J. Phys. Chem. 1982, 86, 1358-1365
1358
Theory of Solvent Effects on the Hypertine Splitting Constants in ESR Spectra of Free Radicals Takehiro Abe,' College of General Educetbn, Tohoku Unlverslty, Kawauchi, Sendal980, Japan
Shozo Two-Kubota, and Yusaku Ikegaml Chemlcal Research Institute of Non-Aqueous Solutbn, Tohoku Unlverslty, Katahlra 2 Chome. Sendai 980, Japan (Received: February 25, 1981; I n Final Form: August 17, 1981)
An expression for the effects of solvation and hydrogen bonding on the hyperfine splitting constants of a free radical has been derived by obtaining r-electron spin densities of the radical in solution by perturbation theory. When no hydrogen bonding occurs between the radical and a solvent molecule, the splitting constant is approximately proportional to the Block and Walker parameter of @(e,) 3e, (In t,)/(e, In t, - tr + 1)- 6/(ln e,) - 2, where 6 is the relative permittivity of the solvent. The expression is succe&sfulyapplied to the di-tert-butyl nitroxide radical, the l-methyl-4-(methoxycarbonyl)pyridinyl radical, and other free radicals. The effects of hydrogen bonding are discussed.
Introduction There are several theoretical studies of solvent effects on hyperfine splitting constants in ESR spectra. The mechanism of charge transfer from the lone-pair electrons of the oxygen atom in a phenoxy1 radical to vacant levels of a solvent molecule was theoretically taken into consideration by Aono and Suhara.' Claxton and McWilliams2 treated all the solvent effects on spin densities in benzosemiquinone anion radicals by changing integral parameters in the LCAO MO method. Griffith et al.3considered the solvent effects on the nitrogen hyperfine splitting constant of the di-tert-butyl nitroxide radical by calculating the change in a-electron density on the nitrogen atom by first-order perturbation theory. They used the Onsager reaction field as a field acting on the a electrons in the radical. By regarding the field due to the solvent as a single external point charge, Spanget-Larsen4calculated the effects of solvation and hydrogen bonding on the splitting constant of the nitrogen atom in an anion radical within the INDO approximation. Recently, Reddoch and Konishi6 obtained a good result for the di-tert-butyl nitroxide radical by using a field due to only a dipole moment of one solvent molecule instead of various reaction fields. The a-electron system of this radical is considerably shielded by two bulky tert-butyl groups from other solvent molecules. All the theoretical treatments proposed hitherto are limited to the individual radicals and do not give an expression generally applicable to the anion or neutral radicals. In the present work, therefore, an attempt has been made to derive a general expression for the effects of solvation and hydrogen bonding on the hyperfine splitting constants of neutral radicals. This will be done by obtaining a-electron spin densities of the radical in solution by first-order perturbation theory. Theoretical Section The ESR spectra of free radicals showing well-resolved hyperfine splittings are usually taken at very low concentrations. Let us consider, therefore, a solution consisting of numerous solvent molecules and one free (neutral) (1) Aono, S.; Suhara, M. Bull. Chem. SOC. Jpn. 1968, 41, 2553. 1968,64,2593. (2) C b n , T. A.; McWilliams, D. Trans. Faraday SOC. ( 3 ) Griffith, 0. H.; Dehlinger, P. J.; Van, S. P.J. Membr. Biol. 1974, 15, 159. (4) Spanget-Larsen, J. Mol. Phys. 1976, 32,735. (5) Reddoch, A. H.; Konishi, S. J . Chem. Phys. 1979, 70, 2121. 0022-3854/82/2088-1358$01.25/0
radical having a a-electron system. For convenience, let the origin of the coordinates be the center of mass of the radical. Effects of the electric and magnetic fields applied to measure the ESR spectrum are ignored in the present treatment. We confine our attention to the a-electron system consisting of m a electrons and n core atoms. The sum of m and n is denoted by N . Let us denote the charge and position vector of the jth particle of these N particles by ej and rj, respectively. The interaction energy W of the system of the N charged particles with an external field due to the solvent is written as N
W = Cej$(rj) j=l
(1)
Here $(rj)is a potential acting on ej owing to the presence of the solvent. As is well-known? $(rj)can be expanded in a Taylor series in terms of the value and derivatives of $(O) at the origin. Neglecting terms higher than the second in the series, we obtain N
+ rj-grad $(O)]
W = Cej[$(O) j=l
(2)
Here -grad $(O) is an electric field R at the origin owing to the presence of the solvent. Since Z e j = 0 for the neutral radical, eq 2 becomes N
W = -CejrYR j=l
(3)
Let us write the perturbation 7f' for the one-electron Hamiltonian operator in the Huckel MO method as H' = H', + 7 f r 2 (4) Here %', is due to the field R and is written according to eq 3 as H', = eR-r (5) In eq 4,Ff'2 is the perturbation corresponding to changes in the Coulomb integral a, at the rth atom and in the resonance integral 0, at the r-s bond by 6a, and 6&, respectively, as a result of the hydrogen bonding between the rth atom and the solvent molecule. We can express &a,and 60, as (6) For example: Davies, D. W. "The Theory of the Electric and Magnetic Properties of Molecules";Wiley: New York, 1967; p 264.
0 1982 American Chemical Society
The Journal of Physical Chemistry, Vol. 86, No. 8, 1982 1359
Solvent Effects on Free Radlcals ( ~ r l 7 f ' d ~ r=) S u r
(6) ( ~ r l % ' n l ~ A= W r s (7) Here xr is the rth AO. The kth MO for the n-electron system of the radical in the vapor is written as n $Oh
=
We assume that orthonormality of From eq 4-8, we obtain ($okls'l$OI) = n
eR p'l
n
n
CCokpCo&(xplrld S=l
(8)
xcokrXr r=l
(dokl$OI)
= 6kl.
n
+ p=l C sC= cl o k p c o & ( X p ~ ~ ' 2 1 X s )(9)
If the terms involving (x,lrlx)for p # s are neglected, eq 9 is reduced to n
($"k1%'l#"I)
n
= e R C cokpcoIprp+ C c o k p c o l p 6 f f r P=l
n
C
n
Pel
+
+ cok&oIp)6bps (10)
~(cokpco& p=l s=l
where (x,lrlx ) is written as rp,because the integral coincides with t i e coordinates (r,) of the pth atom. Even if we average the sum of the terms relating to the positive core charges in eq 3 per electron and add the average of (-Cj=lnejr,-R)/m to 7ff,the average does not contribute to (f$'kl%+#JOI) for k # 1 because of the orthonormality of the MOs. An energy level for (bok is denoted by t o k e From fust-order perturbation theory, the corresponding MO for the r-electron system of the radical in solution is written as
where
In view of the formal expression $k = C C k r X r in eq 11, Ckr can be regarded as a coefficient for the radical in solution.
From eq 12 we approximately obtain
The hyperfine splitting constant arHfor the hydrogen bonded to the rth carbon atom is given by' arH = Q C H ~ P : (14) where p: is the n-electron spin density at the rth carbon in the n-electron system in the solution and QCHH is a cr-r parameter. Since p: = Ck:, the following equation is obtained from eq 10, 13, and 14:
n
(7) McConnell, H. M. J. Chem. Phys. 1966,24,761.
When no hydrogen bonding occurs between the radical and the solvent, the third and fourth terms in the brackets of the right-hand side of eq 15 vanish. The third term is similar to the expression given by Aono and Suhara.l Here we assume that the radical is contained within a spherical cavity with radius a in an isotropic continuous medium of the solvent whose relative permittivity is denoted by e,. The center of the cavity is assumed to be located at the origin. Moreover, let us assume a point dipole pRat the origin for a permanent dipole moment of the radical. Then, the external field R due to the presence of the solvent is considered to be the reaction field of the charges induced by pR on the cavity surface. As described below, we adopt the Block and Walker reaction field8 as R and obtain R = (pR/a3)e(%)
(16)
where
e(t,)
3 ~ In , E, - - -6 cr In t, - t, + 1 In e,
2
(17)
Thus, according to eq 15-17, arHwould be proportional to e(t,) when the radical forms no hydrogen bond with the solvent molecules. Moreover, if Q c H H is known, ( c o k r ) 2 could be experimentally estimated from an intersection of a straight line obtained by plotting arHagainst O(e,).
Discussion A feature of the present theoretical treatment lies in obtaining not a solvation energy but the coefficients of the highest occupied MO for the ground state of the radical, whereas many other theories for the solvent effects on phenomena such as frequency shifts of electronic spectra are characterized by obtaining the solvation energies of states of the solute. Accordingly, the present treatment will be useful to other problems related to solvent effects on the Coefficients and energies of the MO's of the solutes. Strictly speaking,the electric and magnetic fields applied to measure the ESR spectrum must be considered, though they are completely neglected in the present treatment. In eq 15, R can be replaced by other reaction fields due to pRor by a field due to permanent dipole moments of the solvent molecules around the radical. Such replacements do not contain a dispersion effect. In the present treatment, therefore, the dispersion effect is not considered. Consequently, eq 15 cannot be applied to the free radicals having no or small permanent dipole moments. When the solute and solvent molecules having large dipole moments are tightly oriented with respect to each other, eq 16 is unfavorable, because the relative permittivity of the solvent would differ from c, in this case. It should be noted that the MO ( $ k ) given by eq 11 is not normalized. This leads to the unfavorable expectation that eq 15 gives too large a change in the arHvalue with increasing perturbation. According to the theory of Karplus and Fraenkel: the expression for the nitrogen hyperfine splitting constant is complicated. The present method can be extended to the nitrogen hyperfine splitting by applying eq 13 to the nitrogen, oxygen, and adjacent carbon atoms, as will be shown below. On the assumption that Cokr is larger than the second term in eq 12, eq 13 is obtained. When the value of Cokr is very small in eq 12, it will frequently happen that C o k r (8)Block, H.; Walker, S. M. Chem. Phys. Lett. 1973, 19, 363. (9)Karplus, M.; Fraenkel, G . K. J. Chem. Phys. 1961, 35, 1312.
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The Journal of phvslcal Chemistry, Vol. 86, No. 8, 1982
cannot be approximated by eq 13. In this w e , eq 12 must be used without the approximation. Accordingly, in the case of the radical forming no hydrogen bond with the solvent, we must use the following equation instead of eq 15:
As mentioned above, besides the Block and Walker reaction field, the famous Onsager reaction field,'O an ellipsoidal cavity reaction field," Fulton's reaction field,12and Wertheim's reaction field5J3can be used for R in eq 15 and 18. Onsager's, Block and Walker's, and Wertheim's reaction fields have been examined by Reddoch and Konishi for the di-tert-butyl nitroxide r a d i ~ a l . ~Fulton's and Wertheim's theories are evolved for the systems of a cubic lattice and a nonpolar fluid, respectively. Therefore, these reaction fields were not chosen as R in the present treatment, because we apply eq 15 and 18 not to crystalline systems but to solutions consisting of not only nonpolar solvent molecules but also polar ones. Application of the ellipsoidal reaction field is difficult in finding shape factore for ellipsoidal solute molecules. For the derivation of the simplest Onsager reaction field, the local relative permittivity, apparently different from the bulk relative permittivity (E,), is not considered. According to Kober and Fitts," the local relative permittivity around a molecule is considerably lower than the bulk one. It is wellknown that the Onsager reaction field saturatea too quickly as a function of +I6 The Block and Walker reaction field derived from simply taking the local relative permittivity into account does not saturate like the Onsager one5@and can be easily applied. Abboud and TafP found that the Block and Walker reaction field is much improved as compared with the Onsager one in description of experimental results for solvent effects on several phenomena. The values of e(€,) at 20 "C for many common solvents have been reported by them. Thus, we use the Block and Walker reaction field as R in the present treatment. When the u-electron system is screened by bulky groups as in the case of di-tert-butyl nitroxide radical, all the solvent molecules around the radical do not interact to the same degree with the u-electron system, because the distances from the center of the radical to that of the solvent molecules vary with the respective solvent molecules. When only one of the solvent molecules around the radical interacts mainly with the system, the field due to the solvent molecule may be approximately used as R. Moreover, if the interaction between p~ and the permanent dipole moment ps of the solvent molecule is not strong enough to align them with respect to each other, the field must be averaged over all orientations between them as done by Reddoch and K ~ n i s h i . ~ Application Di-tert-butyl Nitroxide Radical. The solvent effects on the nitrogen hyperfine splitting constant aN in the di(10)Oneeger, L.J . Am. Chem. SOC.1936,58,1486. (11)Bt&t&r, C.J. F.; Van Belle,0. C.; Bordewijk, P.; Rip, A. "Theory of Electric Polarization"; Elsevier: Amsterdam, 1973; Vol. 1, p 129. (12)Fulton, R.L. J. Chem. Phys. 1976,62,3676. (13)Wertheim, M.S.Mol. Phys. 1973,25,211. (14)Kober,F. P.; Fitts, D. D. Electrochim. Acta 1966,11,641. (15)For example, see ref 5 and 16. (16)Abboud, J.-L. M.;Taft, R. W.J. Phys. Chem. 1979,83, 412.
Abe et at.
Figure 1. Energy levels and Hkkel MOs for di-tert-butyl nitroxide in the vapor state.
tert-butyl nitroxide radical have been theoretically investigated by Griffith et aL3 and especially by Reddoch and K ~ n i s h i .In ~ the present application, all the data used are taken from those of Reddoch and Konishi6 Among the 34 nonpolar and polar solvents used by them, there are those that seem to interact with the radical or for which relative permittivities at 20 "C cannot be found. For example, butylamine and nitromethane (a Brornsted acid) probably interact with the radical. These unfavorable solvents were omitted. Accordingly, 20 solvents from their nonpolar and polar solvents and chlorobenzene from their anomalous solvents were selected as solvents that formed no hydrogen bonds. The data of dichloromethane, ethanol, methanol, and water were used for those affected by the hydrogen bonding. Almost all the values of e(tJ for these solvents were taken from the paper of Abboud and Taft.I6 The energy levels and Hiickel MO's for the very small u-electron system of the di-tert-butyl nitroxide radical are shown in Figure 1. Of course, there is the relation ( c O ~ ) + = 1. Since the electronegativity of oxygen is greater than that of nitrogen, there is the relation coo > CON. Although the theoretical expression for the nitrogen hyperfine splitting constant is complicated: aNis experimentally expressed as1' aN = (23.9 G)pR + (3.6 G)p&
(19)
From eq 15 and 19, we obtain aN = 23.9 G - (20.3 G)(cON)~ + (40.6 G)eR(CoN)2[1-
Here it is assumed that the oxygen atom in the di-tertbutyl nitroxide radical forms a hydrogen bond with a protic solvent molecule and that only the Coulomb integral for the atom changes by 6ao because of the hydrogen bond. The value of 6ru0 is negative, because the electronegativity of the oxygen atom playing a role of hydrogen acceptor would increase in forming the hydrogen bond with the protic solvent molecule. We assume that the vectors of PR and r N - ro are in the same direction, because the di-tert-butyl nitroxide molecule has approximately Czu symmetry, and its permanent dipole moment of 3.08 D18 (1 D = 3.333 X C m) is probably due mainly to that (2.7 Dig) of the N-0 bond. Putting eq 16 into eq 20, we find that aN should be proportional to e(€,) for the aprotic solvents. According to eq 20, aNshould become much greater for the solvents forming the hydrogen bonds, since 6ruo < 0 and toz- eo1 > 0. Murata and Mataga18 have already stated that the hydrogen-bondinginteraction will increase aNconsiderably. The plot of the aN values (aNoW)vs. the e(€,) values is shown in Figure 2. The relationship between these values agrees with the theoretical expectation based on eq 20. The correlation for the aprotic solvents is fairly good as already found by Reddoch and Konishi.s (17)Cohan, A. H.;Hoffman,B. M. J. Phys. Chem. 1974,78,1313. (18)Murata,Y.;Mataga, N. Bull. Chem. SOC.Jpn. 1971, 44, 354. (19) Vasserman, A. M.; Buchachenko, A. L.; h t s e v , E. G.; Nieman, M. B.J. Struck Chem. 1965,6, 445.
~
The Journal of phvsicel Chemistry, Vol. 86,No. 8, 1982 1361
Solvent Effects on Free Radicals
11.0.
17'5---1 -
17.0
9.0
0
15.0' 0
'
0.1
'
0.2
'
0.3
e w
'
0.4
'
0.5
'
0.6
~lguo 2. plot of aNw vs. B(e,) for dl-tert-butyi nitroxide. The plots denote nonpolar (O),aprotic polar (a),and potic solvents (O), respectively. The straight line is a Ieast-squares fit for the data of 21 aprotic sohrents6
Reddoch and K0nishi6have used the following averaged field due to the permanent dipole moment ps of the nearest solvent molecule lying on the axis of the N-0 bond
R=
=( coth - $) 4ue& x
where = ~ P N O P ~ / [ ( ~ ~ % ) ~ T ~ I(22) Here k is the Boltzmann constant, T, the temperature, 6, the permittivity of vacuum, pNO, the dipole moment of the N-0 bond, and r, the distance from the center of the nearest spherical solvent molecule to that of the N-O bond. Application of eq 21 to the nonpolar solvents leads to R = 0, because eq 21 is derived by considering only the dipole-dipole interaction between the dipole moments of the radical and solvent molecule. In order to avoid R = 0 for the nonpolar solvents, we consider a dipole induced at the solvent molecule owing to the presence of pNp An isotropic polarizability of the solvent molecule is denoted by as, which is given by the Clausius-Mossotti equation. Since the induced dipole moment is 2pNOcyS/kqf, we add the field due to the induced dipole moment to eq 21 and obtain MPr ns2 - 1 X
where NAis the Avogadro constant and MP, 8,and % are the relative molecular weight, density, and refractive index, respectively, of the solvent. In addition to the dipoledipole interaction, the interaction between the dipole of the radical and the induced dipole of the solvent molecule is taken into consideration for eq 23. In application of eq 23 to eq 20, almost all the values of ps were taken from ref 16, and r was taken as r = rN0/2 ro + (3M:/4~N~d~)l/~, where NO is the length of the N 4 bond and ro is the van der Waals radius of the oxygen atom. We adopted rN0 = 1.3 A,5 ro = 1.4 A, and p N 0 =
+
0.1
0.2 0.3
0.4
0.5
s
Flgurr 3. Plots of aNw vs. &e,) for (a) diphenyl nitroxide and (b) dl-p-anisyi nitroxide in aprotic solvents.2'
2.7 D.6 Equation 20, into which eq 16 or 23 was put, was fitted to the data as a function of the corresponding solvent parameter by the leashquares method, and the constants characteristic of the radical in the equation were obtained. By using these constants, we calculated the nitrogen hyperfin splitting constants (aNdd). Correlations of aNa with aNowwere fairly good: We obtained the values of 0.921 and 0.025 for the correlation coefficient and covariance, respectively, in the case of eq 16 and corresponding values of 0.924 and 0.025 in the case of eq 23. The field of eq 16 may be regarded as being derived from taking all the solvent molecules into account, while that of eq 23 is due to only one solvent molecule lying on the axis of p N p Consequently, eq 16 and 23 are two extreme fields. Although the two tert-butyl groups are bulky, it is hardly considered that the N-O bond of the radical is completely screened by them from all the solvent molecules except the nearest one lying on the axis. In view of the correlation coefficients, an actual field is probably somewhere between the two extreme fields in the present case. According to eq 20,the intersection of the line expressed by aNdd = (15.08 f 0.03) G + [(1.22 f 0.08) G]19(e,) in Figure 2 gives the value of 0.695 as coN. The estimations C O N = 0.695 and cog = 0.752 support the canonical structurem for the radical. Diphenyl Nitronide and Di-p-anisyl Nitroxide Radicak The Block and Walker reaction field may be appropriate for the diphenyl nitroxide and di-p-anisyl nitroxide radicals, because their r-electron systems are not screened by any bulky group. Plots of the nitrogen hyperfin splitting constants (aNow)21 vs. e($) are shown in Figure 3. By the least-squares method we obtain the relationships aNdd = (9.06 f 0.09) G + [(2.44 f 0.29) G]B(t,) and aN- = (9.61 f 0.04) G + [(2.01f 0.15) G]O(+) for the diphenyl nitroxide and di-p-anisyl nitroxide radicals, respectively. The correlation coefficients between aNowand a"are 0.908 for the diphenyl nitroxide radical and 0.959 for the di-p-anisyl nitroxide radical. These correlations are good. According to eq 19, the first terms (9.06 and 9.61 G) in the above expression for a N d d approximately correspond to the (20)Knauer, B. R.;Napier, J. J. J. Am. Chem. SOC.1976,98,4396. (21)Mukai, K.;Niehiguchi, H.; Ishizu, K.; Deguchi, Y.; Takaki, H. Bull. Chem. SOC.Jpn. 1967,40, 2731.
1382
Abe et al.
The Journal of Physical Chemishy, Vol. 86, No. 8, 1982
I
0
01
02
03
e(€,)
04
05
I 06
Fbwe 4. pkts of la "J vs. &+) for 2 , 6 d k t & p @ in aprotlc solvents:z' (a) a "(C, or C5): (b) a "(CH,).
+
values of (23.9G)pV (3.6 G)pV,where pko and pB0 are the spin densities at the nitrogen and oxygen atoms, respectively, of the N-O bonds in the radicals in the vapor. According to Ayscough and SargentPaa set of their results calculated by the Hiickel method gives pho = 0.31121 and p r = 0.413 78 for the diphenyl nitroxide radical. These spin densities give the value of 8.93 G for (23.9G)&' + (3.6G)pBo,showing an agreement with 9.06 G. 2,6-Di-tert-butyl-4-methylphenoxyl Radical. Plots of w. the hydrogen hyperfine splitting constants laHo~lzl for the di-tert-butyl-4-methylphenoxyl radical in aprotic solvents are shown in Figure 4.23 By the least-squares method, we obtain the relationships laH (CHJl = (10.87 f 0.02 G ) + (1.34f 0.08 G)e(t,) and la d ( C 3 ) l = (1.72 f 0.01 G ) - (0.24f 0.04 G)O(t,). The correlation coefficients between laHoMland l a H d lare 0.970 for the CH3 hydrogen and 0.841for the C3hydrogen. The correlations ~ e(€,) are good. of a H owith l-Methyl-4-(methoxycarbonyl)pyridinyland 1 Methyl-4-acetylpyridinylRadicakr. Plots of the hydrogen and nitrogen hyperfine splitting constants ( 1 ~ ~ vs.~ e(%) for the 1-methyl-4(methoxycarbonyl)pyridinyl(1)and l-methyl-4-aceQlpyridinyl(2)radicals are shown in Figures 5 and 6. The correlation between the values of I u , ~ land e(e,) is good except for the benzene solvent. Only for the benzene solvent do the plots considerably deviate from the corresponding lines obtained by the leasbsquarea method. The deviations are probably due to a specific interaction such aa a charge-transfer mechanism between these radicals and the electron-donating benzene molecule since the pyridine rings of these radicals may have positive charges
"0
01
02
0.3- 0.4 WEr)
05
06
Flguro 5. Plots of la -1 vs. e(€,) for l-methyi-4+"exycarbonyl~ pyridinyl In aprotlc s o l ~ e n t s :(a) ~ ~a ~"(~C,~or C6);(b) a "(OCH,); (c) a YC, or Ce);(d) a "(NCH,); (e) a '. The letter B denotes a value for benzene solvent.
5F
4
v
(22) Ayncough, P. B.; Sargent, F. P. J. Chem. SOC.B 1966,907. (23) In the CBBB of the hydrogen bonded to the ring carbon atom, the relation of QmH< 0 is well-knownand leads to that of a,".< 0.acCofding to eq 14. Although aHoWis alwaya positive, it is used as bemg identacally equal to a,Hin eq 15. Accordingly, absolute values are taken for aHoM and QcwHin the preaent paper. (24) Kubota, So;Ikegami, Y. J. Phys. Chem. 1978,82, 2739. (26) The hyperfine splitting constanta of l-methyl-rl-(methoxycarbony1)pyridinyI and 1-methyl-4-acetylpyridinylradicals in hexane, ether were measured in the same wav aa in cyclohexane, or diisoDroDY1 ref 24. (26) Groeei, L.; Minisci, F.; Pedulli, G. F.J. Chem. SOC.,Perkin Trans. 2 1977,943.
__
2
1 ) ~ ~
1
0 0
0.1
02
03
04
05
06
BE,) F~~w 8. oPlots of vs. 8(+)for l-m&yl4acetytpyMinyi In aprotk solvents:2c" (a) a (C,or C8): (b) a "(acetyl): (c)a YC, or C,,); (d) a "(NCH,); (e) a '. The letter B denotes a value for benzene solvent.
owing to the presence of electron-attracting methoxycarbonyl or acetyl. In Figures 5 and 6 the values of JaHo~(C or3C,)l for 1 and 2 are small and vary with the or C,)l, therefore, it is solvents. For the case of JaHow(C3 better to use eq 18 than eq 15 in the form
Solvent Effects on Free Radicals
The Journal of Physical Chemistry, Vol. 86, No. 8, 1982 1363
TABLE I: Hyperfine Splitting Constants of 1 and 2 in the Vapor and Their Dependence on the Solvents Pkr
hfs constant for the vapor" compd a H o r a N 1 aH(C20rC,)
a
I/G
4.37 4.29 aH(C3or C,) 0.07 (0.12) 0.00 (0.06) UN 6 22 UH(NCH, ) 5.27 aH(OCH3) 0.76 2 aH(C, or C,) 4.24 3.66 aH(C3or C,) 0.32 (0.38) -0.09 (0.03) UN 5.86 ~H(NCH,) 5.06 aH(CCH,) 1.20 IQcHHI= 23 G and Q c c ~ =, 27 ~ G.
IIIQH iC 0.190 0.187 0.003 (0.005) 0.000 (0.003)
rth atom related C, or C,
S/Gd
-1.71 -1.73 1.54 C, or C, 1.57 0.20 N, 0.79 N, 0.30 0, 0.184 -1.94 C, or C, 0.159 -2.23 0.014 (0.017) 1.95 C, or C, -0.004 (0.001) 1.95 -0.31 N, N; 0.64 0.044 C, 2.86 From eq 15 (eq 24). Equal to (c'kr)'.
PT e
.
0.1430 0.0110 0.1830 0.1830 0.0124 0.1137 0.0272 0.1647 0.1647 0.2461
-0.0638 0.0841 -0.0796 0.0621 0.0044 0.0044 -0.0199 -0.0624 0.0979 -0.0782 0.0507 0.0097 0.0097 -0.1001
Solvent dependency.
-
.
-0.2666 0.1 388 -0.1367 -0.1367 0.0402 -0.2681 0.1366 -0.1566 -0.1566 0.6064 e
McLachlan
spin density.
As expected from eq 15, intersections (I)of the straight lines and the vertical axis obtained from Figures 5 and 6 provide the corresponding hyperfine splitting constants (lQl(cokr)2) of the radicals in the vapor. Each slope (S) of these lines shows a dependence of the hyperfine splitting constant on the solvent and is related to S=
(~~PR-PLJ~~)IQI
(25)
where
Here k , can be calculated by using results of Huckel MO calculations on 1 and 2. The values of I and S estimated from Figures 5 and 6 are listed in Table I. In the table, only the values of I/lQcHHIand I/lQccH,HLarelisted, because the values of QN, QNCH,H, and QOCH are unknown in the present cases. The value of I / l Q c c H ~was l obtained on the assumption that the hydrogen hyperfine splitting constant for the methyl group is simply proportional to the spin density of the atom to which the methyl group is bonded. In order to account qualitatively for the values of I/lQHI (or I) and S, Hackel MO calculations were made on the radicals. The atomic coordinates and Huckel MO parameters used for the r-electron systems of 1 and 2 are listed in Table 11, where hyperconjugationof the methyl groups was neglected. The parameters used are the same as in the previous paper." The results of calculations for McLachlan spin densities (p:") and the C(kr values for the related atoms are shown in Table I. The values of I/lQHI should be equal to the corresponding spin densities. In Table I, all the values of I / lQcHHl are relatively correlated to the McLachlan spin densities. The I values for aN,aH(NCH3),and aH(OCH3) seem to be correlated to the McLachlan spin densities. Only the McLachlan spin density a t the 7-carbon in 2 is too large in comparison with the value Of I/lQwH,Hl. Steric hindrance between the hydrogen atom of the acetyl group and the hydrogen at the 3- and 5-carbon in 2 was inferred to occur on the basis of CPK model building. The calculation on 2 in Table I was made by neglecting the hyperconjugation of the methyl group in the acetyl group and by assuming a planar conformation for 2. So that the effects of the hyperconjugation and steric hindrance could be examined, a calculation in which h7 = 0 and k4,7= 0.9
TABLE 11: Atomic Coordinates" and Molecular Orbital Parametersb for n-Electron Svstems of 1 and 2 atomic coordinate posix/A y/A integralsC tion
'
1 0.00 -2.66 h , = 1.5 2 1.17 -1.95 h , = h , = 0.3 3 1.20 -0.56 h a = 1.0 4 0.00 0.14 h , = 2.0 e 2 5 -1.20 -0.56 k , , 2 = k,, = 1.0 6 -1.17 -1.95 k,,, = 0.b CHI Y 7 0.00 1.60 k,,8 = 1.0 8 -1.06 2.21 k,,9 = 0.8 ' 9 1.18 2.28 " In the case of 2,atom 9 is eliminated, The McLachlan parameter h = 1.2was used. Here and po denote the Coulomb and resonance integrals, respectively, for the carbon atom bonded to the same atom. Coulomb (CY, = a 0 t hrp,) and resonance ( p r s = kr,p,) integrals. *o\c'/o
,b, 7)
were replaced by h7 = -0.5 (an inductive model for CH3) and k4,7= 0.3,respectively, was attempted on 2. The calculation gave a McLachlan spin density of 0.0460 for the 7-carbon. Accordingly, the too large McLachlan spin density at the 7-carbon in 2 in Table I may be due to the neglect of the hyperconjugation and steric hindrance. According to eq 25, each value of S should be mainly correlated to each corresponding value of p b (the pk value along the y axis), which is much larger than that of pkrx for each atom. Table I shows that the S values are roughly correlated to the pkry values except for the cases of aN&d aH(NCH,). In thecase of aN,the S values for 1 and 2 may be accounted for as follows. According to the theory of Karplus and Fraenkel: the nitrogen hyperfine splitting constants of 1 and 2 should be written as aN = Q N p k + ~
Q c N ~ P +E Q C ~ N ~ P E J
(27)
where QN = SN+ 2&cN
+ QNCtN
(28)
Here C and C' denote an adjacent ring carbon atom and an adjacent carbon atom of the methyl group, respectively, SNrepresents the contribution of the nitrogen 1s electrons to the splitting, and QwA is a (M parameter for a nucleus of atom A owing to interaction between a B-C bond and a r-electron spin density on atom C. The values of QBA and QBAAare positive and negative, respectively, and QBA
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The Journal of Physlcal Chemistry, Vol. 88, No. 8, 1982
generally differs from lQBAAlfor A # B? In the present case, p & in eq 27 is taken to be zero, because the hyperconjugation of the methyl groups is neglected. We assume that the same values of QN and QC" for both 1 and 2. Using the McLachlan spin densities for Cok: = pFo and putting the expressions of eq 13 (ck: = p:) for N1, C2,and C6 into eq 27, we have
Abe et al.
D = 0.1647QN+ 0.2274Qc"
ably affected by the hydrogen bonding owing to the presence of the protic solvent molecules of 2-propanol and water. Therefore, their values of QN and QC" cannot be compared directly with the present corresponding values assumed or estimated. The positive S values of aH(NCH3)for 1 and 2 are not correlated to the negative &Ny values. The calculation including the hyperconjugation of the methyl groups for 1 and 2 also gave negative &Ny values. The contradiction may be explained as given below. As to the hydrogen splitting constant of the methyl group bonded to a carbon atom, Underwood and VogeP2 have found a pronounced dependence of the empirical parameter QCCHBH on the excess Huckel charge density on the carbon atom and have presented an empirical relationship. Extending their relationship to the nitrogen atom bonded to the methyl group, we obtain
E = -0.1566QN - 0.5362Qc"
aH(NCH3) = [QNCH?+ J(1 - qN)lp&
If we temporarily assume QN = 58 G and QC" = -16 G, we obtain the following expressions of aN for 1 and 2, respectively, from eq 2 9
where J is a parameter denoting a deviation in the empirical parameter QNcHF and q N is the s-electron density on the nitrogen atom. Smce p k = CkN2 and q N = 2 C z i crN2 + ckN2, eq 31 may be approximately written by using the expression of eq 13 for ciN2 and CkN2 as
aN = D
+ E(2ep~,/a~)8(e,)
(29)
Here, for 1
D = 0.1830QN + 0.2860Qc" E = -0.1367QN - 0.5332Qc" and for 2
aN = 6.04 G
(0.60 G)(!&p~,/a~)8(e,)
(31)
aN = 5.91 G - (0.50 G)(2ep~,/a~)e(c,)
These equations can account for the values of I and S for aN in Table I. As described by B ~ l t o nan , ~estimate ~ of PN+ QNCN is 21.1 G for the 1,2,4,5-tetrazeneanion radiwhere pNrepresents the contribution of spin polarization of the nitrogen lone-pair electrons. Rieger and FraenkeP have given the relation Qc"/QcN'
%
QNC~/QNC'
%
-0.460
(30)
Using QcNc = 14.7 G and QNcc = -47.5 G,%we obtain the estimates QNcN = 21.85 G and Qc = -6.76 G from eq 30. On the assumption that S N + QNC is approximately equal to PN + QNCN, a rough estimate of QN can be made with the use of Q cN = 21.85 G QN = SN+ 2&cN + QNCN a (I"+ QNc$ + 2QNCN= 64.80 G. The value of 58 G temporarily assumed for 8N is close to the estimate of 64.80 G. However, the value of -16 G assumed for QmN is much smaller than the estimate of -6.76 G. Kubota et aL30have reported QN = 42.57 G and QC" = -6.66 G for the anion radicals of heterocyclic amine N-oxides. This QN value is smaller than 58 G. Their s m d @ value seems to be due to small spin densities on carbon atoms bonded to nitrogen atoms in the anion radicals of heterocyclic amine Noxides.g0 In comparison with the spin densities on the carbon atoms in the anion radicals, the corresponding spin densities shown in Table I are comparatively very high. If the spin densities on the carbon atoms in 1 and 2 were very low, the 8N value would be smaller than 58 G, because the D values in eq 29 depend on the spin densities on the carbon atoms in this case. Rakowsky and Dohrmann31 have obtained QN = 25.3 G and QcNN= -2.7 G for the N-hydropyridinyl radical and its related radicals by using their hyperfine splitting constanb measured in 2-propanol containing acetone and water. These constanb are prob-
f
(27)Bolton, J. R. 'Radical Ions";Kaiser, E. T., Kevan, L., Eds.; Interscience: New York, 1968;p 1. (28) Stone, E. W.;Maki,A. H.J. Chem. Phys. 1963,39, 1935. (29) Rieger, P.H.; Fraenkel, 0.K. J. Chem. Phys. 1962 37, 2796. (30)Kubota,T.;Niehikida, K.;Miyazaki, H.; Iwatani, K.; bishi, Y. J. Am. Chem. SOC.1968,90,5080. (31)Rakowsky, T.; Dohrmann, J. Ber. Bonsenges. Phys. Chem. 1979, 83, 495.
Here q o N is the s-electron density on the nitrogen atom N the same as in eq 26, of the radical in the vapor, and C C ~is if k is replaced by i in the equation. The solvent dependence of aH(NCH3)is shown by F. According to Underwood and V0ge1,~~ the J values for aH(CCH3)vary from -5.1 to 105.8 and are almost positive, while the values of QmbHvary from 12.9 to 36.5. The Huckel MO calculation gave for 1 and 2, respectively
Fy = 0.1451J - 0 . 1 3 6 7 Q ~ c ~ ~ ~
Fy = 0.1234J - 0 . 1 1 8 2 Q ~ c ~ ~ ~ In these equations for Fy, we may easily find the J value so that small positive values will be given for 2eRFy of the second term of eq 32. Thus, the positive S values for aH(NCH3)may be accounted for. The absolute value of the sum of HN was smaller than that of PkN The necessity of the above explanation for aH(NCH3)comes from the comparatively large negative values of both &Ny and (1qoN) on the nitrogen atoms of 1 and 2, because in such a case the first term of eq 33 can take the positive sign, different from that of &Ny, as shown above. On the other hand, both the elk, values and the excess charges on atom 9 in 1and on atom 7 in 2 are positive, and so the first terms in the equations corresponding to eq 33 necessarily take the same positive signs as the & , values do. Accordingly, the S values for aH(OCH3)of 1 and for aH(CCH3)of 2 may be simply explained by the corresponding &v values on the atoms bonded to the methyl groups. Conclusion For the field R in eq 15, the Block and Walker reaction field should be used, because the reaction field is derived from simply taking the local relative permittivity of the (32)Underwood, G.R.;Vogel, V. L. J. Chem. Phys. 1969,51,4323.
J. Phys. Chem. 1982, 86, 1365-1371
solvent into account. When the neutral radical forms no hydrogen bonds with the solvent, the expression gives a good linear relationship between the hyperfine splitting constants and the Block and Walker parameters (eq 17)
1305
of the solvents. When the solvent forms hydrogen bonds, the splitting constant9 deviate above the linear lines. The slope and intersection of the line can be qualitatively accounted for by the Huckel MO calculation on the radical.
Hydrogen Bonding Involving the Hexacyanocobaltate( I I I ) Anion. 1. Cobalt-59 Nuclear Magnetic Resonance Studies Donald R. Eaton;
Carol V. Rogerson, and Alan C. Sandercock
Depertmnt of chemlsby, McMester UniversttY, Hemiiton, Ontario L8S 4M1, Canada (Receival: April 28, 1981; In Final Form: October 7, 1981)
sgCochemical shifts,line widths, viscosities, and electronic spectral data are reported for solutions of potassium hexacyanocobaltate(II1)in mixed solvents involving dimethyl sulfoxide,water, formic acid, trifluoroacetic acid, and propionic acid. The chemical shifts cover a range of some 350 ppm, and it in concluded that hydrogen-bonding effects are responsible for the differences. The larger high-field shifts and by inference the stronger hydrogen bonds are associated with the stronger acids. There is evidence for preferential solvation of the hexacyanmbaltate anion in mixtures of dimethyl sulfoxide and acids, but not in waterlacid mixtures. In the dimethyl sulfoxide mixtures the hydrogen bonds become progressively weaker as more acid molecules are incorporated into the second coordination sphere. Interactions with potassium or hydrogen cations do not contribute significantly to the shifts or line widths. The energy of the fmt d-d electronic transition shows parallel changes. The NMR line widths show only modest changes in mixed aqueous solutions, but larger changes (factors of up to several hundred) in dimethyl sulfoxide solutions. Since TIis reduced by a similar factor, “chemical exchange” is not responsible for the broadening. The larger changes in relaxation rate are associated with the formation of the stronger hydrogen bonds. Relaxation rates are not proportional to viscosity, showing that changes in relaxation mechanism rather than simple variations of the correlation time are involved. These results are interpreted in terms of changes in the lifetimes of the hydrogen bonds. The stronger hydrogen bonds (with trifluoroacetic acid) have lifetimes greater than the rotational correlation time of the complex leading to an efficient quadrupolar relaxation mechanism for complexes with unsymmetrically substituted second coordination spheres. Estimates of the quadrupole coupling constants and the rotational correlation times show that this mechanism suffices to account for the observed line widths. The weaker hydrogen bonds (with water) have lifetimes shorter than the rotational correlation times, and other relaxation mechanisms dominate. Formic acid shows intermediate behavior.
Introduction The primary structural feature of a coordination compound is a central metal ion directly bonded to a number of ligands. Additional ligands may also be present not directly bonded to the metal ion, but more weakly held in a second coordination sphere. The nature and the structure of this second coordination sphere are of considerable importance to the understanding of the mechanisms of reactions of metal complexes. The subject has been reviewed by Becks1 Most of the early work in this area was concerned with the participation of ions in the second sphere of charged metal complexes. However, neutral molecules can also function m second-sphere ligands if interactions other than simple electrostatic attraction are involved. Hydrogen bonding offers one obvious mode of interaction, and there is indeed extensive, though scattered, evidence for such complexes in the literaturea2+ There are much more extensive studies of hydrogen-bonding interactions with simpler anions.g (1)M.T.Beck, Coord. Chem. Reu. 3,91 (1968). ( 2 ) B. M.Fung,J. Am. Chem. SOC.,89,5788(1968). (3)A. D.Bain, D. R. Eaton, R. A. Hux, and J. P. K. Tong, Carbohydr. Res. 84,1 (1980). (4) D. Waysbort and G. Navon, J. Phys. Chem., 84,674(1980). (6) S.Kirachner, N. Ahmed, C. Munir, and R. J. Pollock, Pure Appl. Chem., 51, 913 (1979). 0022-3654/82/2086-1365$01.25/0
Data on the enthalphies of formation and lifetimes of second-sphere, hydrogen-bonded complexes are relatively sparse. Enthalphies of 2-3 kcal/mol have been reported for some such complexes,’ but both stronger and weaker complexes are clearly possible in the right circumstances. We have recently initiated studies aimed a t obtaining thermodynamic and kinetic data on hydrogen-bonded, second-sphere complexes. The present paper presents evidence for hydrogen bonding involving the hexacyanocobaltate(II1) anion, compares the effects for several hydrogen donors, and discusses the lifetimes of such complexes. 69C0NMR provides a powerful probe for investigating weak second-sphere interactions. A recent communication8 has pointed out that the chemical shifts are sensitive to hydrogen-bonding effects. The relaxation times are also a potential source of information on the lifetimes of the complexes. The dominant relaxation mechanism for spherically symmetrical Co(II1) complexes has not been unambiguously established, and this leads to some uncertainties in the detailed interpretation. Quadrupolar relaxation, spin-rotation relaxation, and scalar coupling to the nitrogen have all been invoked. (6)L. M.Epshtein,Russ. Chem. Reu. (Engl. Traml.), 48,854(1979). (7)D. R. Eaton, Can. J. Chem., 47,2645 (1969). (8)P.Laszlo and A. Stockis, J. Am. Chem. SOC.,102,7818 (1980).
0 1982 American Chemical Society
