Cnaprnn LL: CoonnrNnrrox CnnvrrsrRv III: Er,ncrRoNIcSpncrna

11.1 ^.

pt There will be (6!)/(313 !): 20 microstates

M1

Mg

-Jt z -U2 U2 3t2raTL +l-o l* 1- o*

+.1

* l- -l--0- 0*

l" 1- -1*1* 0- 0n

0 l- 0- -1-

- 0- -1-- 0* -1-- 0- -l*

1- 0- -l-l* o- -1*1- 0- -1-

l* 0* 1+*t

-i* 1- 1-

-l I-0-0-l-

-t -t I

-l* o- o*

-2+-l-

o -1- 0*-l

Terms: L: 0, S :312: aS (ground state)

L:2,5:112:2DL: l, S: ll2: 2P

p'd' Thercwill be (6!y(1!5!) (I0!y(1!91):60 microstates

Mg

Mt

Terms: L:3, S: | 3F (ground state)

r:3, s:0 'FL:2, S: I 'D

L:2,5:0 tD

Z:1,S:1 tP

Z: 1, S:0 'P

The two electrons have quantum numbers that are independent of each other, because

the electrons are in different orbitals. Because they have different /values, the electrons

can have the same mr and m, values.

-1 0 I

J l- 2- 1- z 1* 2- t- 2-

2l- 1-

0- 2-1* 1-, 1- 1*

0* 2-, 0- 2-

1- 1-0* 2t

I

1- 0-0- 1-1_ ,,_

1* o-, o* l-1- 0*, 0- 1*

-r-2*- -1* 2-

1' 0-0- l-1+ at

0

1-I

0-

-1-

-l

0-I

1* -1-, 1- -l *

o- o*, o* o-

-1* l-. -1- I *

1* -1'0* 0-r* r+

-l I

-t-1-0-1-

0-1-

-l1-

-1* o-, o* -1--1- 0*, 0- -1*t- -2-, l- 2-

-1- 0-0* *1*l* -2*

a1-

-l

0-

1--t

,)--L

-1'-1-, -l- -1-o* -2-, o- 2*

-1- -l -o* ^2*

*J l-

-la- 1-

-lt+ 1+

-t.|_ 1i at

-t -L

panu4uo)

-E- _7,

+! r I

rt- -0oT-f7-

+ I +L

-L -v +L -9

_L- +l +c- _l_I- *o '*I- _o

-0 nI- '*0 -I-_ t +L- +l _L-

-E- _Z

_z- _I_I- _0

_0 _I-_I _Z-

T-t

+Q +uT I-

*0 *0T- T+' +r

1u a(.

77-'77-_L +L +Q _O

T T-.I I--' +'

-o *o '*o -o-I- *I '*I- -l

--c---9L{'!t9

_z _z-

-I I-_0 _0

_I- -IZ- T,

0

+o -v

*Z *I-TO

*0 *I4l a("

_E _z- _z-_z T- ,7 _I-

I *0 I 0_0 +l '*0 _I

-r- *7 '*r- _z

_E _Z-_7, _r-IO

_0 _I_r _z

I+

cT-+e + r

*7 *0*l *I.0 -7,

c r-'q T--L +r +9 -rz *o '*z ,o-I *I '*I -I-0 -7, '-0 -z

-t _I-,z,0_I _I_0 _z

Z+

*t n0

,Z *I,I *Z

€ *0 '*t _0

z *r "*z _r

r *z '*r _z

_E _0

_7, _r

_1 _Z

t+

CT+9 + I

*7 *7

_€ nI '*[ _I--(ez_L +L +L _L

_E _I_z _z

l+c 7'c 79+9+o-9 -t -z S+

I+ 0 T-

t17g

s14J

'lurot f8rouo tso^\ol eqlsl '&lclldltlnru

Q' :g: g'7

d'P

urds lseq8rq eql qll,\r 'O, .,IJ

:7 i(It :I : S 'Z: 7 :s{ueJ

'e n'rl.J

'q

*7- *0 _z- *0 '*z- _0 _z-_0 Z-*I-o0 _I- *0 'T-o _I- _0 I-*0 *0 _0 *0 '*0 _0 _0 _0 0

I-0 I *0 '*I _0 I_0 I+*z *0 -z *0 '*7 _o _z _0 7l

T+ 0 I_

stra6

:saleJsoJcrru 0z aJe oJoqJ ,Prs 'e g'II

?, sl el€ls punor8 oql pue 'f8reue lsel\ol seq f lset\ol Sut.tuq elels eql'pelluJI€q u€q] ssel er? sle^ol qloq eculs 'z't'v:1s€q/, urel eql'l :s'€: 7 :rprd tog

.z/rs sr elelspunor8 eql 'eroJereqf '(lS-Zl : lS+Zl) Kluo 71E:f s"q So ru:s1 eqt'Zlt: S '0 : Z :rdroC Z'II

€rlcods cruo4cela :III {4srtueq] uorl€urprooc II raldsqf,

ttr47

:i

;i

ll4 Chapter 11 Coordination Chemistry III: Electronic Spectra

-2

-2- 0-

-1- -l-0- -2-1- -3-

-2- 0-, -2- 0-

-1- -1*, -1* -l-o--2*, o* -2-1- -3t. l'-3

a + 0-1+

-I .,+

1*_J

1f_I

0*1*

-3-2- -l-r- 20- -3

a- 1+ 't+ -l

-L-t;-L-l

-l- )-, -I- -20- -3-. 0- -3

-2- -l*1+ a+

0- -3-

4 -2- -2--1- -3-

^t- 1+ .tr .,r-L-)

-1- -3*, -1' -3-

/rt aa

i+ a+-l -J

-2- -3- 2- aa-J

.,+-3-

/)+-J

11.5

Terms: L:5,S: l: 3H; L:5,^s:0: 1I1, L:4,,s= 1: 3G; L:4,.s:0: lG;

L:3,,S:1: 3F; L:3,S:0: rF;L:2,.S:1: 3D; L:2,,S:0: rD;

L: l.,S: 1: 3P; L: l,S:0: tP

The lowest energy term is the3H. For this term, /has the values 6,5, and 4. Because

the subshells are less than half full, the lowest value of-/provides the lowest energy:

'Ho.

From problem I 1.1a, for a p3 configuration there are three terms, oS,'D, andzP'

The -Ivalues for each of these are determined below.

it+For a,S: L:0, S:312.

Because J : L + ^S,

Z +'S- 1,

...|L - Sl, the quantum number Jcan only Ae Z^tZ

1ld^tlere is a

slngle state lor 'Ji J:iz.

For2D'. L:2,s:112.

Possible -Ivalues are 512 and312, and the two possible states

are'Dr,randzD312.

F or 2 P: L : l, S : ll2. Possible -/values are 312 and I l2,with states 2 Psn andz P vz.

The lowest energy state is a,S372 (highest multiplicity). 'Dr,, andzD312 are next, at

19233.I8 and 19224.46 cm-r, and2P312 and2Pvz are the highest energy at28838.92

and 28839.31 cm-l.

The difference in energy between the 4,S andzD states is 2fI". From the average ofthe two nearly degenerate

2D states, n"-- 9614.4l cm-l.

The difference in energy between the averages of the2D and2P states is

fI" : 28,839.12 - 19,228.52 : 9610.30 cm-r.

lI"

2iln

ti+

2P -- r-8839.31

--:::r"--- ?8838.92

1 9233. I 8

19224.46

t A I acflte

0

zts(Iz zlt'7.19 : lg - 7l : s 'uuel Q os '7: Z: Z-I-Y0+0+I+I+Z+Z: lW xEW

Z:I+I: ,fircryd4pur urdg S : ZII :sW qvQ aP

'lure] o os '7: z: I-0+l+z:7IN xeINg:I+V: filcqd4lnur urd5 S:Z:sW PJ ,P

o(1, o'r'z'E'r:f

OINJJIEq

Ie^el eql esn?ceq .{1dde 1ou saop elnJ Iensn oql :es€c slql ut utegecun st 1)

zltr'zllr : ls + 7l: t 'uue]1 os '7: 9 : 0+l+I+7a7:t14J xe14

Z: I + 1 : ,$rcrldplnur urdg S : ZII: s7g urds MolqO sP

,,tSn Zlg : f 'uuel S os '7: 0 : Z-I-0+l a7:t1tg xe15

9 : I + 9 : ,Qrcqdrllnu utdS S :719: s1,g urds LlSIq'tO sp 'q

'r' z' t'v : r Ylrt.') I *;,;'1,;53i.t.t.tr:;':1,f ,;5

:sJe^\sue esoq] uI pepnlcul eJ€ sonl?^1

I6r-0I xtl'9=(, so,0I x6I'8xslor-0I " 929'il=ALl = E

,_so,or.u,r=1ffi=L=atJIu 99E=T

ruc, 0l x7,0', _y _ ^,_slrUi ntV't=-=--'|

(, rtur ootl,-s Lu8olx 866'z) ')

,-wJ 006'vz !uuz0v:Lucr_0lxz0'v=- t = l=y,rrrx QQg,l(= A

'p

.{11cexa stZltrT , 'ZlrIJ,

'q

OI'II

'a 6'II

8'II

.J

'q

.E L'II

'c

'q

'e 9'rl

-I_\'/=IouI- "

nuc loIU \(*'oo'r)[ " seool B

olli- =;=-- :--i,=i

-coo'I=1 or'o=y -1Jo-ggg'g=t

,,ul r, rp Jo e1e1s puno.rS eqt stu 7,1 t', zl s',zl L', zl 6 : f rltlt I v

tDr'rp1o e]e1s pellcxe u€ slg t'V'9:f qlL4A rr,tte-'

,p Jo e}€ts petrcxo u€ stu Zlt 'Zl9 : f qlld' CIz

Zl t' Zfi ' Zl l-' Zl €- :sW pue E'Z' I' 0' I-' 7-' E- :ltrry os'T,l E : S' pue E :'J seq l,

I '0'I- :sW pue V't'Z 'l '0'l-'Z-'t-'V-:7W os 'I :S pu€ t :7 seqDE

Zfi'Zly:sW pw Z'l'0'I-'Z-:7W os'ZlI : S pue Z:'I seqQz

BJlreds cruojlcelg f.rlsrureq3 uolleulprooJ 11 ;a;duq3

11.6 Chapter 11 Coordination chemistry III: Electronic Spectra

11.11 [Ni(H2O)6]2* For ds ions, the energy of the lowest energy band is Ao, so A, : 8,700 cm-t'

The bands are split due to Jahn-Teller distortion in the excited state.

ll.lZ a. lCr(CzOq):13 is Cr(III), dt . Luis equal to the lowest energy band, so L": 77,400 cm-r.

b. [Ti(NCS)6]3- is Ti(III), dr.4,, is the energy of the single band;A,: 18,400 cm r.

The band is split due to Jahn-Teller distortion of the excited state.

c. pi(en)r]2n is Ni(II), d8. The lowest energy band corresponds to Lu, Lo: 11,200 cm I'

d. [VFu]t is V(III), d2. Following the example on pp. 434435, we find the ratio vzlvr

and then Lu lB: v2lvy: 1.57 at A,o lB: 26. From the Tanabe-Sugano diagram at L,o:26,

vr: E/B :24.1 E :24.18 : 14,800 cm-r B : 614 cm-'

vz:E/B:31.0 E:37.0|^:23,250cmt B:628cm-1

Average B : 620 cm-t, Ao :26 B: 16,000 cm-r

e. V(III) is a d2 ion. Again following the example on pp. 434435,v2:21,413 cm-r

and v1 : 14,409 cm-t, vrlvr : 1.49. From the Tanabe-Sugano diagram at A,:34.5,v1:ElB:29 E:2gB:14,409cmr B:489cmrvz:ElB:44 E:448:2l,4l3cmt B:489cm-'

Average B:489 cm-', A, :34.5 B: 16,870 cm I

11.13 [Co(NH3)6]2*, d' . As in problem Il.12dv2lv1:2.34 at L"lB :1 l. From the Tanabe-Sugano diagram at Ao : I 1,

vr: E/B: 10 E: 10 B:9,000 cm-r B:900 cm-l

vz: EIB:22.5 E:22.5 B : 21,100 cm-r B : 938 cm-r

Average B: g20 cm-t, Ao : 11 B : 10,100 cm-l

ll.l4 a. tr|er2 The t2rlevel is a triply degenerate asymmetrically occupied state, so it is 7'

b. trr6 This is a nondegenerate state, completely occupied, so it is l.

c. bc3 es3 This is an excited state, with the t2r level uniformly occupied and the er

level doubly degenerate, so it is E'

d. trrt This is a triply degenerate state, Z. (Vacancies in the orbitals can be treated

similarly to electrons.)

e. es Another excited state, this is doubly degenerate, E'

11.15 The complexes with potential degeneracies are those wilh dt, d', do, d7 , and de,low spin d5,

and high ,pin au "onitgurations.

ihe strongest effects are with hiqh sgrl_da,_low spin d7 , and

dn coilplexer, .o.r.rponding to [Mn(NH:)e]3t, ;NilNHr)6lr*, and ICuJNHl)1J'-' Weaker

effects might be seenwith [ii(Ngr)u]r., [V(NH3)6]3'. low spin [Fe(NH3.;6]'*, and high spin

[C'(NH3);3*, all of which are unknown or unstable. Other ligands are needed to stabilize ions

containing these 3+ metal ions.

'e8ed lxeu oql uo elqel JelceJuqc eqlur ue.tr8 or€ sl?lrqro eqlJo sleqel ,{4euufs eq1 'X.rleruiu'ts ntJ e,req sexelduoc eseilJ

:ere de1.reno reln8ue uo pes€q slulrqJopJo ser8reue eq1'doi ol tuoiloq urorg 'yyeren6

(IJ)"az + (rc)"a€(o)"a + (rJ)"az(o)'a + fiJ)"az

fil)"az

,[- r'z

zz[ pue zx

{x

ua

raI

I

0

0

0Ya

z{zx

{xt- x7Z

zT,

I€1OJ

:spue8rl _,O Jo ecuengul 'sl?lrqJo p I€leI I

z

Z

T,

T,

0ua

:spue8ry _lJJo ocuengur 'syelrq;o p le:e6 '(_rO pue _lJ ere spue8rleql) h)oIN pue (n)r3 are suor l€]ew eqt pue 'srouop IL pu€ o qloq er€ _lJ pu€ _,O

0

0

0

0

I0a

0

0Oa

Y^-

xa7

U^-oLx2 7 Loz c-.'UI-L

e2z

I€1OJ

zIzx

[x

,t- r*,,

0

0

0

7oa

.B 6I'I I

'xeloruos Jeqiro JoJ alqlssooosle eJ€ (suorlelrcxe *tL <- 8zt) suorlrsu€4 -IJJJ 'WJJJ roJ olq€llun€ eJ€ slenel 3a req8rq

eqt ,(1uo os 'llqJ e:e ole(NC)eC] Jo s1e're1 327 eqJ 'sle^ol 3a to 8zt reqire 01 slellqro puu8rl eq1

luog tr\IJJC Surrrrolle 'suorlcele g ur€tuoc _r[e(ruC)eUJ Jo sl€irqro aer e\t::oldecce v e puerouop o e sl,NC ereq^\'(np ulds mol) *[e(NJ)eg] pue (rp ulds mol) _e[e(NC)eg] Suueduto3 gI'II

'sseco;d IAtrJJJ e

ur ,(ilsee lsolu uoJlcele u€ esol u€3 pu? Jeuos sr eplpol 'sru:ol reqlo uI 'eplpol JoJ isellBlussr ecueJeJJrp eq1 os ',(?:eue ur Jellturs oJ? srOIAI1'I ot{l pue ',{8reue ur lseq8rq st xeldruoc

eplpol eqlJo OI{OH eqJ 'lJ > rg > I sI spueq raJsuer} e8;eqc eqt;o ,{SreueJo repro eq1 LI'il'iue8e Sutztplxo

Jeiloq B sr 1r isuo4cele ldecce ol olqu Jeileq sr _toutr[ '_tOeUJo s.6yr1 Surpuodser:oc eql ueq]

,{8reue ur ro,rol e;e _rgu1ln;o sl€}rqro pE aqt ruorg .,tyuerur:d pe,tr"rep sl€}IqJo J€lnoelotu eql eculs

'uorgppe u1 '_rgeg rog,(8reue aroru serrnber uortrEtrrcxe IAIJJC e os 'uyq;o slelrqropt eq] ueqlf8reue ur req8rq eJe oUJo slelrqJo pg eql pue 'eseue?ueru uuql re3:e1 ,(lluecgtu8ts sI tunluequ 9I'II

e-rlcedg cruorlcalg :111.,ft1srueqJ uorl€ulpJooJ 11 relduq3

r18 Chapter 11 Coordination Chemistry lII: Electronic Spectra

.^ I

B1

B2

E

Il.2l ^. At 80K: Fs =0.65= {n(n+Z)At 300K: Ps = 5.2= 'lnQt +Z)

1

-II0

I

1

-l0

z

*'-y'xy

(xz, yz)

Each of the representations is labeled with the matching orbital(s).

c. The lowest d orbital has an energy of 2e*(Cl); the next have energies of 2e"(Cl) +

e"(O). Because these are dt complexes, the transition is between these orbitals; it is from

an essentially nonbonding orbital to an* orbital. The interactions between metal and

ligand are generally stronger for a second row transition metal than for the first row,

raising the n* energy in the Mo case.

II.20 ;V(CO)61- < Cr(CO)o < [Mn(CO)6]* As the nuclear charge on the metal increases, the metal

orbitals are drawn to lower energies. Consequently, the CTTL bands should increase

in energy.

n:0.19

n: 4.3

b.

11.22 a.

The complex is near the low spin-high spin boundary of the d6 Tanabe-Sugano

diagram. High spin becomes increasingly favored as the temperature increases'

ML2, using positions 1 and 6, with 02- both a o'and z donor:

a-L (a

0

0

eft

0

0

0

2

2

vo

z

0

0

0

0

xy

xz

1)7

Total_2z

22x -y

If this is a high spin complex, there are four electrons in

the lowest levels (xy, *' - y'), three in the next two (xz,

yz), and one in the highest (2"). Electronic transitions can

be from the middle levels to the top, and from the bottomlevels to the middle and the top-three possibilities inall. According to the reference, the transitions seen are

from the middle and the bottom levels to the top level.

a^'vT.,, .Lctr

trtii v.l

)e i i rl-"ti i I

1 i /o I

: t-'6 |:ilili ir I

v2

: lli llc. Assigning the transitions as in part b: 1{

E :2eo: 16,000 cm-r E :2en:9,000 cm-r

so eo : 8'000 cm-l and en:4'500 cm I

The reference provides a much more detailed analysis, including a discussion of the

paramagnetism of this complex and other factors related to its electronic spectrum.

-'r-/ I

-T--rT--T--Ti-tt tv I rv

lliT-ulTtlI

r^{rrr IIY

-ro]t .lJt\

:leloru eql iuo{ ,(lueurt.rd ere l€q} sle}IqJo o} spu€8ll oplxo eq} ruog .,{lu€tulJd eJe }€q}slelrqJo ruoJJ 'suol}Isusr} I{JJJ Jo ecuenbosuos eq} f1e>1t1 lsout er€ sroloc eseqJ 'e 9z'II

serJes lecrueqcoJlceds oql uI

spu€8rl eseqlJo suolllsod eq] qllltn luelslsuoo sl slqJ ']seleo,tl eq] OzH "V uo tJeJJe lso?uoJls

eql seq ue leql 3ur1ec1pu1 'ser8;eue Surseercur eleq selJes slql uI sJoloc X:elueureyduroo egJ

1y\ollof eSue;o poJ :Joloc,ftelua{ueldluoc

lololl enlq uear? :roloc Pe^Jesqo

*r[E(ue)lNJ {- *.[e(tHN)tN] e -r[e(o'DlNlUE THN

:*z[E(uo)lN] lolol^ turoJ o1 spueSrl tHN xls 11e ecelde.l

uec spue8rl uo ooJql ispue8rl tHN o,r,rl bcelder u€3 uo 'pue8rl eleluoplq e sV 'rr[e(EHN)lN]

enlq e.tr8 ol z[e(O.H)r1q] uee;8 eql ur spue8ll OzH eq] seculder eg5l snoenbeJo uoulppv 9Z'lI

'sJoJSueJl eSreqc Ieletu o] pue3tl 3Je osaqJ 'slullqro Isleur ol slellqJo

pue8rl uro:3 suoJlcele olrcxo ol pepoeu sr ,(8reue ssel 'flluenbesuo3 'set8reue ranoy

o1 ur pe11nd ere sletrIqJo Ieleur eql oseseoJcul I€letu oqlJo e8reqc J€elcnu eq] sV 'J

'-,tonu Pu€ -rtOJJ roJ

rnd 9LI pue _rtOuhtr rog ud 0rI qll^,\ uosueduroc ut 'tud 99I 'ecuelslp ueSr(xo-1e1aut

lsagoqs oql seq _rtoeC 'tr1nser € sV 'suorlcele Surpuoq JoJ uollceJlle 1se?uo-t1s

eql suoxe pue solros cluoJJceleosl slq] ul lseleer8 sI uoJIJo e8reqc Jeelcnu aqJ 'q

'-rtoJJ < -itoulN < -,toeJ < ,tonu sJ

pueJ] IIpJeAo eqJ 'sl€laru ,4 oJ tsJg JoJ u€t{t , aoJ puocos -ro3 ;eleer8 st 1e;eue8 uI pu€

Ieleur eqlJo e]€ls uolleplxo oq] qll^\ ses€ercul /V ''VJo en1e,r lseqSrq oql s€q -.tond 'e n7U

'pue8rl ol JeJSu€Jl eS;eqc s€ slq] u8tsse ,{eur e.t 'pueq re3isuerl

e8reqc , 8reue lso. aol oql wq osle xelduroJ srql ecurs 'slellqJo roldecce ol suoJlcele roJSueJ]

o1 Kcuapuel lselee:8 oql pu€ suo4celoJo uonerluocuoc tsetee:8 oq] s€q (0SgC)(ttgM€(OC)eUxelduoc eql ur Ieletu eql 'oJoJeJeqJ 'sorJes slql ul pue8r1 rouop lse8uoJls eq] sI ElgN

urc \Lg'gt (bSgCXqa$E(OC)eUruc oo€'rI (bsgc)(tqade(oc)auuic 0sz'8t (bsgcx(tqao)a)t(oc)eu Ez'rl

I-I

t-

e.rlcedg cluorlcolg :g1 f.rlsrueqC uolleulprooJ 11 reldeq3

t20 Chapter 11 Coordination Chemistry III: Electronic Spectra

In TcO+-, the separation between the donor orbitals of the O' ligands and the

acceptor orbitals is greater than in MnO+-. As a consequence, TcO+- absorbs light

of higher energy (green) than MnO+ (yellow). Actually, most of the absorption by

TcOi is in the ultraviolet, with the pale red color a result of a tail of the absorption band

extending into the visible.

The metal-ligand interactions in MnO+2- (Mn(VI)) are weaker than in MnO+

(Mn(VII)), and the separation of donor and acceptor orbitals in MnOa2- is smaller,

meaning that less energy (red light) is necessary for excitation than in MnO+- (yellow).

Also worth noting: the Mn-O bond distance is longer in MnOa'- (165.9 pm) than in

MnO4- Q629 pm), an indication of weaker bonding in the former'

11.27 a. At 350 nm: At 514 nm:

c.

A 2.34 A 0.s32

"=b=@ t=r"=@= 11,700 L mol-r cm-

At 590 nm:

=2,640 L mol-r cm-l

At 1540 nm:0.0016A 0.370 Ao-1"-(r.oo..{z.ooxtoav) " lc

;, 1

.so

> 2.4

2.2

2

[Ni(H2O)6]2*[Ni(NH3)6]"

^[Ni(os(cH3)r)6]"[Ni(dma)6]2*

3.062.62

8.812.5

8,50010,5007,7287,576

970860920950

3.11 8.4

1r m.'{oo x toJ tu)

= 1,850 L mol-r cm-r = 8.0 L mol-l cm t

b. Because of their high intensify, the bands at 350,514, and 590 nm are probably

charge transfer bands. However, the low molar absorptivity of the band at 1540 nm

indicates that it is probably a d-d transition (see examples in Figure 1 1.8).

ll.ZB These are all d8 complexes, with three excited states of the same spin multiplicity as the

ground state. For do, Lo: energy ofthelowest energy band. B can be calculated

by using the method of Problem ll.l2.A, is the difference between the transitions

'Ar. -+3T1and'A, -)372; a graph of v2lv1

versus AolB needs to be prepared for d"Ni2* in order to calculate B, as described

in pages 434435. A plot of the ratio ofthe highest energy band to the lowest

energy band is shown here.

Species Ratio A "lB L,(cm-r) B(cm-l)

8.0

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