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NMR in paramagnetic complexes of radicals with organic ligands. I. Method of determination of lifetimes and distances in complexes
ChemicalPhysics
0 North-Holland
(1975) 123-129 Publishing Company
NMR IN PARAMAGNETIC DETERMINATION
COMPLEXES
OF LIFETIMES
OF RADICALS
AND DISTANCES
WITH ORGANIC
LIGANDS.
1. METHOD OF
IN COMPLEXES
N.A. SYSOEVA, A. Yu. KARhlILOV and A.L. BUCHACHENKO Inm’rule of Chemical Physics. Academy of Sciences. Rfoscow V.334. USSR Received 15 hlay 1974
A method for determination of lifetimes and distances between the unpaired electron and ligand protons in paramagnetic complexes with stable radicals is developed, which is based on studying tfte viscosity and concentration depeendences of the linewidths in NhIR spectra of the l&and and the complexed radical. The method allows to determine separately the dipolar (DR. DL) and scalar (CR.C,) contributions to the linewidths of the radical and the &and. Roth the isotropic and the anisotropic molecular rotation of the complex are covered by this method, for the latter being only necessary that the anisotropy should not depend on the viscosity. As an illustration, the dipolar and scalar contributions for hydrogen bond complexes of the nitroxyl radical widt methanol, chloroform, cyclohexanol and ethylene glyeol are determined experimentally and the lifetimes and hydrogen bond lengths of the complexes are calculated. The complex rotation was found to be anisotropic. The lifetimes of the complexes as well as the anisotropy of the molecular rotation are shown to be viscosity independent.
l_ Introduction Stable nitroxide radicals (and a great variety of others) were found to form short lived complexes with various organic molecules (ligands) [ l-81. Transfer of spin density on the ligand molecular orbitals produces the paramagnetic shifts of the resonance lines in NMR spectra. The direction and the value of the paramagnetic shift are determined by the sign and the value of the hyperfine coupling constant. The complex formation can also result in paramagnetic line broadening that is governed by time dependent anisotropic and isotropic (scalar) hyperfine interactions (HFI). The paramagnetic shifts and broadenings are a very sensitive probe of the molecular complexation in liquids. Two problems remain to be solved in order that the molecular structure of the radical complex may be established. The fit one is to ascertain what orbitals of the radical and Iigand are pIaced at the disposal of the complex, i.e., what orbitals are involved in the complex formation. In order to solve this problem we developed a special approach which is based on the concept of competition of two or more ligands for the radical
orbitals, the concentration dependence of the patamagnetic shifts and broadenings of the lignds being detected. This approach will be described later. ‘The second problem is to derive the dynamical and structural parameters of the radical complex from the experimental data. In this paper a method ofextracting this information based on the viscosity dependence of the paramagnetic line broadenings of both complexed radical and ligand will be considered. The method is illustrated by studying nitroxide radical complexes with proton donor molecules (alcohols and chloroform). They were shown to be formed under hydrogen bonding between the ligand hydrogen atom and the hybrid sp* lone pair of the oxygen atom of the nitroxide radical [S] (fig. 1).
2. Theory In case tween the conditions Swift and measured
of fast exchange of the solvent molecule bestates of free molecule and l&and under the IIT2,_re * l/T?=; Aw: the well known Konnick equations for the experimentally paramagnetic shift Aw and line broadening
N.A. Sysoevaet al. fNMR in pammagneticcomplexes of mdicolswith
124
organic
T& = 2 nAv,
= fi2+&&r&
+ f 7:&Tex = 2n(&
T?can
of the complex
of the nitroxide
be written as [9] :
Aw = AwrpL.
(1)
T? = T&,
(2)
where TzL is the transverse relaxation time of ligand
protons in complex, T= is the lifetime of the complex, pi is the molar fraction of complexes, and AwL = - d~&~/4k~~.
(3)
At 298 K the paramagnetic shift measured in ppm is 6 L = AwL/wo
= an,
(4)
where (Y= - 7.5 X 10m5 for protons. From the complexation equilibrium R+S$
L
it follows PL =W%lI(~
+Wll.
(5)
Here [R,] is the total radical concentration, (S] is the concentration of free l&and molecules. Combining eqs. (I). (4) and (5) we have [R,] IS = (I/as)
(l/k + IS]).
I
the complexed radical and of the ligand protons are given by
z
Fig. 1. The molecuku model rxlical with methanol.
ligrm&.
(6)
Using this equation the HFI constant and equilibrium constant can be measured from the concentration dependence of the pammagnetic shift. The transverse relaxation times of the protons of
+ P$&)T~
+ C,),
(7)
where 7~ and rL are the correlation times of the anisotropic HFI with the protons of the complexed radical and with the @and protons, ~~~ is the correlation time of the scalar interaction with the radical protons which results fr’om the electron exchange interaction, T, is the lifetime of the complex, p. and pN are the spin densities of the unpaired electron on the p-orbitals of the oxygen and nitrogen atoms of the radical, rOR and rm are the distances between the radical proton under consideration and the oxygen and the nitrogen atoms, ‘0 and fN are the relevant quantities for the ligand protons, D and Care dipolar and scalar contributions to the line broadenings. Eqs. (S)-(8) can also be generalized for the case of other radicals. Substituting eqs. (5) and (8) into (2) we obtain an equation similar to eq. (6): [R,] /Au = (DL + CL)-l
(k-l t [S] ),
(9)
from which value (DL + CL) can be evaluated. Since the scalar contribution to the linewidth of the protons of the complexed radical depends on the radical concentration through 7ex, the values DR and CR in eq. (7) can be determined separately as will be illustrated in the experimental part. The correlation time 7R is attributed to the rotational motion of the complexed radical only, the value of rL depends on the rotational correlation time of the anisotropic HFI with the ligand protons 7c and on the lifetime of the complex 7,:
(10) The reason is that complex formation and decomposition processes modulate an anisotropic as well as isotropic HFI with ligand protons. If the molecular tumbling is assumed to be isotropic, the rotational correlation time TC is identical
N.A. Sysoeva et aLfNh¶R in pammagnetic complexes of mdicalr with organic ligunds I
125
to TRand is given by the Debye formula: rc = 4na3q/3 kT.
(11)
In solutions of low viscosity TV -s$T, and 7L = rC, then according to eq. (8) and (11) the dependence ALQ(~) is linear and the intercept at T)= 0 gives the value of the scalar contribution CL =(1/2a) X f $alre from which the lifetime T, can be evaluated. In a viscous medium 7C increases and becomes comparable to re and finally at high viscosity, when TC 5 I-~ and ‘L = fe, the line broadening reaches the limiting value of (112s) rfi’Y;Y:@Q/~$
+ P&l&
+f 7~~~17,.
The general form of the A.y(q) dependence is shown in fig. 2 and can be used to evaluate the parameters TV ‘0 and fN, providing the values &-, and pN are known. By the procedures discussed above the dipolar and scalar contributions can be determined separately from the experimental data. Now a method of determination of interatomic distances in the complex will be developed which is based on the viscosity dependence of the dipolar contributions D, and D,. Let the parameters DR, DL, 7~. TC refer to the low viscosity region and the relevant parameters with prirnes belong to the high viscosity region where T= and 7e are comparable. For the detailed analysis of the paramagnetic NMR line broadenings of the complexed radical and &and the relation +JT=
= 7K/TR,
(12)
is useful. Relation (12) implies that the molecular rotational motion is isotropic but it is valid also even though the molecular tumbling is an&tropic. The only condition required for (12) to hold in the anisotropic casis that the rotational anisotropy should not depend on the viscosity. As will be shown in the experimental part, this approximation is well satisfied. It should be pointed out that the rotational anisotropy does not disturb the correctness of the calculations given below, because in this case the expressions for the transverse relaxation times are similar to those for the case of isotropic motion, the only difference being that instead of the correlation times TC and 7~ their effective values are used. The latter are determined through the combination of principal components of the rotational diffusion tensor. Relation (12) permits to avoid using the effective correlation times.
Fig. 2. The Av~(q) dependence for the hydroxyl
protons of
cydohexanol. Substituting eqs. (7), (8) (10) into eq. (12), one can derive a formula to calculate the distances r. and IN between the ligand proton considered and the unpaired electron of the radical. In particular for the hydrogen bond distance O...H between the oxygen atom of the nitroxide radical and the hydroxyl proton of the ligand the formula takes the form:
To derive this formula the spin densities PO and PN were assumed to be 0.5; the N-Q distance in the radical was taken to be 1.26 A [lo] ; the term p$r$ was neglected since $, % &_
3. Experimental
resdts
The PMR spectra of the radical (I) and ligands were recorded at room temperature. The spectrometer used was a high resolution Varian 4H-100 model. The paramagnetic shifts were determined
(0 H3C
CH3
126
NA. Sysoeva et al /NMR in panmagnetic complexes of mdicaiswith organicligandrI
with respect to the internal standard [CgHl2; (CH3)3 SiOSi(CH3),] to avoid correcting for the effect of the magnetic volume susceptibility. As a viscous medium Tween 80, not containing functional groups capable of hydrogen bond formation, was used. As was mentioned above, in order to calculate the hydrogen bond length by eq. (13), the knowledge of the dipolar contributions DL, g, DR, Dk and of the lifetime of the complex 7e are required. The procedure of their experimental finding will be described In details below, taking the methanol complexes as an example. From the paramagnetic shifts of the hydrorjl and methyl proton NMR lines in pure methanol and methanol diluted with CC14 the HFI constant “OH and the equilibrium constant k were determined by use of eq. (6) to be -0.75 gauss and 3.5 Q mole-l respectively. ‘Jhe linewidth tiL = DL + CL of the hydroxyl proton in complex was determined from the experimentally observed linewidth Au by eq. (9) and was found to be 1000 Hz in pure methanol. To estimate separately both the dlpolar and the scalar contributions to the paramagnetic broadening, the viscosity dependence of the linewidth was analyzed in solutions of methanol in Cc14 covering the viscosity range from 0.56 to 0.97 CP. In accordance with eqs. (8) and (11) this dependence was shown tq be linear and the extrapolated value was found to be C, = 250 Hz. This value is in good agreement with that (260 Hz) found independently from the measurement of the relaxation times ratio T1/T2 for the hyclroxyl proton of methanol in the presence of radical I 121. Now one can calculate the dlpokr contribution DL = 750 Hz and the lifetime of the compiex Te = 4 X lo-l1 s. The dlpolar contribution Di was measured in solutions of methanol in Tween 8O([S] = 5 mole Q-l, r) = 61 cP). Using eq. (9) Avt was found to be 2690 Hz and therefore Dt = 2440 Hz. (The scalar contrlbution was assumed to be independent of the solvent viscosity, and it will be proven later that this is the case.) The values of DR. CR. 0; were determined from the NMR linewidth analysis of the complexed radical I. For this purpose the isolated low field line was chosen that belongs to the 8-CH2 protons [1 11.It was ascertained preliminarily that the width of this line
depends on the solvent viscosity and therefore the correlation time 7~ of the radical is governed by molecular rotation rather than by intramolecular inversion of the sixmembered ring. Due to the high frequency ring inversion there is only one line in the NMR spectra corresponding to the average position of the axial and equatorial &proton individual lines, the linewidth being
= nfi2+2, + b&d&+
++
K&&
+ P&Q
&/&)l
r’,(U;t,+
Uiq)Tex
TR
= 2R(&
+ c,),
(14)
are the distances bewherero,. rNax. ‘0 , ‘N tween the 0 and N ato% andyhe axial and equatorial &protons; their values are known to be 4.0,2.8,5.0, and 3.8 A, respectively, and were used to calculate 7~ from eq. (14). In fig. 3 the spectral lines of the 6-CH2 protons of the radical I complexed in the undiluted methanol of low viscosity and in the high viscosity solution in Tween 80 ([S] = 5 mole II-‘; B = 61 cP) are shown. The width of this line is Au = DR + CR + M = 110& ([$] = 1.2mole Q-l) in pure methanol. The intermolecular paramagnetic broadening M was determined from the linewidths of amine H,C
CH3
HZ=
NH
“2C
H2C <
H3C
CH2
with
a structure similar to that of the radical and was found to be 30 Hz in the presence of radical I of the same concentration [R,] = 1.2 mole Q-l as in the previous case. As follows from eq. (14), the dipolar contribution to the linewidth of the radical can be determined, provided that the scalar contribution is reduced to a negligible value. This can be obtained by increasing the radical concentration since the correlation time Tcx is controlled by electron exchange lnteraction which is related to the radical concentration as T
cx = ~f(k[R~
I)-‘,
(13
N.A. Sysoeva et aL fh%lR in pammagnetic
complexes
of radicals wirh organic ligands. I
121
Table 1 tigand
CL(b)
D,_(k)
&(Hz)
D&h)
&(&)
CHsOH CHCl3
250 80 800 100
150 700 3700 840
50 45 70 50
2440 2200
185 175 170 320
CsGOH (CH&OHh
Fig. 3. l-k NMR lines of the 6-CHz protons of the radical I in pure methanol and in the meUxmol solution in Tween 80 (IS] = 5 mole P-t).
where k is the diffusion rate constant of the radicalradical encounters, (is the nuclear spin state factor (f= f ), p denotes the exchange probability (for the strong collisions it is very close to 1). The dependence of the linewith AYR on (Rz]-t is expected to be linear and its extrapolation to [R,]-t + 0 gives a dipolar contribution D, = 50 Hz. That this is indeed the case is shown in fig. 4. The scalar and dipolar contributions (CR, DR) were determined for the solutions of radical I in pure methanol and in the viscous solution ([S] = 5 mole II-t; v = 61 cP) in Tween 80 (OK). In the last case the scalar contribution is negligible. A similar approach has been used to analyze the NMR spectra of radical I and hgands other than methanol. The dipolar and scalar contributions which are necessary to calculate the hydrogen bond length with eq. (13) are listed in table 1. For comparison pur-
~8000 4000
poses the values CL. DL and DR as well as Di and 0; were determined for the same solutions. The HFI constants, the lifetimes of each complex and the hydrogen bond lengths calculated with eq. (13) are given in table 2. There appear to exist correhtions between all these parameters: the shorter the hydrogen bond, the higher the HFI constant and the longer is the lifetime of the complex. It should be emphasized that the method of hydrogen bond length determination described above would be much simpler if the molecular rotation of the complex were isotropic. In this case it would be enough to find only the values CL. D,_. CR and DR from the linewidth analysis of the NMR spectra ofthe ligand and the radical in the same solution of low viscosity where 7c & 7, and therefore ~~ = rc.’ Then the correlation time rR can be determined trsiig eq. (14). The equality is isotropic so that Trc - 7’R holds only if the rotation r_ = ‘R and clin be inserted into eq. (8) to calculate the hydrogen bond length from DL.
But even in the case of isotropic rotation the use of relation (12) is more reliable because for the calculation of rR from eq. (14) one should know exactly the spin densities and the distances between the unpaired electron and the proton in the radical. information that is not always available. From the ESR spectra of the complexed radical one can determine the rotational correlation time 7 which is referred to the averagingof anisotropic dipolar Table 2 Ligand
Fig.4. The ALJR([Rs~-‘)
dependence for the NMR line of in methanol.
the 6-CHz protons of the radical 1 complexed
CH3 OH CHCI3 GHIIOH (CH2)2(OHh
a (saws) -0.75 -0.44
-0.89 -0.45
r(A) 1.6 1.7 1.5 1.7
r&I :x” ‘
g:::
8 x lo-” 4 x lo-”
128
NJ. Syooe~ et aL/NhfR in paramagneticcomplexes of tndicalswfth ognnic ligmdz 1
electron-nitrogen nucleus interaction and of the anisotmpy of the g-factor 1121. Providing the rotational motion is isotropic, this time should be equal lo rR as determined from the NMR spectra of the radical by eq. (14). This was shown not to be the case. For example in pure methanol at -70°C 7 alid rR were 6 X lo-t1 s and 2 X IO-*t s respectiveiy; the difference exceeds the possible error in the evaluation of TR from eq. (14). Moreover the activation energies of the molecular rotation estimated from the temperature dependence of 7 and rR are different
also, they are 4 kcal
mole” and 2 kcai mole-l respectively. These results indicate that the molecular rotation is an&tropic indeed. As was mentioned in section 2 relation (12) holds also for the anisotropic motion. The only condition for this relation to be valid is that the tisotropy should not depend on the viscosity. To confirm this idea it is necessary to compare the dipolar contributions DR and DL at different viscosities in the range where 7C 4 T,. For example in pure methanol the values Of DR and DL are 50 Hz and 750 Hz, while in the solution of methanol in CCl4( [S] =2.6 mole 12-l) the corresponding values 0; and Dt are 75 and 145OHz respectively. The ratios are Dk/DR = T~/T~ = 1 S; Di/DL = T&C = 1.9, i.e., relation (12) is satisfied with good accuracy. They are also close to the ratio of the specific viscosities of these solutions which is 1.67. ‘Ihis fact leads to the conclusion that the change of solution viscosity does not effect significantly the anisotropy of the molecular rotation. This result is in accordance
from which le can be calculated. This behaviour is shown in fig. 2 for cyclohexanol and its solutions in CC14 and 7e were found to be 5 X 10-lts in pure cyclohexanol with high viscosity and 8 X IO-I1 s in its solutions with low viscosity. Their comparison is enough to conclude that the lifetime of complexes and therefore the scalar contribution to the paramagnetic line broadening does practically not depend on the viscosity
with results
obtained
4. Dir&on
The method developed in this paper offers a means of determinin g structural and kinetical informations concerning radical complexes in liquid solutions. It is based on analyses of paramagnetic line broadenings in NMR spectra of radicals and ligands and on the study of their viscosity dependence which permits that the dipolar and scalar contributions be separately determined. The procedure is quite universal because it makes possible fmding all the parameters independently of the mode of molecular rotation - isotropic or anisotropic. The method is illustrated in the particular case of complexes with hydrogen bonds. Practically there are no limitations to the use of the method for investigating different radical-l&and complexes, apart from the knowledge of mutual positions of the radical and ligand in the complex. This is the first problem mentioned in section 1 and it will be discussed in the next paper.
by Freed
et al. 1131 from the ESRstudy of the molecular rotation of a stable nitroxide radical, Fremi salt, in media of variable viscosity.
We have suggested before that the scalar contribution CL and therefore the lifetime of the complex 7e are independent of the viscosity of the solution. If this assumption is correct, TV would be expected lo be the same irrespective of whether it is determined from NMR spectra analyses in low or high viscosity solu-
[l]
tions.
Bu&a&enko. zh. sbukt. khim. ij (1972) 419. ISI AS. Gbankin. CM. Zhidomirov and A.L. Buchachenko,
As was derived in section 2, at high viscosity
where ?C * fe and therefore 7L = 7,. the tiaramagnetic line broadening of the ligand reaches a limiting value:
(16)
N-A. Sysoeva. AL. Buchachenko and AU. Stepanyanta.
Zh. Strukt. khim. 9 (1968) 311. [2] N.A. Syaoeva and AL. Buchachenko, Zh. Strukt. khim. 13 (1972) 42. (31 N.A. Sysoeva and A.L. Buchachenko, Zh. Strukt. Khim 13 (1972) 221. 141 _ _ N.A. Sysocva. f.1. Pckhk. E.T. Litwnaa and A.L.
1. Magn. Reson. 9 (1973) 199. [6] 1. Morishima. K. Endo and T. Yonczawa. J. Amer. Chhem. Sot 93 (1971) 2048. [7J 1. Morishima. T. Inubushi. K. Endo, T. Yonezawa and
K. Goto, J. Amer. Chcm. Sot. 94 (1972)4812. 181 1. MoUma. K. Endo and T. Yonezawa. J. Chem. Plays. 58 (1973) 3146.
N-4.
Syweva
et aL/NhlR
in pammagnetic
19) T.J. SW-XC and RE. Connick. 1. Chem. Phys. 37 (1962) 307. [ 101 Par. I. Laszerowia-Bonnetau, Acta Cryst. B (1968) 24. I1 1 I R. Briere, H. Lemaire. A. Rabat. P. Rey and A.
compleres
of radicals with orgunk l@ndx
I
Rousseau, Bull. SW. Chim. France (1967) 4469.
129
[ 121 J. Freed and G. Fraenkcl, J. Chem. Php. 39 (1963) 326. [ 131 A. Goldman, F. Bruno and C. Fblnaszek. J. CInn.
Phys. 56 (1972) 716.
0 North-Holland
(1975) 123-129 Publishing Company
NMR IN PARAMAGNETIC DETERMINATION
COMPLEXES
OF LIFETIMES
OF RADICALS
AND DISTANCES
WITH ORGANIC
LIGANDS.
1. METHOD OF
IN COMPLEXES
N.A. SYSOEVA, A. Yu. KARhlILOV and A.L. BUCHACHENKO Inm’rule of Chemical Physics. Academy of Sciences. Rfoscow V.334. USSR Received 15 hlay 1974
A method for determination of lifetimes and distances between the unpaired electron and ligand protons in paramagnetic complexes with stable radicals is developed, which is based on studying tfte viscosity and concentration depeendences of the linewidths in NhIR spectra of the l&and and the complexed radical. The method allows to determine separately the dipolar (DR. DL) and scalar (CR.C,) contributions to the linewidths of the radical and the &and. Roth the isotropic and the anisotropic molecular rotation of the complex are covered by this method, for the latter being only necessary that the anisotropy should not depend on the viscosity. As an illustration, the dipolar and scalar contributions for hydrogen bond complexes of the nitroxyl radical widt methanol, chloroform, cyclohexanol and ethylene glyeol are determined experimentally and the lifetimes and hydrogen bond lengths of the complexes are calculated. The complex rotation was found to be anisotropic. The lifetimes of the complexes as well as the anisotropy of the molecular rotation are shown to be viscosity independent.
l_ Introduction Stable nitroxide radicals (and a great variety of others) were found to form short lived complexes with various organic molecules (ligands) [ l-81. Transfer of spin density on the ligand molecular orbitals produces the paramagnetic shifts of the resonance lines in NMR spectra. The direction and the value of the paramagnetic shift are determined by the sign and the value of the hyperfine coupling constant. The complex formation can also result in paramagnetic line broadening that is governed by time dependent anisotropic and isotropic (scalar) hyperfine interactions (HFI). The paramagnetic shifts and broadenings are a very sensitive probe of the molecular complexation in liquids. Two problems remain to be solved in order that the molecular structure of the radical complex may be established. The fit one is to ascertain what orbitals of the radical and Iigand are pIaced at the disposal of the complex, i.e., what orbitals are involved in the complex formation. In order to solve this problem we developed a special approach which is based on the concept of competition of two or more ligands for the radical
orbitals, the concentration dependence of the patamagnetic shifts and broadenings of the lignds being detected. This approach will be described later. ‘The second problem is to derive the dynamical and structural parameters of the radical complex from the experimental data. In this paper a method ofextracting this information based on the viscosity dependence of the paramagnetic line broadenings of both complexed radical and ligand will be considered. The method is illustrated by studying nitroxide radical complexes with proton donor molecules (alcohols and chloroform). They were shown to be formed under hydrogen bonding between the ligand hydrogen atom and the hybrid sp* lone pair of the oxygen atom of the nitroxide radical [S] (fig. 1).
2. Theory In case tween the conditions Swift and measured
of fast exchange of the solvent molecule bestates of free molecule and l&and under the IIT2,_re * l/T?=; Aw: the well known Konnick equations for the experimentally paramagnetic shift Aw and line broadening
N.A. Sysoevaet al. fNMR in pammagneticcomplexes of mdicolswith
124
organic
T& = 2 nAv,
= fi2+&&r&
+ f 7:&Tex = 2n(&
T?can
of the complex
of the nitroxide
be written as [9] :
Aw = AwrpL.
(1)
T? = T&,
(2)
where TzL is the transverse relaxation time of ligand
protons in complex, T= is the lifetime of the complex, pi is the molar fraction of complexes, and AwL = - d~&~/4k~~.
(3)
At 298 K the paramagnetic shift measured in ppm is 6 L = AwL/wo
= an,
(4)
where (Y= - 7.5 X 10m5 for protons. From the complexation equilibrium R+S$
L
it follows PL =W%lI(~
+Wll.
(5)
Here [R,] is the total radical concentration, (S] is the concentration of free l&and molecules. Combining eqs. (I). (4) and (5) we have [R,] IS = (I/as)
(l/k + IS]).
I
the complexed radical and of the ligand protons are given by
z
Fig. 1. The molecuku model rxlical with methanol.
ligrm&.
(6)
Using this equation the HFI constant and equilibrium constant can be measured from the concentration dependence of the pammagnetic shift. The transverse relaxation times of the protons of
+ P$&)T~
+ C,),
(7)
where 7~ and rL are the correlation times of the anisotropic HFI with the protons of the complexed radical and with the @and protons, ~~~ is the correlation time of the scalar interaction with the radical protons which results fr’om the electron exchange interaction, T, is the lifetime of the complex, p. and pN are the spin densities of the unpaired electron on the p-orbitals of the oxygen and nitrogen atoms of the radical, rOR and rm are the distances between the radical proton under consideration and the oxygen and the nitrogen atoms, ‘0 and fN are the relevant quantities for the ligand protons, D and Care dipolar and scalar contributions to the line broadenings. Eqs. (S)-(8) can also be generalized for the case of other radicals. Substituting eqs. (5) and (8) into (2) we obtain an equation similar to eq. (6): [R,] /Au = (DL + CL)-l
(k-l t [S] ),
(9)
from which value (DL + CL) can be evaluated. Since the scalar contribution to the linewidth of the protons of the complexed radical depends on the radical concentration through 7ex, the values DR and CR in eq. (7) can be determined separately as will be illustrated in the experimental part. The correlation time 7R is attributed to the rotational motion of the complexed radical only, the value of rL depends on the rotational correlation time of the anisotropic HFI with the ligand protons 7c and on the lifetime of the complex 7,:
(10) The reason is that complex formation and decomposition processes modulate an anisotropic as well as isotropic HFI with ligand protons. If the molecular tumbling is assumed to be isotropic, the rotational correlation time TC is identical
N.A. Sysoeva et aLfNh¶R in pammagnetic complexes of mdicalr with organic ligunds I
125
to TRand is given by the Debye formula: rc = 4na3q/3 kT.
(11)
In solutions of low viscosity TV -s$T, and 7L = rC, then according to eq. (8) and (11) the dependence ALQ(~) is linear and the intercept at T)= 0 gives the value of the scalar contribution CL =(1/2a) X f $alre from which the lifetime T, can be evaluated. In a viscous medium 7C increases and becomes comparable to re and finally at high viscosity, when TC 5 I-~ and ‘L = fe, the line broadening reaches the limiting value of (112s) rfi’Y;Y:@Q/~$
+ P&l&
+f 7~~~17,.
The general form of the A.y(q) dependence is shown in fig. 2 and can be used to evaluate the parameters TV ‘0 and fN, providing the values &-, and pN are known. By the procedures discussed above the dipolar and scalar contributions can be determined separately from the experimental data. Now a method of determination of interatomic distances in the complex will be developed which is based on the viscosity dependence of the dipolar contributions D, and D,. Let the parameters DR, DL, 7~. TC refer to the low viscosity region and the relevant parameters with prirnes belong to the high viscosity region where T= and 7e are comparable. For the detailed analysis of the paramagnetic NMR line broadenings of the complexed radical and &and the relation +JT=
= 7K/TR,
(12)
is useful. Relation (12) implies that the molecular rotational motion is isotropic but it is valid also even though the molecular tumbling is an&tropic. The only condition required for (12) to hold in the anisotropic casis that the rotational anisotropy should not depend on the viscosity. As will be shown in the experimental part, this approximation is well satisfied. It should be pointed out that the rotational anisotropy does not disturb the correctness of the calculations given below, because in this case the expressions for the transverse relaxation times are similar to those for the case of isotropic motion, the only difference being that instead of the correlation times TC and 7~ their effective values are used. The latter are determined through the combination of principal components of the rotational diffusion tensor. Relation (12) permits to avoid using the effective correlation times.
Fig. 2. The Av~(q) dependence for the hydroxyl
protons of
cydohexanol. Substituting eqs. (7), (8) (10) into eq. (12), one can derive a formula to calculate the distances r. and IN between the ligand proton considered and the unpaired electron of the radical. In particular for the hydrogen bond distance O...H between the oxygen atom of the nitroxide radical and the hydroxyl proton of the ligand the formula takes the form:
To derive this formula the spin densities PO and PN were assumed to be 0.5; the N-Q distance in the radical was taken to be 1.26 A [lo] ; the term p$r$ was neglected since $, % &_
3. Experimental
resdts
The PMR spectra of the radical (I) and ligands were recorded at room temperature. The spectrometer used was a high resolution Varian 4H-100 model. The paramagnetic shifts were determined
(0 H3C
CH3
126
NA. Sysoeva et al /NMR in panmagnetic complexes of mdicaiswith organicligandrI
with respect to the internal standard [CgHl2; (CH3)3 SiOSi(CH3),] to avoid correcting for the effect of the magnetic volume susceptibility. As a viscous medium Tween 80, not containing functional groups capable of hydrogen bond formation, was used. As was mentioned above, in order to calculate the hydrogen bond length by eq. (13), the knowledge of the dipolar contributions DL, g, DR, Dk and of the lifetime of the complex 7e are required. The procedure of their experimental finding will be described In details below, taking the methanol complexes as an example. From the paramagnetic shifts of the hydrorjl and methyl proton NMR lines in pure methanol and methanol diluted with CC14 the HFI constant “OH and the equilibrium constant k were determined by use of eq. (6) to be -0.75 gauss and 3.5 Q mole-l respectively. ‘Jhe linewidth tiL = DL + CL of the hydroxyl proton in complex was determined from the experimentally observed linewidth Au by eq. (9) and was found to be 1000 Hz in pure methanol. To estimate separately both the dlpolar and the scalar contributions to the paramagnetic broadening, the viscosity dependence of the linewidth was analyzed in solutions of methanol in Cc14 covering the viscosity range from 0.56 to 0.97 CP. In accordance with eqs. (8) and (11) this dependence was shown tq be linear and the extrapolated value was found to be C, = 250 Hz. This value is in good agreement with that (260 Hz) found independently from the measurement of the relaxation times ratio T1/T2 for the hyclroxyl proton of methanol in the presence of radical I 121. Now one can calculate the dlpokr contribution DL = 750 Hz and the lifetime of the compiex Te = 4 X lo-l1 s. The dlpolar contribution Di was measured in solutions of methanol in Tween 8O([S] = 5 mole Q-l, r) = 61 cP). Using eq. (9) Avt was found to be 2690 Hz and therefore Dt = 2440 Hz. (The scalar contrlbution was assumed to be independent of the solvent viscosity, and it will be proven later that this is the case.) The values of DR. CR. 0; were determined from the NMR linewidth analysis of the complexed radical I. For this purpose the isolated low field line was chosen that belongs to the 8-CH2 protons [1 11.It was ascertained preliminarily that the width of this line
depends on the solvent viscosity and therefore the correlation time 7~ of the radical is governed by molecular rotation rather than by intramolecular inversion of the sixmembered ring. Due to the high frequency ring inversion there is only one line in the NMR spectra corresponding to the average position of the axial and equatorial &proton individual lines, the linewidth being
= nfi2+2, + b&d&+
++
K&&
+ P&Q
&/&)l
r’,(U;t,+
Uiq)Tex
TR
= 2R(&
+ c,),
(14)
are the distances bewherero,. rNax. ‘0 , ‘N tween the 0 and N ato% andyhe axial and equatorial &protons; their values are known to be 4.0,2.8,5.0, and 3.8 A, respectively, and were used to calculate 7~ from eq. (14). In fig. 3 the spectral lines of the 6-CH2 protons of the radical I complexed in the undiluted methanol of low viscosity and in the high viscosity solution in Tween 80 ([S] = 5 mole II-‘; B = 61 cP) are shown. The width of this line is Au = DR + CR + M = 110& ([$] = 1.2mole Q-l) in pure methanol. The intermolecular paramagnetic broadening M was determined from the linewidths of amine H,C
CH3
HZ=
NH
“2C
H2C <
H3C
CH2
with
a structure similar to that of the radical and was found to be 30 Hz in the presence of radical I of the same concentration [R,] = 1.2 mole Q-l as in the previous case. As follows from eq. (14), the dipolar contribution to the linewidth of the radical can be determined, provided that the scalar contribution is reduced to a negligible value. This can be obtained by increasing the radical concentration since the correlation time Tcx is controlled by electron exchange lnteraction which is related to the radical concentration as T
cx = ~f(k[R~
I)-‘,
(13
N.A. Sysoeva et aL fh%lR in pammagnetic
complexes
of radicals wirh organic ligands. I
121
Table 1 tigand
CL(b)
D,_(k)
&(Hz)
D&h)
&(&)
CHsOH CHCl3
250 80 800 100
150 700 3700 840
50 45 70 50
2440 2200
185 175 170 320
CsGOH (CH&OHh
Fig. 3. l-k NMR lines of the 6-CHz protons of the radical I in pure methanol and in the meUxmol solution in Tween 80 (IS] = 5 mole P-t).
where k is the diffusion rate constant of the radicalradical encounters, (is the nuclear spin state factor (f= f ), p denotes the exchange probability (for the strong collisions it is very close to 1). The dependence of the linewith AYR on (Rz]-t is expected to be linear and its extrapolation to [R,]-t + 0 gives a dipolar contribution D, = 50 Hz. That this is indeed the case is shown in fig. 4. The scalar and dipolar contributions (CR, DR) were determined for the solutions of radical I in pure methanol and in the viscous solution ([S] = 5 mole II-t; v = 61 cP) in Tween 80 (OK). In the last case the scalar contribution is negligible. A similar approach has been used to analyze the NMR spectra of radical I and hgands other than methanol. The dipolar and scalar contributions which are necessary to calculate the hydrogen bond length with eq. (13) are listed in table 1. For comparison pur-
~8000 4000
poses the values CL. DL and DR as well as Di and 0; were determined for the same solutions. The HFI constants, the lifetimes of each complex and the hydrogen bond lengths calculated with eq. (13) are given in table 2. There appear to exist correhtions between all these parameters: the shorter the hydrogen bond, the higher the HFI constant and the longer is the lifetime of the complex. It should be emphasized that the method of hydrogen bond length determination described above would be much simpler if the molecular rotation of the complex were isotropic. In this case it would be enough to find only the values CL. D,_. CR and DR from the linewidth analysis of the NMR spectra ofthe ligand and the radical in the same solution of low viscosity where 7c & 7, and therefore ~~ = rc.’ Then the correlation time rR can be determined trsiig eq. (14). The equality is isotropic so that Trc - 7’R holds only if the rotation r_ = ‘R and clin be inserted into eq. (8) to calculate the hydrogen bond length from DL.
But even in the case of isotropic rotation the use of relation (12) is more reliable because for the calculation of rR from eq. (14) one should know exactly the spin densities and the distances between the unpaired electron and the proton in the radical. information that is not always available. From the ESR spectra of the complexed radical one can determine the rotational correlation time 7 which is referred to the averagingof anisotropic dipolar Table 2 Ligand
Fig.4. The ALJR([Rs~-‘)
dependence for the NMR line of in methanol.
the 6-CHz protons of the radical 1 complexed
CH3 OH CHCI3 GHIIOH (CH2)2(OHh
a (saws) -0.75 -0.44
-0.89 -0.45
r(A) 1.6 1.7 1.5 1.7
r&I :x” ‘
g:::
8 x lo-” 4 x lo-”
128
NJ. Syooe~ et aL/NhfR in paramagneticcomplexes of tndicalswfth ognnic ligmdz 1
electron-nitrogen nucleus interaction and of the anisotmpy of the g-factor 1121. Providing the rotational motion is isotropic, this time should be equal lo rR as determined from the NMR spectra of the radical by eq. (14). This was shown not to be the case. For example in pure methanol at -70°C 7 alid rR were 6 X lo-t1 s and 2 X IO-*t s respectiveiy; the difference exceeds the possible error in the evaluation of TR from eq. (14). Moreover the activation energies of the molecular rotation estimated from the temperature dependence of 7 and rR are different
also, they are 4 kcal
mole” and 2 kcai mole-l respectively. These results indicate that the molecular rotation is an&tropic indeed. As was mentioned in section 2 relation (12) holds also for the anisotropic motion. The only condition for this relation to be valid is that the tisotropy should not depend on the viscosity. To confirm this idea it is necessary to compare the dipolar contributions DR and DL at different viscosities in the range where 7C 4 T,. For example in pure methanol the values Of DR and DL are 50 Hz and 750 Hz, while in the solution of methanol in CCl4( [S] =2.6 mole 12-l) the corresponding values 0; and Dt are 75 and 145OHz respectively. The ratios are Dk/DR = T~/T~ = 1 S; Di/DL = T&C = 1.9, i.e., relation (12) is satisfied with good accuracy. They are also close to the ratio of the specific viscosities of these solutions which is 1.67. ‘Ihis fact leads to the conclusion that the change of solution viscosity does not effect significantly the anisotropy of the molecular rotation. This result is in accordance
from which le can be calculated. This behaviour is shown in fig. 2 for cyclohexanol and its solutions in CC14 and 7e were found to be 5 X 10-lts in pure cyclohexanol with high viscosity and 8 X IO-I1 s in its solutions with low viscosity. Their comparison is enough to conclude that the lifetime of complexes and therefore the scalar contribution to the paramagnetic line broadening does practically not depend on the viscosity
with results
obtained
4. Dir&on
The method developed in this paper offers a means of determinin g structural and kinetical informations concerning radical complexes in liquid solutions. It is based on analyses of paramagnetic line broadenings in NMR spectra of radicals and ligands and on the study of their viscosity dependence which permits that the dipolar and scalar contributions be separately determined. The procedure is quite universal because it makes possible fmding all the parameters independently of the mode of molecular rotation - isotropic or anisotropic. The method is illustrated in the particular case of complexes with hydrogen bonds. Practically there are no limitations to the use of the method for investigating different radical-l&and complexes, apart from the knowledge of mutual positions of the radical and ligand in the complex. This is the first problem mentioned in section 1 and it will be discussed in the next paper.
by Freed
et al. 1131 from the ESRstudy of the molecular rotation of a stable nitroxide radical, Fremi salt, in media of variable viscosity.
We have suggested before that the scalar contribution CL and therefore the lifetime of the complex 7e are independent of the viscosity of the solution. If this assumption is correct, TV would be expected lo be the same irrespective of whether it is determined from NMR spectra analyses in low or high viscosity solu-
[l]
tions.
Bu&a&enko. zh. sbukt. khim. ij (1972) 419. ISI AS. Gbankin. CM. Zhidomirov and A.L. Buchachenko,
As was derived in section 2, at high viscosity
where ?C * fe and therefore 7L = 7,. the tiaramagnetic line broadening of the ligand reaches a limiting value:
(16)
N-A. Sysoeva. AL. Buchachenko and AU. Stepanyanta.
Zh. Strukt. khim. 9 (1968) 311. [2] N.A. Syaoeva and AL. Buchachenko, Zh. Strukt. khim. 13 (1972) 42. (31 N.A. Sysoeva and A.L. Buchachenko, Zh. Strukt. Khim 13 (1972) 221. 141 _ _ N.A. Sysocva. f.1. Pckhk. E.T. Litwnaa and A.L.
1. Magn. Reson. 9 (1973) 199. [6] 1. Morishima. K. Endo and T. Yonczawa. J. Amer. Chhem. Sot 93 (1971) 2048. [7J 1. Morishima. T. Inubushi. K. Endo, T. Yonezawa and
K. Goto, J. Amer. Chcm. Sot. 94 (1972)4812. 181 1. MoUma. K. Endo and T. Yonezawa. J. Chem. Plays. 58 (1973) 3146.
N-4.
Syweva
et aL/NhlR
in pammagnetic
19) T.J. SW-XC and RE. Connick. 1. Chem. Phys. 37 (1962) 307. [ 101 Par. I. Laszerowia-Bonnetau, Acta Cryst. B (1968) 24. I1 1 I R. Briere, H. Lemaire. A. Rabat. P. Rey and A.
compleres
of radicals with orgunk l@ndx
I
Rousseau, Bull. SW. Chim. France (1967) 4469.
129
[ 121 J. Freed and G. Fraenkcl, J. Chem. Php. 39 (1963) 326. [ 131 A. Goldman, F. Bruno and C. Fblnaszek. J. CInn.
Phys. 56 (1972) 716.