hyperfine splitting in aromatic free radicals

56 Pages·2017·8.93 MB·English

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<ty of thhaiss thseye.nsn tee mx- gecta-
·i:iivaolnu e,
./ .·'.: (2)
whe::re _ni sa_ (�f)u ncatsisoonc iwaittethdh eob neT'rob,l aD:ed ·o/ (�)J�·:_··�l�e
:ra.·1Y\�.,, �1.uch·:ltciclo1..1nc .s·c r..,iGbheee lcsc ·t:cosnto..i tec ' vhI'\.,e snp anx.st :he c·o n11)lete
=,=
"\ ·v
s:9acUe� :.sdp.inc om:..· dai:(rt1 e·s,o szt) h e!f electx·=o nsx, ...._� (9'1' ,::, :::. _.. .)o( ::)
. . . ' .. "'I\,. . . . I\., ·. I\,'v�.J.. • . l\:.,J . 'J\,
.is e:q;:t\1gn�sneerda,al·s, inSa Ul) erpositoifoc no nfigurationThsu.s·,, -
(3):., .
uhei'·:ee a.ch-�(i�sg).i vebnyt hee.n·t ic�uoetriz:�d prosd-tu;c,t·pg al_reCit r;"i ctlhee
),.
molecular _sp�-or�(:£i1ta�lrsbi cro.'O'h·k -...�t u·1iJ":in n.., es.cro mbinatioonfts h e
completsee � .of o�ritbtoamilc¢s ( x):
i
or ( h,.)
where Tis
oi ·
orbitals¢ into ·tha·tm.o 1ecu1.e.r orbit�al�s":u · The atomic' orbi·tals c1re: character-
"' 4'\.,
izedb yth e·f ourfosly.awdo·l v( n=,P, ., m," :sniu·ca h ma )nn,e rint ne.t:
' ., fi
t�::
�v·)= R { nr.� ) (Y 0, �) f .. ( m ) (5)
.- "" n[ "'n:.. b s
UCRL 9998
-3-
�1heree ,(�r )a�r et hes pherip�oalla cro ordionaftt ehese l ectron
y. 8n (�)
witrle1s Cptet ot hen ucieus deperiodnlsir otnh ed istanc
�
\
r1•oma ndvY (eq,,)i'a · sap herihcaarlm o�{is�e�� ifnosrt ance:
. .em _
t;
Ref.. p( 7... )·. .A.5l. 7sJ.)o· . . ·· th..a ez n11:1i.t .a. lqu. .. a· nt��:um be.,r i.n .d icates
thei rred.u cibl� repro.e rtshe. en· s tpa,a ttiioanl -s. ynunet;py,d ,(. a�,. }�·
. . . • , ., • • +, . I . . '
..· and m the _particouf.lt arh-�2c.e·o. m1 .·p·f oon,J.eddne tg enersattae·st · e
:' I
o:r·o rp1taar1igu ia··r mome.,n twumh11ne,· . . the prqu1ann�t:t:umnp umab1e r
·
di'stingu·it shh�e.s- �;ri�u1,s· 1:.t:t htsehst aamt·eec:sr··a nsformation
.
' '
prope_i?btuywt i tdhi �ei�e�nnte:r gyF.i naltlhyes pifnun �tiofn� ,
�
i.� equa.1 toa · (?(3.:r a �cortdoiwn hge th��a·r= ,+� o�- �. ..
.
l!• aKr:�• .• i • . . '
The ·given.: apprboy.ex 1in�1haeotrne e.� 1ry trho�1 1ow1ng
.
twoc·o nventi•oen:itap.lsr ieo�nrls;e e. f.o ·ir, n sa(tri cRee f. ).,, p , o(2; 372):
·.·,:.. .A...•;. . '.'·.•.. , t, .··.,h� . '� -.Bys,' . 1 . .... a·.. i .'....e . ; ...�. .P. .·'.�.t. u.\l'.'i ��l.g.e o�,.� c.d.1 e-: '.( VB.B) ���.(.1 8:� )( 9):
. =,hr�H t�
. : .: �K-= )�v° k-2�)< ·� '2•[ tk·1if�1��1( �)· l,- DK. {G)a
..: /·.·:·": · B·, th"i;JenYH9 ._ lec·t.iolfabirt a.1m'ent hod'de( vMeOl)o bpye d·
(lo)· :
HUck;e·1a.ri dMi llike(n1 i) : ' : : . . .,.
.
;. .. . .
. ·:.· ;· :·. .... '. .. .. .. '. . ., ..' .. m ··1: ..
. . 1.[ llrk.1 <::s.21<.>!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
<iiv�.n= o
.'A cu=r �-l n= �-nx- - �
n r
r3
of by
Theen ergayp artiicntl� ies m agneftiie�il sdg iven
the
classHiacmaill toofen lieacnt rod(ynsameifecq sir n sta(n7c)e
units throughtohuits
p.108[)a tomica rues e_d develo-pmseenet
Append(i x) ] ;
l ' 2
H =Z i p c�)n
2 ( +p otenEnteiragly
..... k
k
thet ransition
Where toqu antmume chainsia ccsh ideb vyre eplacing
them omentpum· btyh e 1 Vi ft he don ot
opera-tor particles
�· 11V ' •
posssepsisn F.� t;trn e lectwriot�nhp ins�=a ,nidn trinsic mag-
netimco me·n!:: et =13 �· g.,•a na dditicoonntarli buttoit ohnee nergy
,s'.' .:·." c;• a,••. ..1 • :a :· r• .
arisefsr otmh e' produ!:cet• � n· Thee lectrostianttiecr -
actiobne twetehnen ucleaunsdt hee lec-tcrhoanr gcelo udasl so
·
contribtuott ehsee nerg(yqu adrupole isn onz eroon iy
t�rms)�but