The spin magnetism of α, α′diphenylβpicrylhydrazyl (DPPH)P. Grobet, L. Van Gerven, and A. Van den Bosch Citation: The Journal of Chemical Physics 68, 5225 (1978); doi: 10.1063/1.435589 View online: http://dx.doi.org/10.1063/1.435589 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/68/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Low-dimensional magnetism of spin-½ chain systems of α- and β-TeVO4: A comparative study Low Temp. Phys. 38, 559 (2012); 10.1063/1.4734010 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 ElectronSpinResonance Studies of DPPH Solutions J. Chem. Phys. 36, 1676 (1962); 10.1063/1.1732796 ParamagneticResonance Study of Hyperfine Interactions in Single Crystals Containing α,αDiphenylβPicrylhydrazyl J. Chem. Phys. 33, 541 (1960); 10.1063/1.1731181

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The spin magnetism of a, a'-diphenyl-J3-picrylhydrazyl (DPPH)

P. Grobeta) and L. Van Gerven

Laboratorium voor Vaste Stof-Fysika en Magnetisme, Katholieke Universiteit Leuven, Leuven (Belgium)

A. Van den Bosch

Materials Science Department, S.C.K./C.E.N .. Mol (Belgium) (Received 14 November 1977)

Magnetic susceptibility measurements are performed on DPPH-benzene complex and solvent-free DPPH in the temperature range 300--2.2 K and in a field range 6-20 kOe. The experimental values of the DPPH-benzene complex fit the Brillouin function for noninteracting paramagnetic centers (S = 1/2); at temperatures below 4 K; however, a systematic deviation is observed. The values in solvent-free DPPH obey the same law at temperatures above 150 K. Below this temperature a strong deviation occurs, and below 10 K the susceptibility even decreases with decreasing temperature. This deviation is attributed to electron spin pairing. In solvent-free DPPH less than 1 % of paramagnetic centra is left at 2.2 K.

INTRODUCTION pie 2 is identical to sample DPPH (I) in the work of Weil et al. , 8 but sample 1 may not be identified with DPPH (II); indeed, our sample is not dried or heated in vacuo but saturated with benzene in a 1 : 1 ratio.

Sample 1

In the framework of a study on the low temperature properties of nonionic organiC free radicals, the static magnetic susceptibility of a, a' -diphenyl-j3-picrylhy­drazyl (DPPH) has been measured by means of the Faraday method. l In the past there have been several susceptibility measurements on DPPH2

- 5 over a wide temperature range, but most investigators did not take care to indicate the preparation and to identify the exact chemical composition of their samples. Since it is well known that complex formation with the solvent, from which it is crystallized, is common in solid DPPH, this has lead to a lot of confusion. In our measurements two extreme cases are conSidered: the first one deals with a sample in which the DPPH molecules are separated by benzene molecules (DPPH· CaD6 1 : 1), whereas the sec­ond one deals with a solvent-free sample. 6 Susceptibil­ities have been measured as a function of temperature between 2.2 and 300 K for six different fields. The nominal values of the strength of these fields are 20.6, 18.7, 14.7, 11. 9, 9.0 and 6.1 kOe. They will be re­ferred to by the subscript i, numbered from 1 to 6.

A plot of the mass susceptibility of sample 1 is given in Fig. 1. The values indicated by the 0 signs are Xl'S; those given by the A signs X6' s. The other XI are omitted for clarity. The plot shows that the X values at the high­er temperatures fit the equation

The reported experimental results are discussed using a model based on electron spin pair formation.

EXPERIMENTAL RESULTS

The DPPH' C6D6 sample (sample 1) was crystallized from a very dilute solution of DPPH in CaD6; the DPPH powder was supplied by Eastman Kodak Co. Deutero­benzene was used in order to avoid proton signals from solvent molecules in our previous proton resonance measurements. 6 Pumping on the recrystallized powder is restricted to a minimum.

The solvent-free sample (sample 2) was prepared from a very dilute solution of DPPH in ether and purified in a chromatographic column.7 Afterwards it was crystal­lized and dried by pumping at room temperature. Sam-

a"Onderzoeksleider" of the Belgian "Nationaal Fonds voor Wetenschappelijk Onderzoek."

(1 )

The values of AI and CI are temperature independent. The first term in the right-hand side of Eq. (1) is the Curie law, which expresses the behavior of noninteract­ing paramagnetic centers. The temperature independent

- T/K

1 5 3.3 2.5 2.0

X 11O-4emug-1 11:. 11:.

3.0 11:. 0

11:. 0 0 0

2.0

1.0

FIG. 1. The magnetic susceptibility of DPPH' CsDs (1: 1) measured at 20.6 kOe (0) and 6.1 kOe (6).

J. Chern. Phys. 68( 111. 1 June 1978 0021·9606178/6811·5225$01.00 © 1978 American I nstitute of Physics 5225 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:

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5226 Grobet, Van Gerven, and Van den Bosch: Magnetism of DPPH

TABLE I. The calculated spin concentration of sample 1 from susceptibilities fitted to the Brillouin function.

Ci X 107 C i'x107

Bi (emug-1) (emug-1)

1 0.973 -5.6 -4.4 2 0.976 -4.1 -4.3

3 0.978 -3.1 -4.2

4 0.976 -3.2 -4.0

5 0.987 -4.7 -3.8

6 0.979 -3.1 -3.3

part is attributed to the susceptibility of the rest of the material. In the low temperature region a systematic deviation from the Curie law is observed: saturation oc­curs in the magnetization. Therefore, the magnetization has to be fitted to the Brillouin function B( T, H), for non­interacting paramagnetic centers (S=-!). For each field strength a fitting has been carried out using the param­eter B j , the free radical concentration, given by the ratio of the number of paramagnetic centers to the total number of complex molecules. The BI values have been chosen so that the computed values xL

I -B B(T,Hj ) C' XI - i HI + I,

minimize, in the low temperature region, the sum of the weighted squares of the deviations

N

D = L [W(XI - Xi)21n n,1

(2)

(3)

of the N measurements which have been taken at tem­peratures above 7 K. As the magnetization is higher at lower temperatures the weighting factor was taken pro­portional to the reciprocal temperature. The Ci' s are fitted values obtained from the susceptibility data taken at T> 100 K. Indeed, at the higher temperatures the Curie term is the smaller one resulting in a better pre­cision on the CI values. In fact, the results have been obtained in an iterative process wherein, (i) the B/ s are the fitting parameters in the low temperature region us­ing for C/ the values obtained from the high temperature data, and (ii) the C/' s, on their turn are the fitting pa­rameters using a "most probable free radical concen­tration" as known BI constants. The most probable free radical concentration is taken to be the average of the precedingly obtained B j values, assuming that the con­centration is equal for all six magnetic field strengths. The iterative process started with the theoretically ex­pected va lues B j = 1 and C/ = Xa, the diamagnetic suscep­tibility of the substance. The diamagnetism of the sam­ple has been estimated, from the data of Haberditzl9 and Dorfman1o to be

Xa = - 4. 8x 10-7 emu g-1 .

The obtained Civalues are systematically slightly dif­ferent from Xa so that the presence of a saturated ferro­magnetic impurity may be assumed. Therefore we used

(4)

where Xa and K are constants and H j is the magnetic fie ld. The assumption requires an intermediate step in the fitting procedure. This step is carried out by choos­ing the value of K so that it minimizes the standard de­viation

S = I 1 • I (L:t (C. _ C/ )2)1/2

6-1 ' (5)

using for Cj the value obtained for C; in the preceding high-temper.ature fitting. The procedure finally yields the values collected in Table I.

The standard deviation s = O. 9 xl 0-7 emu g -1 for K = O. 9x10-3 emuOeg-1. The most probable free radical concentration is B = 0.978 ± 0.005. The relative devia­tions of the susceptibilities measured at the different fields, from those calculated from Eq. (2) using B,

~ = 100 (Xi - xll/xi , are plotted in Fig. 2 vs the temperature.

Sample 2

Susceptibility values of sample 2, the solvent-free DPPH, are given in Fig. 3. While in the high-tempera­ture region the paramagnetism is almost identical with that of the preceding specimen, it is strongly reduced in the low-temperature region. The similarity in behavior of the two samples at the higher temperatures justifies a similar analysis of the data. For the solvent-free DPPH also the iterative process has been started with the theoretical values B = 1 and C/ = Xa' The diamagne­tism of the solvent-free DPPH is estimated to be - 4. 5 X 10-7 emu g-1. The resulting values of C/, as obtained for T> 150 K, are given in Table II together with the corresponding B I • The most probable free radical con­centration in the solvent-free DPPH is B = 0.972 ± O. 006. The relative deviations of the measured susceptibilities from those calculated, using B j = Band Ci = the average of the C; values in Eq. (2), are plotted vs temperature in Fig. 4, for i=l (0 signs) and i=6 (A signs).

r: I I

1:::.1% 6

.' 4

2 . . .. -.1 , .-0 ;h : ;.~ .. .':~ .,

c :, .' . '. J -_. . .

.f. ~ •• !.~.- . -2 .

i :.

-4

-6

-8

-10 I

1 10 T/K 100 .. flG. 2. The proportional deviation of the measured magne­tization of DPPH· C6D6 (1 : 1) from the Brillouin function at different magnetic fields.

J. Chem. Phys., Vol. 68, No. 11, 1 June 1978

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Grobet, Van Gerven, and Van den Bosch: Magnetism of DPPH 5227

..... It----T/K

~ 10 5 3.3 2.5 2.0

X/1O-5emug-1

~

4.0 ~ ~

€J ~

I!)

3.0 0

~ '" 2.0 ~ 8

/1; 0 4D ~

~ , ~ a;,

/1;0 c:t> 0

0.2 0.3 0.4 0.5 r 1/K-1 __

FIG. 3. The magnetic susceptibility of solvent-free DPPH measured at 20.6 kOe (0) and 6.1 kOe (8).

DISCUSSION

Sample 1

The values of the magnetic susceptibility of the a, a'­diphenyl-j9-picrylhydrazyl sample 1, in which the radi­cal molecules are isolated from each other by deuter­ated benzene, fit the values expected from the Brillouin magnetization f~nction for an unpaired electron spin con­centration of 0.978 ± 0.0005. The concentration, which is somewhat less than unity, can be explained by the presence of diphenylpicrylhydrazine and by the assump­tion that the composition of the sample is not stoichio­metric, i. e., the DPPH/CsDs ratio is not exactly 1. An indication supporting this assumption is the observation that the composition of the sample is not very stable: the specimen lost O. 6% of its weight during two of the three days which separated its preparation from the in­stallation in the apparatus. To prevent further escape of benzene the sample was then kept at temperatures below 175 K for the whole period during which the sus­ceptibility measurements were carried out. The treat­ment seems to be effective: no change in time of the measured susceptibility has been observed.

The measured values of the susceptibility deviate from the values expected from the most probable unpaired electron spin concentration. The spread of the relative deviations at the higher temperatures in Fig. 2 is due to scatter in the force determination. Indeed, at these temperatures, the force on the specimen is small com­pared to the force on the balance pan: the ratio is about 3 x 10-2 at 170 K. At lower temperatures the ratio is higher. From the point of view of force measurements,

TABLE II. The calculated spin concentration of sample 2 from susceptibilities fitted to the Brillouin function at high temperatures.

B j

C; Xl07 (emug-1)

1 0.963 -4.8 2 0.970 -4.5 3 0.979 -4.0 4 0.977 -4.1 5 0.975 -4.2 6 0.969 -4.5

average 0.972 ± O. 006 -4.3 (s=0.3)

therefore, the precision on the susceptibility values should increase with decreasing temperature. In agree­ment with this reasoning is the spread of the deviations, which is found to be smaller on the left side of Fig. 2. The mass of the sample, 1. 024 x 10-4 g, was chosen to optimize the precision of the measurements in the low temperature region. At the lowest temperatures one might expect deviations due to temperature errors. In order to check this, the sample temperature has been estimatedll using superconductive transition tempera­tures as reference points: the error is less than 0.01 K. Consequently the systematic deviation from the Brillouin behavior below 4 K, as observed in Fig. 2, is expected to be a real effect. We attribute it to the for­mation of pairs of radicals; at the lowest temperatures pair formation reduces the "high-temperature" unpaired electron spin concentration up to about 2% at T = 2.2 K. More direct information about this pair formation is found in proton magnetic resonance measurements.12,13

This effect shows up also in sample 2 even more pro­nounced and it will be discussed below in the section of sample 2.

Ferromagnetic impurities cannot be avoided always. If the field dependence of the magnetic susceptibility at the higher temperatures should be attributed to more or

-40 a

I -60

-80

FIG. 4. The proportional deviation of the measured magne­tization of solvent-free DPPH from the Brillouin function at 20.6 and 6.1 kOe.

J. Chern. Phys., Vol. 68, No. 11, 1 June 1978

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5228 Grobet, Van Gerven, and Van den Bosch: Magnetism of DPPH

less saturated iron, present in a not too dispersed form, one could calculate its mass concentration because K is the ratio of the impurity mass to the sample mass, mul­tiplied by the magnetic moment of one gram of the im­purity.14 This moment for bulk iron is 221 ergOe-1 g-l. Our K value of O. 9 x 10-3emu Oe g-l results in abou t 4 ppm of iron to be sufficient for explaining the field de­pendence. This explanation implies the assumption that a piece of 4 x 10-10 g of iron case still be represen­tative for the bulk. This weight is considered to be the detection limit for iron in the DPPH sample as the standard deviation s is of the same order in magnitude as the susceptibi lity differences between the C1 values, which effect suggests the presence of ferromagnetic impurities.

Sample 2

Unlike the just discussed DPPH· C6D6, solvent-free DPPH is more stable at room temperature. It has been possible therefore, to measure susceptibilities up to 300 K and to observe that at temperatures above 150 K the susceptibility also fits the value expected from the Brillouin magnetization function. The unpaired elec­tron spin concentration in this sample is O. 972 ± O. 006. The 2.8% deviation from unity may be due to the pres­ence of nonoxidized diamagnetic hydrazine; stable or­ganic free radicals are generally difficult to prepare in pure form. 5

At lower temperatures the magnetization of the sample is drastically smaller than the value expected from the Brillouin function with the "high-temperature" concen­tration of unpaired electrons. Such a large effect can only be explained by some transformation in the unpaired electron spin. system by which paramagnetic centers are eliminated. One can speculate about the nature of the elimination of the unpaired electrons in solvent-free DPPH, a phenomena which also occurs, however weak­ly, in DPPH· C6D6 at much lower temperatures. From crystallographic considerations15 and the like in most neutral free radicals, the molecules of DPPH are thought to lie one upon another to form a one-dimension­al magnetic system with parallel chains. The distance between chains is greater than the distance between nearest molecules in the chain and therefore the ex­change coupling between nearest-neighbor electrons in different chains is much weaker than between nearest­neighbor electrons in the same chain. The chain of DPPH molecules can form a regular or an alternating one-dimensional array of exchange-coupled molecules. In the case of a regular one-dimensional chain we can look for two different models: the linear Heisenberg model and the Ising model.

In the Heisenberg model the susceptibility as a func­tion of temperature displays a rounded maximum. From calculations of Bonner and Fisher16 one can de­duce that:

(6)

at

(7)

where Tm is the temperature corresponding to the maxi­mum value Xm and J is the exchange interaction energy between unpaired electrons. If we eliminate J from Re­lations (6) and (7) we get a theoretical value:

(8)

From our experimental results in solvent-free DPPH we derive a value of 0.121 ± 0.002.

This model predicts also a finite nonzero susceptibil­ity value at T = O(XT=O) which is related to the parameter J in the following way:

XT=O/ (i /-L~/ I JI ) = o. 05066 . (9)

If we calculate IJI from Relation (7)- with our experi­mental value Tm = 10.5 K (see Fig. 3)-and use Relation (9) we obtain a value XT=O =2. 36x10-5 emug-l, which has to be compared with our average experimental value X = (4. 3±0.1)X10-e emu g-l at 2.3 K. We may say that both theoretical results (8) and (9)-and in particular (9)-do not agree with experiment and so we conclude that the regular linear Heisenberg model is inappropri­ate to describe the magnetic system in solvent-free DPPH.

A linear ISing model which describes the susceptibil­ityas

X = (N!!/-LV4kT) exp(J/kT) , (10)

(with N= number of molecules per gram), is not satis­factory either. In Fig. 5 the susceptibility data at 6.1 kOe are shown together with the best Ising fit (J/k =11. 5 K).

A better fit is obtained if we analyze the experimental results in solvent-free DPPH on the basis of a singlet­triplet model. In this model we assume that the system consists of alternating one-dimensional chains of ex­change-coupled molecules. We suppose that the chains are formed by pairs of nearest-neighbor radical mole­cules which form units with no or weak exchange inter­action between the unpaired electrons on adjacent units. The two "unpaired" electrons on a unit may be in either

10

11~--~~~~~~10~--~~~~~1~0~0--~~

T/K-----FIG. 5. The magnetic susceptibility of solvent-free DPPH measured at 6.1 kOe. The solid curve is based on the Ising model [Eq. (10].

J. Chern. Phys., Vol. 68, No. 11, 1 June 1978

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Grobet, Van Gerven, and Van den Bosch: Magnetism of DPPH 5229

10

5

11L---L~-L~~ll10--~--~LLLLW1~00---L~

T / K----lI_-FIG. 6. The magnetic susceptibility of solvent-free DPPH measured at 20.6 kOe (0) and 6.1 kOe C"). The solid curves are based on a pair model [Eq. (13)].

an antiparallel-spin singlet state or a parallel-spin triplet state. The exchange interaction in a unit is taken to be antiferromagnetic so that the exchange integral is positive and the singlet state is the ground state. The gram susceptibility is then given by

x = (NgJ.LB/2H)sh(gJ.LBH/kT)/

[exp(~/kT) + 2ch(gJ.LBH/kT) + 1] , (11)

where ~ is the singlet-triplet energy separation and equals 21 J I; J is the exchange interaction energy be­tween the "unpaired" electrons on a unit of two radical molecules. If gJ.LB «kT one obtains from Relation (11) the better known and special case expression

x = (N,t J.L~S(S+ 1 )/2kT)/[3 + exp(~/kT)] . (12)

Relation (11) describes the ideal case where all radical molecules do form pairs. Since in practice there al­ways will be breaks in the linear alternating Heisenberg chains, giving rise to isolated paramagnetic centers, we have to add a second purely paramagnetic term to our Eq. (11) in order to fit our experimental suscepti­bility data:

x = (ctNgJ.LB/2H)sh(gJ.LBH/kT)/

[exp(~/kT) +2ch(gJ.LBH/kT) + 1] + C2N,tJ.LV4kT . (13)

C1 and C2 are the concentration of unpaired electron spins which form pairs and of isolated paramagnetic centers, respectively. The result of the analysis of the experi­mental data by means of Relation (13) is given in Fig. 6; the adjusted parameters are C1 = 99%, C2 = O. 8%, and ~/k=17.5K.

Another way of explaining the deviation of the low­temperature experimental data from the pure singlet­triplet model is to make use of the alternating Heisen­berg linear chain model of Duffy and Barr17 where the isotropic Hamiltonian is described by:

N /2

JC(N, a) = - 2J f.; (~1~1-1 + a~/~1+1) .

Here J« 0) is the exchange integral coupling of a spin with its nearest right neighbor and aJ is the exchange integral of a spin with its nearest left neighbor. For a = 1 this model reduces to a regular Heisenberg linear chain, for a = 0 we get the pure singlet-triplet model. Even though this generalized model of Duffy and Barr does not completely describe the low temperature tail of the susceptibility data in solvent-free DPPH either, we do find that the factor a has to remain well below 0.2. However, we also believe that a is nonzero, i. e., that there is a weak exchange interaction between the electron spin pairs, since we have a strong indication from our NMR data6,13 that triplet excitons are present in solvent-free DPPH at low temperatures. In the para­magnetic exciton model18,19 a spin-paired unit in the chain is excited to its triplet state and this excitation can propagate through the chain as a triplet exciton by means of the weak exchange interaction between the pairs. This leads to the wipeout of the proton hyperfine structure we see in our NMR data6 for solvent-free DPPH. If this triplet exciton bandwidth (2aJ) is small, as we assume, compared to the singlet-triplet excita­tion energy (2J) the electron spin susceptibility will be nearly that of a collection of isolated pairs. 19 Thus this exciton model does not contradict our analysis of the susceptibility data on the basis of a singlet-triplet mod­el; conversely the susceptibility measurement does not provide us with a sensitive means for determining the exciton bandwidth.

As mentioned above pair formation occurs in the DPPH' C6De sample as well but at much lower tempera­tures « 2 K); in this case pair formation is hindered by the presence of benzene molecules between the free rad­ical molecules which weaken the interaction. The NMR results also show that heating up the DPPH' C6D6 sam­ple for 48 hours at 80 0 C in vacuo does not restore total­ly the possibility of pair formation at low temperatures. This heat treatment of DPPH crystallized from benzene, which has been thought to be an equivalent method to achieve solvent-free DPPH, clearly does not remove all benzene molecules from the crystal lattice of the complex. Although we have not yet performed suscep­tibility measurements on such dried DPPH-benzene complexes ourselves, we believe that the results should show a mixture of the susceptibility data of the solvent­free and the DPPH-benzene (1: 1) complex. This is probably the answer to the puzzling high and low temper­ature Curie-Weiss laws and the reduction of the spin concentration of about 50% between room temperature and 4.2 K found by several investigators, 3,4 and ex­plained through a "narrow-band model" by Kommandeur et aZ. 20

Our susceptibility measurements agree very well with those of Fujito et aZ. 21 in the same temperature range. A slight difference at low temperatures in the case of solvent-free DPPH is probably due to sample prepara­tion. However since they had no NMR results to com­pare with, they were unable to give a clear physical pic­ture.

J. Chern. Phys., Vol. 68, No. 11, 1 June 1978

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5230 Grobet, Van Gerven, and Van den Bosch: Magnetism of DPPH

CONCLUDING REMARKS

In solvent-free DPPH (i. e., DPPH crystallized from ether) pair formation is observed at low temperatures. From our susceptibility measurements it is not possible to deduce whether or not this dimerization is due to a phase transition in the crystal lattice at a certain criti­cal temperature as is the case for Wurster's blue perchlorate. 22 The pair formation in solvent-free DPPH as observed from our susceptibility data, supports a paramagnetic exciton model which has been used to de­scribe the disappearance of the proton hyperfine spec­trum in our NMR measurements. 6

In the DPPH' C6DS sample, where the free radical molecules are in some way isolated by deuterated ben­zene, a hint of pair formation is observed at much lower temperatures than in the solvent-free sample. A speci­men in which all free radical molecules would be isolated by even larger diamagnetic molecules than benzene, and which would be stable, would be of interest for therm­ometry as its magnetization is than expected to follow precisely the Brillouin function.

ACKNOWLEDGMENTS

This work has been performed in the framework of an association between the "Katholieke Universiteit Leuven" and the "S. C. K. -C. E. N." Mol (Belgium). We are much indebted to the Belgian "Interuniversitair Instituut voor Kernwetenschappen" and the Belgian "Nationaal Fonds voor Wetenshcappelijk Onderzoek. "

lA. Van den Bosch, Vacuum Microbalance Techniques, edited by H. K. Behrndt (Plenum, New York, 1966), Vol. 5, p. 77.

2H. J. Gerritsen, R. Okkes, H. M. Gijsman, and J. Van den Handel, Physic a (utrecht) 20, 13 (1954).

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(1968). 5W. Duffy, Jr. and D. L. Strandburg, J. Chem. Phys. 46,

456 (1967). 6R. Verlinden, P. Grobet and L. Van Gerven, Chern. Phys.

Lett. 27, 535 (1974). 7T. Laederlich and P. Traynand, C. R. Acad. Sci. Paris

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15D. E. Williams, J. Am. Chern. Soc. 89, 4280 (1967). 16J. C. Bonner and M. E. Fisher, Phys. Rev. A 135, 640

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J. Chern. Phys., Vol. 68, No. 11, 1 June 1978

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