San Jose State University From the SelectedWorks of Juana Vivó Acrivos December, 1961 HYPERFINE SPLITTING IN AROMATIC FREE RADICALS Juana Vivó Acrivos,San José State University Available at:https://works.bepress.com/juana_acrivos/79/ 5].· UNIVERSITOYF CALIFORNIA LawrencRea diatiLoanb oratory BerkeleCya,l ifornia ContraNcot. W -7405-eng-48 HYPERFINE SPLITTINIGN A RO·lv'IATIFCRE E RADICALS J.V. Acrivos Decembe1r9 61 .. :.JV A.CR IVOS \ DepartmoefCn hte mistrLya,w reRnacdei atLiaobno ratory UniversoifCt ayl iforBneirak,e lCeayl,i fornia .I The h;me1s"tf:riuncGto ufrc· thEe� "=!s pectraf' .ceo:refa diciaGl s a prol)c:ro·ftt hy0 syosfte elemc troannds n uclewih ich constthe, mio lteuctuel e. Itar ises from.the einneterrgya c9.tfoi fot nh e unpaired elect�ons end nuclear S!)in·no ·hiisco hft he.f orm 11hcrei sa.T t ens..oo f1s ecornanldt ,I ist h�n uclesapri o.nn d J the elteoc·-tal � I � � ;£ t. troa..nri gular mo1:wntuIm.I?,o. t he·rw orad n,n ucleus o�s es1p-ia...rp.cea o probe tot hee lect,rsotnriucc to,furea conrplmeo:i-l:c ctftrelearr adiceTlh.em,- ..;asure- rento ft his· coupliinsgi n enegerngye ral_,,,i lo:10if m. p:9o:rtenbcecc,au se it pcrrtilsit h:ed irecdtc terr;,o-fht iha.::::et licoc..nf ·cadn e nsitenide si,tt sh eorc·G:i.ce.l tu:.r"C. Inp articulairt;; :niost un co!!ImOni' or thes pEeSRc torfa:rr cc:i- :e.di.nic alo solutionpso ssteoas· hys p dr:f'isnet ruct;c�sn' heo,w inn Fig. l for the p benzosenicquinaonne.$'o d :r iw ohni cthh e J:·c.diinod:ut.c·iecodrn m1 sit:!.i�ot nheo Paschen-:eack. haipg}?hr md.f'miaeo.rtleid o nc ovebrynt ehdeB ol:n.-> relo:i;ionship: -1- .uCRL·9 998 hw iathee neiy;i·d ifferebnectwee etnh ee lectronic lZeeevemanl ins the ab O . �f sencet hehyp erfininet eracta.nidol\.n io a cocnohtaanrta �teri.sottfhei c . . .. n . . ·. . .. . . z free re.d.ical. andn uthcel enu,s gyroof� gnetic ratio H ist he applied rn�·. externalrr .sgnetf'iice ld.In ·t he aroma.tir,c- elcctrfreoen r e.dicatlhzes, i f;!I!,a 1 bondperdo to·nws:t atphi In = are rcoponaifbol:rte h eo bs.esrvterdu cttn'e. 2 . . i Th:!.se x:ge:rimenteavli debanac el·e dt hereftooret hec onclutf3haito n tshep in and polarizatiiostn r unotmitc clt hrougha valenbcoenb de t1-;tehee an- 'fr- electrc�lUt�) t "'ot. h:all.ttiime c hw erceo n�dsereo.ds nionnte ractgrionugp s. 1 2 Weissmanand McCon.nehallveb roughfto :r.1t-hceih dee tall c.uts o riginally propobsyeA db ragam. llorowiPry ctez3 ianntd h.e ir sotftud hye l2Yr>e:-L"f'i1?,e OIJltit ingo ft hei onoo ft het ransit1i11.eotna c;lc1 i1cst,h i'bso nding cbane e x plaihien.te drms of. amn {3Ueti�cn t dencitmayt ,rix.i nt- 1hicahl lt hee ):citcd coni'igura.tions cmt1.ott rhieg'b 1u·t0is,ngt.i.. a-ritdte hr oug·h.th ec orrel.a.tiinotenr actiboent m�tehen tt -rgorO lll?S wohulad.v teo b e incluT'dniesda. .p :proo.wchhi,c· h .has beesnu ccess�deyv elopanedd appltione idur. �rcoauss eins t hel iterature, ·will now be gidevte�inl ..in: tsrswo�ime?llb e :moe.:f'td heed ons:lmattryix for 4 malismd evelobpeydLo wdin end._McWeeney.� UCRL 9998· -2- The D�nsityF orm.J:.'iunle.:ttiroiXn 1 11 · .The electrsoysnitecm d escribbye·�d .:. toimn?tri � leculeissg iven, within .. · . 6. . . i set th.eB orn-Oppenheimearp proximtioinn,t erms ofe completeo fa tomic . ' \ . orbitals undreesrt ritchteti haotnt heP aulpir incibpeleo beyed�A direct- n lymJa sui"�bplbyes ico9I1emipcraolp er!t2 k>··· t.1 �,iNCc( D�'K)(,=Jj = (-"l)P fl .. . - . . .. . ; \ . .. . .. ' ;?(b) w.� <.�e_-P��-� ,� h}.-S ��l�te.r �tde�inant. .·:. ..· . •;·,ft�D .(. l).��.,fr. . : .{l)11 :�(:..:1,) .. · ....k .l ..k2 .· kn 1<_2,) t��c2>, -�_1('_2_, > ;,, -2 - 1 . The eigenvac;>lfut:eh es piins i ndicabtye· das uperscrai bpatr, _ ,•, "' .'-.-o =,, I • I • • • •' I +. -fo�rIlls� _�l/a�2:n dn- ot��;fn��grm �= ��/�•2. ��--��---��-��----��.�-��-��---��--�--�-� .. .. . ' '' ... . . . '. 6 . -. '. .. . t Jg·i\n terchangets� � pinin then :p aiorfso rbi-wt�sc arhe b ondteodg ether �no. · . E permuttheeesl -ectamornognt sh sep in·o-z,bitwuilst,h correszpx>anrid:l;iinge s �he· ran dp .Th et ransformat%iin o Enq ll 4{)in thvael enbcoen VBd , methiosdt he unit matrixw hehybnr id orbhaivteba elestn ak einn taoc coun··t �. UCRL 9998 -4- The functio""nf!2' . '\, (x.).ig se neIin ra elxp an. •de d in ' .te nriso fz·e r.1; � onetw,o ; · etca.r tJ.'i:co lep eratqrs: .( 7) �nda ccordtiongE q. (2)e.°:h.i1:)tesc tavtailounie s :: .· ·. . •.·..,, + - 2 .(8 ) ·whe·tre he o·p eratiinsoinde theb );'a.ckeits c urrioeudtb e.f oret hep rin1es ign • ' . • 1 ise l-r.i•·in•a.t.H cedr p, p•••.Pi �� define.de. s,-o.�t·h,te w eot,c e.l ectron � � 2 c1.c nsitmayt rices Ni *'2•• • (•:£J.� ,'� )• f•/:• : ._) P1( �;�={ ), :fe(:f.]_, �j) ( f�-kJJ)!, Pi:f.i•�;tCI«,:£i��,�:IN >�)...< •.:£J. * ,•·� •�• ><�> fl o •. D·o• • o oo o o • o11 o e 1> 00 0 Q O O O O O & OQ O • and (9) The inr9ortance·of-thema trix is dtuoet_ h ep hysicsailgn ificance density ofth e diagonale lements.Th us: > .. f � �1(�1 1 �l:.� -�umbe� �fp articliens� he.. sysmteum�li !)liebdy t he pl"obaboiflif tinyd ing one with::tLh'l'le · voellumee mendt� ,c en- . . . ... : . . - . . ·uCRL· 9998 -5- p2(1!,2��. .�2 )ld ;1!:�d � 2.£ =2 x numbreo_f p ?,irisnt ehs ysetm . , .. . .' . . . . by.thper obabiloift y ·m ulltiiepd simultalnye·o ufsinding· . . . 1 onpea rtiicnel aec ohft hveo lumeel ementasnd_d d£� 2 i c:��t�readb outa.n �q-,P r• espe�voetloy .cAorddng:t t�. qE�· 3·.)(t1 he n:. 2.· ... . ..:. ...· . ·.. ,2.•.; 1 1 1 Prh2;;:;,,nll ·�)n� � P P(I0\!1,2.,n.,; 21'J,"n·') IO, n .. ' . . . . .. . . . (9}, :w here * PKA= CK CA = Pn( .,12 J1�•.-n I •. 2•l'., •, n •') • J 1 1 (N�!� IJ!(i,2�.�•'i'n*,(·1·�<·;2N··,;:)• �• N n)�() ) K witthh ree latiobnsehtiwpse uecnc esdseinvsemi attyr i�es: 1 (Nn)�n�(la�20n,f·1�2·�ni·)·= g I J 1 1 P+(12,,• • n·, ln1 +'2,,. •�;n ,+nl) nl � +l brevty are For � thc�o ordinaitnedsi edcb aytt hpea rtiicnldee x. Alsot hsep aacnesd p icno ordimnaanytoe bwse -sepaarcactoerdd ing toM cWeeny; · * * . . a a . a(3 . p f3 (KAl);l')= p (K.1;,1'A)Ia (la) 1 '{)p (+K.,AJla;l()l '()1 ') 1 1 . . *. . ·.1· . . a� · . .· (3 (3·· .'4n .. , p·(+.,KA·J1;1�_1(f)) .a p,((Kl.7�A J)lt3�21( )l '()f3i '.) 1 1 · . ·. · (10) ·wherteh e· .pares piniesdse nsity.matorbitcaeisnb eydi ntegrating 1 p ovetrh sep in.coo•�.dTh iens aptipenrs o dtuoc- tw htihceh 1 spatfiuanlc tbieolno insgi sn dicbayta er da isseymdb o+I.n particiuflt ahre,r e aenxaxi iss otfsqu antiz�a'tt ihosenp in direction .c ompoinnet nhta t is: .UCRL :9 989 -6- ..· - z f (S>= [��(l1)'p1)i,]=( ild; �l l\f a. a � � · =2 (p(1;1 )- p {1·1,)]d £l 1 1 . . ""½i· : '· ql_l(; 1)d £1 (11) spin Fois�t ateosfd efinistpei tnh·e s ·pleisnsa nd densimtayt rices ·P.i and..a rqet hen; 1 P1( 1;�.1 ) = K::A}: p . '}p\[-? p. , (j1K ;Al_: ' .):+ p , (l·.K I�l . J l :'·) ] qll j{ l')=.. P�� [p (�i\Jl ; .:�'·) P-i(K Af l;1' )] (12) l K witthh.e f ollopwhiynsgi csailg ntfiocft·ah nec·edfl;oi naal elements: any· p(11J )df .= probabiolffi itnyd ineg leotw�iothni n 1 1 . . .. the volumee�e mendt£l centeraet�d 1 • · q1( lJ· 1d)� l .= P::r9ba.lbiitoyf f i.fl:d.i·..nan Ug..l' 1�rpeade lectron -� . spwii+nt 1h/ 2w ithitnh ev olumee lemednt·a t · :_:1 !:i that itw'i tshp in _. ..minus off inding' 1/02· . UCRL -7- 9998 THE HYPERFINEI NTERACTHAIMIOLNT ONIAN Them agnetiinct �raotion isa betwpeaernt iclerse lativistic 2 .effecFte.rm ii d�rivtehdee xpressfioortn h e ofi nter- ' energy . . between 1 theory action theel ectarnondnu clsepairfn r oDmi �sa c _relativAi ty.. consistw��n:tt h of d�r1vat1on thepsreC> p��.r� ta:is . 14 b_Cya simi13r andF·e rreials f ollowTsh.e. develop�d hyperfine energiys byc.o nsidetrhienm·go tioonra ,nie lectrionn obtained thfei eld, �n= curl� n i�ducbeydt he·nluecuosfm omen�t" where potential· n thvee ctor 1 � ata frotmh e is by: n _d ist�a nce hucleusd·enf ined

hyperfine splitting in aromatic free radicals

Similar hyperfine splitting in aromatic free radicals