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UNTVERSITI SAINS MALAYSIAPEPERIKSAAN KURSUS SEMASA CUTI PANJANGACADEMIC SESSION 2008/2009JUNE 2OO9JIK 317 - QUANTUM CIIEMTSTRY AND GROUP THEORYIKIMIA KUANTAM DAN TEOM KAMPULAN]Duration: 3 horns[Masa : 3 jamJPlease ensure that this examination paper contains FIVE printed pages together with a20 printed pages of Appendix JIK 317 before you begin the examination.Answer FIVE questions. You may answer either in Bahasa Malaysia or English.All answers must be written in the answer booklet provided.Each question is worth 20 marks and the mark for each sub question is given at the end ofthat question.Sila pastikan bahawa kertas peperilcsaan ini mengandungi LIMA muka surat yangbercetak bersqma dengan Lampirun JIK 317 sebanyak 20 muka surat bercetak sebelumanda memulakan peperiksaan ini.Jawab LIMA soalan. Anda dibenarkan menjawab soalan sama ada dalam BahasaMalaysia atau Bahasa Inggeris.Setiap jawapan mesti dijawab di dalam bulat jawapanyang disediakan.Setiap soalan bernilai 20 marknh dan markah subsoalan diperlihatkan di penghujungsubsoalan itu.2LL at1.-2- urK 3l7lList the symmetry elements of the following molecules and classi$r eachmolecule into specific point group.Senaraikan unsur-unsur simetri bagi molela,tl-molekul berilafi dan kelaskan setiapmolekul kep ada htmpul an titik tertentu.(a)(b)cl"(c)oil'/\.,CIF| ,,,,,Ft-f :"I'F(d)(e) O=C=S(staggered)120 markslmarkahl2L2 ...3/-2.-3-Reduce the fo llowing reducible representations.Turunkan perw akilan-perw akilan terturunkan b erikut :(i)lJrK 3l7l(a)(iiDfl} marks/markahl(b) Set up the correlation diagram for CH+ molecule. Consider the 2s and2porbitals of carbon and the ls orbital of each hydrogen atom.Lukis gambar rajah korelasi bagi molekul CH4 Atom karbon melibatknnorbital 2s dan 2p manakala setiap atom hidrogen melibatkon orbitql Is.lI0 markslmarkahl3. (a) Find the number, and symmetry species of the Raman and infrared activevibrations of boron trifluoride (Dlr,). Show your calculation.Kira bilangan dan spesies simetri spelctrum Raman dan inframerahdaripada getaran aktif molekul boron trifluorida (fua). Tunjukkanpengiraan anda.a/"\,lI0 markslmarkahl(iDFI213...4/-[JrK 317]O) With appropriate calculation predict the hybrid orbital responsible foro-bond at carbon atom in ethylene molecule, CH2 = 911r.Dengan menunjukkan pengiraan yang berkaitan ramalkan orbital hibridyang terlibat dengan ikatan-o pada atom karbon dalam molelail etilenaCH2 =gPt.[10 marks/zarkahfWrite out the results of experiment that produce the phenomenon known as thephotoelectric effect. Which of those results cannot be explained using classicalwave theorf How could the photoelectric effect phenomenon be explained byEinstein's hlpothesis of quantization of light?Tulislran keputusan-keputusan el<sperimen yang menghasilkan fenomena yangdikenali sebagai kesan fotoelehrik. Antara keputusan-keputusan itu, manakahyang tidak dapat dijelaskan dengan penggunaan teori klasik gelombang?Bagaimanaknh hipotesis Einstein yang menyatakan bahawa cahaya adalahterlanntum berj aya menj elasknn fenomena ini?120 markslmarkahl-4-4.5. (a) Write out the postulates of quantummechanics.Nyatakan postulat-postulat mekanik lanntum.(b)115 markslmarknhlA state of quantum system is given byVt =01+2Qr+3Qr+4QoCalculate the expectation value for measurement of energy, given thatud= h'AUO'=2hvt'UO'=Zn'A'frdo= 4hvLo21"4-5- lJrK 3171Keadqan satu sistem lruantum diberikan olehV = d+202+3(r+4(oKirakan nilai jangkaan bagi pengukuran tenaga, diberi baha,yanO' = h'hfrdr=2hvQ,nA, =Zlt'Afrdo= 4hvQn15 markslmarkahl6. A particle of mass rr is confined to a one-dimensional box of length z.Satu zarah be$isim m dihadkan dalam satu Intak satu dimensi yang panjangnyaL.(a) Find the wavefunction of the particle in the box by solving the relevantSchroedinger equation, with appropriate boundary conditions.Dapatkan fungsi gelombang untuk zarah dalam tatok tersebut denganmenyelesaikan persamaan schroedinger yang berkaitan, dengan syiat-syarat sempadan yang bersesuaion.ll2 markslmarkahl(b) calculate the probability of finding the parricle in the regions o = * = %and %= * <3%. Evaluate the expressions for general values ofquantum number n obtained from 3(a).Kirakon kebarangkolian untuk mencari zarah tersebut dalam ruang,=*=% dan %=*<3%. Tuliskan iawapan untuk nilai nomborkuantum nyang umum daripada 3(a).[8 markslzarkah]- oooOooo -2l_ 5216APPEI\DIX JIK 3I7QUANTUM CHEMISTRYAI{D GROUP THEORYICHARACTER TABLE]2L'.7itxj*ri "r^ >ll**----T_----li dlj rl* il* F-T--'Hl- TIIIrl,-. *I15iu t<t--c.lvXzfY)s,III,^IXlial sFl.-Scll >\-/lNXINFl*grr l+ ",1,l* t9.l-l- ^t\In^lxt*l3l^l*t-\l-',xlr-INIF 'Xl|_l-I_----i--N | /--"4--mlr\ | J(\'/ l*'uI,'T I x\JI*'UIIIJI I *.* -| \-J-T---nlu l<hXc,lN"l^ X>rNNNX>)EXxFXt-N>\,x xFE.fsFF5(oL''F u,co_(.) =-c (n() Iv tFto \-./tr>txdb=v)@v a>a;=o.(EEO- >\.ar t'd,d A.t-),LilP+) lJ-UESL(t,-UNr)f r'l__T_-clb l* -H i..ll?)la-t$'YrlPlr{l l\)-IUIlq)dtk k N <Fq218INTRODUCTORY GROUP THEORY FOR CHEMISTSr.reoMXzfY'ls>r*x6 A, 6t^tx?r\l+'Nol* eJ9\otsc{xd;,tlvTlx6Acl^xN n-L6l:NN?e 5(r|trC\lXo)llINIA,a,H>.>4 l-e.NXXF t-d.vv>.d.x&,N\d.FNXFFcl >rNXi'i. KJ-t- N** ->{T :tFH= U \! r9 l./'trtl.rF *Fl F{ tu lU ll, lulllt?H F.l lD la, l9 U,trtlttllF{ H.d -rllF fi .i.HllHdF.FI,, /j-It R-H lu lu tr, lu'l+dd*uu\rv-FFIH--\-\tF ]IFgp.1 lu I t! lulllHHFFFtsrll-HHF{-- \+/h \oUaloU'-AaN:>&. tse,aNxxF l-d.vvA* * -clg t! ru \u \, (.il*L* -PFU\,UUL,,U$UnUe.lOOrr'lF{H-- ll$UUq()r7'l.Ta).iv,soUsUq)st-{ Nrq219<Fq rqr'-c-tvXzrY)dAPPENDIXFIF{.<.dH-.H.d llllHHd-HFIH-rlllFl Fl .H.F F -.d .HH-H--#FF\_-tr-i-\ri-v-J^2\. /--\tF r-t-t*t g tU lU .i.r tJ \,G*xn^ ct'i,K t-L^l al*t>t9f-trNXoilru"d.Gd,FE,t**'F|.-E>^|Tlxn^.t'i.Kn+^liNN? e.i'@F6tXoltUda,tsoExxl- d,Ic.,Il& lF-:ruu.H.Hvutrlllg' .,7g-l U t9.d.i U Urlllllltr€U@Ua"l€QsU€r()FUr+t-()nrUNr(J--^-4rA.JF .*tcl (\1 6.?)guu\ruvu*r*c.la.loo.16:utrtrrurull,* ilFoo.rfdq!--U\r\rUt!te '|(olGloo:l*F{\,t!rJttu\,*ttFolc.l6ogUTUTYUUTUH**---d\.+r-\.J14 dpq d FTq).sac)c1so\()rt;Sf(tF il+gF{ \r lt.d.- tr, vllllfT'l2'zoINTRODUCTORY GROUP TIIEORY FOR CIIEMISTSt+FlF{F{NIf--caMXl-{zfY'lsNN(.1^ cl ?J-t^.N* tae]r+Ic,x&\JN>&. F-^nNXFF \./XNr.itri.Nc!hI_l_ |'Nqr- xdNd>le{->x NXXN>rt-irr-rOllJF{-HOllol\UelNc'lol!+OllNUUC\Ex4.N>d. l-s*FFNQ(flUc.l-t t-f -f rf OltXNU\c.lUNNUrtlxxXd. d. e'niiFFFH-tsHllHFts-tl**OII--Cl HF{-F{eilvasot\q.)iSriC-ldN< < tr FqrqH6l<<rq2"-1-HNO<EEFq-Hoo'I-deilclAPPENDIXF{ F{ t-{ F( O OttF{FiFlFrOOtlFi--HHF llFT F{ F{ F{ F{ F{lllF{ Fr !i i{ C{ C{t-caVXzrTlsIrr}I&xd,vNXd,FXXFF v-FrF{F(C{OItll\6lUca-aqUraalUU(\l\oUc{hXe}Nsl>rXolNt\h+alXhria ANi, K?.+^l' Noli< -bt'&x&x>.d. l-NXFFoo.+N$F--,-,8 Iooc..l c{ne.{iNicl<<FqFCElrrlaI .+f- sfts*'-, I 6ooc{ c{rnUc.T14\q)sq)?1a,S'()aq)FeF222-o.ldd<<F1E1f..co\lXzfY'lsINTRODUCTORY GROTIP TIIEORY FOR CIIEMISTS-rHHHotlFlHd-Otl--HH(\IxNN-ct]ia c.lt?l'T.N*rtGINNd'xx NXXN>,N6 .4,i,i,K+t-* T. i'Sd. d.rliFrfII4xt,xFXFNXGIUfrlHHHF CAtlFUFHHs C..ltlHF{Hts fI]I-*NL)$aortq)FSt-{ {{d'd'rt223d6lt<<F] UF{F{OOId Fi (\ (\.lAPPENDIXNNF4FIF{FtFlOOItF{F{F{FaOOl'lFr F{ F{ H e'l OlF{F{F{F{HF llF{ F{ F{ Fi F( HlllsF.Fi-{Nc{tr-caVXzrYls.hxKN^lN6lhXIr-Idxd.xxt-NN6l>r-Lc!xhtlia ,ANi, K?-L^lt NstT< el9dxdFxt-oo$ c'l*t\-r-r88OOc.lNa{hQc{13caabeoc{()6l\oUc\l6l+f-'+F.u)u)d- o o.()OC\NrnUc.le(J\Sa)sc)%sLeuq)sFra\oU dC.ldNda:l<<FCFqrrlFr2'24deJdhl<<trl rqINTRODUCTORY GROUP THEORY FOR CIIEMISTStr-caF-XzE]3,I@INNXNctxhh N-Lt^::N** ->d^.FXxxdt-F\./ v*a- c.q^ ^ii K-l-r6'..1Ni<5 t)ef)C..lXc)tl1E .'Fguru-uulllHHH-Hdlll+tFtsuru*luu**gUU*rrUdFdHFlH\/dFl .H.FHH.H.<trtl- H .H .i F{ F{.i .dtlttddFlHrHd- \/HddgE--d tttlt F{.H.d t g.r .Ftltl€Fl--HF{Hd ltllf*-qlJugUU.ti tlllld-.F.i-d.H.dtltttEiF-H-Fl tlllt-HHF ll9b\inis<Fq rq <n H'x >F & .6NxNx&,FFd,V\JXotNor- X>rN"r' l$X>."af* iriiddt-tst()rqHHd#tl!+rnvQ9bi:r<Fq<m*FtsHrr'lANv2$fh€L)q)sc\225APPENDIXt--cawhXzf r'lsalxN^^Ni,K?J N* .>5\otrc{X0)lt\,xx FN^t-NXd.dF \/ \./Io\IF{F{r+:F{-F{F{-F{dHtllllliT ll lF li-- tu \, \, \rF{H U lu U UtttlllHddHF(ddH#d-d lllllliF IF :F :IFHd U U U UFiF{ \, \, U Ulrlrltl& .ti t 'lFF{Ft lU ll, \, UF{Fl I \, U UrlllllllFttFlFFltsFadF{- llllli*. - lt.x- Gt 6l lF cil NHlrlglUU-U\rgur'*"*.l(.6rNi'FdNH \, t, lr, l!F( lu l! lu ulllll{e rtgerN.iF'dNtFF{ \, tf, !, 19F{ l! t t, U^t* .K*d!r\rullit,UrrrUREIah(t)\oUNoU'lt 'Y".lidNilFNa.tgUUtUU-TYUUV:lF *i\ o l+ al el tFi lU U lr, UF{ tU l! U Ul+ tF*cilcltFNolp1 U lJ ll, tU-f iU U U Udd:H:--H--\- a-J \-Y--L,/-JH-:FHdg-dF{F-\-\-A-vJo\hv)onor(t)tUhUNU**lFl*F{ F{ \, U rr, \, F{ Ft \, \, l9 19tlllllF(-F{F{FiF{F{F{F{--FltllllTFIEIF'tsHF{U\r\r\UgdtrlyrUUllllllll16l+oN cr lF N ol tF f)-\DUUTUHUUUUV.!F 16 JF :'F:-. tu tu U Ud= lu lu tu \,rlllllNfr'lba?l\\{:ril r'1 dchU R $*'114 < Fq Irlc!b)<Fq\\)s.soU2so(5€(5a)sNq.r- xNaFlq!xI_l_ |.N*r9?',26t--Hcr)w.XZrYlsNNol.rl>xuXXN>lINTRODUCToRY GRoUP THEoRY FoR CTIEIVIISTSjjJ |jffNNxFrno.lcNUcaUolxNUUNN()rrlec{l^3ftaa,)r\t\HHHHHHH-tttltsHH**-HFtttltsTHHH*HFtttl_HHHHHHHlttlHEHHH.d€Ftttl-HHHHHHHH-OserOllHHOg-OllF_HFtF{F{ llH-C-il--(\IIri^NiiK+r^i3 g/^Nl- x*d,' l-x'xFd,vvHiHtls-J IIItfHHC-.lHHOllllqbb-ia:ss;<NoaHdo<FqFqFA<m44€dra\\': Clr H cl\<<H<<s122',7APPENDIXtr-ca\lXzr4scl- xL\nsli,nK-Ll^' tr N*t'->af€Ni Nid.F l-d,oooo.+ c.l $ (\l<. r-. .+ r-F{-t ) u, rt) rr>'-- I8ll8Ic{N I lof c,tltraac\tIIooc\ '+F\ {'u) u,ooC)Oe\ c{ltooc\ -+f- .tFlaa-,-r I INC\oooo+c\ $(\sf\ sFt-F{--- r, ul-- rn uloo ooO() OO(\l c.l o.l c'looooa{ s o.l .+t.*<. f-tF{Hd- t) ul-* ul qzoo oooo (J()(\l 6t C\l c'.1r: C-l O.l -. -l N (rlh()C\rT'ls-OO*HOOrltlF{HOO--OOllbr.)NN-.,^i,i,KJ-l^* T. i'SF{i<dF{OFierefprOtlllHFiF{FfOt-{-f-fetOllllnrr)c\l{:balUrnNh(Jc\Ft F( F{ F{ Ol Fi F{ rr -.(\lllll&t-XNxdFFv\Jc{c!FIF{Fl-(\F{F{F{Fl(\ trlll--c-iloilF{d(\N ttllFiFtFigO*ei*-rOllllFa-F.lF{OF{-lrr-OllllF{FiddOr-tFl!-rF{OI I r'l Ir< Ft F{ F{ ({ t-{ -< -r rr OIlldF{Fi-rOelgF(F{OllllF{FlFlF(NFaFiFfF{61\e{UN6lOc.lNUsU6t\ \ -\ \ia.,ldNnqHN<<rq14<<Hrrl{.fd.foji.id-i dATaq).SsocasaU€aq)t'rC-i2'2,8INTRODUCTORY GROUP TIIEORY FOR CIIEMISTStr-c.)VXzrY'l!FxFxd.Xd.HHHFOO-F{F{dOOrtll-HHFlt\Ic.ilHHF{d(\l(\ltlrllldHdHOOtsHHHOOttll-HHHH:Hi-HHHmcob€aC\ac..l\6lUc.,NUraNUQ(\Uc\tfT'l H H F{ F C.il t\l Ft H F{ Fi Ol 6l€F{HFIHOOHH#TOOtrll-F{H-(\{e.lH--HOllC.ltrllllIO.lF{HFIF{HF{HH--HH llllFF{Fl-le{C{F1 dFlHN(\lttlttlII,l<-tsHOOF{Fl*-OOltllHHHHFHH-HHHH ll tlHHHdHHH:F{HHdI'l I ltlbbbbbr:tii|:st*q$qNHd']qlHNHc-.1<<FqEH14<<FqFCF4rq\s):s.ssc)ra$s(5*laa)FsrX^ c.r^xh!\lNal>XNNd+NX229t---HcaVf-XZfi'l3,r0aHH-Ho (\ltlHH-Ho .<tl I6l.UF{dHH(\ CaIoUd-:Ho 6ltl:-d-(\ tr1APPENDIXdF{(>HHOllF{F{dF{F{HHHH-HH lt-s(\€-61 fllFtF{dHoooll-HFIHOOOtlFiF{F{dC{(\lSl tlF{F{F{FrClOC\tt>IHHFrHoailc)IHdHHC{ONll>I--HHe.l 6lt\xNNri-dB,iJlroli(-9s$6lUsccUo€(t)c.l9UC\6a6lF{Ht\F{F{C\ ttlF{-{OFrF{OllxX>.x'.' NrtNX>G.GF CE,xNxxd, t-F d,\/vIcaIAxid,Fxi xie,d. FF\/vd.x4vFNNXd, FFvFv6l6lUc.lalUtu)(\l4soU'r3aq)st\rab*$nalA-rCl:l<<rq<<tr]t{d.d'r'r {230i$a6tiGto<<FCFqHrqr4INTRODUCTORY GROUP TIIEORY FOR CHEMISTSFFF-oooooltHOOOOOtlts-FFN(\lt\O.l(\lHHC{N-sNNgeOO--OOtlHHFi-O6IO(\IOF{HHHHHC-ila*tsHC{N<-6161 FHtsHSl(\le{(\l(\letlisRF-L^l*stsFmVXzfr'tsXat' ^lr\e.{. NJ9e6lNsl+olXe,xd,t-t{NxE. FF\/HFOO-sOOtlo. o- o o-r|. ol $Nrf, t-- .if f-HH*- H HTT g HNO{ NNllr!+Ish+ tu+ \or-- r(r F- +-H-* B ai.i *,*, d55 | | UE \oc{N c\lc{ll?Fj{ fiIr.|(ANac\F{HHFIC.)F{O-EOtt> t>IH-H.tsHHC-l-- ttlt.olUN(t)(\oU6lsrAc!ioUc.lS(n6loor+ c\tr+ f-rt> .t)C)oc..l Nol .+t--rfv) v)ooo()c.l N.+N$r--- Ga ca*-oo(J()NNooOil \f,f\\l.F-acDcaH-vvo(-)NN6lUc\Ut.lHHH-(Y)HO-trrrt> t>Ia).sac)4soU€aa)FSt\{ .i.f'i',iii'i-$ 3a { { d'd'r{ FT d gI gT2 31,APPENDIX**Hslu*r9!,lll.**gUU-UUF{EtsFlFlF{\.--, V^A.* l-- --.t .\- I -, ,,, l:1.- u *r,llttFlH.H.HHd.H.FtttlFFFFFlllltr-eo\lXzs,x1NotNXNNNh+GIx€tre{9rX(l)ilttac.'-e.ji * *- l-d,hTl x.,*hR-.1- | 6*35catsolUtlu,I(alI3Fj;dt'NNXssRf.l $xx \?d,xd.vF|rNXEl- Fv-r* Y*t.-.-*, utllld+:fOl-riU"rusrU-r,rL)lll'll :lFHH rU \r.F.H r! UlltllF :tFF{ F{ \, lU .* .< tU lDtlll----t-{F{ lll*,FgtrU-9lJNU+-\HH.i.Flld:.H.xHH.F!Fr..ltlllHts:-F{FIHF\+rr\/F{Ft-H tlHH.-.HllH--- V4$a6"it)sF.t drqo{rn 14{m d gT232<ta r{rrlINTRODUCTORY GROUP THEORY FOR CHEMISTStr-caMXzrYls,otINXNx,irlK-+- N"ixNi-I- al hc{- r{ xx\/v>.FXHFF.IId>lIclx6lt' | 'X-.--.N-{- d"i {$J-NT<c,]9--*O- trtl-HOF{ ---O-r F{lllli-OdHll**O-HIIssa\odUcoU@rrlc1a-s'L..a()q)sl-rI\oec.l\oaooqrt)\oaltC)ilNUcrlqU\oalO\oUoorq{:rtlt-rHHH(\F{ HtltrOFdF{O Olls-r-O- F{rtl(Yr s - (\ Cq C?llllrl*t-N- F{ItlbborUSiiS:!nc.,ls:Nicl ?Jid<<IqF E-<<14F FdrO-llFl Fi e'l -Ie-*QI-*QeIHF{t\Cf)H-tsO-I4aIRE- 1-iiEI-i*d. l-HHoIHIH*OdIHF{HO O-t-l-<61tl--t\(rt CTtFFGlcilHHN-H ll-r-t-OOI-: c.l ci cr)233nNrd<<fqF{F{tr-caVXzfrlHs- d o o.oI- E (\ c\l C.il+l,irnH.5eilililil[-ieJ*eqo<<rqHrqAPPENDIXNXd. d,--ooFl Fl (\ 6lHHOOI- H c.l eilH#OOI-{-iOQIFH(.-l(\lGRXsRF-l- ^l*se\FNXFF'g' e6lrt) aYY 8 8I lctntIEalU6>tTlx- Aot^i, Ki+.1. NN? -)5tt8v)Nd.xd.FxNXFdFIc\Ic.lr2 v)..-,8It\t c{IdHolC\ltlttt\l'autoooor\ c\c\I'v)u) ooooNNUgIQOIR8aeeelt\l co'?AU)v)ooo()()C)r{NNEUg8Uc.I8UsseoE\sq).s{€8a\\Jet?sr.()$.FSt:234IAPPENDTX JrK 317]Reducing Formulaai = l/hIXs"Xs,Nsh ; total number of operations in certain point group.Xt* ; Character (X) for reducible representation.Xs, ; Character (X) for reducible representation (from the character Table)Ns ; Number of syrnmetry operation for each type or class of operation.- tt2BUIAPPENDTX JrK 317] 'contribution for the character, 1(R), for each unshifted atom in fsNCg', Cs' i 0-t9-236IAPPENDTX JrK 317]Notations of the Character Tablea. Schoenflies sSrmbols for point groupb. lists the s1'rnmetry operations (by classes) for that goupc. lists all the characters, for all ineducible representations" of each class of eachoperationd. shows the irreducible representations for which the six vectors ,Tx, Ty, Tz, Rx, Ry,Rz, provide the basese. shows the funtions which are binary combinations of x, y,z(e.g.xy,* ) provide basesfor certain ineducible representationsf . iists conventional symbols for the irreducible representations called Mulliken symbols.All one -dimentional ineducible rep. Are labelled as A or B, all two-dimentional as E,all three-dimentional as T (in certain texts it is given the label F), four-dimentional asG and five-dimentional as H.In addition to the letter, most Mulliken symbols possess certain subscripts and/orsuperscripts. For two- and higher - dimentional irreducible representations they can beregarded as lebels. For one-dimentional representations, they have the followingspecifications.A : One-dimentional irreducible rep. if it is symmetry about Cn axis, i.e.(1 :+1),2 anusymm. ), ft:-1)Sub. i : In. Rep is symmetry with respect to Cz I Cn (if no Cz), thenlrr. Rep. Is symmetry with respect to o,nSub.2 : In. Rep is antisymmetry under conditions as those in Subr of above.Sub.u : (gerade) irr. rep. are symm. With respect to inversion at an iSub. ,,: (ungerade) in. rep. are antisymm. with respect to an i: irr. Rep are symm with respect to reflection in a on: irr. Rep. Are antisymm with respect to reflection in a o5B:23',7-20 -238

JIK317 - QUANTUM CHEMISTRY AND GROUP THEORY JUN 2009

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JIK317 - QUANTUM CHEMISTRY AND GROUP THEORY JUN 2009

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