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Gerade Ungerade

1) The document discusses how to determine the gerade and ungerade symmetry of molecular orbitals. It provides examples of orbitals formed from s-s, p-p, s-p, and p-d orbital overlap. 2) Comments on the post clarify that molecules without inversion symmetry, like those examples, cannot be strictly labeled as gerade or ungerade. Their symmetry is determined by the point group. 3) It is not correct to label the orbitals in the examples as g and u, as the author did, since they lack inversion symmetry. Their symmetry depends on the molecule's point group.

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657 views2 pages

Gerade Ungerade

1) The document discusses how to determine the gerade and ungerade symmetry of molecular orbitals. It provides examples of orbitals formed from s-s, p-p, s-p, and p-d orbital overlap. 2) Comments on the post clarify that molecules without inversion symmetry, like those examples, cannot be strictly labeled as gerade or ungerade. Their symmetry is determined by the point group. 3) It is not correct to label the orbitals in the examples as g and u, as the author did, since they lack inversion symmetry. Their symmetry depends on the molecule's point group.

Uploaded by

Divij
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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11/7/2016

Howtodeterminegerade&ungeradesymmetryofaMOorbital?ChemistryStackExchange

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Howtodeterminegerade&ungeradesymmetryofaMOorbital?
J.D.LeewritesinhisbookConciseInorganicChemistry:
[...]Analternativemethodfordeterminingthesymmetryofthemolecularorbitalistorotatetheorbitalaboutthelinejoiningthe
twonucleiandthenrotatetheorbitalaboutthelineperpendiculartothis.Ifthesignofthelobesremainsthesame,
theorbitalisgerade,andifthesignchanges,theorbitalisungerade.
Now,itcanbedetectedeasilywhichMO,formedduetotheoverlappingofssorpporbitals,isgeradeorungeradeasshowninthesepics:

Butwhataboutthemolecularorbitalsformedduetotheoverlappingofsporbitalsorpdorbitals?moduetotooverlappingofsporbitals:

moduetooverlappingofpdorbitals:

http://chemistry.stackexchange.com/questions/42877/howtodeterminegeradeungeradesymmetryofamoorbital

1/2

11/7/2016

Howtodeterminegerade&ungeradesymmetryofaMOorbital?ChemistryStackExchange

IfIrotateaboutthefirstorbitalaboutanaxisperpendiculartotheinternuclearaxis,thesmallerlobegoestotherightonlythesignalways
remainssamejustthepositionofthelobehasbeenchanged.Butinthefirstpicture,onlythebondingmoisgeradewhiletheantibonding
moisungeradeI'mnotgettinghowbyrotatingalongtheaxisperpendiculartotheinternuclearaxis,thesignoftheantibondingmo
changesmakingitungerade.
Cananyonepleasehelpmehowtoapplytheprocedureforthemolecularorbitalsformedduetotheoverlappingofsp&pdorbitals?
molecularorbitaltheory

editedDec28'15at18:09

askedDec28'15at17:16

MAFIA36790
1,678

16

37

3 ThoseMOssimplycannotbelabelledasgoru.MOsofnoncentrosynmetricmolecules(i.e.moleculesthatdonot
possessacentreofinversion)cannotbelabelledgoru.LookattheMOdiagramofwater(C2v)noneoftheorbitals
havegorulabels.orthocresol Dec28'15at17:48

@orthocresol:So,doyoumeantosaythoseinthepiccannotbelabelledgoru? MAFIA36790 Dec28'15at17:53

2 That'sright,theycannotbelabelledassuch.orthocresol Dec28'15at17:55

@orthocresol:Buttheauthordidlabelthoseorbitalsasg&u:/ MAFIA36790 Dec28'15at17:57

IthinkthepointofallthisisaboutMOorbitalsymmetry,nodes,bondingandantibonding.Fortheseasymmetric
examples,considertheorbitallobesbetweenthenucleiiftheyaresigmaorpioverlap,andiftheorbitalformed
betweenthemhasgenadeorungeradesymmetry.SpontificationDec28'15at22:49

2Answers

Thebetterwaytodoitistocheckwhathappensunderinversion(i or1
).Iftheorbitalstays
thesame,itisg,otherwiseu.

However,asOrthocresolmentionedinthecomments,checkingthatisonlypossibleiftheentire
moleculecontainsinversionsymmetry.Notallpointgroupsdo,andthevastmajorityof
moleculesdoesnot(partlybecauseC islikelythemostprevalentpointgroupoutthere).
1

Forexample,considertransitionmetalsdorbitals.Inoctahedralcomplexes,theyarelabelled
t and e .Intetrahedralcomplexes,whichdonothaveinversionsymmetry,theyare t and e.
2g

answeredDec28'15at22:40

Jan
22.5k

44

Hmmm...couldyoutellwhatpointgroupis?Also,ifthereisnoinversionsymmetryinthoseorbitals,whydidMr.
Leelabelledthoseorbitalsasgandu ? MAFIA36790 Dec29'15at12:04

@user36790Ifyoucheckoutwhichsymmetryfeaturesamoleculehas,yourealisethatthesehappentoforma
mathematicalgroup,i.e.theresidentity,theresaninverseelementtoeachelementandwhenaddingtwooperations
together,theyexhibitcommutativity.Onlyahandfulofdifferentgroupsactuallyexist,andsincetheyhelpsomuch
withsymmetryconsiderations,theyaretaughtinsecondorsoyearofchemistrystudies.IllcheckoutifIfinda
questionhereonchem.SEaboutthem^^JanDec29'15at12:17

So,shouldIsaytheauthorisnotrightinmarkingthoseorbitalsasgandu? MAFIA36790 Dec29'15at12:27

Unfortunately,thereisnobasicquestionaboutgrouptheoryhereasfarIcantell.Feelfreetoaskone^^' JanDec
29'15at12:28

118

2 @user36790Yes,itdoesnotmakesenselabellingsomethingasgoruifthereisnoinversionpresentinthemolecule.
JanDec29'15at12:29

Ifoppositelobeshaveinversioncentrei.e.thecentreofsymmetrywithrespecttophaseofwave
functionsthentheorbitalsaregeradeotherwiseungerade.
answeredJun7at2:55

user30828
1

http://chemistry.stackexchange.com/questions/42877/howtodeterminegeradeungeradesymmetryofamoorbital

2/2

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