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ParamagneticResonance Study of Hyperfine Interactions in Single Crystals Containing α,αDiphenylβPicrylhydrazyl Robert W. Holmberg, Ralph Livingston, and William T. Smith Jr. Citation: The Journal of Chemical Physics 33, 541 (1960); doi: 10.1063/1.1731181 View online: http://dx.doi.org/10.1063/1.1731181 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/33/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The spin magnetism of α, α′diphenylβpicrylhydrazyl (DPPH) J. Chem. Phys. 68, 5225 (1978); 10.1063/1.435589 Electron paramagnetic resonance (EPR) and electronnuclear double resonance (ENDOR) of hyperfine interactions in solutions of α, α′diphenylβpicryl hydrazyl (DPPH) J. Chem. Phys. 59, 3403 (1973); 10.1063/1.1680483 Electron Paramagnetic Resonance Absorption Studies of NeutronIrradiated α,αDiphenylβPicryl Hydrazine J. Chem. Phys. 38, 1453 (1963); 10.1063/1.1733877 ParamagneticResonance Studies of Irradiated HighDensity Polyethylene. I. Radical Species and the Effect of Environment on Their Behavior J. Chem. Phys. 33, 395 (1960); 10.1063/1.1731155 Use of ParamagneticResonance Techniques in the Study of Atomic Oxygen Recombinations J. Chem. Phys. 31, 1196 (1959); 10.1063/1.1730570 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.240.225.44 On: Sat, 20 Dec 2014 07:47:41

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Page 1: Paramagnetic-Resonance Study of Hyperfine Interactions in Single Crystals Containing α,α-Diphenyl-β-Picrylhydrazyl

ParamagneticResonance Study of Hyperfine Interactions in Single CrystalsContaining α,αDiphenylβPicrylhydrazylRobert W. Holmberg, Ralph Livingston, and William T. Smith Jr. Citation: The Journal of Chemical Physics 33, 541 (1960); doi: 10.1063/1.1731181 View online: http://dx.doi.org/10.1063/1.1731181 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/33/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The spin magnetism of α, α′diphenylβpicrylhydrazyl (DPPH) J. Chem. Phys. 68, 5225 (1978); 10.1063/1.435589 Electron paramagnetic resonance (EPR) and electronnuclear double resonance (ENDOR) of hyperfineinteractions in solutions of α, α′diphenylβpicryl hydrazyl (DPPH) J. Chem. Phys. 59, 3403 (1973); 10.1063/1.1680483 Electron Paramagnetic Resonance Absorption Studies of NeutronIrradiated α,αDiphenylβPicryl Hydrazine J. Chem. Phys. 38, 1453 (1963); 10.1063/1.1733877 ParamagneticResonance Studies of Irradiated HighDensity Polyethylene. I. Radical Species and theEffect of Environment on Their Behavior J. Chem. Phys. 33, 395 (1960); 10.1063/1.1731155 Use of ParamagneticResonance Techniques in the Study of Atomic Oxygen Recombinations J. Chem. Phys. 31, 1196 (1959); 10.1063/1.1730570

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Page 2: Paramagnetic-Resonance Study of Hyperfine Interactions in Single Crystals Containing α,α-Diphenyl-β-Picrylhydrazyl

THE JOURNAL OF CHEMICAL PHYSICS VOLUME 33, NUMBER 2 AUGUST, 1960

Paramagnetic-Resonance Study of Hyperfine Interactions in Single Crystals Containing a,a-Diphenyl-t3-Picrylhydrazyl

ROBERT W. HOLMBERG AND RALPH LIVINGSTON

Oak Ridge National Laboratory,· Oak Ridge, Tennessee

AND

WILUAM T. SMITH, JR.

Department of Chemistry, University of Tennessee, Knoxville, Tennessee

(Received March 7, 1960)

a,a-!Jiphenyl-i3-picryl~ydrazyl, with and without Nil, contained in single crystals of the corresponding hydrazme has been stud!ed by the paramagnetic-resonance method. All resolved hyperfine effects arise from the t~o .hydrazyl ~tro?en atoms. The tensors describing the hyperfine interaction for each nitrogen and the pnnclpal-axes dlrectlOns have been deduced. The tensors have been interpreted on the basis of an s-p model. with the following electron densities: for the a nitrogen a,"=O.Ol1 and a,,'=0.263 with the two parts havmg the same sign of spin density; for the fI nitrogen a.2=0.024 and a,,2""0.396 or a,"=0.010 and a"t=~.605: The tw~ choices for the fI nitrogen arise from an ambiguity in interpreting the hyperfine tensor, but WIth either chOIce the two parts have the same sign of spin density.

INTRODUCTION

THE stable free radical that has most frequently been observed by the paramagnetic-resonance

method is undouhtedly a.a-diphenyl-t3-picrylhydrazyl (DPPH). The first observationl was made on a poly­crystalline powder, and a single, sharp absorption line was seen with a g value very close to that of the free electron. The sharpness of the line and lack of hyper­fin,e ~tructure was attributed to exchange interactions; thIS mterpretation has been borne out in many later studies. Subsequently, others have investigated single crystals of D PPH, and a very small aniostropy in g value2 and line width3 have been reported. The closeness of the g value to that of the free electron is typical of the more complex free radicals which exhibit essentially complete quenching of orbital angular momentum.

A number of solution studies, usually in benzene, have been made. If the solution is sufficiently dilute so that exchange and dipole-dipole interactions are greatly reduced, then a nearly resolved five-line spec­trum can be observed.2 The spectrum arises from hyperfine interactions of the electron with the two hydrazyl nitrogen nuclei.2.4 Each N14 nucleus (I = 1) gives a triplet splitting which, in general; giv.es a com:­posite spectrum of nine lines. The five lines have been interpreted as arising from the special case of essentially equal coupling of the two nitrogen nuclei which causes some of the nine lines to be superimposed within the limits of the resolution of the observed pattern. More recently a detailed analysis of the five-line spectrum in

* Operated for the U. S. Atomic Energy Commission by the Union Carbide Corporation.

I (a) A. N. Holden, C. Kittel, F. R. Merritt, and W. A. Yager, Phys. Rev. 77, 147 (1950); (b) C. H. Townes and J. Turkevich, Phys. Rev. 77,148 (1950).

2 C. A. Hutchison, Jr., R. C. Pastor, and A. G. Kowalsky, J. Chern. Phys. 20, 534 (1952).

3 G. Berthet, Compt. rend. 240, 57 (1955). • H. S. Jarrett, J. Chern. Phys. 21, 761 (1953).

dilute solution has been made,S and the ratio of the couplings of the two nuclei has been reported to be 0.82. Only hyperfine effects arising from the contact hyperfine interaction are seen in solution.s No informa­tion is obtained on the dipolar contributions; their effects are averaged out by the tumbling motions in solution.

In the present study both the isotropic contact hyperfine interaction and the anisotropic dipolar inter­action have been measured in single crystals containing DPPH. Normal DPPH, both hydrazyl nitrogens being N14, and labeled DPPH, one of the nitrogens being Nib, have been used. The {j position (Fig. 1) was labeled with N15. The single crystals studied were diamagnetic a,a-diphenyl-t3-picrylhydrazine (DPPH2) containing a small amount of DPPH. (The formula of DPPH2

differs from that of DPPH in that its extra hydrogen atom is located on the (3 nitrogen.) Both DPPH7 and DPPH28 grown from benzene solutions are monoclinic with two molecules in the unit cell plus two molecules of benzene; however, their space groups are different. DPPH has space group Pa while DPPH2 has P21

(monoclinic angle 111° 14'). An x-ray diffraction exam­ination of crystals of DPPHz containing small amounts of DPPH showed no change from that of pure DPPH2•

Hyperfine interactions from the two N14 nuclei of the hydrazyl, in general, would give a spectrum of nine lines. This would be doubled to 18 lines because there are two molecules in the unit cell. The symmetry of the dilute crystals is such that if the applied magnetic field is parallel to the crystallographic ac plane then hoth molecules appear alike, and at most a nine-line spectrum would be expected. If one of the nitrogens is replaced by Nl5 (I =!) a six-line spectrum doubling to 12 lines

5 R. M. Deal and W. S. Koski, J. Chern. Phys. 31,1138 (1959). 6 S,1. Weissman, J. Chern. Phys. 22,1378 (1954). 7 M. Sternberg, Compt. rend. 240, 990 (1955). • R. D. Ellison and R. W. Holmberg, ActaCryst.13,446 (1960).

541

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Page 3: Paramagnetic-Resonance Study of Hyperfine Interactions in Single Crystals Containing α,α-Diphenyl-β-Picrylhydrazyl

S42 HOLMBERG, LIVINGSTON, AND SMITH

(a)

( b)

FIG. 1. a,a-Diphenyl-/3-picrylhydrazyl. Two reso­nant structures are indi­cated.

(since there are two molecules) would be expected. This type of spectra has been observed. Their measure­ment has allowed the elements of a phenomenological hyperfine-interaction tensor to be evaluated for each nitrogen. These elements have then been interpreted in terms of sand p atomic orbitals for each nitrogen.

EXPERIMENTAL

Single crystals of DPPH2 weighing up to !g and con­taining small amounts of DPPH were grown from benzene solution by a slow-evaporation method and also by a thermal-gradient method. The latter was more generally successful. Typically, a gram of DPPH2 and 20 mg of DPPH in 10 ml of benzene were placed in a IS-ml test tube. The lower part of the tube was heated to about 60°C and, with luck, after several days well­developed single crystals formed in the upper, room­temperature, portion of the tube. The crystals contained approximately 0.1 % DPPH. The DPPH labeled with Nl5 had to be synthesized. The starting material was 98% Nl5 as nitric acid as obtained from the Oak Ridge National Laboratory Isotope Division. The acid was converted to dry NaN150a. The nitrite was prepared from the nitrate by heating with granular lead for 16 hr at 375°C under an argon atmosphere and was recovered by leaching of the matrix with water. This was followed by the preparation9 of a,a­diphenylhydrazine-{1-NI5 which in turn was convertedlO

to DPPH2 and then to DPPH. In growing crystals from solution, both the DPPH2 and DPPH had to be labeled.

(b)

(c) (d)

FIG. 2. Spectra of a single crystal con­taining N15-labeled DPPH; the mag­netic field was par­allel to the ac plane. The field directions relative to the c axis were (a) 70°, (b) 45°, (c) 40°, and (d) 0°.

9 A. Murray and D. L. Williams, Organic Syntheses with Iso­topes (Interscience Publishers, Inc., New York, 1958), p. 1830.

10 R. H. Poirier, E. J. Kahler, and F. Benington, J. Org. Chern. 7,1435 (1952).

If the DPPH2 was not Nl5 labeled rapid exchange of the {1 hydrogen completely destroyed the labeling.

The crystal habit was determined by comparing interfacial angles, measured with an optical goniometer, with those calculated from the cell parameters deter­mined by x rays.s Usually the 100 and 001 faces were well developed and measurements with the magnetic field parallel to these planes could be conveniently carried out by laying the crystal on the appropriate surface in the bottom of the microwave cavity. For measurements parallel to the ac plane the crystal was cemented to a rod which was then inserted into the microwave cavity.

180

160

140

120

~wo w a:: '" ~ 80

60

40

20

40

a oxis ~-------------

c axis

GAUSS

FIG. 3. Measured values and calculated curves for the hyperfine separations in a single crystal containing N15-labeled DPPH; the magnetic field was parallel to the ac plane. The solid circles are measurements of unresolved lines.

A simple 9Ooo-Mc paramagnetic-resonance spectrom­eter was used. It employed a rectangular cavity oper­ating in the T EI01 mode, 60-cps field modulation, and oscilloscope presentation of the spectrum. The mag­netic-field direction could be altered by rotating the magnet. Fields were measured with a proton-magnetic­resonance probe. Most measurements were made at room temperature; some were made at nOK to improve the signal intensity. Comparisons of the spectra at the two temperatures were made, and no significant change in line spacing or width could be observed. The lines at the lower temperature could, however, be much more readily power saturated.

Measurements were made with the normal (NIL-NI4) and labeled (N14_NI5) crystals and in each case with the field at a number of settings parallel to the ae, ab, and be crystallographic planes. Resolved hyperfine components had a full width at a half-height of about seven gauss. For many orientations this

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Page 4: Paramagnetic-Resonance Study of Hyperfine Interactions in Single Crystals Containing α,α-Diphenyl-β-Picrylhydrazyl

PAR A MAG N E'T I eRE SON A ~ CEO Fa, a - DIP HEN Y L - ~ - PIC R Y L H Y D R A Z Y L 543

FIG. 4. Measured values and calculated curves for the over-all hyperfine separa­tions in a single crystal contining N16_ labeled DPPH. The solid and dotted curves represent the two symmetry-re­lated molecules. (a) The field was parallel to the be plane. (b) The field was parallel to the ab plane.

180

40 30 20

exceeded the spacings between components and, conse­quently, the number of resolved data was quite limited. The N14_N15 crystals gave spectra with fewer hyper­fine components; resolved patterns could be seen over a greater range of angles. These data were used to evaluate the hyperfine tensor elements. Measured values obtained from the N14_N14 crystals at a number of orientations were in excellent agreement with the N14_N15 results. The use of N15 no't only facilitated resolution of the spectra but also allowed an unam­biguous assignment of the two hyperfine tensors to the appropriate nitrogens. The most useful data were obtained for the magnetic field parallel to the ac plane for the Nl~N15 crystals. Typical spectra are shown in Fig. 2, and measured values are given in Fig. 3. At most, only six lines appear. For one orientation [Fig. 2(a)] the hyperfine interaction for the N14 is zero and only the doublet for the N15 remains. Upon changing the orientation each component splits into a triplet, and contributions of both nitrogens to the hyperfine pattern are seen. Measured values for other planes are shown in Fig. 4. Only the outermost lines were suffi­ciently well resolved to be measured accurately.

The appropriate spin Hamiltonian to which the data were fitted is

where (3 is the Bohr magneton, H the applied magnetic field, S and I the electron- and nUclear-spin operators in units of n, A the hyperfine tensor, and g refers to the electron. The subscripts ex and (3 refer to the two nitrogens as labeled in Fig. 1. It was found, experi­mentally, that the anisotropy in the electron g value was negligibly small. It centered at about g= 2.003 with a variation of approximately ±O.OO1. This is similar to that observed2 in concentrated single crystals of DPPH. Accordingly, the Zeeman energy of the electron was regarded as isotropic and the hyperfine interactions

(0 )

-0 oxis-

(b)

d''.

1 I

,I ,I

"

30 20 W 0 10 20 30 GAUSS

180

160

140

120

en

1::0 i

60

40

20

o

were treated as a small perturbation. The spacings of hyperfine components from the unperturbed line position (center of symmetric hyperfine multiplet) are given by

b.H =mra(H, N, H) }+mr(J(H' N· fI) ~l, (2)

where b.H is the spacing in magnetic-field units, mr is the nuclear magnetic quantum number, H is a unit vector in the direction of the applied field, A 2 = A· A is a rank-two symmetric tensor and the allowed transitions have been taken to be for b.mr=O. In a principal-axis system Eq. (2) becomes

b.H =mr,,[.L:h i2 A ii2],,!+mr(J[.L:hl AjjZ](Jl, (3)

where the h's are direction cosines of the applied mag­netic field with respect to the principal axes, and the A's are written in component form. (A d) = (A 2) ii. It is apparent that no information on the absolute or relative signs of the principal values of A can be de­duced from Eq. (3); the spectra depend upon their magnitudes. In addition to separate tensors for each nitrogen, from the symmetry of DPPHz one would expect a second pair of tensors corresponding to the second molecule in the unit cell. Only the tensors for one molecule need be determined since those for the other molecule can be obtained by the appropriate symmetry operation, a twofold rotation about the b crystallographic axis.

In general the fitting of data is a 12-parameter problem, six parameters for each tensor. One approach would be to choose an arbitrary axis system, deduce the elements of A2 using Eq. (2), diagonalize and then deduce the diagonal elements of A. Fortunately, there are simplifying features that allowed one of the tensors to be determined directly in diagonal form. From Eq. (3) it is apparent that the only way a zero hyper­fine splitting can occur is for a principal value to be

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Page 5: Paramagnetic-Resonance Study of Hyperfine Interactions in Single Crystals Containing α,α-Diphenyl-β-Picrylhydrazyl

544 HOLMBERG, LIVINGSTON, AND SMITH

zero and the magnetic field to be applied along the corresponding axis direction. Thus the zero splitting for N14 as shown in Fig. 2(a) must mean that the field was along a principal-axis direction and the corre­sponding diagonal element of Aa is zero. A zero splitting (zero tensor element) is fortuitous, and finding the appropriate direction to be with the magnetic field parallel to the ac plane at first appeared as an even more remarkable coincidence. This suggested that the Aa tensor was axially symmetric and an entire plane of zero-splitting orientations would occur with this crystal. Indeed, zero splittings were found for three widely spaced orientations in addition to the one found in the ac plane. These orientations defined a plane and con­firmed axial symmetry. In moving the magnetic field out of the ac plane, splittings from the two molecules appeared partly superimposed, and there were resolu­tion problems. There was an intensity anomaly, how­ever, which will be described more fully later. Although spacings of hyperfine lines from each molecule ap­peared normal, one molecule gave lines with only about one-third the intensity of the other. Good measure­ments could be made by confining observations to the strong family of lines. A strong doublet (each com­ponent threefold degenerate) was observed super­imposed on a family of six very much weaker lines. The symmetry axis was overdetermined in this way and found to make angles of 126°, 62°, and 36° with the a, b, and c crystallographic axes, respectively. From the principal-axes directions and from the data of Fig. 3 the only nonzero element of Aa was easily evaluated to be 18.7. Deducing the elements of A~ proceeded in a more conventional manner. Only over-all splittings of the hyperfine pattern were needed. The elements were deduced by using the values for Aa , the data of Figs. 3 and 4, and Eq. (2).

The magnitudes of the tensor elements are

o 5.8

Aa= o and 5.8

18.7 27.5

Both are axially symmetric, and the principal-axes directions (symmetry axes) are given in Table I for one of the two molecules in the unit cell. The angle between the two symmetry axes is 13° with an estimated un­certainty of ±2°. The elements of the tensors are in units of gauss and refer to N14. The tensor deduced for N15(A~) has been converted to the appropriate N14 value by mUltiplying each element by I gJ4 III g16 I = 0.7129. This facilitates comparisons between the two nitrogens. Although it is difficult to estimate errors in the tensor elements, spectra calculated from the two tensors and the principal-axes directions agree with the measured values to within a gauss. This is indicated in Figs. 3 and 4. Small deviations of the two tensors from

axial symmetry might fit the data equally well. For example, the zero elements of Aa represent hyperfine components merging to a true singlet. This is illustrated in Fig. 2 by a pair of triplets collapsing to a pair of singlets. Consideration of line widths and intensities indicated that the merging of lines was, indeed, quite complete and the small elements of Aa could not exceed one or two gauss.

INTERPRETATION AND DISCUSSION

Without loss of generality, the hyperfine tensors may be resolved into isotropic and anisotropic (traceless) parts. There are, however, ambiguities since the resolu­tions must be made for all combinations of signs of the elements. The Aa tensor gives the least ambiguity with the following result:

o 6.3 -6.3

6.3 + -6.3

18.7 6.3 12.5 (4)

The only other choice is with the sign of every element of each tensor reversed. The simplest and most obvious model for describing the tensors is a combination of s and p atomic orbitals. The choice of signs made in Eq. (4) gives both parts a positive spin density. The only other choice woujd be for both parts to be negative. The three possible resolutions of A~ are

5.8 113.0

1+

-7.2

(5) 5.8 13.0 -7.2

27.5 13.0\ 14.5

-5.8

-5.8

27.5

5.3 I -11.1

I 5.3 1+ -11.1 (6) === i I

5.31 I

I 22.21

5.8

-5.8

27.5

9.1 -3.3

-14.9 I (

(7) 9.1 + 9.1 18.31

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Page 6: Paramagnetic-Resonance Study of Hyperfine Interactions in Single Crystals Containing α,α-Diphenyl-β-Picrylhydrazyl

PAR A MAG NET I C RES 0 NAN CEO Fa, a - DIP HEN Y L - {J - PIC R Y L H Y D R A Z Y L 545

The third resolution given by Eq. (7) contains a dipolar tensor that departs greatly from axial symmetry, and for this reason is physically unacceptable. A quenched p orbital should give an axially symmetric tensor. It will later be shown that a p orbital centered on the adjacent nitrogen atom will not greatly affect the tensor elements. This view is further supported by the elements found for Aa where the same argument applies and where, without ambiguity, the dipolar part is axially symmetric. For the physically acceptable choices, Eqs. (5) and (6), there is still the ambiguity in the signs of each element. The choice written is for a positive spin density for the sand p parts. In each case the other choice requires both parts to be negative.

The detailed form of the hyperfine interaction is given by the Hamiltonian of Eq. (1) where the portion S·A·I is given by

S· A· I = { (811'/3) S / iI(O) /2 - (S/r) + (3· S· rr/r") }

·gNi3NI. (8)

As indicated in Eq. (1), there will be two terms of this form, one for each nitrogen, where i3N is the nuclear magneton and gN is the appropriate nuclear gyromag­netic ratio. The eigenvalues have been discussed else­where,u If we use the same nomenclature for an s-p model, the tensor elements, as defined in this paper, are

A.=a.2(811'/3) / iI.(O) /2gNi3N (9)

Ap=tap2 (1/r)pgNi3N, (10)

where A. is an element of the isotropic part of the tensor and Ap is one of the elements of the dipolar tensor, and a.2 and ap

2 are the probabilities of having the electron on the nitrogen in question in the sand p states, re­spectively. The element given for Ap in Eq. (10) is the unique one which corresponds to the applied mag­netic field being along the symmetry axis of the quenched p lobe (8=0° in the nomenclature of footnote reference 11) .

The significance of the zero splitting (zero tensor element) was discussed above in terms of the phe­nomenological treatment. In terms of a detailed treat­ment using sand p states it can be seenll that the field at the nuclear position from an electron in an s state is always along the externally applied field direction. On the other hand, the contribution from a p state at the nuclear position will always have a perpendicular com­ponent unless the externally applied field is along the symmetry axis (0°) or perpendicular to the symmetry axis (90°). The sand p parts can only cancel for these two angles, and only if there is the appropriate ax­mixture. The cancellation can only occur at 90° if the two parts have the same sign of spin density (the case for DPPH) and at 0° for opposite signs.

11 H. Zeldes, G. T. Trammell, R. Livingston, and R. W. Holm­berg, J. Chern. Phys. 32, 618 (1960).

TABLE I. The symmetry-axes directions for the hyperfine tensors.

a

126S

118.0°

Crystallographic axis

b c

When the electron is considered to be on one nitrogen there will be some magnetic interaction with the adjoining nitrogen nucleus. This interaction could cause the dipolar part of the hyperfine tensor to depart from axial symmetry. Calculations using Eqs. (15) and (19) of footnote reference 12 and taking the p lobes to be perpendicular to the N-N bond direction and taking the hydrazine N-N distance of 1.45 A showed the effect to be less than the experimental un­certainty in the tensor elements.

The value used for / iI.(O) /2 was 32.0X 1024 cm-3 as deduced from Hartree13 wave functions for a 2s electron on N(4S). The corresponding value for (l/r) for a 2p electron was 22.SX1Q24 cm-3• This is an 8% increase from the value deduced from the Hartree function as discussed by Dousmanis.14 This value was used for interpreting Afj. In interpreting Aa the electron is regarded as being on the a nitrogen with resonant structures of the type indicated in Fig. 1 (b). To account for the decrease in screening because of the positive formal charge on the a nitrogen the value of (1/r3 ) was increased by a factor of 1.30 as indicated by Townes and Schawlow.15

U sing the preceding values, we obtain the following results: For the a nitrogen a.2 =0.011 and ap2 =0.263. The spin densities of the two parts have the same sign. The total electron density on this nitrogen is 0.274 of which 4% is s character. For the nitrogen in the {3 position there are two choices: a.2=0.024 and ap2= 0.396 or a.2 =0.010 and ap2 =0.605. For either choice, the spin densities of the sand p parts have the same sign. The total electron density on this nitrogen is 0.420 or 0.615 of which 5.7% or 1.6%, respectively, is s character. With either choice the electron density on the f3 nitrogen is greater than that on the a nitrogen indicating that a resonant structure of the type given in Fig. 1 (a) predominates. This is the structure a chemist would normally write for DPPH. The fore­going values are substantially different from those calculated by a molecular-orbital method15 which gave densities for the unpaired electron of 0.1416 and 0.1518 for the a and f3 nitrogens.

12 G. T. Trammell, H. Zeldes, and R. Livingston, Phys. Rev. 110,630 (1958).

13 D. R. Hartree and W. Hartree, Proc. Roy. Soc. (London) A193,299 (1948).

14 G. C. Dousmllnis, Phys. Rev. 97, 967 (1955). 15 C. H. Townes and A. L. Schawlow, Microwave Spectroscopy

(McGraw-Hill Book Company, Inc., New York, 1955), p. 239. 16 R:Bersohn, Arch. sci. (Geneva) 11, 12 (1958).

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Page 7: Paramagnetic-Resonance Study of Hyperfine Interactions in Single Crystals Containing α,α-Diphenyl-β-Picrylhydrazyl

546 HOLMBERG, LIVINGSTON, AND SMITH

There are other magnetic nuclei in the system that can interact with the unpaired electron. These are the hydrogens and nitrogens attached to the aromatic rings. There were no experimental indications of splittings from these nuclei. The approximate 7 -gauss line width of a resolved hyperfine component indicates these interactions to be weak; moreover, a substantial part of the width could arise from intermolecular magnetic dipole-dipole interactions. This is consistent with the electron being rather highly localized on the two hydrazyl nitrogens where either 0.694 or 0.889 total electron density is found depending on the choice made for the f3 nitrogen.

In the experimental discussion it was pointed out that a line-intensity anomaly was present. The hyper­fine lines from one molecule in the unit cell were about three times as intense as those from the other molecule. The spacings were not anomalous. The effect could not be attributed to any asymmetry in the experimental configuration, and we are forced to conclude that there are different numbers of DPPH molecules in each of the two cell positions. This is inconsistent with the space group for DPPH2• ()nly small amounts of DPPH were contained in the DPPH2 crystals and distortions may have been present that were not observed in the x-ray­diffraction work. Since DPPH has a different space group than DPPH2 there must ultimately be a change as one is added to the other to form a solid solution. Presumably, even with small amounts of added DPPH, the host lattice does not accommodate it well, and there are distortions not seen by x rays at such low concentrations; the "symmetry-related positions" are not occupied with equal probability. This may be related to the finding that 2% DPPH (compared to DPPH2) had to be placed in solution to obtain a crystal containing only 0.1 % DPPH.

It was hoped that a comparison of spectra calculated from the isotropic part of the hyperfine interactions [Eqs. (4)-(6) ] with observed spectra in solution would remove the ambiguity in the resolution of A{3. Although one choice is favored, some doubt remains. In making the comparisons the over-all splitting from first to fifth

component of the five-line solution spectra is used. Although a number of studies of the solution spectrum have been published, most authors have not stated measured values of the splitting. The first value re­ported2 gave the separation between components as approximately 10 gauss or an over-all separation as approximately 40 gauss. We have remeasured this value for DPPH in benzene solution (0.002 and 0.005 M) and carbon-disulfide solution (0.005 M) with and without the solutions being saturated in DPPH2•

The spectra were essentially the same in all cases with an over-all splitting of 34± 1 gauss. There is some uncertainty due to lack of complete resolution, but we use this number for comparisons. The isotropic part of Aa is 6.3 [Eq. (4) ] while the two choices for A{3 are 13.0 and 5.3 [Eqs. (5) and (6)]. With the larger value for the isotropic part of A{3 a seven-line spectrum would be expected in solution with an over-all splitting of 38.6 gauss. The ratios of interactions for the two nitrogens is 0.48. The over-all splitting is only a little large, but the other features are in complete disagreement with the observed solution spectrum. With the smaller value for the isotropic part of A{3 a five-line spectrum would be expected with a ratio of interactions for the two nitrogens of 0.86 to be compared with the value of 0.82 recently deduced5 from solution studies. Although this agreement is excellent, the calculated splitting is 23.2 gauss, which is quite small. These findings give some preference to the smaller value for the isotropic part of A{l. This is the choice that gave as

2 =0.010, ap

2 =0.605, a combined density of 0.615 for the (3 nitrogen and a combined density of 0.889 for the two nitrogens. An examination of the results show that the isotropic parts of the interactions, the only parts ob­served in solution, represent a minor portion of the electron density. The small amount of s admixture might vary with the environment of the DPPH, which casts some doubt on the validity of comparing values in the solid with those in solution. Finding the same values in a few different solutions was reassuring, but, perhaps, it would be more significant to make the present measurements with different host crystals.

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