Magnetic circular dichroism and absorption spectra of the mononegative and dinegative ions of [16] annulene

Cbemt;al Physics 8 (1975) 3X-347 Q North-Holland Pubkhing Company

In recent years son?* irl~esti~~ti5ns 0i th2 Wgll& circular rjichroisnl of ncgxivc ions of aromatic hydracarbonshave been published [I .I!j. showingthat !K’D is a valuabletool to get speztrascop~c tnformcltion about these compounds. Interesting ~SJXCK of neyrive ions are the possibility of hwng a dcgeneratc ground state and the rather k~rge v;liut~ d.4/fl that sometimesare observed. A study of 0th et 31.[;I, using ESR. NXIR, W* absorption and poiaro~rap~e techmques.showed that the mono- and dinegativeions of [ 16]annufsnc behave quite differently from the correspondingneutral mole. cule. Both kinds of ions are much more stable in solu8011 than the MokCUk.

detzrmin~d and compxcd with theoretical data. obtained by means of an SCF calculation with ~on~~ur~t~on interaction ;Ind using Sfatcr rypr atomic orbitals and B/L~ vz~tuss xe

I. Introduction

For the dinegarive

sew& stability ww crpccted

ion rhr ob-

from the Eitickel(~I~&l)

ruic. The ions might hsve a (planar) DJh structure, whereasthe molecule can have two ~on~Eur~[ion~in a dynamiceq~librium. probably of S, and C, sym. metry. These authors also calculated energy levels, usins the (mriablefl) I-fMf3appro.uimarion. In order to investigatethe symmetry on a~ optical time Sc3Ieand to get more information about the spcctroscop~cstates. we have measured the hfc~ spectra of these negativt ions. The e~~rjm~nt~l A/D

2. Experimental

The MCDspectm were measured with 3 modified Jouan dIc~ogr~ph model Il. of which the p~otornulti. plwr was placed about 90 cm behind its original posttlon in order to have room for 3 Siemens SLNA 60171/l 10 superconducting magnet with a n?3~irnu~ field strength of 60 kG. By changing the ma_cneric field (H) we obtained a good MCDbaseline and che&ed the: signal ta be linear in H. hfost mrasuremcntz

wre done with 2 magnetic field of 30 I&. For ~hc

lo~v-~ernper~l~r~ me3suremen~s a unit ~ons~s(in~ ci two permanent rn~~nets was used, giving a field S~r~n~~h of 2.75 kG [I] at a pole distance or’IOmm. In this unit a small quartz Dewsr ceil could be ploxd. The temperature of the snmple,could be lowered down to -160°C by passing;I stream of cold nirrug?n over it and was measured wirh a cooper-const~ntait~ thermocoupie, attached to the cuver by means of ruif polish,near the focus of the light beam; the temwa-

R.E. Komn,e, P.J. Zandsrra/MCD ture WZIS stable within

2 percent. With

3 stream

and absorption

of

warm nitrogen the optical windows were prevented has rhe besr signal

from fogging. Since ihe dichrograph

to noise ratio with samples of an optical density be-

1S, spectra had to be recorded at several dilutions. The CD c;llibration of the appa-

tween about 0.5 and

sprcrra of /16]anmrkrrc

339

ions

p-

I 16t

I. :: II

:

;: ::

00 I

;: :I

l?-I/

I

I

::

ratus WAS done with a solurion of epiandrostcrone in dioxun. The optical absorption spectra were measured with 3 Gary I4 spectrophotometer. For the low-temperature spectra the same Dewar cell was used as mcnrion-

The spectra 31 room temperature have hecn published before 131, but are measured agin for

ed above.

reasons of comparison.

[ 161Annulene W;IS kindly given to us by Dr. Rottele of the University oi Karlsruhe, and stored under nitrogen at -‘_O’C in the dark. The solvenrs tetrahydrofuran. 3-methyl-tetrahydroiuran and doglyme were dried on NJ~SO~. purified on an A1203 column. distrlled under vacuum and stored on 3 Na-K alloy and a Na mirror respectively. The rndical anion and the dianion

were formed by reaction of the hydro-

carbon solution

with

a mirror

of rhe alkali merals Na

and K. We did noI observe appreciable diiference

be-

FI;. I. Absorption spwtrJ

of a mllture

of

[ 16~annulcnc xnd

IIF mononqarn’c and dincpanvc ions in MTHT. icrcnt tcmprralurc5. rc,pcclircly Jnd -119”C(-

-28 (---

JI IIIKY dll).-6X-.-.)

- - -).

the t’;lct that the reactic)n mixture can be described by the following

equilibrium

tween the spectra of solutions in THF and in MTHF and also not between the spectra with Na or wth K as counterion. In diglyme the reaction was somewhat

The equilibrium

slower. but rhe spectra were nearly 111~same.

be espressed in rhe dipole strenyrh

2V&,+bll--.

sorption

constant

Kr.

T. can

at ;f tempwture

of lhc various ab-

bands. The dipole strength

of3

band is given

by 3. Results 0=(9.1834X

3. I. 77re kttrprra~trrc

dcpettdctm

IO-3/CI)

nj rite absorprbr

spectra

where D is in debye?,

P-l. I is the optic;ll Short reaction of the hydrocarbon solution wth the alkalimetal resulted in a mixture of [16]annulenc and its mono- and disnion. In order to obtain values of the dipole strength of the negative ions and 10

check temperature absorption and MD

effects in the spectra, we did SOme measurements iII vrlrious tempe-

j- (OD/v)du. b.md

C is the concentration

in mole

path length in cm. OD is the optical

density and the integral is the zcrorh moment sorption

moments of the most intense absorption hl- and hl’-

(35000.3_6500

temperature

Trespectively

(hl’-+-,

of

ab-

of a given band [4J. If we write the zeroth bands of hl.

and 24800 cm-l) as (hl$,

the espression ofKr

(hl-$-

a1 a

and

bccomzs.

ratures. The changes in the absorption

spectra are very

large, as is shown in fig. I. where we can see that

cooling of Ihe solution favours the formation of the ion and lowers the concemration of

mononegative the molecule

and the dinegstive

The occurrence

ion.

of isosbestic points dcmonstraIes

where A(M) derivation

means: iRl)r, of rhis equation

So by dctermming bands at different

-(hf)q

with 7’1 < T’,. A

is given in the appendix.

rhe integrated temperatures.

absorption

of the

KT can be calculared

R.E. Koninx?p.P.J. Zar~dsrra/r\lCD

340 Table I Some parameters,

exlractcd

from thr tcmprr;:urc

arid abrorptiorr

spectra o/ ]I 61 annlrlene

ions

21

dcpcndcncc

of the opticA absorptmn sp-ctra

In K

!

t

2!4- ==? M t hl’-

o!-

K = 7 (Lll?O°C) AH = 5.0 = 0.7 kczd mole Ci = 22 3 f 3.4 cd rn&-‘k-’ -21

D~polcrtrengrh: bl

D = 88 debye’ D = 95 dcbyc’ D = l-18 debyc“

: 35000 cm-’

bl- : 26500 cm-’ hl’-:

24800 cm-’

knodng

the initial

function

of krnpersture.

concentrations

\

3----

5

I

.---_

qunntiries

order

.lOj

In h’ hxs

to delermme

Mand

6 +

The rcsulls of lhese cakul~-

versus I/Tin

therrnodvnamic

\

o\

and 35 ;I

tions arc given in table I and in 6s. 2. where bezn plotted

-L

___-

without

‘,\‘\

I

L

rIF. 2 A ~10~ O[ In A’ 3s J iunclion ol fhL’rcciprocdl oi lhc _,b-

the

AJ of [hc CCJUI~I~.

rium. The vulues of AH and AS are con~putcd

\uIu(~ t~mpcmrurc.

by

means of a least squares procedure out of the inkgrated absorptlons of the bwds, rchich have beet) COP

In 111~case of the MCD spectra of solulions a good q. protimalion dfi is 3 gaussian I1~41ape. whereas/,

for shrinlrage of the solution. The dipole strengths of the :6500cm-’ bJnd ui the mononeglive ion and of thr 3800 cm-I hxtd oi the dinegalive ion are expressed In the dipole srrznsth oi the 35000 cm-l band of the molecule bq’ rhe iollowing equations:

IS S-shxpzd. Thr psramcters .-I and C are both due 1; the splitting of degenerate levels by the magnclic fitld, so rhsy can be prescnr only if the point group sym-

rrcted

metry allows degeneracy. The B wrrn is presrtnr ftir e\rry transition because it describes the magneti< field induced mixing of slates. ‘k expressions of 1l1c ..I, 8 2nd C parameters. for the ekcrronic transition A - J. Jr\: ;ivPn by:

Knowing the value of LlAI (88 &bye’-). rhe unknown qtzmtilies DA,-and DNz-arc easily oblained (we rnbfc I ).

The theory

of MCD

by Stephens [j] and will bz @en

X Im ~alrrr,lj)


11)

has been estensivelg descnbcd some pcrrinent formulae

only

here. Usu~~lly the mobr

eliiplkity

[o]\f

prr unit magnetic field is expressed 3~ 3 function of rhe wvenumb~r v by means of three parsmeters A, B and Cand IWO lineshape functions I1 and 12 [3]: PI\,

= -33.53

[(B+~w-)fi

where s

bind

(f,/u)dll=

+.4fJ.

+

C~olmli~X(klm~P)*~ilplk)~Tro~, tb)

k#j

(3)

where m is fhe electric dipolc moment is the magnetic moment

I.

opsrator.

opsrJ[or 3ndp

The sumrn3lwn has

10 be carried out over the degenerate

componcnls

10)

of the ground stale and lj) of the excited staw. whik

dA is the degeneracy ui the ground state;fiwb means the difference in energy between the states I&Jand la>. The hiCD and absorption spectra of the onion of

are given in fig.3, where we can recog nize 3 isrge S-shapedband due to 3 Faraday Asrcrm. In addition we see pretty large:iO],, values in spectra1 ~~~~~n~ulene

ranges where the absorption rntensiry is low. in the ~5: of the dine&ve ion thereart?WYlarge

d-terms for the smailabsorption bands in the red se* gion of the spectrum, whereas in the W part a smaller h1CDband agreeswith a strongly allowedabsorption band, as can be seen in fig. 4. In order to compare the e~perirn~nta~ spectrum with calculated valuesby meansof eq. (3), it is necessary to assumeband shapes for the electronic transi-

tkons, after whicha curve fitting procedure 1’3~lead to the values of A. 8 and C. Another method however. which IS independent of the lineshspc, is the method

of mon~ent~fG.7j. where numericalintegralsover the absorption and MCtJbands arr: used. The main difl’iculty with this method is the way ta unravel ovcrhpping bands. The rrth moment of MCD is defined by: (Ol,f =

I

~[U]*~/~~~~d~.

(71

hand $o

usingeq. (3) one finds the followingexpressions

(&, = -33.53 (5 + CfkT),

(6)

@I, = 33.53 [A- (B+C/kT)C],

(9)

Table 2 Eqxrlmcntal values of the hICD parameters of rhc anion and dianion of [16~~nnulrne ;It room wmpwrurc vo”’

(1-b ion

(2-J

ion

;ct

,r/Dd~

{~/~)e) x 1oJ

Ltf)

2’770

0.40~)

.I

65

26600 2l-m5 17668

26440 _

OS? 0.52 0.52

4

95 10 In

29990

30060

0.01

::

i% n

-5

-

17166

1 17

-1.3

7

IS074

18013

07lb)

-I

7

247.52 35740

24872 -

O.Oj 0.05

17066

3

I-%

t I

peaks does not

lh2 anion and the dianion. With the psramet?r vdues of table 3 3 jimulJkxl uf the hf(JD spectn hx bren carried out. UsinS~3uss type band shapesf9). Some ~broni~ pans of the bands \vere sinlulstcd with the A and B WhXS Of the 13rSez.lpeak. Siy alternation. possible if the eic~tront~

-

11659

between the positive and native change when WCgo down a hundred degrees in temperature. The szmz WE SCM car the monone~~tiv~ ion. so the vrtlue of C/D is Zero for both

eSpeciaJ]y the ratio

iysnjiriottis allowed by more than 8 sit@ nbratronal modz. ws not seen.

4. c3lculstions

30

3) ProbJbly lhls i, not u ml pJr3melcr. but Compowd B-terms ofdrlicren~ sign.

Oi [Ku

Theoretical values of spectral parameters have bctn by means of the LCAO SCF CI method of

sakulated P&cr,

Parr and Poplc,

while repulsion integrals ;1c-

cordq IO hlatagaare used. The geometry of the [ i6jannulene negativeions was first choosers 10 b2 a5 symnztric 3s posstble. wtthin D,J~symmetry. This nleans that $1 bond lengths are I .4 ii and nit bond zm$es 135 degrees. The results of these ~a~cu~ati~ilj where ii is the ratio bi-[we?n th< first and zeroth mumznt of absorption [4]. defined in exactly the same way 3s eq. (7). with E instead of ftZJ])f. The vaiucs oi_4fD and BID. dcuiared by means

of the moment analysis are given in table 7. In this analysis the spectral regions of a band xc sstimarcd by ~xtrapofarion of bell~shiqxd 4-&h

absorption

bands.

Itd to 3 dIff~rrnc~ of its than 10 p-a-u

be-

tween various spectra. On cooling the solution

of a mixture

ol[l6]an-

nuient:and its anionswe got e~clctlythe same equiiihrium shift in MCDgs h3s been seen with the low rcm-

are shown in fig.7. Another possible choice is piv?n by 0th et al. 131, who minimized the strain energy. in order to investigatethe dependence of the BiCD parameterson the molecular geometry we dso tried such a model. usingthe coefficients of Allinger ct ai. the bending and the Van der Wa3Ij With our second geometry (see fig. 6) t&tl:e 10 the first one the gain in sigma bending eneri;y is about 22 kcai mole-l and the loss in Van der Waals energ is 5 kcal mole-‘, taking 17,5”as the mlmmum unstrained sngie. The ~eo~~tr~ was not optin~l~ed, [lo]

to calculate

enew.

prrature absorption mrasurzmems (fig. 53) In this iigure we have a much lower sign&to-noise ratio 3s in tigs. 3 cmd 9, because a ~~rrnanent magnet with 3

because the due of the bending energy is strongly dcprndent on the choice of the minimum unstrained angle. Wth these models the energy schemes of the mono-

weak f?eld had to be used for these low tempzraturs mwwemwts. With the permanent magnet it was not possible to observe thz equilibrium shift in the (JV

wl dinegative ions have been calculated with rrspcctiwly 43 and 27 configurations. In order to calcuize A and B terms according 10

range becattse the MID signalof the dianion ws too at the optimum conditions [8] foprical density between 0.5 and I.?). h

Wh 3 solution that contained only the dinegrttive dependency was present. as is shown in fig. 5b. Herewe see that the iinzshspc 3nd

(3) 3rd (6). in the first place complex cornbin3~t~~s of :he real functions $ of degenersre gales are iurmed: which are diagonal in the angular momentum

operator:

ion. I-IO t~~ipe~tur~

\fr=2-1j2($0

2 ir]lb).

,

, 550

t

I 600

------4

The Cl

functians \I, are evahsred

h tnml

in the SCF mok~ular

orbitalsQ[ II], givin_g realexpressions for the matris

(IOl

elements.These hlOsare then expressedin atomic or* bitalsx, with coefficientsc i Of the magneticmoment operator Pz, we only take

the orbilal pxt I,, related to it by !.I:= - (Po/fi)lz, where40 is the 3ahr magneton: this can be done bee causethe spin-orbit couplingissmall (31.UsingSlater atomicorbirals,the magnetictr3ffs~~ton moment betww~the hlOsq, and @,canbe calculated[I 1 by eq. (10).

wherep = Q,$+ q is the effective nuclearchargefor the carbonp3 orbit& (= I.625 f f ,121),aw is rhe Bohr radius (=0.S2S);Xlp and Yf are the artesian coordi-

n3tesof atomi with respectto the centerof gravity3s origin:Rii is the distanceof atomsi andi andCgi,Cbj 3~2tlzearornicorbital coefficients. The resultsof the calculations are shown in the tables 3 and 4. Variation of the resonance integnlfi

344

20-

==: -

-----ET

I_

.

-

e-.--E;

..-.-x.

-

--..-“A:

lff-

resultsin rcvsonablcchsngesof the tmnsition liequrn. ties, but the other parametersdo not 41er vex’much. ~~~liz~~i~n of thr second geometry has very litlIe influencean V,but somewhatmote on rhe rest.

5. Discussion

. prcsencr: of 3

degrnerJIe staw. On ESR time sC3fe D#, symmetrywzs found [3j. Our rest&sindizxe that rix symmetry Dqh may 31sogive 3 nthttr good ~e~criptlon cn optical timesc3le.Other symmetriesxc not Wry likely. Accordingto the term-schemeof rig 7 one expects that the spectrumMl consistof t\vo allowedtnnsie tions. %tu -r ?E; 3n(r?A?” + ‘$snd possiblyof someorbit~iiyforbidden.but ~bronjc3l~}f alloived transitions.In the absorptionspectrum twit large bands arc seenat ~6~OOcm*i 2nd 30~~~cm”’of whichrhe first one (IA?, -+2Ei)exhibirs considerable vibranicstructure (see also fig. 11.In the AICD spectrum the ?Ei transitionis the one, whichgives3 kqe

A-tcrm.wheress

the ~E~‘transition

gives a signal that

i5 even m&r

than j@]*rin the red pxt of the spectrum. ~~~rn~~~imaIysisgtvesthe P~~UI?S of tabk 3.

4Dis respectively0.52 and 0.01 far ~&SE two Comparingthese numberswith the theoretical ones of table 3, we see that 3 very good ~~r2ernent mists for the strong ?Ei trrtnsition,where~/D--0.3. where

bmds.

This 1ue3nsthat the dynamic Jahn-Teller

eifrct.

IT

present, will ml be wry kg Tfle .4/D @fue of [he ~~~[~~~siti~n doa not agree 31311wiIh the t~i~oret~c~~

resuhs.bcingU.01 instead of the calculated -0.5. in explanation 111terms of Jahn-Teller effect is not wrl probabletendsnother possible esplsnation may b? th3.t3 tibronic bsnd ofthe ZEl,transition coincides with the main band of the “EGtransition, Becrtus~ these two bands have opposite A/D a very smallrcsuiting value may follow. The reason why the f$ll value will not cancel in such a case will be esplukd brlo\v in this discussion. 0th et al. [3] found front charge density cdcuI3~ tbls an “All; ground state, whereas in our c&ul.aions Re always find ZA.,, 3s the ground state, howe~~cr with ?Atu fying only about 450cm-’ above this VW.

URf~rtun~Ielyit is not possible by means of MCD me~suremen~sto d~stin~uisbbetween these OWL) p@+ sibilities,because both the transitions ?A?,,+ ‘$afld

-I.-l -I 6 -1.8 -I .sbt -2 0

23610 29668 30779 30120 31881

172 281 298 161 2%

0 363 0.391 0512 0.361 0.532

1.19-1122=0.97 I.18 - n.30 = 1.18 1.13 - 0.1 I = I 02 I 28 1.62 -- 0.33

-2.2

32993

301

o-r51

1.76-037-1.39

I .3J - 0.X

q

I 08

q

30271 31_75!2 3x72

7.73 8.84 10.5-t

-0.479 -0.501 -O.C??

31981

9.23

-n.;so

33309

I I .J9

-0.513

-0.93 + 0.72 = -0.71 -I .08 + 0.26 = -0.82 -I 3-1+030= -0.92 -0.9 I + 0 1I - -n.SO -1.35 +O.H = -1.01

31366

14.23

-OS-~?

-l.48+0.37=

” l?x [irst nunlbvr ,ivc% rhc conrrlbulion oi the firrt prr oi q. (6). Ihc wcond number rhJt OT Ih.: orhcr prt. h)Th csc ~31~s .IW caiculat~d with anotlttir gL’orn~!rry 01’IIIL~icn (~IOI 211dnclcr arc ~‘qu31). c.) Of the three low-tying 2E,. \13fc\ ;ttso 4/D uhes ;II.Z alculJted N’irh J = - 1.8 thcw rducc arc rerpcLliscly -1.38. ? 1.035.

% where

-t ?EI: will have an A/D v31ue of + + l I,) PO. (/i,;s

Ille espwlation

lar momentum

wlue of[k

orbital

3nsu-

of the ?Ec (only 3 ground sure with B

symmetry uould give 3 negative s@n). Wilh sow

-1.11

3.071) 3nd

For thr 22700crn-t transition also tin S-shaped hand is seen. tlo\vever. no degenerate state has been calculstcd in this region. so we tried to sirnulltc 3 spectrum, rrlww this bsnd ws considered as ;1 vibronic

ms~hematicai mzmipul~tions It was powblr

to change

part of the ?AIU + ZEb rransirion.

the sequence of the SCF FlDs in such 3 U>

IIIDI {cc

this IVJ)’Icd to wry e&oneous rcsul~s. Also the ,4,/D v.dues. dewrrnmcd by nlomtnt analysis arc different.

go1 rhe scheme

of 0th

et 31. (fig.

I? of ref. 131) bur

but simulation

in

after configuration interaction again 3 !A-,, ground ws found. no\r with -‘A ,,,lymg 15cm-~ 3bow it. this

so w must conclude (hat it is really another tnnsilion. The S~sh~pe can be explained if we assume that

picture seems very unrcalis~ic because such 3 nttar.degrnrracy would cause 3 remperaturz depcndenr hlCD spectrum and in addition rhc calrul~wd dipole sirengths of 111eIWO rransirions to lhs “Es sI3tes wre contrary 10 c’sperimenl. So. we 3ssume for pracrlcal reasons that rhz gound state is of symr:lctr!’ ?A,,.

the band consists of IWO transitions 10 very close

- I .4

10109 I1409

O.aJ?. 0.037

2.106 ?.I 13

25099 26335

1,700

0.031

2.1 18

17571

483

12760

0.033

t ,895

27290

33-1

-0.t85 -0 184 -0.18-l -0.182

0.030

2 I23

18807

484

-0.18J

0.028

3.126

30033

W

-0.183

-1.6 -I 8 -1.8”) -2.0

1398-1

-2.2

15263

a) See note b of table 3.

-182 483

lying escired swes. in which case the two B-terms have a diflkent sign [ i3]. In the term scheme we see J lot of close lying vibronically allowed SIDW which can exhibir an S-shaped rransirron. In the red p3rl of Lhe spectrum WC find prelfy lxgc IN-D vah~es compared to very small dipole strengrhs. The large /3-rerms in the red and rhroughou[ rhc whole spectrum can be explained by [he field induced mixing into the ground state. The first part of tq. (6) can have 3 large value if (kJ&Jo) differs from zero and pi the energy denominator Awh is small. Both rhzse conditions are fulfilled in the case of the [ 16]annulene anidn, where Ik). 1-1?and lo) have the symmetry A,, , A,, and A?, respectively. while Rw~ was culculatzd at &out 450 cm-*. This part of the B.term has been calculated for the two allowed transitions. Also the other part ofa, according to the mixing i~o the excited rrates has been calculated, but this cslculation was rcstr:cled to the influence of the states 2E. E and ZEf’onro each other because no.other close lying SMICS have the proper symmetry

and other 2Eg s~atcs

differ too much in energy. As can be seen from fabjc 3 the mixing into the ground state is much larger thsn the mixing into the excited sta!c’. The 0~~~r~Ji i&uhted B-term h3s the ri@t sign and a pretty good numcrieal agreementwith the experiments1values. c 3 &,...U>“.‘ ni,r@o,lr;,w in,, C._. .% ,“.. ‘ilw MCD spectrum of

tht! [I ti/annuiene (I!-1 ion

shows transitions which are 311more or less S-shaped (lig. 4). In the rernrrchemr of this ton two poss~bic &wed transitionsart:possibleat f3OC10 and at X000

6. Conclusiorls

Q’CT tttan~Dr. Rot& of the

university

of ~rJsf~hr

providingus with 3 sample of the ~16)annul:ne. Wekindly ~~~no~~edgereferees suggestions~ws~ming the derivation in the appendix. The present we+ @[ion fus been supported by the PJetherla& FPJ& tion for Chemical Research (SON) with finanal aid tbr

Wch

is eq. {I).

sions and with

Also with

it is easy to derive In the kw~?

Appendix

the use of these cxpra-

of the dipole

the definition deri~t~on

ar resonance

frequency

of such u band can asily lemprratures and higher. ht M”arld

pre~~rrcd the USC of mead of the optical

WC

integrated absorption bands density

Howr*er

the Ilneshape

on cooling.

At lower

bands become narrowa

the linewidths

considered

s;tmc %I~ (see fig.

bzrxuse

change

the absorption

Xi2

strength.

cq. (2).

of the. bands

here do no1 change

of

in I~C

1f.

References

1I J P.J Zsndari. D 1. Schaltcne and R.E. Konmg. J. Chrrn Phyr. 57 (197213821; P J. Zt~ncidra .md B C. Van Borg’. J. Chsm. Phys. 59 (1973)5101.

(51 P.J. Swphens. J. Uwm. P~Js. 52 (19701 3489. ;6] C.14 Henry. S.E. Schnattcrly and C.P. Slichter. Phy’c. RL’I. 137 (1965) X.583.

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Substitution the

of these equalions

into the expwion

of

~q~i~ib~un~ c~nsl3n~ girrs [ I 71 H.C. Longuer-Higgins. Spewi) Ckmical

Publieatjon No. 31 CThc

Socrety, London, 1967) p. 109.