The Journal of Physical Chemistry, Vol. 82, No. 19, 1978 2105
ESR Study of Substituted 3-Nitropyridines (7) T. A. Moore and P. S. Song, Nature(London),New 8/01.,242, 30 (1973). (8) T. Takemura, P. K. Das, G. Hug, and R. S.Becker, J. Am. Chem. SOC., 98, 7099 (1976). (9) T. Takemura, P. K. Das, G. Hug, and R. S. Becker, J. Am. Chem. SOC., 100, 2626 (1978). (10) W. H. Waddeli, A. M. Schaffer, and R. S. Becker, J. Am. Chem. Soc., 95, 8223 (1973). (11) W. H. Melhuish, J. Opt. SOC. Am., 52, 1256 (1962). (12) (a) E. J. Bowen and J. Sahu, J. Phys. Chem., 63,4 (1959); (b) W. H. Meihuish, J. Opt. Soc. Am., 54, 183 (1964); (c) G. Heinrich, S. Schoof, and H. Gusten, J. Photochem., 3, 315 (1974-1975). (13) C. A. Parker, "Photoluminescence of Solutions", Elsevler, London, 1968, pp 220-232. (14) (a) In the case where there are two species (designated by subscripts 1 and 2) in solution and emission of one (designated by subscript 1) is much stronger than the other, the excitation spectrum Exz(X) are given bys and quantum yield, d, Eh,(X) = A(h)[l - 10-A'h)]-lI~(h')
=
i(Wfi(A')
application of (A), (B), and Beer's law (Le., A(X) = A1(A) i- A2(X)) gives cA(X)-' = constant X el(X)-'[4
&(A)-'
(16) (A) (B)
(17)
where is the excltln wavelength, A' the monitoring wavelength, A()! = total absorbance, I is the observed A(X) = Ai(X) fluorescence intensity arid, d, (A) and @') represents Intrinsic quantum yield and intrinsic fluorescence shape, respectively. Applying eq A and B to the equllibrium represented by
(18) (19) (20)
+ ROH 2P-HOR
(22) (23)
d,app(W
= A(xjiA
I(X)dl(N
+
P
(21)
and assuming that only the H-bonded complex emits and that the excited states of the free and H-bonded forms do not interconvert, we obtain
+ (K,hC)-'] + e*(A)ej(X)-'h-'(C + KH-')]
€(A)-' = COnStant x €I(~)-'d,1(~)-'[C-' h-'
d,app(A)-i = d,l(X)-'[l
= constant X e1(A)-'4,(A)-'[4
4app(A)-1 = @Jl(A)-'[I (15)
+ K,-'c-']
(E)
+ &-'c'](F)
+ %(A)€l(A)-1(2 + G-'cl)l (GI
wlth eq E being applicable at a wavelength where the absorptlon of monomer is negligible. We note that because of rapid cooling and slowness imposed by the rigidity of the solutlon the equilibrium constants probably correspond to equlllbria at a temperature higher than 77 K. Also, the equilibrium constants for H-bond formatlon as obtained from the emission data are probably smaller than those for true ground state equilibria because of posslble interconversion involvlng the excited states of the free and H-bonded forms (P. K. Das, G. Hug, and R. S. Becker, to be published). K. Brederick, T. Forster, and H. G. Oesterlin in "Lumlnescence of Organic and Inorganic Materials", H. P. Kallman and G. M. Spruchs, Ed., Wiley, New York, N.Y., 1962, p 161. (a) N. Mataga, T. Kalfu, and M. Koizumi, Bull. Chem. Soc. Jpn., 29, 373 (1966); (b) N. Mataga, !bid., 31, 459 (1958). W. R. Moomaw and M. F. Antor, J. Phys. Chem., 80, 2243 (1976). P. K. Das and R. S. Becker, to be published. T. Takemura, G. Hug, P. K. Das, and R. S. Becker, J. Am. Chem. Soc., 100, 2631 (1978). R. S. Becker, R. Bensasson, J. Lafferty, E. J. Land, and T. G. Truscott, manuscrlpt in preparation. J. P. Daiie and 8. Rosenberg, Photochem. Phot06ioi., 12, 151 (1970). (a) Taking all-trans C,, aldehyde (2 X M in 3M# at 77 K) as an example and using the apparent equilibrium constants given in Table IV, we find that as the concentration of TFE is increased from 1 X lo4 to 1 X 10" M, h e fraction of molecules that are hydrogen bonded should increase from 10 to 93%, (b) Sample calculations using equllibrlum constant data (Table IV) for dimer formation of all-trans C, aldehyde (3MP, 77 K) show that, as the concentration is increased from 1 X to 5 X lo-* M, the fraction of molecules that are dimerized increases from 13 to 72%. (a) B. Honig, B. Hudson, 8. D. Sykes, and M. Karplus, Proc. Natl. Acad. Scl., U.S.A., 68, 1289 (1971); (b)B. Honig, A. Warshel, and M. Karolus. Acc. Chem. Res.. 8. 92 (1975). R. M. Hochstrasser, D. L. Narva, and A. C. Nelson, Ccem. Phys. Lett., 43, 15 (1976). P. K. Das and R. S. Becker, work in progress.
-
(c) (D)
where e's are the extinction coefficients and h and c are the concentrations of hydrogen bonding agent and polyenal, respectively. (b) For the equilibrium
(24)
P + P S D
(26)
(25)
- -
An Electron Spin Resonance Investigation of Substituted 3-Nitropyridines Radical Anions M. Barzaghl, A. Gamba,' G. Morosl, and M. Slmonetta" C.N.R. center for the Study of Structure/Reactivity Relations and Institute of Physical Chemistry, University of Milan, 20 133 Milan, Italy (Received April IO, 1978)
The radical anions of 3-nitropyridine, 2-amino-3-nitropyridine, Z-amino-3-nitro-4-methylpyridine, 2-amino3-nitro-5-methylpyridine, 2-amino-5-nitropyridine, 2-amino-3-methyl-5-nitropyridine, 2-amino-4-methyl-5nitropyridine, 3-nitro-4-aminopyridine, 3-nitro-5-aminopyridine, 3-nitro-5-nicotinate,3-nitro-5-methylnicotinate, 3,5-dinitropyridine, Z-methoxy-3-nitropyridine, Z-methoxy-5-nitropyridine, 2,6-dimethoxy-3-nitropyridine, and 2,6-dimethoxy-3,5-dinitropyridine have been studied by ESR spectroscopy. Cepstral and autocorrelogramanalysis were applied as routine techniques to extract the hyperfine coupling constants from the experimental ESR spectra. The assignment of the hfscs to the nuclei was made through methyl substitution and quantum mechanical calculations (INDO and McLachlan methods). The Hammett equation was used to correlate ESR data; also, it is proposed as a tool to complete and to verify hfsc's assignment. Introduction Few types of radical anions have been more widely and comprehensively investigated by ESR spectroscopy than those generated by chemical or electrochemical reduction of aromatic nitro derivatives.2 In our laboratory we have performed detailed experimental and theoretical investigations on the spin distribution of nitrostyrenes,3p4 nitrodiphenylethylene~,~?~ nitroben~ophenones,~ nitro0022-3654/78/2082-2105$01 .OO/O
pyridines,&ll and nitropyridine N-oxides6radical anions. In this paper we investigate the influence of a second substituent on the reactivity of 3-nitropyridine, and in particular we consider substituents (-NH2, -0CHJ that exhibit a mesomeric effect opposite to the nitro group. As the reactivity at different nuclei of a radical anion depends on the electron distribution, ESR spectroscopy is a straightforward tool for studying the variations of re0 1978 American Chemical Society
2108
The Journal of Physical Chemistry, Vol. 82, No. 19, 1978
Simonetta et al,
activity determined by different substituents. The complete lack of symmetry in 3-nitropyridine derivatives, combined with the large number of magnetic nuclei, makes it very difficult both to analyze the ESR spectra and to assign the experimental hfscs to the proper magnetic nuclei. In this view, we have implemented numerical methods, such as cepstral12 and autoc~rrelogram~~ analysis, as routine techniques for interpreting the ESR spectra. The assignment of the experimental hfscs was made through the combined use of chemical substitution and quantum mechanical calculations. We have also used the Hammett linear free energy relationship to correlate ESR data and to solve any ambiguity in proton hfscs assignment. Experimental Section Materials. 3-Nitropyridine was obtained by oxidation of 3-aminopyridine14 (Fluka) and separated on a silica column (mp 36 "C from ethane-ethyl acetate). 2Amino-5-nitropyridine was a Fluka product (mp 188 "C from water). 2-Amino-3-nitropyridine was obtained15by nitration of 2-aminopyridine (Fluka), followed by thermal rearrangement of the corresponding pyridil nitramine and vapor stream distillation (mp 164 "C from water). The same method16(nitration and thermal rearrangement) was from used to obtain 2-amino-3-methyl-5-nitropyridine 2-amino-3-methylpyridine(Fluka, mp 255 "C sublimated), 2-amino-3-nitro-5-methylpyridine from 2-amino-5methylpyridine (Fluka, mp 190 "C, sublimated), and 2amino-3-nitro-4-methylpyridineand 2-amino-4-methyl5-nitropyridine from 2-amino-4-methylpyridine (Fluka). 2-Amino-3-nitro-4-methylpyridine(mp 136 "C from chloroform) was separated from 2-amino-4-methyl-5nitropyridine (mp 220 "C from chloroform) on a silica column using chloroform as an eluent. 3-Nitro-4aminopyridine was prepared from isonicotinhydrazide16 (Fluka) via nitration and hydrolysis of the corresponding carbamate (mp 201 "C from ethanol). 3,5-Dinitropyridine was obtained following the method suggested by Plazek17 (mp 106 "C from ethanol). 3-Amino-5-nitropyridine was synthesized through the following s t e p ~ : lesterificationm ~'~ of nicotinic acid N-oxide (Fluka), nitration by p-nitrobenzoil chloride and anhydrous AgNO,, reduction21 by PCl,, hydrolysis of methyl 5-nitronicotinate; 5-nitronicotinic acid was treated with S0Cl2 and the resulting benzoil chloride was added with NaN,; acid hydrolysis of the crude 5-nitronicotinazidegave 3-amino-5-nitropyridine; product was purified on a silica column, using chloroform as an eluent (mp 141 "C from chloroform). Nitration of 2,6-dimethoxypyridine (Fluka) gave 2,6-dimethoxy-3nitropyridine after 10 min at 0-5 "C (mp 97 "C) and 2,6-dimethoxy-3,5-dinitropyridine after 30 min at 50 "C (mp 135 "C). 2-Methoxy-3-nitropyridine and 2-methoxy-5-nitropyridine were K & K Labs., Inc., products. The purity of all the samples was confirmed by NMR, IR, and UV spectroscopies.19 Preparation of Radical Anions and Measurements. Radical anions were obtained in vacuum cells by controlled potential electrolysis using N,N-dimethylformamide as a solvent. The technical details and the vacuum apparatus were previously d e s ~ r i b e d . ~Reduction ~ ~ J ~ potentials for each compound were slowly obtained in small increments until the first radical was detected. A solution of 0.03 M tetrabutylammonium perchlorate (Fluka) in N,N-dimethylformamide was used as a supporting electrolyte. The N,N-dimethylformamide employed was Carlo Erba RS, further purified by drying over anhydrous potassium carbonate followed by distillation at reduced pressure and storing under vacuum. ESR spectra were recorded with
I
I
I
I
I
1
I
I
,
-20
-15
-10
-5
0 gauss
5
10
15
20
Flgure 1. ESR spectra of the 2-amino-3-nkropyridine anion radical and its methyl derivatives, obtained by electrolytic reduction In N,N-dlmethylformamide at room temperature: (solid line) simulated spectra; (points) experimental spectra. Simulations were performed with the hfscs collected in Table 111, assuming Lorentzian line shape: (A) 2-amlno-3-nitropyridine (Ilne width 0.339 f 0.006 Gauss); (B) 2amino-3-nitro-4-methylpyridine (line width 0.326 f 0.010 G); (C)2amlno-3-nltro-5-methylpyridine (line width 0.327 f 0.007 Gauss).
a Varian E-Line Century Series spectrometer, equipped with a 9-in. magnet, a Varian field/frequency lock E-272B, and a Hewlett-Packard 5340A frequency counter. The home-made apparatus used for experiments at low and high temperatures is described elsewhere.* As the ESR spectra did not change significantly with temperature variations, all data reported in this paper are referred to 20 "C. Analysis of the ESR Spectra The interpretation of ESR spectra (see Figures 1-4) was obtained through an iterative line shape fitting procedure, as described p r e v i ~ u s l y According .~~~ to the method of least squares, the best fit is obtained by minimizing the function NP
F(P) = Cb, - Y(%P)12 i=l
(1)
with respect to the set of parameters p. y i is the ith experimental data point and y(xi,p) is a model function which is nonlinear in its parameters p. The least-squares method to be efficient requires that the starting parameters po approach the values p* of minimum F(p). Wrong guesses normally do not lead to convergence or they may give rise to local minima. Several derivatives of 3-nitropyridine produce spectra too complex to be completely resolved. The presence of seven groups of nonequivalent magnetic nuclei make up 648 theoretical lines for the amino derivatives, and 1296 lines for the aminomethyl derivatives. This fact makes selection of even the major coupling constants an ambiguous procedure when stick spectra are simply conglomerated and compared with experimental spectra,
The Journal of Physlcal Chem;stry, Vol. 82, No. 19, 1978 2107
ESR Study of Substituted 3-Nitropyridlnes
I
-20
I
-15
I
-10
I
-5
I
I
I
I
0
5
10
15
I
I
20
-20
gauss
I
I
-15
-10
I
-5
I
I
0
5
,
10
I
I
15
20
gauss
Figure 2. ESR spectra of the 2-amino-5-nitropyridine anion radical and its methyl derlvatives, obtained by electrolitlc reduction in N,N-dimethylformamlde at room temperature: (solid line) simulated spectra; (points) experimental spectra. Simulations were performed with the hfscs collected in Table 111, assuming Lorentzian line shape: (A) 2-amlno-hitropyridine (line width 0.245 f 0.01 0 G); (6)2-amino3-methyld-nltropyridine (line width 0.300 f 0.014 G); (C) 2-amino4-methyl-5-nitropyridine (line width 0.215 f 0.007 G). In parts B and C the scatter between experlmental and calculated spectra is due to a considerable broadening caused by electron spin relaxation, as usually found in several aromatic nitro derivatives.‘ Attempts to evaluate the contribution of the electron spin relaxation to the line widths through a least-squares line shape fitting procedure‘ did not give significative results, owing to the large number of parameters to be refined (11, at least).
which may contain on the order of 100 lines. Therefore the choice of a good set of parameters to enter the iterative least-squares fitting procedure presents a very difficult task. The cepstral analysis12 and the autocorrelation technique13 appear very effective methods for guessing hyperfine splitting constants. The methods are based on Fourier transformation of the experimental ESR spectra. The Fourier transform, or characteristic function, of a function y(x) is defined by
Figure 3. (A) ESR spectrum of the 3-nitro-5-aminopyridineanion radical, obtained by electrolytic reduction in N,Ndimethylformamide at room temperature: (solid line) simulated spectrum; (points) experimental spectrum. Simulation was performed with the hfscs collected in Table 11, assuming Lorentzian line shape and line width (0.147 f 0.007 G). (B) Autocorrelogram of spectrum A. The lines corresponding to an hfsc are marked by a disk (see also Table I). (C)Cepstrum of spectrum A. The lines corresponding to an hfsc are marked by a disk (see also Table I).
peak position, and a function g(x/w), usually Lorentzian or Gaussian with line width w,which defines the line shape
By using the convolution theorem,22it is straightforward to obtain the Fourier transform of eq 4, i.e. NL
Y(s) = G(sw) C exp(-isxi) j=l
(6)
where G(sw) is the Fourier transform of g ( x / w ) ,assumed in this work to be identical for every line. The position of the jth line, to a first-order approximation, is given by N.
with the inverse y(x) = ( 2 ~ ) - ~ / ~ 1 + ~exp(isx) Y ( s ) ds
(3)
The independent variable s in the complex Fourier plane has a dimension which is the inverse to that of x ; therefore it is referred as “spacial frequency”. An ESR spectrum is a sum of NL lines
!2
y(x) = j=l g
(7)
(4)
Any line j of the spectrum (4) can be considered as the convolution of a delta function 6(x - xi), which states the
where xo is the symmetry center of spectrum, N A is the number of paramagnetic nuclei, ak is the hfsc of the kth nucleus with spin I k , and mjk is the spin quantum number of the kth nucleus in the jth transition. Then
where H(s,ak)is a characteristic function of the hth nucleus and is defined as follows: +Ik
H(S,Uk) =
c
mp=-Ik
eXp(-iSUkmjk)
(94
2108
The Journal of Physical Chemistty, Vol. 82, No. 19, 1978
Simonetta et al. A
2rk
H(S,Uk) =
j=O
Cos [sake - lk)]
- sin [(sak/2)(2& + l ) ] sin (sak/2)
. I
(9b) (9c)
Expressions 9b and 9c point out that H(s,ak) is a real function. The power spectrum of eq 4 is given by the product Y(s)Y*(s). I t frequently happens that as a consequence of symmetry several nuclei have the same hyperfine splitting. If the set of Nk nuclei of spin I k have the common hfsc ak, then the power spectrum is Ni
Y(s)Y*(s) = G(sw)G*(sw)IT H(S,Uk)2Nk (10) k=l
where the product is taken over the N i equivalent nuclei sets interacting with the free electron. The inverse Fourier + Ikak - nkak), i.e. a set transform of H(s,ak) is of (211, + 1)delta functions symmetrically placed about the origin at multiples of ak. The inverse Fourier transform of H(s,uk)2Nkcan be obtained by using the convolution theorem
c,=,,%(x
r
I Ii
C
1
I
-20
I
I
-15
-10
I
-5
I
I
I
I
0
5
10
15
I
20
gauss
u,,,=2Nk
(11)
The Wiener-Kintchine theorem22states that R(x,ak)is the autocorrelation functionB for a set of Nk equivalent nuclei. The sum in eq 11is over all the terms which satisfy the condition Cnk=021kvnk = 2Nk,where the vnk (nk = 0,1, ...,21k) are integer numbers. Equation 11points out that R(x,ak) is proportional to the number Nk of equivalent nuclei, while the areas of the component delta functions are proportional to 1/nnk=owkvnJ and decrease on increasing 1x1. The inverse Fourier transform of G(sw)G*(sw)is the autocorrelation function of the line shape; it is proportional to g(xl2w). The experimental ESR spectra are in general obtained as first derivatives of the line shape function; by using the differentiation theorem,22we have ( 2 ~ ) - ' / ~-m1 + ~ g ' ( x / exp(-isx) w) dx = -is G(sw) (12) so that the power spectrum of the line shape results s2 G(sw)G*(sw),while the autocorrelation function is proportional to g"(x/2w). We may now conclude that the autocorrelation function of an ESR spectrum will be a convolution of g"(x/2w) with the autocorrelation function of the stick spectrum 11,so that the autocorrelogram will be similar to a second derivative ESR spectrum. The autocorrelation function is a measure of the correlation between the values of a function at values of the variable differing by an amount x; in other words, the autocorrelogram is a graph of the frequency of occurrence of all spacings within a spectrum. Therefore it can be used to extract the hfscs. Furthermore, the relative intensities of the various maxima in the autocorrelogram give a number of equivalent nuclei with the same hfsc. Let us consider now the natural logarithm of eq 10 NIA
In [Y(s)Y*(s)] = In [G(sw)G*(sw)]+ 2cNk In IH(s,ak)l k=l
(13) where H(s,ak)is defined by eq 9c. Then, by using the
Flgure 4. (A) ESR spectrum of the 3-nh-4-aminopyridineanion radlcai, obtained by electrolytic reduction in N,N-dimethylformamide at room temperature: (solid line) simulated spectrum: (points) experimental spectrum. Simulation was performed with the hfscs collected in Table 11, assuming Lorentzian line shape and line width (0.196 f 0.007 G). (B) Autocorrelogram of spectrum A. The lines corresponding to an hfsc are marked by a disk (see also Table I). (C) Cepstrum of spectrum A. The lines corresponding to an hfsc are marked by a disk (see also Table I).
Fourier series expansion of the natural logarithm of the absolute value of a sine f ~ n c t i o n , we ' ~ ~obtain ~~ +m
In IH(S,Uk)(= C (l/h!)[COS (shah) - COS (shak(2lk + I))] h=l
(14)
whose inverse Fourier transform is C(X,Uk) = (&-'I2C (l/h!)[6(x h=l
-
hUk) + 6(X
hak) - 6(x - hak(2lk + 1))- 6(r
+
+ hak(2Ik + I))] (15)
Equation 15 is known as the cepstrum of the hfsc of the kth nucleus and defines a set of delta functions of decreasing strengths, symmetrically placed about the origin and separated by the hfsc ak. Of course, the cepstrum of the experimental spectrum is given by the inverse Fourier transform of eq 13 NIA
c(X)= c ( X / W ) + 2cNk C(X,ak) k=l
(16)
where C(x/w) is the cepstrum of the line shape. Equation 16 shows that the cepstral technique decouples the nuclear hfscs, allowing them to be readily identified and evaluated. Moreover, the relative intensities of the lines can be used to determine the number of equivalent nuclei having the same hfsc. The use and effectiveness of autocorrelogram and cepstral analysis in obtaining the hfscs is illustrated in Figures 3-5. Since autocorrelogram and cepstrum
ESR Study of Substituted 3-Nltropyridines
The Journal of Physical Chemistry, Vol. 82, No. 19, 1978 2109
TABLE I: Hfscs Evaluated through Cepstral and Autocorrelogram Analysis and Refined by the Least-Squares Method least-squares line shape fitting cepstrum au tocorrelogram no. of line re1 line re1 equivaposition, ampli- position, amplilent comod G tude G tude Hfsc, G nuclei spin 1 1 1 11.253 f 0.004 1 11.26 11.25 2-amino-5-nitropyridine 1 1 4.062 f 0.008 3.97 2 112 3.95 1 2.856 i 0.012 1 2.37 112 2 2.85 1 1.322 f 0.008 1 1.12 1 1.30 112 1 1 1.099 i: 0.005 1 1 1.054 f 0.006 4 1.05 2 0.469 f 0.006 1 0.50 2 0.56 112 1 1 11.240 f 0.003 1 11.25 1 11.25 2-amino-3-methyl-5-nitropyridine 1 1 4.095 i: 0.005 1 3.95 3.95 112 1 3 2.686 f 0.003 2.85 112 2 2.85 1.211 f 0.015 3 112 1.161 f 0.015 1 1.10 2 1 3 1.10 1.082 f 0.004 1 1 2 0.609 t 0.007 0.60 2 2 0.65 112 1 1 1 11.10 1 11.093 f 0.003 2-amino-4-methyl-5-nitropyridine 11.05 1 4.008 f 0.005 1 3.80 1 4.00 112 3 2.85 3 1 2.866 f 0.005 2.35 112 1 1.40 2 1.438 f 0.009 1.40 2 112 1 1 1.161 i: 0.004 0.95 2 3 0.95 1 1 0.941 i: 0.005 2 0.45 0.484 i: 0.010 0.45 2 2 112 1 1 2-amino-3-nitro-4-methylpyridine 12.20 12.20 3 12.156 f 0.004 2 1 1 3.324 f 0.006 2.75 1 2.75 112 3 3.218 f 0.005 3 3 3.20 3.30 112 1 1 1.359 i 0.002 1.15 112 1 1 0.620 i: 0.001 4 1 1 0.60 2 0.55 0.540 f 0.003 2 0.431 f 0.003 1/22 3-nitro-5-aminopyridine 1 1 1 1 9.462 f 0.003 9.50 9.46 1 1 1 4.075 f 0.009 4.05 4.04 112 1 4.028 i: 0.009 112 2.572 f 0.005 2.57 2.60 1 1 1 1/2 1.26 P 1 1 1.229 c 0.002 1.20 2 1 2 0.50 0.318 f 0.003 112 1 0.221 f 0.002 1 3-nitro-4-aminopyridine 11.45 11.45 1 2 11.465 f 0.004 1 7 1 3.45 1 3.45 3.451 f 0.004 1 112 2.80 2.45 1 1 3 2.651 f 0.006 112 1.45 1.40 1 5 1.429 t 0.007 1 112 1.20 1.20 3 1 1.161 f 0.003 7 1 0.70 0.70 1 1 1 2 0.742 f 0.004 0.25 2 2 0.219 f 0.003 112
transforms involve two successive Fourier transforms, the abscissa units of the cepstrum and the autocorrelogram will be the same as the units of the abscissa of the ESR spectrum. The first major lines then occur at the same field value as the hfscs of the ESR spectrum. According to eq 11 and 16 the intensity of the lines should be determined by the number of equivalent nuclei having the same hfsc. The intensity of a given line is roughly indicated by the height of the line and more accurately determined by the integral of the line over the width of the line. The autocorrelation function of the line shape will appear as a strong line at the origin of the autocorrelogram; the same thing occurs in the cepstrum. As noted previously, the lines in the autocorrelogram are second derivative (Lorentzian or Gaussian) functions with twice the line width of the original ESR spectrum. On the contrary the lines in the cepstrum resemble impulsive functions, as shown by eq 15 and Figures 3-5. Therefore overlappings are less significant in the cepstrum than in the autocorrelogram, allowing a better evaluation of the amplitude of the cepstral lines (see Table I). The experimental ESR spectra were digitalized “by hand” over 500-600 points. The cepstrum and the au-
tocorrelogram were calculated by using the fast Fourier transform a l g ~ r i t h m ,and ~ ~ then ? ~ ~ analyzed by a slightly modified version of the method reported in ref 13. The method locates the maxima in the cepstrum and in the autocorrelogram, assuming that the most intense peak corresponds to a splitting constant. The remaining maxima are then scanned in order of decreasing intensity and systematically examined for the integral relationships which indicate whether a maximum corresponds to a hfsc or to a combination of previously determined hfscs.13 In practice both overlap of lines and the presence of nonequivalent nuclei with nearly equal hfscs may prevent the extraction of all the hfscs from the cepstrum or the autocorrelogram. However the comparison of the number of nonequivalent magnetic nuclei in the radical, deduced on the basis of symmetry considerations, with the relative amplitudes of the lines in the cepstrum and in the autocorrelogram are useful to resolve such an ambiguity. The hfscs derived in this way were entered to the iterative leastisquares program5for final refinement. Convergencies were achieved in 5-10 iterations. The results of such a procedure are compared in Table I. The required computer programs were written in Fortran and runned on an
2110
The Journal of Physical Chemistry, Vol. 82, No. 19, 1978
Simonetta et ai.
TABLE 11: Experimental and Calculated (INDO, McLachlan) Hfscs (G)for Magnetic Nuclei in 3-Nitropyridine Derivatives compd 3-nitropyridine
2-amino-3-nitropyridine
2-amino-3-nitro-4-meth ylpyridine
nucleus
ring position
INDO expta>b
1 2 3 4 5 6
3.720 1.092 4.577
1 2
0.588 0.588
3 4 5 6
10.120
1 2
0.620 0.540
1.323 3.180
8.928
4.786 1.133 4.786
0.431
2-amino-3-nitro-5-methylpyridine
3 4 5 6
12.156
1 2
0.616 0.616
3 4 5 6
10.087
1 2
1.099 1.054
3.21 8 1.359 3.324
4.782 1.163 4.782
C
tS2) = 0.78 (S')= 0.75 - 1.744 - 1.680 - 3.122 - 2.810 10.207 10.200 - 3.782 - 3.471 1.981 1.818 - 3.141 - 3.362 ( 8 ' )= 0.78 - 1.290 0.417 -0.330 9.598 -3.185 1.674 - 2.591 ( 8 ' ) = 0.78 - 1.366 0.455 - 0.297 10.053 3.871 1.620 - 2.375
tS2) = 0.78 - 1.252 0.417 - 0.360 9.446 - 3.347 - 2.321 - 2.699 ( S z )= 0.78
2-amino-5-nitropyridine
2-amino-3-methyl-5-nitropyridine
0.469 1.322 2.856
3 4 5 6
11.253
1 2
1.161 1.082
4.062
0.609 1.211 2.686
3 4 5 6
11.240
1 2
1.161 0.941
4.095
-1.593 0.228 -0.459 1.674 - 3.131 9.636 - 2.645 (S') = 0.79 - 1.935
0.341 - 0.594 - 2.321 - 3.239 9.256 - 3.779 ( 8 ' ) = 0.78
2-amino-4-methyl-5-nitropyridine
3-nitro-4-aminopyridine
0.484 1.438 2.866
3 4 5 6
11.093
1 2 3 4
1.161 3.451 11.465 0.742
4.008
0.219
5 6 3-nitro-5-aminopyridine
1 2 3 4 5 6
1.429 2.651 1.229 2.572
9.462 4.075
0.221 0.318 4.028
d
- 1.859 -0.341 -0.540 1.890 3.309 9.408 - 3.725
( S 2) = 0.77 - 1.517 - 2.915 10.015 0.114 - 0.405 1.242 - 2.483 (27') = 0.78 - 1.707 - 3.077 8.346 - 3.671 -0.152 0.243 - 3.293
(S') = 0.75
McLachlane -1.151 - 2.257 8.862 - 3.253 1.047 - 3.776
- 1.239
- 0.527
0.451 - 0.248 9.578 - 3.503 1.751 - 2.802
0.029 0.016 9.172 - 5.147 1.418 - 4.223
(8')= 0.75
- 1.352
- 0.844
0.563 -0.263 10.141 6.253 1.751 - 2.627
0.662 0.356 10.080 - 2.720 1.044 -4.217
(6'') = 0.75 - 1.239 0.338 - 0.248 9.465 -3.503 - 2.452 - 2.977 ( S ' ) = 0.75 - 1.578 0.225 - 0.525 1.751 - 3.328 9.690 - 2.802 (23') = 0.75 - 1.916 0.338 - 0.701 -2.452 - 3.503 9.240 -4.028 (5'' ) = 0.75 - 1.803 - 0.338 -0.525 2.102 4.957 9.465 -4.028 ( S z )= 0.75 - 1.465 - 3.153 10.029 0.113 - 0.438 1.401 - 2.627 ( S z )= 0.75 - 1.690 -3.328 8.338 -3.853 -0.113 0.263 - 3.503
- 0.580 0.090 0.049 9.300 - 4.958 1.617 -4.435
- 1.020 1.099 -0.591 1.014 - 2.490 11.820 - 3.298
- 1.055 1.032
- 0.554
1.292
- 2.298
11.970 -3.547 - 1.065
0.921 - 0.495
0.621
- 0.436
12.170 - 4.860
- 1.414 - 4.546 10.250 0.334 - 0.180 -0.373 - 2.799 -0.927
- 1.628 9.048
- 4.180 0.499 - 0.268 - 3.136
The Journal of Physical Chemistry, Vol. 82, No. 79, 1978 2111
ESR Study of Substltuted 3-Nitropyridines
TABLE I1 (Continued) compd
nucleus
ring position
C
d
tS*) = 0.77 - 1.404 - 2.375
tS2) = 0.75
1 2 3 4 6
1.391 3.505 9.235 3.505 5.014
1 296 395 4
1.476 4.890 3.462 3.333
1 2 3 4 5 6
1.022
- 1.404
tSZ)= 0.75 - 1.352
8.707 5.240 1.292 4.904
0.000 8.725 - 3.887 1.997 - 3.347
0.175 8.676 -4.204 2.101 - 3.678
1.424 0.338 1.078 3.154 10.443 3.929
t S 2 )= 0.78 - 1.669
t S Z )= 0.75
1 2 3 4 5 6
- 1.690
- 1.120
0.032 1.782 - 2.807 9.256 - 3.293
0.053 1.927 - 2.977 9.240 - 3.503
0.779 1.091 - 2.921 10.950 - 2.965
( 5 " )= 0.78
1 2
1.226 0.434 10.947 4.055 1.137
- 1.593
t S Z )= 0.75 - 1.578
0.018 9.256 -3.725 1.944 0.032
0.035 9.240 - 4.028 2.102 0.053
t S 2 )= 0.77
t S Z )= 0.75
3.712 0.032 0.210 - 12.719
3.692 0.009 0.208 - 13.661
N(-N=) H(OCH3) N(NO2 1 H H
H 2-methoxy-5-nitropyridine
2,6-dimethoxy-d-nitropyridine
-1.352
N( -N= ) H(OCH3) N(NO2) H H H(OCH3)
3 4 5 6
N(-N=) H(OCH3) N(NO*1 H
1 276 335 4
- 2.627
10.254
10.205 -2.861 - 2.537
- 2.977 - 2.802
tSZ) = 0.78
t S 2 )= 0.75
8.308 - 3.347 - 3.779
8.338 - 3.678 - 4.028
- 1.707 - 3.347
- 1.690 - 3.678
( 8 ' ) = 0.75f - 2.03 - 4.48 2.13 - 1.21
(S2) = 0.78 2-methox y-3-nitropyridine
McLachlane
3 4 6 N(-N=) H
3,5-dinitropyridine
expta*b 1.327 3.407 9.824 4.320 3.407
1 2
3-nitro-5-nicotinate
3-nitro-5-methylnicotinate
INDO
- 1.352 -2.872 8.573 - 2.534 -4.323
- 2.070 - 5.630
3.979 0.359 -0.766 0.824 9.293 -4.577 1.350 -4.174
-0.732 0.686 11.350 - 4.381 1.095 0.345
0.006 0.519 4.563 5.752 6.069 -8.267 a In N,N-dimethylformamide. The experimentally assigned proton hfscs are in italics. INDO wave function. INDO wave function after quartet spin component annihilation. Hydrogen spin densities were translated into hfscs by the parameter 1751.47 ?: 84.44 G,instead of the original value 711.25 G.29 e amH= (- 20.05 ?: 0.80)pcn;U C H = (-90.16 i 1 0 . 7 O ) p c ( ~ ~ , ) * ; a N 1= 1 ,(-13.97 ~ * 0.g7)pNT;aNHzN= (26.00 ?: 4 ! 5 8 ) p ~ " ; ~ -=~ (7.43 = ~ ? 3 . 8 0 ) p ~ n+3(-2.74 2 0.5O)(pcT t pct"); UNO,^ = (32.64 rt 0 . 7 2 ) ( 2 p ~ "- PO"). RHF + CI INDO wave function, from ref 7.
2,6-dimethoxy-3,5-dinitropyridine
Univac 1106. The calculated cepstra, autocorrelograms, and ESR spectra were displayed by a Calcomp plotter. A few examples are shown in Figures 1-5. Calculations Spin densities calculations were carried out by means of the McLachlan m e t h ~ d , ~based ' on the a / r approximation, and by means of the INDO m e t h ~ d , ~ which *y~~ includes all valence electrons. For the anion radical of 2-amino-3-nitropyridine the experimental geometry of the parent neutral molecule30 was used. Model geometries6 were assumed for the remaining radical anions. a! and P integrals required for McLachlan calculations were inferred from the l i t e r a t ~ r e .Hfscs ~ ~ ~were ~ ~ obtained from McLachlan spin densities through the McConnell type relationships reported in Table 11. In Table I1 the results of McLachlan and INDO calculations are compared with the experimental values.
Hfscs Assignment The assignment of hfscs to specific nuclei is a quite difficult task because the considered molecules contain seven types of nonequivalent nuclei. Only the splittings of the amino and methyl protons can be unequivocally assigned, as they are associated to a 1:2:1 triplet and a 1:3:3:1quartet, respectively. In the other cases an aid for correct assignment comes from a combined use of chemical substitution, theoretical predictions, and an accurate analysis of the substituents effects through the Hammett relationships. Nitrogen Hfscs. By examining the whole set of hyperfine patterns, it emerges that the largest nitrogen splitting is easily assigned to the nitrogen of the nitro group.6-11 On the other hand, the assignment of the two other small nitrogen splittings is difficult as in general the two hfscs are nearly identical, Their relative signs and magnitude ratio were predicted by theoretical methods (see
2112
The Journal of Physical Chemistry, Vol. 82, No. 19, 1978
Slmonetta et ai.
TABLE 111: Assignment of Proton Hfscs of 2-Amino-3-nitropyridineand 2.Amino-5-nitropyridine Radical Anions through Methvl ring nucleus position
compd 2-amino-3-nitropyridine
N(-N= ) N("2) H("2) N(NO2) H H
methyl derivatives 0.620 f 0.540 i 0.431 f 12.156f
0,001 0.003 0.003d 0.004 3.218 i: 0.005 1.359 f 0.002 3.324 0.006 1.161 f 0.015 1.082 i 0.004 0.609 f 0.007d
1 2
3 4 5 6 1 2
0.616 i 0.008 0.616 f 0.008
unsubstituted
0.588 f 0,008 0.588 i: 0.008
10.087 f 0.002 10.120i: 0.003 4.782 i: 0.003 4.786i 0.007 1.163 f 0.007 1.133 i: 0.018 H 4.782 i 0.003 4.786 i 0.007 2-amino-5-nitropyridine N(-N= ) 1.161 i 0.004 1.099 f 0.005 N("2) 0.941 f 0.005 1.054 f 0.006 0.484 f O.OIOd 0.469 i 0.006d W H ,1 H 3 1.211 r 0.015 1.438 i: 0.009 1.322f 0.008 4 2.686 i: 0.003 2.866 i: 0.005 2.856 f 0.012 H N(NO2) 5 11.240 f 0.003 11.093f 0.003 11.253 f 0.004 H 6 4.095 f 0.005 4.008f 0.005 4.062i 0.008 a In N,N-dimethylformamide. Hfscs in gauss. Methyl protons hfscs are printed in italics. They are associated with a 1:3:3:1 quartet. Associated with a 1:2:1 triplet,
.
iiii I I :
A
l.ii i
B
I
I
I
I
I
0
2
4
6
8
I
I
10 12 gauss
I
I
I
14
16
18
I
20
Figure 5. Autocorrelogram (A) and cepstrum (9)of the ESR spectrum of 2amino-4-methyi-5-nitropyrldine anion radical (see Figure 2C). The lines corresponding to an hfsc are marked by a disk (see also Table 1).
Table 11),even if the isotope substitution (15N)only could give a conclusive answer. Proton Hfsc of 2-Amino-3-nitropyridine and 2Amino-5-nitropyridine Radical Anions. The chemical substitution of ring protons by -CH, was necessary to obtain unequivocal assignment of the corresponding hfscs. The experimental results for the unsubstituted and the methyl-substituted radical anions are collected in Table 111. The introduction of a methyl group slightly modifies the spin distribution of the corresponding aminonitropyridine radical anions, with the exception of 2-amino3-nitropyridine, in which the presence of a methyl group in position 4 causes variations of the spin densities that can no longer be considered a perturbation. From Table I11 it emerges that methyl substitution allows a conclusive assignment of the proton hfscs of the two considered radical anions, i.e., la(5-H)I < la(4-H)I 5 la(6-H)I for 2amino-3-nitropyridine and la(3-H)I < la(4-H)J< la(6-H)I for 2-amino-5-nitropyridine. Proton Hfscs of the Unsubstituted 3-Nitropyridine Radical Anion. The assignment of hfscs to the specific protons of the unsubstituted 3-nitropyridine radical anion is not straightforward. A comparison with 2-amino-5nitropyridine suggests that the lowest hfsc (1.092 G) is
located at position 5. In a recent works the ion pair of the 3-nitropyridine radical anion with the sodium cation was compared with the corresponding ion pair of the 3,5-dinitropyridine radical anion. The two ion pairs were found to have very similar spin distributions, as 3,5-dinitropyridine appears as a 5-substituted 3-nitropyridine where the nitro group at position 5 is only a small perturbing substituent. When sodium tetraphenylborate is added to the ethereal solution, the 3,5-dinitropyridine ion pair exhibits cation transfer between the two nitro groups, which affects the line widths of the doublets of 2 and 6 protons dramatically, allowing the assignment of the corresponding hfscs and, by exclusion, of the hfsc of 4 proton.8 These results can be transferred to the 3nitropyridine radical anion in a natural way, so that the hfscs of 3.180 and 4.577 G are assigned to 2,6 protons and the hfsc of 3.720 G to the 4 proton. However, more information is required to assign the two hfscs to the 2 and 6 protons specifically. In the following section the Hammett linear free energy relationship will be proposed to correlate ESR data and to complete our assignment of ring protons hfscs in the 3-nitropyridine radical anion and its 5-substituted derivatives.
Hammett Linear Free Energy Relationship Also the Hammett equation was originally intended to apply to equilibria and reaction rates, there have been many efforts to utilize it in order to correlate physical measurements. Two of the most widely investigated of these have been IR and NMR spectroscopies. As far as we know, the first relevant attempts to correlate ESR data by means of the Hammett equation are reported and critically discussed in ref 31 and 32. In particular, Bowers31 noted that the logarithm of the hfscs observed for the nitro group nitrogens of a series of para-substituted nitrobenzenes was approximately linearly related to the u values of the substituent. Furthermore the author suggested an iterative least-squares fitting procedure to obtain a new set of refined u values. As the hfscs are directly related to the spin density on the corresponding nuclei and they can be measured with high precision, one can expect the u values obtained by ESR data to describe the total electronic influence of the substituent. Identification of the u values with measures of substituent total electronic effects allows the identification of the p values as the relative susceptibility of the hfsc (i.e., the electron spin density) of a particular nucleus to a change in the substituent in the ring.
The Journal of Physical Chemistry, Vol. 82, No. 19, 1978 2113
ESR Study of Substituted 3-Nltropyridines
o,D
TABLE IV: Estimated Values of u 0 Based on Hfsc Measurements (in N,N-Dimethylformamide) for Substituted 3-Nitropyridines
-0.8
-1.0 I
,
-0.4 I
0.4
0.0
I
I
0 I4
'
~
/
0.8 I
,
a:(* I
I
U0
substitueni? rn-NO, P-NO~ rn-NH, P-"2 rn-COO-
this workbic
ref 33
ref 31
0.975 f 0.006 0.79 0.73 2.58 0.828 t O.OISd -0.059 i 0.002 -0.14 -0.241 f 0.002 -0.38 -0.24 - 0.1e -0.100 f 0.002 p-coo0.133 t 0.002 0.oe rn-COOCH, 0.34 0.083 f 0.002 0.186 f 0.013d p-COOCH, 0.46 0.60f -0.161 ?: 0.002 p-OCH, -0.16 -0.16 Meta and para position with respect to the paramagnetic group chosen as an "indicator". Obtained by the iterative least-squares fitting procedure described in ref 31. If not otherwise stated, the nitro group was The 2 proton is the "indicachosen as an "indicator". tor". e From ref 34. f Calculated by the hfsc obtained from ref 5 and the p parameter from ref 31.
We have attempted to apply the Hammett equation to derivatives of 3-nitropyridine in order to obtain a better understanding of the substituent effect and to complete our assignments of the hfscs to the corresponding nuclei. The existence of Hammett a-p correlations between a(NO,) and a(-N=) and the meta substituents has been ascertained. When a(N0,) was used as an "indicator", NH2 and OCH3in the para position to the nitro group were also included. When ring protons were used as "indicators:', all combinations of unassigned hfsc were fitted to a a-p equation; the best fit, chosen on the basis of the best correlation coefficient, allowed us to assign the hfscs to specific ring positions, provided that at least one hfsc was previously assigned. This procedure requires as the only assumption that the ESR data can be fitted through linear free energy relationships, that is really the case.31~32In this view, the Hammett correlation appears as a useful self-consistenttool to assign hfscs. Correlation Of log (ayX/ayH),with Y = NO2,2-H, -N=, X = NOz, NHZ, COO-, COOCH3, OCH3,and substituent constants axo33 proved to be approximately linear (see Figure 6). The agreement is within the acceptable limits of precision of the data (cf. Tables IV and V), The Bowers iterative procedureS1was applied to refine the a values for meta and para substituents. The results of calculations are collected in Table IV. The corresponding Hammett plots are shown in Figure 6; their slopes are reported in Table V. It should be noted that our refined a values for the nitro group are just intermediate between a0 and 6,as expected for those groups which are strongly electron withdrawing by resoThe Hammett correlations between the substituent and the hfscs of the 4 and 6 protons (i.e., ortho to the substituent) were also checked by using para a values. Only rough correlations have been obtained, with a general scatter that is beyond the reasonable limits of precision
-01'
'
-04
'
'
0.0
a
0.8 I
1.9 I
'
1I. 6 ( 1 : ( 0 ) 1
Flgure 6. Hammett plots of NO2, 2-H and -N== hfscs vs. literaturew u values (0,lower scale) and refined u values (e,upper scale) for 3-nitropyridine anion radical derivatives in N,N-dlmethylformamMe obtained by electrolytic reduction at room temperature.
of the data. The corresponding p values, collected in Table V, can be considered to be only indicative. From the results of Tables IV and V it appears that the absolute value of the hfscs of NO2 and 4-H increase ( p < 0) with the electron-donating power of the 5-substituent (a < 0). The reverse trend is observed for 2-H, 6-H, and -N= ( p > 0). It is also evident from Table V that the 5-substituent perturbs the spin distribution of the 3nitropyridine radical anion in the order NOz > 2-H > 4-H > 6-H N -N=. Owing to the small number of points used for the correlations of Figure 6, our results cannot be considered conclusive. However they support the suitability of the linear free energy relationships for fitting ESR data. On the other hand, they allow an unequivocal assignment of the hfscs for the protons in the 3-nitropyridine radical anion and its 5-substituted derivatives. Results of Calculations In Table 11, the ring proton hfscs that were assigned experimentally (i.e., by methyl substitution or Hammett correlations)are printed in italics. By the comparison with the calculated values, the reliability of the McLachlan and INDO methods in spin density calculations of the investigated class of compounds can be checked. The greatest disagreement is found for the 3-nitropyridine and the 2-amino-5-nitropyridineradical anions, as la(4-H)I < la(6-H)I according to experimental evidence and McLachlan calculation, while the T S F ~ order G is predicted by the INDO method. Still both INDO and McLachlan methods are unable to give 44-H) = 46-H) for 2amino-3-nitropyridine and its 5-methyl derivative, and
TABLE V: Estimated Values of p Based on Hfsc Measurements in N,N-Dimethylformamide Pa
indicator b C d NO2 -0.318 ?r 0,074 (0.907) -0.422 f 0.001 (0.999) -0.319 2-H 0.207 * 0.044 (0.947) 0.232 0.019 (0.983) 4-H -0.075 * 0.031 (0.810) -0.093 i. 0.034 (0.776) 6-H 0.068 ?r 0.029 (0.816) 0.048 t 0.040 (0.612) -N= 0.067 * 0.019 (0.909) 0.055 f 0.028 (0.806) a The correlation coefficients are reported within brackets. Obtained by using the original u values.33 Obtained by using refined u values (see Table IV). From ref 31; see also ref 32.
~
2114
The Journal of Physical Chemisfty, Vol. 82, No. 79, 1978
44-H) 46-H) for 3-nitro-5-aminopyridine, as found experimentally. However it should be noted that both methods predicts the equivalence of the 2 and 4 protons in 3-nitro-5-methylnicotinatecorrectly, and the equivalence of the 2 and 6 protons in 3-nitro-5-nicotinate with fair approximation. As shown in Table 11, the naive McLachlan method gives on the whole a more satisfactory interpretation of the experimental spin distribution than the INDO method, both for the unsubstituted and for the methyl-substituted aminonitropyridines. This finding is not surprising if considering that the INDO method is parameterized to reproduce ab initio results, which at present do not give a faithful interpretation of this observable. That being so, a properly parameterized naive technique, such as the McLachlan one, should be more qualified for interpreting the hfscs of large radicals, than other more accurate methods. In this view, the McLachlan method can be used successfully as a good interpolating technique for spin densities calculation of new derivatives, both of the benzene6 and the pyridine series. Therefore proton hfscs of 3-nitro-4-aminopyridine, 2-methoxy-3-nitropyridine1 2-methoxy-5-nitropyridine, and 2,6-dimethoxy-3-nitropyridine were assigned on the basis of McLachlan spin densities. However identical assignment are predicted by the INDO method.
Concluding Remarks By examining the effect of the substituents on 3nitropyridine, it appears that the amino group causes a reduction of spin density at the substituted position; conversely, an increasing of spin density occurs at the nitrogen of the nitro group. The effect of the methoxy group parallels that of the amino group, except for 2methoxy-3-nitropyridine.In general the electron donor effect of the methoxy group is less than that of the amino group, as can be argued by comparing the magnitudes of the nitro group nitrogen hfscs. When a ring proton is substituted by a methyl group, no significant change in the spin density of the nitro group is observed, with the only exception of 2-amino-3-nitro-4-methylpyridineradical anion, in which the two substituents in the ortho position to the nitro group cause a large increase of the nitro group spin density. This effect could be ascribed to steric hindrance, which forces the nitro group to spend more time out of the plane of the pyridine ring, so that a larger localization of spin density on the nitro group of this radical anion than in the other aminonitropyridines is observed. The increasing of spin density at the nitro group of 3-nitropyridine,caused by an electron donor substituent, is correctly reproduced by the McLachlan method. On the contrary, the INDO method predicts an opposite effect; this result could be explained by an overestimate of the inductive effect of the substituent with respect to the resonance one. In fact, when the predominant inductive effect causes a decrease of the experimental hfsc of the radical anion, nitro group, as for 2-methoxy-3-nitropyridine the INDO method correctly reproduces this trend. With regard to the redistribution of the spin density among the ring protons in the substituted 3-nitropyridine, the state of affairs is not easy to rationalize, owing to the concomitant and opposite effects of nitro, amino, and aza groups. Even for the meta-substituted 3-nitropyridines the Hammett equation was found to correlate the ESR data satisfactorily, it is clear that the concomitant effects of several substituents cannot be correlated by simple
Simonetta et al.
linear relationships. This type of failure is probably due to the existence of considerable direct resonance between the ortho and para substituents and the reaction center, in this case, the paramagnetic nucleus chosen as an indicator. A significative example is given by 3-nitro-4aminopyridine and 2-amino-3-nitropyridine; in these radical anions the nitro group hfscs differ by 1.3 G, even if the only relevant difference in their structures is the position of the amino group in each of the two possible ortho positions with respect to the nitro group.
Acknowledgment. The authors express their gratitude to Dr. V. Malatesta, who supplied samples of 2-amino3-nitropyridine and its methyl derivatives, 2-amino-3methyl-5-nitropyridine,2-amino-4-methyl-5-nitropyridine, and 3-nitro-4-aminopyridine. His helpful suggestions and discussion in the preliminary part of this work are also acknowledged. References and Notes Institute of Physical Chemistry, Unlversity of Sassarl, 07100 Sassarl, Italy. For reviews see (a) E. T. Kaiser and L. Kevan, Ed., “Radlcal Ions”, Interscience, New York, N.Y., 1968; (b) F. Gerson, “Hlgh Resolution ESR SPectroscoav”. Wilev. New York. N.Y.. 1970. A. Gamba, V. M’aiatesta,.G. Morosl, and M.. Simonetta, J. Phys. Chem., 76, 3960 (1972). M. Barzaghi, A. Gamba, G. Morosi, and M. Simonetta, J. Phys. Chem., 78, 49 (1974). M. Barzaghi, P. L. Beitrame, A. Gamba, and M. Slmonetta, J. Am. Chem. Soc.. 100. 251 (1978). A. Gamba, V: Malatesta,‘G. Morosi, C. Oliva, and M. Slmonetta, J. Phys. Chem., 77, 2744 (1973). A. Gamba, G. Morosl, C. Oliva, and M. Simonetta, Gazz. Chim. Ita/., 105, 509 (1975). M. Barzaghi, P. Cremaschi, A. Gamba, G. Morosi, C. Oliva, and M. Slmonetta, J . Am. Chem. Soc., 100, 3132 (1978). P. Cremaschi, A. Gamba, G. Morosl, C. Ollva, and M. Simonetta, J. Chem. SOC., Faraday Trans. 2, 71, 189 (1975). A. Gamba, C. Oliva, and M. Simonetta, Chem. Phys. Lett., 36,88 (1975). P. Cremaschi, A. Gamba, G. Morosi, C. Oiiva, and M. Simonetta, Gau. Chim. Ita/., 106, 337 (1976). D. W. Klrsme, J . Magn. Reson., 11, 1 (1973). K. D. Bieber and T. E. Gough, J. Magn. Reson., 21, 285 (1976). 0. von Schickh, A. Binz, and A. Schulz, Chem. Ber., 69, 2593 (1936). L. N. Pino and W. S. Zehrung, J. Am. Chem. Soc., 77, 3154 (1955). J. W. Clark-Lewis and R. P. Singh, J. Chem. SOC.,2380 (1962). E. Plazek, Recl. Trav. Chim., Pays-Bas, 72, 569 (1953). M. Nakadate and Y. Takano, Chem. Pharm. Bull., 13, 113 (1965). R. Azzimonti, Thesis, University of Milan, 1977. G. R. Clemo and H. Koeging, J. Chem. SOC.,Suppl., 231 (1949). E. Ochiai, J . Org. Chem., 18, 534 (1953). D. C. Champeney, “Fourier Transforms and Thelr Physical Appllcations”, Academlc Press, New York, N.Y., 1973. The cross-correlation function between two functions f(x) and g(x) Is a functlon of x defined by
1t m
R(x) = l t m -_f ( u ) g*(u+ x ) du =
f(u- x ) g’(u) d u
It is a measure of whether any correlation between the two functions exists. For f(x) = g(x) we have the autocorrelation functlon of f(x), which is a measure of the correlation between the values of f(x) at values of the varlable differing by an amount x . M. R. Spiegei, “Fourier Anabsls”, McGraw-Hili, New York, N.Y., 1974. J. W. Cooley and J. W. Tukey, Math. Comput., 1% 297 (1965). W. T. Cochran, J. W. Cwley, D. L. Favin, H. D. Helms, R. A. Kaenel, W. W. Lang, G. C. Maling, Jr., D. E. Nelson, C. M. Rader, and P. D. Welch, Proc. I€€€, 55, 1664 (1967). A. D. McLachlan, Mol. Phys., 3, 233 (1960). J. A. Pople, D. L. Beveridge, and P. A. Dobosh, J. Chem. Phys., 47, 2026 (1967). D. L. Beveridge and P. A. Dobosh, J. Chem. Phys., 48, 5532 (1968). R. Destro, T. Pilati, and M. Simonetta, Acta Cwstallogr., Sect. B , 31, 2883 (1975). K. W. Bowers in “Radical Ions”, E. T. Kaiser and L. Kevan, Ed., Intersclence, New York, N.Y., 1968, Chapter 5. E. G. Janzen, Acc. Chem. Res., 2, 279 (1969). R. W. Tan, Jr., J. Phys. Chem., 64, 1805 (1960). D. H. McDanlel and H. C. Brown, J . Org. Chem., 23,420 (1958).
