For instance, the coupling constant at the 4 position in “acenaphthalene” (using the nonstandard numbering system) would be found as follows: (1) Use symmetry operators to minimize the position of the coupling constant. This gives the 1 position. (2) As a result, the alkyl bridge is moved to the 4 (and 5) positions, giving the equation for the coupling constant as aI + *Ai4 (the “A” superscript indicates that the additivity parameter is for the alkyl bridge substituent).
ADDITIVITY
OF ESR COUPLING
CONSTANTS
517
Consider now the more complicated example of the coupling constant at position 3 in “2-t-butylacenaphthalene ; .” Symmetry operators transform the 3 position into the 2 position, moving the alkyl bridge into the 4 (and 5) positions and the t-butyl group into the 3 position. The equation for the coupling constant is then a3 + *Az4 + TA23 (where the superscript “T” indicates that the additivity parameter is that of a t-butyl substituent). Table 6 gives the parameters and observed and calculated coupling constants for this additivity relationship. The R values for the two independent parameter sets, 0.067 and 0.163 G, suggest that the assumption that the alkyl bridge in acenaphthene; is a small perturbation is a reasonable one. The assignments for “2-, 3-,” and “4-t-butylacenaphthalene 7” given in Table 6 have been checked by calculating the additivity relationship when the ambiguous pairs of coupling constants are exchanged. As far as we have been able to determine, the assignments given result in the lowest possible values of R; i.e., the given assignments give the best possible agreement between the calculated and observed coupling constants. Methyl-substituted naphthalene anion radicals. Moss et al. (3) in a substantial paper, successfully applied the additivity relationship to a series of polymethyl-substituted naphthalene anion radicals. In this study we have redetermined coupling constants for naphthalene; both mono-methylnaphthalenes;, all ten dimethylnaphthalenes;, 1,2,3,4- and 1,3,5,7-tetramethylnaphthalene;, 1,2,3,4,5,8-hexamethylnaphthalene;, and octamethylnaphthalene;. Our observed coupling constants are in good agreement with those previously reported (3, 22-24) for these compounds. The tables include data for the previously unreported asymmetric dimethylnaphthalenes; , 1,2-, 1,3-, 1,6-, and 1,7-dimethylnaphthalene;, 1,3,5,7-tetramethylnaphthalene;, 1,2,3,4,5,8-hexamethylnaphthalene ;, and octamethylnaphthalene ;. Using the observed coupling constants reported in this study, together with the observed coupling constants for 1,4,5,8-tetramethylnaphthalene; reported by Moss et al. (3) and for 2,3,6,7-tetramethylnaphthalene; reported by Bolton (29, we determined the additivity relationships given in Tables 7 and 8. (a) Ring proton coupling constants. The agreement between our observed coupling constants and the coupling constants predicted by the additivity relationship based on the literature values can be improved by altering a number of the assignments used by Moss et al. Specifically, the coupling constants for the 2 and 3 positions in 1,8-dimethylnaphthalene;, 1 and 5 positions in 2,3-dimethylnaphthalene ;, and 1 and 4 positions in 2,6-dimethylnaphthalene; need to be exchanged. Making these changes in assignment results in a decrease in the R value from 0.087 to 0.060 G, and 0.083 to 0.078 G for the al and a2 parameter sets, respectively. We consider that the improvement in the agreement between the observed and predicted coupling constants is sufficient to justify the suggested changes in assignment in 2,3- and 2,6-dimethylnaphthalene;. The improvement in agreement produced by the change in the assignments in 1,8-dimethylnaphthalene; is small (from 0.083 to 0.078 G) and we are less confident that the improvement is significant. The complete set of assignments, and the coupling constants predicted by the additivity relationship on the basis of the literature assignments and the best least-squares
BAKKER,
518
CLARIDGE,
AND KIRK
TABLE 7 Ring Protons for Methylnaphthalene
Anion Radicals
Part A : Least squares*ddltl”lty mmetersa Parameter “due Parameter “due (0) (Cl (0) CC) 4.972~0.040b
=1
4.965~0.027
a2 A21
-0.280_+0.036
%2
-0.570s.
*14
0.166+0.027 039
0.34930.039
0.367f3.027
A
0.116_+0.034
0.099~0.023
16
-0.273~0.036 0.111~0.036
%3 Part
B : Observed
Position
‘23
-0.571~.027
d 15
P 17
1.940~0.030 -0.44*_+0.030
-0.191_*0.025
0.145_+0.039
%3
1.940~0.032 -0.457_+0.032
‘24
-0.353~0.025 O.llg*O. and
Calculated
Equation
025
0.406+0.036
0.406*0.034
0.058_+0.033
0.043+0.031
AZ5
-0.379~0.033
-0.3s9~0.029
‘26
-0.539~0.033
-0.539~0.031
‘27
0.386~0.032
p28
0.309+X
Coupling Literature
0. 336_tO. 032
030
0.319?0.030
Constants *ssignmnt
Best
Least
squat-*9
Assignmnt Ikpt.
Cahc
DiPI.
i3xpt.
ca1c.
d DiPf
(0)
IG)
(G)
(0)
(G)
(G)
na9btbalem~ l
4.965
4.972
-0.007
4.965
4.965
1.842
1.940
-0.098
1.842
1.940
2 a2J21
1.409
1.483
-0.074
1.409
1.492
-0.083
’
‘Ztd24
1.964
1.998
-0.034
1.964
1.987
-0.025
4 al+%4
4.408
4.403
0.005
4.408
4.339
5 =1+%5
5.372
5.321
0.051
5.372
5.332
6 a2+d25
1.529
1.561
1.529
1.552
2
al a2
l-mthylnaphthalane
0.000 -0.098
:f
-0.032
0.040 -0.023
7 a2+p28
2.290
2.250
2.290
2.259
0.031
8 5+*1g
5.031
5.083
-0.052
5.031
5.083
-0.052
4.764
4.692
-0.090
4.764
4.774
-0.010
2-methyl"a9bthalene 1 %+‘%Z 3
*2+43
0.040
0.020
-P
2.322
2.346
-0.024
2.322
2.346
-0.024
4 %+A13
5.063
5.111
-0.054
5.063
5.132
-0.069
’
*1+%6
5.063
5.088
-0.025
5.063
5.064
-0.001
’
a2+A26
1.331
1.402
-0.071
1.331
1.402
-0.071
’
‘z+%
2.269
2.326
-0.057
2.269
2.326
-0.057
4.602
4.692
-0.090
4.602
4.60,
-0.005
8 al+47
a Experimental coupling constants from indicated references, calcoupling constants from the additivity relationship. b Errors given are the estimated standard deviation. c Calculated using the assignments from Ref. (3). d Calculated using the assignments which give the best agreement with the additivity relationship. e From this work, error is 20.015 gauss. f From this work, error is +0.006 gauss. g From Ref. (3). ‘From Ref. (25). culated
ADDITIVITY
OF ESR COUPLING
519
CONSTANTS
TABLE l-Continued Part B : Observed and Calculated Position
Equation
coupling
Literature
constants Assignnan+,
Best lnaat
squares
Asaigmmt Pzpt.
cahc
Dir-f.
!apt..
ca1c. d DifP
(G)
(0)
(0)
(0)
(0)
(0)
naptitila1*ne=
2.305
2.404 -0.100
2.303
2.393 -0.090
4.502
4.548 -0.044
4.502
4.555 -0.053
5.423
5.437 -0.014
5.423
5.431 -0.008
1.010
1.022 -0.012
1.010
1.013 -0.003
2,648
2.635
2.648
2.645
4.693
4.810 -0.117
4.693
4.723 -0.032
0.013
0.003
* a2+41+43
1.880
2.889 -0.009
1.880
1.898 6.018
4
5*42+44
4.242
4.122
0.120
4.242
4.197
5 a1+45+47
5.074
5.048
0.026
5.074
4.974
0.100
6 az+45+47
2.032
1.947
0.085
2.032
1.937
0.091
7 a2+46+4A
1.759
1.711
0.048
1.759
1.720
0.039
* ‘1+46+48 1.4-dimethylnaphthalBne"
5.239
5.199
0.040
5.239
5.182
0.057
1.663
1.541
0.122
1.663
1.541
0.122
5.416
5.432 -0.016
5.416
5.450 -0.034
1.829
1.870 -0.041
1.829
1.870 -0.041
1.132
1.104
0.028
1.132
1.104
0.028
2.443
1.307
0.028
2.443
2.307
0.136
4.490
4.513 -0.023
4.490
4.506 -0.016
a a2t41+46
I.103
0.944
0.161
1.105
0.954
3 aa+824+A27
2.362
2.384 -0.022
2.362
2.374 -0.012
0.045
0.151
4 al+A14+b17
4.102
4.130 -0.028
4.102
4.031
5 al+P12*d15
5.124
5.041
0.083
5.124
5.141 -0.01,
0.071
' a*+A*3+A28
2.762
2.657
0.106
2.762
2.665
0.097
8 al+A13+A18 1.7dimethylnaphthQlene:e
5.378
5.228
0.150
5.378
5.249
0.129
0.014
* a2+A21+d27
1.892
1.869
0.024
1.892
1.878
' a2+A24eP16
1.441
1.460 -0.018
1.441
1.450 -0.010
' "1+b14+p16
4.488
4.519 -0.031
4.488
4.487
0.001
5 al+A13+AlS
5.532
S.466
0.066
5.532
5.498
0.034
6 a2+A23+~25
1.949
1.967 -0.018
1.949
1.958 -0.009
8 a1+A12+~18
4.837
4.803
0.034
4.837
4.892 -0.055
1.657
1.792 -0.135
1.714
1.811 -0.097
1.714
1.619
1.657
1.600
1.8-dimetllylnapbthalene"
0.095
0.057
520
BAKKER,
CLARIDGE,
KIRK
7-Continued
TABLE Fart B : Observed and Calculated Po.¶ition Equation
AND
coupling
Literature
constants *ssignment
Best Least Squares Assignmnt
iapt.
ce1c.= Diff.
Bxpt.
Calc.d
Diff
(G)
(0)
(0)
(0)
(G)
(0)
naphthalene~* 4 *1+%4+%5
4.662
4.751 -0.089
4.662
4.755 -0.093
l %%2%3
4.773
4.837 -0.064
5.033
4.940
0.093
5 *1+%6+41
5.033
4.816
0.217
4.733
4.706
0.027
' a2+d16+A27
1.797
1.787
0.010
1.797
1.787
0.010
1 al+A12+A16
4.681
4.808 -0.127
4.835
4.873 -0.038
3 a2+A23+All
2.724
2.732 -0.008
2.724
2.732 -0.008
4 al+A13+A17
4.835
4.844 -0.009
4.681
4.774 -0.093
2,3dimst~l"aphthalen*"
2.6dimethylnaphthale"e~
2.7dimethylnaphthaleDe'B l al+A12+A17
4.413
4.419 -0.006
4.413
4.416 -0.003
3 a2+A23+A26
1.797
1.808 -0.011
1.797
1.808 -0.011
' al+A13*A16
5.231
5.234 -0.003
5.*31
5.230
5 al+A15*A16+A17+618
5.167
5.275 -0.108
5.167
5.191 -0.024
' a2+b25*~~6+~~7+A~8
1.730
1.717
0.013
1.730
1.717
0.013
0.001
1.2.3,4-tetraoothyl~~phthalena:f
1.3.5,7-tetramt"ylmphthalene
:f
= a2+41+A23+A15+47
1.958
1.895
0.063
1.958
1.895
0.063
' al*A12+A14+A16*A18
4.440
4.349
0.091
4.440
4.414
0.026
1.411
1.4'11 -0.060
1.411
1.471 -0.060
4.680 -0.040
4.640
4.681 -0.041
I.318
1.198
1.318 -0.120
1.4.5.8-tetFamethyl~phthalene'8 = aa+41+A24+A25+Aa8 2.3.6.7-tetramethylnaphtha~~u~ ' a1*A12+A13+A16*b17 1.2.3.4.5.8-h*xaDBtbylnaphthalene
Th 4.640 +I
6 aZ+~Z1+A~4*A~5+A26*A2,*628 1.198 Standard owi*tion
-0.120
(in Gauss)
a1 p.wametef‘ set
0.087
0.060
"z parameter
0.083
0.078
set
assignments, are given in Part B of the Table 7. The additivity parameters determined from the two sets of assignments are given in Part A of Table 7. Refinements utilizing different sets of coupling constants give some indication of the sensitivity of the R value to various factors. A refinement using only the same coupling constants as were available to Moss et al., but using our values for the coupling constants, gave the following results. For the aI set of coupling constants, the coupling constants of Moss et al. gave an R factor of 0.075. A refinement using data from the
ADDITIVITY
OF
ESR
COUPLING
CONSTANTS
521
present study gave an R factor of 0.060. The R factors for the a2 coupling constants were 0.074 for the data of Moss et al. and 0.078 for the present study. The improvement in the R factor for the al set is substantial whereas the R factor for the a2 set is slightly worse in the present study. This would indicate that, overall, two factors should decrease the R factor. These are improvements in the precision with which the coupling constants are determined, and the use of coupling constants from one study where all the coupling constants have been determined under the same experimental conditions, The importance of these two factors relative to one another cannot be determined on the basis of the available data. The other factor to emerge from a cc mparison of various refinements is the sensitivity of the R factor to increases in the number of coupling constants used in the refinement. In going from the 36 coupling constants available to Moss et al. to the 65 coupling constants of the present study, there has been no improvement in the R factor for the al coupling constants and a slight increase in the R factor for the a2 coupling constants. This would indicate that a major component of the R factor is therefore inherent deviations from the additivity relationship, so that each successive coupling constant added to the refinement would contribute an increment to the sum of the squares of residuals that balances out the decrement in the R factor resulting from a increase in the number of coupling constants. It should be noted that when the additivity relationship was first being determined for the data presented in this work the coupling constants for positions 4, 5, and 8 in 1,7-dimethylnaphthalene (26) were found to be in extremely poor agreement with the additivity relationship. Reinvestigation of the spectra (20) showed that the coupling constants were in error. Reinterpretation of the observed spectra produced a better fit of the simulated to the observed spectra, giving coupling constants in much better agreement with the additivity relationship. (b) Methyl coupling constants. The availability of the data from the asymmetric dimethylnaphthalenes has given sufficient observations to allow a complete additivity relationship to be determined for the methyl coupling constants in the methylnaphthalene series. The additivity relationship determined is given in Table 8. The fit of the additivity relationship is considered reasonable. CONCLUSIONS
For deuterium-substituted benzene anions, the observed coupling constants agree well with the additivity relationship determined, and no conflict of assignment was found. For cyano- and methyl-substituted benzene anions, the agreement with the additivity relationship was very poor. This is considered to be due to changes in the highest occupied molecular orbital as substituents are added. The agreement between observed coupling constants and those calculated on the basis of the additivity relationship is considered satisfactory for methyl-substituted biphenyl anions. Changes in assignment are suggested for the 2-methylbiphenyl anion. The solution to the ESR spectrum of 2,4,6-trimethylbiphenyl; is felt to be incorrect, and we believe that this compound and 2-methylbiphenyl both warrant reinvestigation using modern ESR techniques.
522
BAKKER,
CLARIDGE,
AND KIRK
TABLE 8 Methyl Substituent of Methylnaphthalene Part A : Least Squares Refined Additivity Parameter
"*l"e
Anion9
Parameters
Parameter
"ahe
(Cl
(01
81
3.886+0. 051b
%Z
0.379~0.090
=2
1.719?0.021
621
0.202~0.0,0
A13
-0.02.3~0.084
623
%4
-0.606+0.085
%4
A15
0.489+0.087
%I
-0.370~0.039
'16
0.196~0.092
'26
-0.512+0.036
617
-0.264+0.087
%r
0.484~0.039
%8
0.640?0.092
%8
0.488_+0.038
Part
B
Position
: Observed
and Calculated
Equation
-0.049fl.036 0.108_+0.038
CoupIing Constants nest LBae ?,qvares *.ssignmenta Expt.
CEtlC.
DIPP.
(0)
(0)
(G)
3.854
3.866
-0.032
1.729
1.719
0.010
l-mwtbylnaPhtbalene'C 1
a1
Z-net~lnapbtbalenec 2
3
1.2-5imet~lnapbthalea
;d
1
=1+*12
4.375
4.265
0.110
2
a2+A21
1.943
1.921
0.022
1.3dimetbylnaphtbalene
;d
1
%+A13
3.950
3.862
0.088
3
a2+%4
1.867
1.827
0.040
3.300
3.279
0.021
4.387
4.375
0.012
1.4-di~thylnapbtbalene;d 1
al+%4
1,S-dimethylnaphthalene-d 1
Y+*ls
1,6dimetbylnaphthale~=~ 1
%+'I6
3.975
4.082
-0.107
6
%%5
1.308
1.349
-0.041
1.7dimetllylnapbtbalene;d 1
%+%7
3.492
3.622
-0.130
7
pl+A28
2.184
2.208
-0.024
’ Experimental coupling constants from the indicated references, calculated coupling constants from the additivity relationship. b Estimated parameter standard deviation. ’ This work, error is +0.006 gauss. d This work, error is +O.O15 gauss. e From Ref. (3). ‘From Ref. (25).
ADDITIVITY
OF ESR COUPLING
CONSTANTS
523
TABLE &.-Continued Part
B : Dbserved and Cakulatad
Position
Beat ‘east
1,8-dimettlylnaphthalene
sd
1 =1+*18 2,3-di~thylnaphthalene
75
2 =l+% 2.6-di‘mthylnaphthalene
Td
2
Coupling Constants
Equation
%*'26
2 'a+"27 l.Z.3.4-tBtrP~thglnaphthalene;c
2
ca.10.
(0)
(0)
Diff. (0)
4.560
4.525
0.035
1.714
1.670
0.044
1.222
1.207
0.015
2.200
2.203
-0.003
75
Z,,-dimttlyl"aphthalene
1
Squarea Aaaignwnta
Fxpt.
a1+A12+"13+"14
3.650
3.636
0.014
aa+A21+%3*A24
1.917
1.980
-0.063
al+A13+"15+A17
4.110
4.087
0.023
a2*b24c"26+b28
1.786
1.804
-0.018
4.354
4.406
-0.054
1.620
1.642
-0.027.
1,3.5,7,-tetramethylnaphthalene" 1 3
1,4,5,8-tetraoethyl"aphthalene?B 1
=1+%4+%5+48
2,3,6.7-tetramethylnaphthalene
3
7. a2+b23*b26+b27 1,2.3,4,5,8-hexamethylnaphth~l~"*~ 1 2 5
al+*12+A13+A14+*15+A16
4.675
4.764
-0.089
~Z+~llt~23+6Z4~~ZStb28
2.115
2.099
0.017
al+b14+615*P16+~17+%8
4.483
4.340
0.143
1.2.3.4.5,6.1.6-0ot-t~lnaphthalene'o 1
al+bl*+*13+d14+A15+*16+*17+~*
4.660
4.696
-0.036
2
al+P21+dZ3~b24+bZ5*A~6~~~7+A~~
2.095
2.070
0.025
Standard Deviation
(in Gauss)
a1 parameter
set
0.11s
a2 parameter
set
0.049
The literature assignments for the coupling constants of t-butylacenaphthene anions were found to be in poor agreement with those giving the best agreement with the additivity relationship. By treating the peri-alkyl bridge in acenaphthene as a substituent on a naphthalene skeleton it was possible to produce an additivity relationship including data from t-butylnaphthalenes and so produce unambiguous assignments for all tbutylacenaphthene coupling constants. This use of the additivity relationship with more than one substituent gives the possibility of successfully predicting the coupling constants for compounds including a variety of different substituents. Additivity relationships for both ring proton and methyl coupling constants for
524
BAKKER,
CLARIDGE,
AND KIRK
methyl-substituted naphthalene anions were calculated. This suggested changes in assignment in 2,3- and 2,6-dimethylnaphthalene 7. On the basis of the preceding discussion and earlier work, we would conclude that, where sufficient coupling constants are available, an additivity relationship is a better method of assigning and predicting coupling constants than MO calculations. In cases where there are serious deviations from the additivity relationship, further investigation into the causes of such deviations may be warranted. Our work also indicates that increasing the number of coupling constants will not substantially improve the R factor. It also indicates that improving the precision of the coupling constants, and improving the consistency of the data by determining all the coupling constants under the same conditions, will improve the R factor slightly. EXPERIMENTAL
The ESR spectra were recorded on a Varian E-12 spectrometer. All spectra were recorded at -85°C in 1,2dimethoxyethane, with potassium as counterion. The temperature was controlled by a Varian V4557 temperature controller to +3”C. The spectra of l- and 2-methylnaphthalene ;, 1,2,3,4-, and 1,3,5,7-tetramethylnaphthalene;, and 1,2,3,4,5,8-hexamethylnaphthalene; were fitted using a modified version of program ESRCON (20, 27) to fit the complete spectra. The remaining spectra were fitted using normal simulation techniques. ACKNOWLEDGMENT This work was supported in part by the University Grants Committee of New Zealand, and one of (M.G.B.) is grateful for a postgraduate scholarship held during the course of this work.
US
REFERENCES B. VENKATARAMAN, B. G. SEGAL, AND G. K. FRAENKEL, J. Chem. Phys. 30, 1006 (1959). J. A. PEDERSON, Mol. Phys. 28, 103 1 (1974). R. E. Moss, N. A. ASHFORD, R. G. LAWLER, AND G. K. FRAENKEL, J. Chem. Phys. 51, 1765 (1969). I. B. GOLDBERG AND B. M. PEAKE, J. Phys. Chem. 81,571 (1977). M. G. BAKKER, R. F. C. CLARIDGE, AND C. M. KIRK, J. Chem. Sot. Perkin Trans. 2 1735 (1986). W. R. BUSING AND H. A. LEVY, “Oak Ridge General Least Squares Users Manual.” ORNC-TM-27 1, 1962. 7. P. R. BEVINGTON, “Data Reduction and Error Analysis for the Physical Sciences,” McGraw-Hill, New
1. 2. 3. 4. 5. 6.
York, 1969. 8. 9. 10. II. 12. 13. 14. 15. 16.
G. LAWLER AND G. K. FRAENKEL, J. Chem. Phys. 49, 1126 (1968). T. JONES, S. METZ, AND T. C. KUECHLER, Mol. Phys. 33,3866 (1972). R. BOLTON AND A. CARRINGTON, Mol. Phys. 5,2 1 (1962). V. NELSON AND A. VON ZELEWSKY, J. Am. Chem. Sot. 97,6279 (1975). H. RIEGER, 1. BERNAL, W. H. REINMUTH, AND G. K. FRAENKEL, J. Am. Chem. ISHIZU, M. OHNISHI, AND H. SHIKATA, Bull. Chem. Sot. J. 50,76 (1977). C. CHRISTIDIS AND F. W. HEINEKEN, Chem. Phys. 2,239 (1973). K. ISHIZU, Bull. Chem. Sot. J. 37, 1093 (1964). K. ISHIZU, H. HASEGAWA, H. CHIKAKI, N. NISHIGUCHI, AND Y. DEUCHI, Kogyo
R. M. J. G. P. K. T.
1522 (1965).
Sot. 85,683
Kaguku
(1963).
Zusshi
68,
ADDITIVITY 17. K. ISHIZU, (1975).
F. NEMOTO,
K. MUKAI,
OF ESR COUPLING M. KOHNO,
CONSTANTS
AND H. HASEGAWA,
Bull.
525 Chem. Sot. J. 48, 1635
ISHIZU, F. NEMOTO, K. YAMAMOTO, AND M. NAKAZAKI, Bull. Chem. Sot. J. 48,2168 (1975). P. DINSE, R. BIEHL, AND K. MOBIUS, J. Chem. Phys. 61,4335 (1975). G. BAKKJZR, Ph.D. thesis, University of Canterbury, 1985. S. HUFFADINE, B. M. PEAKE, AND L. W. DEADY, J. Chem. Sot. Perkin Trans. 2, 1263 (1975). GERSON, B. M. PEAKE, AND G. M. WHITESIDES, Org. Magn. Reson. 4,361 (1972). GERSON, B. WEIDMANN, AND E. HEILBRONNER, He/v. Chim. Acta 47, 1951 (1964). BRUMBY, J. Magn. Reson. 40, 157 (1980). 25. J. R. BOLTON, Ph.D. thesis, Cambridge University, Cambridge, 1963. 26. C. M. KIRK, Ph.D. thesis, University of Canterbury, 1975. 27. Program ESRCON, by J. Heinzer, Quantum Chemistry Program Exchange, Program No. 197. 28. J. P. COLPA AND E. DE BOER, Mol. Phys. 7,333, 1964. 29. S. F. NELSEN, J. Am. Chem. Sot. 89, 5925, 1967. 18. 19. 20. 21. 22. 23. 24.
K. K. M. A. F. F. S.
OF MAGNETIC
RESONANCE
74,503-525
(1987)
Applicability of the Additivity Relationship to ESR Coupling Constants MARTING.BAKKER,RODNEYF.C.CLARIDGE,ANDCHRISTOPHERM.KIRK Chemistry Department, University of Canterbury, Christchurch, New Zealand Received February 13, 1987 The application of the additivity relationship to a number of radical anions is reported. The coupling constants calculated from the additivity relationship for deuterobenzene anions agree well with the observed coupling constants. The poor agreement for methyland cyanobenzene anion radicals is ascribed to changes in the HOMO. New assignments of coupling constants in some t-butylacenaphthene and methylbiphenyl anion radicals are suggested. Coupling constants for the asymmetric dimethylnaphthalenes, 1,3,5,7-tetra-, 1,2,3,4,5,8-hexa-, and 1,2,3,4,5,6,7,8octamethylnaphthalene are reported. The additivity relationships for both proton and methyl group coupling constants for methyl-substituted naphthalenes were determined. Changes in the assignment of coupling constants in 2,3-, 2,7-, and 1,8-dimethylnaphthalene anion radicals are proposed. o 1987 Academic press, ITIC. INTRODUCTION
Since the concept of an additivity relationship was first postulated by Fraenkel and co-workers (1) in 1959, this relationship has been applied to a wide variety of systems (2-4). The relationship has been used principally in the assignment of coupling constants, but has also been used to determine compound structure (5). We present here an account of the application of the additivity relationship to a number of series of compounds, aimed at evaluating the accuracy and applicability of the relationship. Use is made of data from the literature and of our own results for the methylnaphthalene anion radicals. The concept of an additivity relationship arises naturally from perturbation theory, where the assumption is made that only first-order perturbations are significant. An additivity relationship exists within a series of compounds if the effect of several substituent groups on the spin density at any position can be represented by the sum of the effects due to the individual substituents. This is subject to the assumption that all other factors are kept constant so that the addition of a substituent(s) is the only difference between two compounds of a series. Some factors which can cause this assumption to be violated are: (a) If the coupling constants used come from a number of different sources, there must inevitably be some differences in experimental conditions, which will result in small, but significant differences in the observed coupling constants. Such differences cannot be accounted for by the additivity relationship. (b) The coupling constants of some series are very strongly affected by the solvent chosen, so that an additivity relationship determined from coupling constants measured in a number of different solvents, may not fit the 503
0022-2364181 $3.00 Co~yi8ht 0 1987 by Academic F’res, Inc. AI1 rights of reproduction in any form reserved.
504
BAKKER,
CLARIDGE,
AND
KIRK
observed coupling constants very well. (c) Nonlinear changes in the electronic or molecular structure when substituents are added is another factor. Examples of such changes are ion-pairing effects, distortions in the molecular skeleton due to steric interaction between the substituents, and strong conjugation of substituents. METHOD
The nomenclature that will be used throughout this account is based on that of Goldberg and Peake (4) and is as follows: in the parent compound of a series (i.e., in the absence of any substituents), the coupling constants will be denoted aI, u2, . , . . . Where there are symmetry-equivalent positions, the smallest possible subscript is used. The effect on the coupling constant at position k due to a substituent at position 1 is defined as Au. Symmetry considerations are used to minimize the subscript k. For example, consider 1,2,4-trimethylnaphthalene. The proton splitting at the 5 position would be calculated as follows: Symmetry operators are used to change the position of the 5-proton to position 1; this transforms the methyl groups at the 1, 2, and 4 positions into substituents at the 5,6, and 8 positions, respectively. The proton splitting constant is then aI + A,, + Ai6 + Ai8. For all series of compounds studied in this investigation the number of parameters (the ai’s and Akl’s) is less than the number of observed coupling constants. This requires that the value of the parameters be optimized for a given set of assignments. This optimization is carried out using the method of minimization of least-squares residuals. That is, the values of the parameters are chosen to minimize the sum of the squares of the differences between the observed coupling constants and the values of the coupling constants calculated from the additivity relationship. The program used to perform this minimization was a modified form of ORGLS (6), which produces as output a listing of optimized parameters with estimated standard deviation, observed and calculated values with differences, and the R factor. The R factor is a measure of goodness of fit and is defined as
R= where 0, are the N observed coupling constants, C,, are the calculated coupling constants, and k is the number of variable parameters, The output from program ORGLS was checked against a second least-squares minimization program, program REGRES (7). The results of the two programs were in excellent agreement. If the parent compound of a series of compounds has two or more nonequivalent positions, then the sets of parameters a,, A,, , , An2, A,, 3, - * * and a,, A,,, , , Am2, - * for m # n, are independent. When this occurs, the independent sets of parameters were refined separately. RESULTS
AND
DISCUSSION
Deuterium-substituted benzene radical anions. Using the coupling constants reported by Lawler and Fraenkel(8), we determined the additivity parameters given in Table
ADDITIVITY
OF ESR COUPLING
CONSTANTS
505
TABLE 1 Deuterobenzene Anion Radicals” Part A : l.*ast squaresR*Cl”ed*&iitivity Parametem Parameter Value (G)
a
3. *oo+o.Ollb
pa
o.leo_+o.oot
b3
0.190_*0.009
Compound
Position
ECJUEltiO”
Best Least s.Juams *saignments hpt.
ca1c.
oirr.
(0)
(0)
(0)
ba!mne’
1
P
3.807
3.800
0.007
d-benzene-
*
a+&*
3.9.3,
3.990
-0.006
1 A-d-bemener 1,3-d-benzene-
1,3.3-d-banzeneStandard Deviation
3
a+A)
3.98, 3.990 -0.006
,
=+,A,
3.43,
3.,,9
2
.W2+L13
4.163
4.181
192 4.181
2
a+2A2
,.
4
WIZ+d,
3.628
192 ,.
3
a+lA3
,.
2
a*ZdZ+b,
3.836
CR)
3.639
0.005 -0.018
0.011 -0.011
180
0.012
3,830
0.006 0.013 Gauss
a Experimental coupling constants taken from Ref. (S), calculated coupling constants from the additivity relationship. b Error given is the estimated parameter standard deviation.
1. The four parameters were determined from nine coupling constants, and hence were overdetermined. The agreement between the observed coupling constants and those calculated on the basis of the additivity relationship is excellent. The largest difference between an observed and a calculated coupling constant is 20 mG. The substitution of deuterium for hydrogen is clearly a small perturbation. It should be noted, however, that the addition of deuterium results in a change of 0.35 G in the para position, which represents a substantial change in the coupling constant at this position. Methyl-substituted benzene radical anions. From the coupling constants of a number of methylbenzene radical anions reported by various authors (8-11) the additivity parameters given in Table 2 were determined. The agreement between observed and calculated coupling constants is very poor, with a difference of 1.1 G between the observed and calculated coupling constants for 1,3,5-trimethylbenzene radical anion. Discarding this coupling constant improves the fit somewhat, and reduces the largest difference between observed and calculated coupling constants to 0.6 G. This is still a very substantial difference. The observed coupling constants are drawn from four
506
BAKKER,
CLARIDGE,
AND KIRK
TABLE 2 Methylbenzene Anion Radicals” Part I : Least squares RePinsd Additivity ParaEetsr
Parameters
Value ,a,
a
3.908_*0.424b
%
1.188_+0.267
13 4
1.604~0.324 -3.633-4.39,
Part B : Obaewsd and Calculated Com9ou"d
Position
Proton Coupling Constants
Eg"atiO"
Least squares *ssignments Ifxpt.
ca1c.
(0)
(G)
DITP. (0) -0.101
benzene”
1
a
3.807
3.908
tO”le”e*
2
“‘4 =+a, E4+.A4
5.167
3.093
0.072
3.419
5.512
-0.093
0.41,
0.272
0.143
3
6.930
6.700
0.230
4 -f
1.810
1.877
-0.067
3 4 l.z-dimetbylbmene~
l.3-dimet~lbsn!mne~
2
a+2 4
6.830
6.283
0.367
4
“‘$+A4
1.460
1.460
-0.000
3
a+24
7.720
7.116
2
a+$+4
3.420
6.700
-1.280
a+2 4+ A4
2.370
2.648
-0.078
0.604
1.4-diatky1t.mene~
1.3.3~trimthy1bmzsne'g 2 Standard Deviation
CR)
0.389 Gauss
a Experimental coupling constants from indicated reference, calculated coupling constants tram the additivity relationship. b Error given is the estimated parameter standard deviation. ’ From Ref. (S), dFrom Ref. (9X ‘From Ref. (25), ‘From Ref. (IO), BFrom Ref. (II).
different sources. A variety of solvent systems were used. It would be expected that some of the differences between the calculated and observed coupling constants would result from these two factors. However, comparisons of the coupling constants reported by different groups for the same compound indicated that differences of about 0.1 G would be expected rather than the 1.1 G found. A possible explanation appears to be that the poor agreement between the additivity relationship and the observed coupling constants results from a change in the electronic structure of the molecule. The ground state of benzene differs from that of a number of methyl-substituted benzene anions.
ADDITIVITY
OF ESR COUPLING
CONSTANTS
507
In benzene the lowest unoccupied molecular orbital is doubly degenerate. One of the two orbitals is symmetric to reflection, the other is antisymmetric. The effect of adding a substituent is to remove the degeneracy of the two orbitals. The pattern of substitution appears to determine which of the two orbitals is more stable. As the spindensity distributions in the two orbitals are different it would be expected that the additivity relationship would fail to fit accurately observations taken from a group of methylbenzene anions containing compounds in both states. Cyano-substituted benzene radical anions. From the results of Rieger et al. (12) the additivity relationship given in Table 3 has been determined. The agreement between TABLE 3 Cyanobenzene Anion Radicals” Part I : Least squares Aeflned 9sMitivity ParamteP
Paran%t*rs
Value (0)
a
2.m3~o.855b 0.0939.558
5 %
-1.609~0.558 ..519*0.992
d4
Part B : Observed and Calculated comgounds
POSitiQ”
temene" cyanoteneene
1 -4
1 .l-dicyanobnza"a
1.3-dicyanobanz.ena
1.4-dicyanobeneene
Proton co”pli*
Equation
a
Constants
sxgt.
cat.
(0)
(0)
(G)
3.801
2.873
0.934
2
a*$
3.630
1.966
3
B+A3
0.300
1.165
4
'*A4
8.420
7.452
oi*r.
0.664 -0.965 0.968
r*
3
~*dl+d3
0.420
1.358
-0.938
4
B+b3+A4
4.130
5.343
-1.713
-1.619
* 2
a+tb2
1.440
3.059
4
++A4
8.290
7.545
5
C3+2tJ3
0.080
-0.344
0.4*4
a+Al+A3
1.590
I.358
0.232
&b2+2A3
1.110
-0.158
1.268
0.745
.d 2 Id
1.2.4.5-tetracyanobenzeoe 5
a Experimental coupling constants from indicated reference, calculated coupling constants from the additivity relationship. b Error given is the estimated parameter standard deviation. ’ From Ref. (8). dFrom Ref. (12).
508
BAKKER,
CLARIDGE,
AND KIRK
TABLE 4 Methyl-Substituted
Biphenyl Anion Radicals”
Part I : Least Squares Refined ldditivity Parameter
Value
Paramet*r
Paramet& Parameter
"due (Cl
(0)
(G)
0.466_+0.036 -0.22po.
43 44 45 46 42 ’ 43,
0.16320.066
*34
0.159yJ.061
635
-0.141~0.070
-0.322+0.064
'36
-0. zzz_+o. 064
632'
0.043_+0.066
&33*
-0.077~0.064
45,
-0.01*_+0.066
d3s.
'26'
-0.121~.056
%S#
&34*
Part B : Observed and Calculated Equation
d42
-O.Z%?O. 058
d43
-0.233?0.105
0.035~0.051
%4'
Posltlon
5.439~0.075
a4
051
-0.238_*0.066 0.193~0.064
"ahe
0.057~0.051 -0.126+0.089 -O.l2l~.OSl -0.091+0.070 0.039_*0.05l
Cou~lirs
Literature
44'
-0.079?0.156
45e
-0.063?0.105
'46'
-0.032*0.058
Constants *ssigments
Best Least
Squares
*ss1glments sxpt. d Ccllc. (0)
(0)
Mfr. (G)
rapt. e ca1c.
IllI-P.
(G)
(0)
(G)
0.036
bi9benyl'f 1
a2
2.660
1.734 -0,074
2.660
2.624
3
a3 a4
0.410
0.470 -0.060
0.410
0.466 -0.056
5.310
5.439 -0.129
5.310
5.4*9 -0.179
4
2-methylbi9henyl=6 2'
%+%2'
2.860
2.556
0.305
2.360
2.402 -0.042
3
83+%2
0.330
0.218
0.112
0.330
0.139
0.091
3'
a3+%2'
0.610
0.501
0.109
0.610
0.523
0.087
4
a4*642
5.300
5.136
0.164
5.300
5.197.
0.108
4'
a4+A46'
5.440
5.481 -0.041
5.440
5.456 -0.016
5
=3+'36
0.610
0.480
0.130
0.610
0.501
0.109
5'
'3+%6,
0.610
0.483
0.127
0.610
0.505
0.105
6
%+'26
2.100
2.315 -0.115
2.200
2.302 -0.102
’ Experimental coupling constants from indicated references, calculated coupling constants from the additivity relationship. b The additivity parameters given are those calculated on the basis of the best fitting assignments. ’ Errors given are the estimated parameter standard deviations. d Assignments as given in the references cited, calculated coupling constants calculated from the additivity relationsihp determined from these assignments. ’ Assignments as given in the text, calculated coupling constants calculated from the additivity relationship determined from the assignments given. ‘From Ref. (13). gFrom Ref. (14). hFrom Ref. (16). ‘From Ref. (17). ‘From Ref. (18).
ADDITIVITY
OF ESR COUPLING
509
CONSTANTS
TABLE &-Continued Part 8 : Observed PODitioll
and Calculated
Equation
Couplisg
Literature
Constants *ssignmnta
Beat
.3qu*ren
Least Assignments
Bxpt. d talc.
Ilie.
hpt.'
ca10.
(0)
(0)
(0)
(0)
(0)
2.860
2.671
0.189
2.360
2.504
Diff. (0)
biphenyl sr 6'
-0.144
*
2.790
2.689
0.101
2.790
2.787
0.003
2'
2.710
2.609
0.101
2.710
2.667
0.043
3'
0.340
0.340
0.340
0.340
4
5.220
5.224
5.220
5.255
0.000 -0.004
o.ooP -0.035
.'
5.390
5.394
-0.004
5.390
5.425
-0.035
5
0.290
0.327
-0.037
0.290
0.325
-0.035
5'
0.340
0.371
-0.037
0.340
0.375
-0.035
6
2.430
2.609
-0.179
2.430
2.387
0.043
6'
2.610
2.789
-0.179
2.610
2.607
0.003
2.830
2.889
-0.059
2.S60
2.540
0.020
2.830
2.817
0.013
2.560
2.547
0.013
0.570
0.613
-0.043
0.570
0.625
-0.055
0.290
0.330
-0.040
0.290
0.345
-0.055
5.410
5.613
-0.203
5.410
5.410
o.oG.3
2,6-dimetk,lbipba,,yl-b a2+42’+46’
2.340
2.492
-0.252
2.340
2.281
a3+dj2+%6
0.210
0.228
-0.018
0.210
0.273
-0.063
0.059
-0.081
a33*%2*+$6’
0.480
0.515
-0,035
0.480
0.561
a4+2d42
4.990
4.832
0.158
4.990
4.897
0.093
a4+2b46 I
5.580
5.525
0.057
5.530
5.424
0.156
2.2,'-dimth,Qbipher,ylTi a3+%Z+%2’
0.260
0.249
0.011
0.260
0.295
‘4+‘42+46
5.210
5.178
0.032
5.210
5.160
-0.035 0.050
‘3*46*Q6’
0.510
0.493
0.017
0.510
0.539
-0.029
a2+A26+A26’
2.270
2.252
0.018
2.270
2.181
0.089
0.001
3,3’-di&h9lbiOhsnyl?J a2*b23+A23’
2.430
2.565
2.430
2.429
a4+643*645’
5.220
5.179
-0.135 0.041
5.220
5.192
0.028
a3+A35+A35*
0.270
0.233
0.037
0.270
0.235
0.035
a2+A25+%5’
2.810
2.665
0.145
2.810
2.769
0.041
‘2+‘24*‘24’
2.730
2.695
0.035
2.730
2.740
-0.010
a3*A34+A34*
0.470
0.472
-0.002
0.470
0.504
-0.034
2.220
2.299
-0.079
2.204
-
4.4’diathylbiphe,,yl~~
2,4,6-tri~t~lbiphsnl~h a2+A22’+624’+%6*
-
510
BAKKER,
CLARIDGE,
Part B : ObJerved and Calculated Equation
KIRK
4-Continued
TABLE
Position
AND
Coupling Constanta
Literature
Aasignwnts
Beat Least Squares Assigmnts
Pmt. d ca1c. (0)
(0)
DiPf.
Bxpt.'
Calo.
(Cl
(0)
(Cl
Diff. (Cl
-
biphenyl si 3
=3+%l+A34+%6
0.000
0.371 -0.371
-
0.433
3’
*)+A32'*A$,'+$6'
0.000
0.37. -0.314
-
0.441
-
4’
*,+b,,.q6'
3.900
3.69,
-
5.346
-
0.203
2.4.6.4'-tetr~thglbiphenyl:h 7.’
a2+A24+%~+A24'+A26'
2.380
2.434 -0.074
2.380
2.397 -0.01,
3
a3'A32+A34+A36+A34'
0.300
0.230
0.070
0.300
0.311 -0.011
3’
a3+4j,+42,+4,,+s6,
0.610
0.317
0.093
0.610
0.600
0.010
a3+42+44+42'+44*
0.390
0.232
0.138
0.390
0.333
0.057
a3+A34*A36tA34'+A36*
0.610
0.,96
0.114
0.610
0.377
0.033
a2+AA4+A26+%4'+%6'
2.310
2.213
0.097
2.310
2.297
0.013
2,4,2',4'-tetraz&bylbiphenyl:h
2,6,2',6'-tetranrt~lbipbeql~h 3
a3+~2+~6+‘J2,+~6'
0.330
0.*73
0.037
0.330
0.369 -0.039
4
*,+a A,2+2 A,6'
4.660
..916
-0.236
4.660
4.332 -O.l,Z
3,3,3',3'-tetramet~lbipb~~l~f 2
a2+43+45+43'+43~
2.530
2.496
0.034
2.330
2.374 -o.o,,
4
a,+2A,,+2 43
4.900
4.919 -0.019
4.900
4.096
Standard Deviation
I
0.00,
(in Gauss)
*2 parameter
set
0.139
0.082
a3 parameter
set
0.175
0.081
a, parameter
set
0.119
0.137
calculated and observed coupling constants is clearly very poor. As, with one exception, all the coupling constants were determined by the same group under the same conditions, it is clear that either the electronic structure must change within the series, or the addition of multiple cyano substituents is not additive, that is, second-order perturbations become significant. In view of the effect of the lifting of the degeneracy discussed for methyl benzene anions, above, the poor agreement of the additivity relationship to the observed coupling constants could be attributed to the lifting of the degeneracy of the symmetric and antisymmetric molecular orbitals. Methyl-substituted biphenyl anions. By use of coupling constants from a number of sources (13-18) it has been possible to determine the additivity relationship for this series of compounds. The literature assignments and the coupling constants calculated from the additivity relationship using these assignments are given in columns 3 and 4 of Part B of Table 4. When the observed and calculated were compared, three
ADDITIVITY
OF
ESR
COUPLING
CONSTANTS
511
constants were found to give especially large differences (column 5). These were the coupling constants assigned to the 2’ position in 2-methylbiphenyl;, and the 3,5 and 3’,5’ positions in 2,4,6-trimethylbiphenyl;. The coupling constants of 2,4,6-trimethylbiphenyl; were reported by Ishizu et al. (26) in 1965, from an ESR investigation. Eliminating these results entirely from the additivity relationship results in a considerable improvement in the least-squares fit to the additivity relationship. We believe that the reported solution to the ESR spectrum is incorrect. The coupling constants used for 2-methylbiphenyl; were those determined by Christidis and Heineken (14) using ENDOR. These authors assigned the methyl coupling constant on the basis of the intensity ratios of the ENDOR peaks. However, it is now well recognized that ENDOR intensities are not determined solely by the number of resonating protons (I 9). Examination of the coupling constants predicted by the additivity relationship and those reported by Christidis and Heineken suggested the possibility of interchanging the coupling constants assigned to the methyl protons at position 2 and the protons at positions 6’ and 2’. This resulted in considerably better agreement between the observed coupling constants and the coupling constants calculated from the additivity relationship. A check on the reasonableness of this change in assignment was made by simulating the ESR spectra using the two sets of assignments and comparing the simulated spectra with the observed ESR spectra published by Ishizu (15). Neither simulated spectrum agreed well with the observed ESR spectrum. In complicated spectra with large numbers of coupling constants, minor changes in the values of coupling constants will often produce substantial changes in the simulated ESR spectrum, so that, unless the coupling constants are very close to the correct values, the simulated ESR spectra will not agree with the experimental spectra (20). The new assignments and the coupling constants calculated from the additivity relationship determined from the new assignments are given in columns 6, 7, and 8 of Part B of Table 4. The additivity parameters are given in Part A of Table 4. The changes described result in a decrease in R values from 0.189, 0.175, and 0.179 G to 0.082,0.08 1, and 0.137 G for the u2, a3, and a4 parameter sets, respectively. In view of the improvement in agreement resulting from the changes discussed above, we believe that 2-methylbiphenyl; and 2,4,6&methylbiphenyl; both warrant reinvestigation using modern ESR techniques. t-Butyl-substituted naphthalene and acenaphthene radical anions. From the results of Huffadine, Peake, and Deady (21), the additivity relationship for the t-butyl-substituted acenaphthene radical anions has been determined. As all coupling constants
FIG. 1. Nonstandard numbering system.
numberingsystemfor acenaphtheneand
derivatives;
based on substituted
naphthalene
512
BAKKER,
CLARIDGE,
AND KIRK
TABLE 5 t-Butyl-Substituted Acenaphthene Anion Radicals” Part
I
: Leant
Parameter
squares
rmrinfl.5
Value
*d*iti”ity
Parametsr
parameters Value
(0) 82
1.080
A23
0.180
A24
-0.230
A25
0.110
426
-0.230
b21
0.240
Part
0.069
83
1.430
Value (0)
0.017
a,
4.236
0.058
A42
0.069
0.013
A32
-0.440
0.020
A34
-0.330
0.021
0.080
43
0.106 0.106
A35
0.210
0.027
A45
0.080
A36
0.240
0.027
A46
0.106
A31
0.120
0.020
A447
B : Observed
Position
PalWWt*F
(0)
Equation
806
Calculated
Literature
coupling Assi6nrmnts
Fxpt.
cake
DiPP.
(0)
(0)
(0)
-0.27,
0.034 -0.127 0.139
0.073
0,095 0.073 0.073
conatanta Best fkpt. (0)
Least
Squares ca1c.
d
Assignments DiPP.
(0)
(0)
“AcenaDhthalene’” 2 3 4
*2 *3 a4
1.040
1.423
2.420
2.260
4.170
4.236
‘“a-t-butylaosnapbthalene’” 3 4 5 6 7
a3+A32 B4+A42 a4AA41 a3+A31 a2+A2l
-0.333 0.160 -0.066
1.040
1.080
-0.040
2.420
2.430
-0.010
4.170
4.236
-0.066
(3-t-butylacenaphthe~~~)’ 2.560
2.720
2.000
1.990
0.010
4.330
4.305
0.025
4.330
4.305
0.025
4.400
4.315
0.025
4.400
4.375
0.025
1.320
1.480
2.560
2.550
0.010
2.000
1.000
1.320
1.320
0.000
“3-t-butylacenaphthalene’”
-0.160
-0.160 0.000
(4-t-butylace”apbthe”e7Jp
1
=2+b23
2.670
2.288
0.332
1.300
1.260
0.040
4
a4+A43
4.000
3.959
0.041
4.000
3.953
0.041
5
%+‘46
4.150
4.109
0.041
4.150
4.109
0.041
6
a3+A36
1.300
1.300
0.000
2.670
2.670
0.000
0.890
0.508
0.382
0.390
0.850
0.040
7
e2tA26 “4-t-butylacenaphthalene’”
1 3
a2tA24 L3+A34
15-t-butylace”aphtbene’~p 1.100
1.100
0.000
0.850
0.350
0.000
0.850
0.850
0.000
2.100
2.100
0.000
5
a4+A45
4.270
4.210
0.000
4.270
4.270
0.000
6
‘)+A35
1.250
1.250
0.000
2.640
2. MO
0.000
7
a2+A25
2,640
2.640
0.000
1.250
1.250
0.000
a Experimental coupling constants from indicated references. A nonstandard numbering system is used to give compatibility with Table 6.The correct systematic names are given in parentheses. b Error given is the estimated parameter standard deviation. ’ Calculated from the additivity relationship determined from the assignments given in Ref. (21). d Calculated from the additivity relationsihp determined from the assignments discussed in the text. ’ From Ref. (28). rFrom Ref. (21). gFrom Ref. (29).
ADDITIVITY
OF
ESR
TABLE
COUPLING
513
CONSTANTS
5--Continued
PartB : Observed andCalculated couplingconstants Position
Equation
Literature
Assigameots
Best Least
Squares Assignments
Bxpt..
cahc
DUP.
Expt.
ca1c. '
DiPf.
(0)
(0)
(G)
(0)
(0)
(0)
.AC~"~phth~k"~'" (3.8di-t-butylacenaphtb~~~~)'
"2.7di-t-butylacenapbthalene:" 3
a3+A32+A37
7,. 100
1.940
0.160
2.100
2.100
-0.010
4
a,+A,2+A17
,.
4.445
-0. oz5
4.420
,. ,,5
-0.025
420
"3,6di-t-butylacenaphthaleoe:"
(4,7-di-t-b"tylaacena~hthe"e'~g
2
aZ+*23+b*6
0.990
1.373
-0.383
0.990
1.030
-0.040
4
a,+A,3*A,6
3.790
3.831
-0.041
3.790
3.831
-0.041
a2 s*t
OP parameters
0.765
a3 **t
OP paramters
0.320
0.020
0.075
0.075
a, set OP parameters
0.080
are from one source, any variability in the additivity relationship will not be a result of differences in solvent or in experimental technique. To increase clarity in the following discussion, a nonstandard numbering system will be used. Acenaphthene will be treated as a 1,8-disubstituted naphthalene, and referred to as “acenaphthalene,” and the compounds will be numbered accordingly (see Fig. 1). To indicate that the numbering used is nonstandard, compounds named using this system will be given in quotation marks, in both text and in Tables 5 and 6. Part B of Table 5 compares the observed and calculated coupling constants for the t-butyl-substituted acenaphthene radical anions. Columns 3 and 4 give the observed coupling constants and the coupling constants calculated on the basis of the additivity relationship for the assignments given by Huffadine et al. Column 5 gives the difference between columns 3 and 4. Columns 6 and 7 give, respectively, the observed coupling constants and the coupling constants calculated using the additivity relationship for the assignments which give the best fitting additivity relationship, as will be discussed below. A detailed examination of the agreement between the observed coupling constants and those predicted using the additivity relationship (column 5) suggested that some of the assignments given by Huffadine et al. may have been incorrect. These authors gave assignments for the monosubstituted compounds, based on MO calculations, such that the coupling constants at the 3, 6 positions were smaller than those at the 2, 7 positions. It was found that, by assuming the coupling constants at the 3, 6 positions were in fact larger than those at the 2, 7 positions, the agreement between the observed and calculated coupling constants could be improved dramatically. The R value for the coupling constants from the 2,7 positions (i.e., the a2 set of parameters) decreases from 0.77 G using the assignments given by Huffadine et al. to 0.080 G using the assignments given in columns 1 and 6 of Part B of Table 5. Similarly the R
BAKKER,
CLARIDGE,
AND KIRK
TABLE 6 t-Butyl-Substituted Naphthalene and Acenaphthene Anion Radicals” ml-t
B
and Calculated
: Observed
cGnpouod
Position
Coupli~
Equation
"4-t-butylacenaphthalene:"
Constants neat least
squares A.¶signmmts
Ekpt.
cam
Oil-f.
CC)
(0)
(0)
0.168
(5-t-b"tylacenaphtbene:)e
2
‘2+A41+T44
1.250
1.082
3
a2+A44+T41
2.100
2.232 -0.132
5
al+A44+T4*
4.270
4.182
0.088
6
a2+A44+T4*
2.640
2.505
0.135
7
a2+A41+T43
0.850
0.966 -0.116
'?,7di-t-butylacenaphthalene;"
(3.8di-t-butylacenapbth~~~~~*
3
aZ+A44+T43+T46
2.100
2.287 -0.187
4
a2+A44+T43+T46
4.420
4.426
'1,6di-t-butylacenaphthalane:"
-0.006
L4.7~i-t-butylaceMphth~~=~)f
2
a2+A41+T43+T46
0.990
1.054 -0.064
4
ai+A44+T42+T47
3.900
3.932
al+T4*
4.632
4.702 -0.070
a~+T%
2.035
2.155 -0.120
5.013
4.948
0.065
5.212
5.085
0.127
1.631
1.523
0.108
2.035
2.003
0.032
-0.032
2-t-butylnaphthalene= 1 3 4 5 6
‘1+T46 a,+T 46
7
a2+T47
8
al+T47
4.731
4.835 -0.104
aZ*T41+T 44
1.769
1.719
5.124
5.188 -0.064
aZ+T45+T48
1.769
1.876 -0.107
a1+T42+T46
4.846
4.861 -0.015
%.+T%3+ T627 T T al+ %3+ Al7
2.200
2.287 -0.087
4.846
4.856 -0.010
T al+ 42+
4.677
4.611
0.066
a2+Td23+T%6 T T %+ %3+ '16
1.817
1.808
0.010
5.050
5.106 -0.056
a*+T41+T43
1.957
2.037 -0.080
al+T42’T44
4.463
4.476 -0.013
5.180
5.162
0.018
1.957
1.852
0.105
1.637
1.680 -0.042
5.060
5.020
0.040
2.100
1.887
0.213
1.4-di-t-butylnaphthalene'g 2 5 6
al+T43+T48
0.051
2,6-di-t-butylnaphthalem~ 1 3 4 2.7-di-t-butylmphthaUTg 1 3 4
T
%7
2,3-di-t-butylnaphthalene~ 2 4 5 6
al+T43+T47 a2+T43+Tb27
7
a2+T46+T48
8
a1+T46+T48
1,3.5-tri-t-butylnaphthal~~e~~ 2
“z+T41+T43+T45
ADDITIVITY
OF ESR COUPLING
CONSTANTS
TABLE 6-Continued Part
II
: I,*a?t
PaIWWter
Squares
Rerinad
dddltivity
hl"B
eammetsrr
P*l-amFtW
"Pl"*
(0) *1
(0)
4.927~0.03lb
**14
-0.680_*0.033
TA12
-0.224~0.035
TAl3
0.021~0.036
Y4
1.307~0.093
*2 **21 *A 24 =*u
-0.227~.046
-0.733~.090 0.419_+0.086 -0.117+0.091 0.2*4~0.072
TA*3 TA24
-0.033~O.llS
TA15
0.321~0.049
=*25
-0.151_*0.092
TA16
0.13*_*0.034
Tb26
-0.347$l.0,3
%7
-0.09*~0.039
-0.065_*0.039 L Part B : Observed and Calculated compound
PoSitioll
naptltmene*
acenaphthene -d
0.133_+0.090
x7
0.136~0.099 TAz8 Coupling Constants
Eq"*tion
oe*t Least &y*re*
*asignments
mpt.
ca1c.
(0)
(0)
OiPf. (0)
4.940
4.921
0.013
1
81
2
*1
1.323
1.870 -0.045
2
*z+ AA21
1.040
1.117 -0.077
3
==2+I Aa4
2.420
2.349
4
*1+ AA14
4.170
4.243 -0.07*
"2-t-butylacenaphthalene'"
0.071
(3-t-butylaceMphthene')e
3
*2+ A A24+TA23
2.560
2.634 -0.074
4
al+ AA14+T A13
4.330
4.263
0.062
5
%+ A '14+ T'16
4.400
4.406 -0.006
6
%+ A '24+ T'26
2.000
7..002 -0.002
7
*1+ AA14+T A27
1.320
1.149
"3-t-butylacenaphthelene'" 2
0.071
(4-t-butylacenaphthe~~~)=
4.000
4.023 -0.023
3
*a+A 41* T%3 A T *1+ %4+ 42 *1+A 44+ TAl7
4.150
4.156 -0.006
6
a*+A%4+T47
2.670
2.482
0.1**
7
a2+A41tT46
0.890
0.770
0.120
4
1.300
1.401 -0.101
a Experimental coupling constants from indicated reference, calculated coupling constants were calculated from the additivity relationship. Additivity parameters superscripted “T” are those for the t-butyl group, those superscripted “A” are for the alkyl bridge in the acenaphthenes. A nonstandard numbering system is used for the t-hutylacenaphthenes to assist in comparison with the t-butylnaphthalenes. the standard compound names are given in parentheses. b Error given is the estimated parameter standard deviation. ’ From Ref. (8). dFrom Ref. (28). “From Ref. (21). fFrom Ref. (29). gFrom Ref. (4).
515
516
BAKKER,
CLARIDGE, TABLE
PaeB
: Observed
COWGWld
and
Caloulated
Positlo.
AND
KIRK
6-Continued Coupling Constants
Equation
Best
Least apt.
Squares Ca.10.
Asslgnmants DifP.
(G)
(0)
(G)
4.411
0.021
4
a1+T42+i44+T4*
4.432
6
aZ+T41+T45+T4,
1.426
1.135
7
aZ+T44*T46+T46
1.426
1.643 -0.219
8
a1+T44+T46+T46
4.764
4.793 -0.029
-0.309
1.3,6-tri-t-butylnaphthalene'B 2
aZ+T41+T43+T46
1.134
1.690
4
“I+T4*+T44+T4,
4.406
4.383
0.021
5
VT
42+T46+T 47 aZ+T 43+T46+T 48
4.984
4.936
0.046
2.196
1.964
0.232
a1+T43+T46+T46
4.984
5.040 -0.036
7 8 Standard Deviation for
0.044
(in Gauss)
a1 parameter
set
0.067
Par a* parameter
set
0.163
value for the coupling constants from the 3, 6 positions (i.e., the a3 set of parameters) decreases from 0.320 to 0.020 G. The assignments made by Huffadine et al. are based on MO calculations made for individual compounds, whereas the assignments made on the basis of the additivity relationship are made using data from a set of compounds. The use of a set of data would tend to average out measurement errors in the individual coupling constants. The assignments of some coupling constants are still ambiguous. The additivity relationship fits equally well when the following pairs of coupling constants were exchanged; positions 4 and 5, and positions 3 and 6 in “3-t-butylacenaphthalene;,” positions 2 and 7, and positions 4 and 5 in “4-t-butylacenaphthalene T,” and positions 2 and 7, and positions 3 and 6 in “5-t-butylacenaphthalene;.” Some indication of the correct assignment of these pairs of coupling constants can be found by considering the additivity relationship that can be derived by including the coupling constants of the series of t-butyl-substituted naphthalene radical anions reported by Goldberg and Peake (4). If the assumption is made that the presence of the saturated alkyl bridge in acenaphthalene is a small perturbation, then an additivity relationship can be determined for both t-butyl-naphthalene and “t-butyl-acenaphthalene” radical anion series simultaneously. This is done by treating the saturated alkyl bridge as a substituent added to naphthalene. For instance, the coupling constant at the 4 position in “acenaphthalene” (using the nonstandard numbering system) would be found as follows: (1) Use symmetry operators to minimize the position of the coupling constant. This gives the 1 position. (2) As a result, the alkyl bridge is moved to the 4 (and 5) positions, giving the equation for the coupling constant as aI + *Ai4 (the “A” superscript indicates that the additivity parameter is for the alkyl bridge substituent).
ADDITIVITY
OF ESR COUPLING
CONSTANTS
517
Consider now the more complicated example of the coupling constant at position 3 in “2-t-butylacenaphthalene ; .” Symmetry operators transform the 3 position into the 2 position, moving the alkyl bridge into the 4 (and 5) positions and the t-butyl group into the 3 position. The equation for the coupling constant is then a3 + *Az4 + TA23 (where the superscript “T” indicates that the additivity parameter is that of a t-butyl substituent). Table 6 gives the parameters and observed and calculated coupling constants for this additivity relationship. The R values for the two independent parameter sets, 0.067 and 0.163 G, suggest that the assumption that the alkyl bridge in acenaphthene; is a small perturbation is a reasonable one. The assignments for “2-, 3-,” and “4-t-butylacenaphthalene 7” given in Table 6 have been checked by calculating the additivity relationship when the ambiguous pairs of coupling constants are exchanged. As far as we have been able to determine, the assignments given result in the lowest possible values of R; i.e., the given assignments give the best possible agreement between the calculated and observed coupling constants. Methyl-substituted naphthalene anion radicals. Moss et al. (3) in a substantial paper, successfully applied the additivity relationship to a series of polymethyl-substituted naphthalene anion radicals. In this study we have redetermined coupling constants for naphthalene; both mono-methylnaphthalenes;, all ten dimethylnaphthalenes;, 1,2,3,4- and 1,3,5,7-tetramethylnaphthalene;, 1,2,3,4,5,8-hexamethylnaphthalene;, and octamethylnaphthalene;. Our observed coupling constants are in good agreement with those previously reported (3, 22-24) for these compounds. The tables include data for the previously unreported asymmetric dimethylnaphthalenes; , 1,2-, 1,3-, 1,6-, and 1,7-dimethylnaphthalene;, 1,3,5,7-tetramethylnaphthalene;, 1,2,3,4,5,8-hexamethylnaphthalene ;, and octamethylnaphthalene ;. Using the observed coupling constants reported in this study, together with the observed coupling constants for 1,4,5,8-tetramethylnaphthalene; reported by Moss et al. (3) and for 2,3,6,7-tetramethylnaphthalene; reported by Bolton (29, we determined the additivity relationships given in Tables 7 and 8. (a) Ring proton coupling constants. The agreement between our observed coupling constants and the coupling constants predicted by the additivity relationship based on the literature values can be improved by altering a number of the assignments used by Moss et al. Specifically, the coupling constants for the 2 and 3 positions in 1,8-dimethylnaphthalene;, 1 and 5 positions in 2,3-dimethylnaphthalene ;, and 1 and 4 positions in 2,6-dimethylnaphthalene; need to be exchanged. Making these changes in assignment results in a decrease in the R value from 0.087 to 0.060 G, and 0.083 to 0.078 G for the al and a2 parameter sets, respectively. We consider that the improvement in the agreement between the observed and predicted coupling constants is sufficient to justify the suggested changes in assignment in 2,3- and 2,6-dimethylnaphthalene;. The improvement in agreement produced by the change in the assignments in 1,8-dimethylnaphthalene; is small (from 0.083 to 0.078 G) and we are less confident that the improvement is significant. The complete set of assignments, and the coupling constants predicted by the additivity relationship on the basis of the literature assignments and the best least-squares
BAKKER,
518
CLARIDGE,
AND KIRK
TABLE 7 Ring Protons for Methylnaphthalene
Anion Radicals
Part A : Least squares*ddltl”lty mmetersa Parameter “due Parameter “due (0) (Cl (0) CC) 4.972~0.040b
=1
4.965~0.027
a2 A21
-0.280_+0.036
%2
-0.570s.
*14
0.166+0.027 039
0.34930.039
0.367f3.027
A
0.116_+0.034
0.099~0.023
16
-0.273~0.036 0.111~0.036
%3 Part
B : Observed
Position
‘23
-0.571~.027
d 15
P 17
1.940~0.030 -0.44*_+0.030
-0.191_*0.025
0.145_+0.039
%3
1.940~0.032 -0.457_+0.032
‘24
-0.353~0.025 O.llg*O. and
Calculated
Equation
025
0.406+0.036
0.406*0.034
0.058_+0.033
0.043+0.031
AZ5
-0.379~0.033
-0.3s9~0.029
‘26
-0.539~0.033
-0.539~0.031
‘27
0.386~0.032
p28
0.309+X
Coupling Literature
0. 336_tO. 032
030
0.319?0.030
Constants *ssignmnt
Best
Least
squat-*9
Assignmnt Ikpt.
Cahc
DiPI.
i3xpt.
ca1c.
d DiPf
(0)
IG)
(G)
(0)
(G)
(G)
na9btbalem~ l
4.965
4.972
-0.007
4.965
4.965
1.842
1.940
-0.098
1.842
1.940
2 a2J21
1.409
1.483
-0.074
1.409
1.492
-0.083
’
‘Ztd24
1.964
1.998
-0.034
1.964
1.987
-0.025
4 al+%4
4.408
4.403
0.005
4.408
4.339
5 =1+%5
5.372
5.321
0.051
5.372
5.332
6 a2+d25
1.529
1.561
1.529
1.552
2
al a2
l-mthylnaphthalane
0.000 -0.098
:f
-0.032
0.040 -0.023
7 a2+p28
2.290
2.250
2.290
2.259
0.031
8 5+*1g
5.031
5.083
-0.052
5.031
5.083
-0.052
4.764
4.692
-0.090
4.764
4.774
-0.010
2-methyl"a9bthalene 1 %+‘%Z 3
*2+43
0.040
0.020
-P
2.322
2.346
-0.024
2.322
2.346
-0.024
4 %+A13
5.063
5.111
-0.054
5.063
5.132
-0.069
’
*1+%6
5.063
5.088
-0.025
5.063
5.064
-0.001
’
a2+A26
1.331
1.402
-0.071
1.331
1.402
-0.071
’
‘z+%
2.269
2.326
-0.057
2.269
2.326
-0.057
4.602
4.692
-0.090
4.602
4.60,
-0.005
8 al+47
a Experimental coupling constants from indicated references, calcoupling constants from the additivity relationship. b Errors given are the estimated standard deviation. c Calculated using the assignments from Ref. (3). d Calculated using the assignments which give the best agreement with the additivity relationship. e From this work, error is 20.015 gauss. f From this work, error is +0.006 gauss. g From Ref. (3). ‘From Ref. (25). culated
ADDITIVITY
OF ESR COUPLING
519
CONSTANTS
TABLE l-Continued Part B : Observed and Calculated Position
Equation
coupling
Literature
constants Assignnan+,
Best lnaat
squares
Asaigmmt Pzpt.
cahc
Dir-f.
!apt..
ca1c. d DifP
(G)
(0)
(0)
(0)
(0)
(0)
naptitila1*ne=
2.305
2.404 -0.100
2.303
2.393 -0.090
4.502
4.548 -0.044
4.502
4.555 -0.053
5.423
5.437 -0.014
5.423
5.431 -0.008
1.010
1.022 -0.012
1.010
1.013 -0.003
2,648
2.635
2.648
2.645
4.693
4.810 -0.117
4.693
4.723 -0.032
0.013
0.003
* a2+41+43
1.880
2.889 -0.009
1.880
1.898 6.018
4
5*42+44
4.242
4.122
0.120
4.242
4.197
5 a1+45+47
5.074
5.048
0.026
5.074
4.974
0.100
6 az+45+47
2.032
1.947
0.085
2.032
1.937
0.091
7 a2+46+4A
1.759
1.711
0.048
1.759
1.720
0.039
* ‘1+46+48 1.4-dimethylnaphthalBne"
5.239
5.199
0.040
5.239
5.182
0.057
1.663
1.541
0.122
1.663
1.541
0.122
5.416
5.432 -0.016
5.416
5.450 -0.034
1.829
1.870 -0.041
1.829
1.870 -0.041
1.132
1.104
0.028
1.132
1.104
0.028
2.443
1.307
0.028
2.443
2.307
0.136
4.490
4.513 -0.023
4.490
4.506 -0.016
a a2t41+46
I.103
0.944
0.161
1.105
0.954
3 aa+824+A27
2.362
2.384 -0.022
2.362
2.374 -0.012
0.045
0.151
4 al+A14+b17
4.102
4.130 -0.028
4.102
4.031
5 al+P12*d15
5.124
5.041
0.083
5.124
5.141 -0.01,
0.071
' a*+A*3+A28
2.762
2.657
0.106
2.762
2.665
0.097
8 al+A13+A18 1.7dimethylnaphthQlene:e
5.378
5.228
0.150
5.378
5.249
0.129
0.014
* a2+A21+d27
1.892
1.869
0.024
1.892
1.878
' a2+A24eP16
1.441
1.460 -0.018
1.441
1.450 -0.010
' "1+b14+p16
4.488
4.519 -0.031
4.488
4.487
0.001
5 al+A13+AlS
5.532
S.466
0.066
5.532
5.498
0.034
6 a2+A23+~25
1.949
1.967 -0.018
1.949
1.958 -0.009
8 a1+A12+~18
4.837
4.803
0.034
4.837
4.892 -0.055
1.657
1.792 -0.135
1.714
1.811 -0.097
1.714
1.619
1.657
1.600
1.8-dimetllylnapbthalene"
0.095
0.057
520
BAKKER,
CLARIDGE,
KIRK
7-Continued
TABLE Fart B : Observed and Calculated Po.¶ition Equation
AND
coupling
Literature
constants *ssignment
Best Least Squares Assignmnt
iapt.
ce1c.= Diff.
Bxpt.
Calc.d
Diff
(G)
(0)
(0)
(0)
(G)
(0)
naphthalene~* 4 *1+%4+%5
4.662
4.751 -0.089
4.662
4.755 -0.093
l %%2%3
4.773
4.837 -0.064
5.033
4.940
0.093
5 *1+%6+41
5.033
4.816
0.217
4.733
4.706
0.027
' a2+d16+A27
1.797
1.787
0.010
1.797
1.787
0.010
1 al+A12+A16
4.681
4.808 -0.127
4.835
4.873 -0.038
3 a2+A23+All
2.724
2.732 -0.008
2.724
2.732 -0.008
4 al+A13+A17
4.835
4.844 -0.009
4.681
4.774 -0.093
2,3dimst~l"aphthalen*"
2.6dimethylnaphthale"e~
2.7dimethylnaphthaleDe'B l al+A12+A17
4.413
4.419 -0.006
4.413
4.416 -0.003
3 a2+A23+A26
1.797
1.808 -0.011
1.797
1.808 -0.011
' al+A13*A16
5.231
5.234 -0.003
5.*31
5.230
5 al+A15*A16+A17+618
5.167
5.275 -0.108
5.167
5.191 -0.024
' a2+b25*~~6+~~7+A~8
1.730
1.717
0.013
1.730
1.717
0.013
0.001
1.2.3,4-tetraoothyl~~phthalena:f
1.3.5,7-tetramt"ylmphthalene
:f
= a2+41+A23+A15+47
1.958
1.895
0.063
1.958
1.895
0.063
' al*A12+A14+A16*A18
4.440
4.349
0.091
4.440
4.414
0.026
1.411
1.4'11 -0.060
1.411
1.471 -0.060
4.680 -0.040
4.640
4.681 -0.041
I.318
1.198
1.318 -0.120
1.4.5.8-tetFamethyl~phthalene'8 = aa+41+A24+A25+Aa8 2.3.6.7-tetramethylnaphtha~~u~ ' a1*A12+A13+A16*b17 1.2.3.4.5.8-h*xaDBtbylnaphthalene
Th 4.640 +I
6 aZ+~Z1+A~4*A~5+A26*A2,*628 1.198 Standard owi*tion
-0.120
(in Gauss)
a1 p.wametef‘ set
0.087
0.060
"z parameter
0.083
0.078
set
assignments, are given in Part B of the Table 7. The additivity parameters determined from the two sets of assignments are given in Part A of Table 7. Refinements utilizing different sets of coupling constants give some indication of the sensitivity of the R value to various factors. A refinement using only the same coupling constants as were available to Moss et al., but using our values for the coupling constants, gave the following results. For the aI set of coupling constants, the coupling constants of Moss et al. gave an R factor of 0.075. A refinement using data from the
ADDITIVITY
OF
ESR
COUPLING
CONSTANTS
521
present study gave an R factor of 0.060. The R factors for the a2 coupling constants were 0.074 for the data of Moss et al. and 0.078 for the present study. The improvement in the R factor for the al set is substantial whereas the R factor for the a2 set is slightly worse in the present study. This would indicate that, overall, two factors should decrease the R factor. These are improvements in the precision with which the coupling constants are determined, and the use of coupling constants from one study where all the coupling constants have been determined under the same experimental conditions, The importance of these two factors relative to one another cannot be determined on the basis of the available data. The other factor to emerge from a cc mparison of various refinements is the sensitivity of the R factor to increases in the number of coupling constants used in the refinement. In going from the 36 coupling constants available to Moss et al. to the 65 coupling constants of the present study, there has been no improvement in the R factor for the al coupling constants and a slight increase in the R factor for the a2 coupling constants. This would indicate that a major component of the R factor is therefore inherent deviations from the additivity relationship, so that each successive coupling constant added to the refinement would contribute an increment to the sum of the squares of residuals that balances out the decrement in the R factor resulting from a increase in the number of coupling constants. It should be noted that when the additivity relationship was first being determined for the data presented in this work the coupling constants for positions 4, 5, and 8 in 1,7-dimethylnaphthalene (26) were found to be in extremely poor agreement with the additivity relationship. Reinvestigation of the spectra (20) showed that the coupling constants were in error. Reinterpretation of the observed spectra produced a better fit of the simulated to the observed spectra, giving coupling constants in much better agreement with the additivity relationship. (b) Methyl coupling constants. The availability of the data from the asymmetric dimethylnaphthalenes has given sufficient observations to allow a complete additivity relationship to be determined for the methyl coupling constants in the methylnaphthalene series. The additivity relationship determined is given in Table 8. The fit of the additivity relationship is considered reasonable. CONCLUSIONS
For deuterium-substituted benzene anions, the observed coupling constants agree well with the additivity relationship determined, and no conflict of assignment was found. For cyano- and methyl-substituted benzene anions, the agreement with the additivity relationship was very poor. This is considered to be due to changes in the highest occupied molecular orbital as substituents are added. The agreement between observed coupling constants and those calculated on the basis of the additivity relationship is considered satisfactory for methyl-substituted biphenyl anions. Changes in assignment are suggested for the 2-methylbiphenyl anion. The solution to the ESR spectrum of 2,4,6-trimethylbiphenyl; is felt to be incorrect, and we believe that this compound and 2-methylbiphenyl both warrant reinvestigation using modern ESR techniques.
522
BAKKER,
CLARIDGE,
AND KIRK
TABLE 8 Methyl Substituent of Methylnaphthalene Part A : Least Squares Refined Additivity Parameter
"*l"e
Anion9
Parameters
Parameter
"ahe
(Cl
(01
81
3.886+0. 051b
%Z
0.379~0.090
=2
1.719?0.021
621
0.202~0.0,0
A13
-0.02.3~0.084
623
%4
-0.606+0.085
%4
A15
0.489+0.087
%I
-0.370~0.039
'16
0.196~0.092
'26
-0.512+0.036
617
-0.264+0.087
%r
0.484~0.039
%8
0.640?0.092
%8
0.488_+0.038
Part
B
Position
: Observed
and Calculated
Equation
-0.049fl.036 0.108_+0.038
CoupIing Constants nest LBae ?,qvares *.ssignmenta Expt.
CEtlC.
DIPP.
(0)
(0)
(G)
3.854
3.866
-0.032
1.729
1.719
0.010
l-mwtbylnaPhtbalene'C 1
a1
Z-net~lnapbtbalenec 2
3
1.2-5imet~lnapbthalea
;d
1
=1+*12
4.375
4.265
0.110
2
a2+A21
1.943
1.921
0.022
1.3dimetbylnaphtbalene
;d
1
%+A13
3.950
3.862
0.088
3
a2+%4
1.867
1.827
0.040
3.300
3.279
0.021
4.387
4.375
0.012
1.4-di~thylnapbtbalene;d 1
al+%4
1,S-dimethylnaphthalene-d 1
Y+*ls
1,6dimetbylnaphthale~=~ 1
%+'I6
3.975
4.082
-0.107
6
%%5
1.308
1.349
-0.041
1.7dimetllylnapbtbalene;d 1
%+%7
3.492
3.622
-0.130
7
pl+A28
2.184
2.208
-0.024
’ Experimental coupling constants from the indicated references, calculated coupling constants from the additivity relationship. b Estimated parameter standard deviation. ’ This work, error is +0.006 gauss. d This work, error is +O.O15 gauss. e From Ref. (3). ‘From Ref. (25).
ADDITIVITY
OF ESR COUPLING
CONSTANTS
523
TABLE &.-Continued Part
B : Dbserved and Cakulatad
Position
Beat ‘east
1,8-dimettlylnaphthalene
sd
1 =1+*18 2,3-di~thylnaphthalene
75
2 =l+% 2.6-di‘mthylnaphthalene
Td
2
Coupling Constants
Equation
%*'26
2 'a+"27 l.Z.3.4-tBtrP~thglnaphthalene;c
2
ca.10.
(0)
(0)
Diff. (0)
4.560
4.525
0.035
1.714
1.670
0.044
1.222
1.207
0.015
2.200
2.203
-0.003
75
Z,,-dimttlyl"aphthalene
1
Squarea Aaaignwnta
Fxpt.
a1+A12+"13+"14
3.650
3.636
0.014
aa+A21+%3*A24
1.917
1.980
-0.063
al+A13+"15+A17
4.110
4.087
0.023
a2*b24c"26+b28
1.786
1.804
-0.018
4.354
4.406
-0.054
1.620
1.642
-0.027.
1,3.5,7,-tetramethylnaphthalene" 1 3
1,4,5,8-tetraoethyl"aphthalene?B 1
=1+%4+%5+48
2,3,6.7-tetramethylnaphthalene
3
7. a2+b23*b26+b27 1,2.3,4,5,8-hexamethylnaphth~l~"*~ 1 2 5
al+*12+A13+A14+*15+A16
4.675
4.764
-0.089
~Z+~llt~23+6Z4~~ZStb28
2.115
2.099
0.017
al+b14+615*P16+~17+%8
4.483
4.340
0.143
1.2.3.4.5,6.1.6-0ot-t~lnaphthalene'o 1
al+bl*+*13+d14+A15+*16+*17+~*
4.660
4.696
-0.036
2
al+P21+dZ3~b24+bZ5*A~6~~~7+A~~
2.095
2.070
0.025
Standard Deviation
(in Gauss)
a1 parameter
set
0.11s
a2 parameter
set
0.049
The literature assignments for the coupling constants of t-butylacenaphthene anions were found to be in poor agreement with those giving the best agreement with the additivity relationship. By treating the peri-alkyl bridge in acenaphthene as a substituent on a naphthalene skeleton it was possible to produce an additivity relationship including data from t-butylnaphthalenes and so produce unambiguous assignments for all tbutylacenaphthene coupling constants. This use of the additivity relationship with more than one substituent gives the possibility of successfully predicting the coupling constants for compounds including a variety of different substituents. Additivity relationships for both ring proton and methyl coupling constants for
524
BAKKER,
CLARIDGE,
AND KIRK
methyl-substituted naphthalene anions were calculated. This suggested changes in assignment in 2,3- and 2,6-dimethylnaphthalene 7. On the basis of the preceding discussion and earlier work, we would conclude that, where sufficient coupling constants are available, an additivity relationship is a better method of assigning and predicting coupling constants than MO calculations. In cases where there are serious deviations from the additivity relationship, further investigation into the causes of such deviations may be warranted. Our work also indicates that increasing the number of coupling constants will not substantially improve the R factor. It also indicates that improving the precision of the coupling constants, and improving the consistency of the data by determining all the coupling constants under the same conditions, will improve the R factor slightly. EXPERIMENTAL
The ESR spectra were recorded on a Varian E-12 spectrometer. All spectra were recorded at -85°C in 1,2dimethoxyethane, with potassium as counterion. The temperature was controlled by a Varian V4557 temperature controller to +3”C. The spectra of l- and 2-methylnaphthalene ;, 1,2,3,4-, and 1,3,5,7-tetramethylnaphthalene;, and 1,2,3,4,5,8-hexamethylnaphthalene; were fitted using a modified version of program ESRCON (20, 27) to fit the complete spectra. The remaining spectra were fitted using normal simulation techniques. ACKNOWLEDGMENT This work was supported in part by the University Grants Committee of New Zealand, and one of (M.G.B.) is grateful for a postgraduate scholarship held during the course of this work.
US
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