Anomalous+electron+configurations+and+associated+energies-1 PDF

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Notes over Anomalous electron configurations and associated energies for Inorganic Chemistry ...

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Whyaresomeelectronconfigurations'anomalous'?  TherearemanyexamplewheretheAufbauprincipleappearstobedisobeyed.Forexample,the groundstateelectronconfigurationofCuis[Ar]4s13d10,andnot[Ar]4s23d9asmightbeexpectedbased onitspositionontheperiodictable.Bydefinitionthegroundstateisthelowestenergyelectron configuration,sotheremustbeareasonwhya'higherenergy'orbital(suchasthe3dorbitalinthis case)fillsbeforethe'lowerenergy'orbital.Thereason,infact,isthatinCuthe3dorbitalisindeed lowerinenergythanthe4sorbitalforthisatom.Thereareseveralcompetingfactorsthatcontributeto this:  Recallthatshieldingisthereasonthatorbitalswiththesameprinciplequantumnumber differentiateinenergy.Ansorbitalwithnoplanarnodeswillalwaysexperienceagreatereffective nuclearcharge(duetoahigherprobabilityoffindingtheelectronnearthenucleus)thanap‐orbital (withoneplanarnodeatthenucleus),followedbythedandtheforbitalswithtwoandthreenon‐ sphericalnodes,respectively.Withoutshieldingitisexpectedthatthe3dorbitalwouldhaveexactlythe sameenergyasthe3sorbital,farbelowthatofthe4sorbital.Asthenuclearchargeincreases(acrossa rowoftheperiodictable),alloftheatomicorbitalsarecompressed(thisistheoriginoftheperiodic trendinatomicradii).Orbitalswhichareinherentlysmallerarenowmorelikelytoshieldlargerorbitals fromthenuclearcharge.Recallthattheaverageelectronicradiusofanorbitalisdeterminedonlybyits principlequantumnumbern.Therefore,orbitalswithasmallervalueofn(a3dorbitalforexample)will becompressedatahigherratethananorbitalwithalargervalueofn(a4sorbitalinthiscase).This eventuallycausestheshieldingeffectstoreverse.  Inaddition,itshouldbenotedthatpairedelectronswithinasingleorbitalexertarepulsive effectoneachother,aformofCoulombicrepulsion.Thistypeofrepulsionismoresevereinsmaller orbitals,butitisalwayspresent.Therefore,placingasecondelectroninanyorbitalalwaysrequires significantlymoreenergythanplacingthefirst.ThisisoneaspectthatcontributestoHund'srule (favoringdistributedunpairedelectronsspreadoverdegenerateorbitals).Itisoften(butnotalways) thecasethatanomalouselectronconfigurationsintransitionmetalsretainasingleunpairedelectronin theoutersorbital.Thiscanberationalizedbythefactthatplacingthesecond(paired)electroninthe outersorbitalwouldbemoreenergeticallyexpensivethanplacingitinthe(nowcompressed)d‐orbital.  Finally,onelastenergytermcontributestoelectronconfigurationsbasedonaquantum mechanicaleffectcalledexchangeenergy.Thisenergytermfavors'identical'electrons,whichhavethe samen,l,andmsquantumnumbers(butdifferentvaluesofml).Theprecisenatureofthisenergyterm isoutsidethescopeofthiscourse,butitseffectsarewidespread.Thisis,forexample,thereasonwhy thegroundstateelectronconfigurationforanatomlikenitrogenhasallofitsunpairedelectronsinthe samespinorientation('maximizedspin'),andthereasonwhyferromagneticmaterials(suchasmetallic iron)spontaneouslymagnetizeduetoalignmentofelectronspins.Inshort,whentwoormore electronsare'identical'(inasetofdegenerateorbitalswithlikespins),theirwavefunctionsarecoupled throughan'exchangeinteraction'.Thisinteractionresultsinanincreasedaveragedistancebetweenthe particles(whichcanberationalizedasanelectrostaticrepulsionbetweentwoparticlesthatcannot occupythesameregionofspaceduetothePauliexclusionprinciple).Thisincreasedseparation decreasestheshieldingexperiencedbyeachoftheparticles(theydonotshieldeachotheraseffectively astheywouldotherwise),whichlowerstheirenergy.Thistermscalesnonlinearlyaccordingtothe followingformula:

Eexchange(n)(n‐1)/2 wherenisthenumberof'identical'electrons.Forexample,increasingthenumberof3delectronsin chromiumfrom4to5wouldaltertheexchangeenergybyaratioof6to10,respectively(allofthed‐ electronsareidenticalsincetheywouldhaveidenticalspinsintheirgroundstate).Thisenergyterm favorshalf‐orfully‐filledsubshells,inwhichthenumberofidenticalelectronsismaximized. Allofthesefactorstogetherfavor'unexpected'electronconfigurationswhenanelement:

  

hasahigheffectivenuclearcharge,causinginnerorbitalstocompressandexperienceless shielding hasashellthatislessthanhalf‐filled,orfullyfilled,butcanobtaintheseconfigurationsby 'borrowing'otherhighenergyelectrons

Herearesomeexamplesofgroundstateelectronconfigurationsthatfitthispattern: Cr:[Ar]4s13d5 Cu:[Ar]4s13d10 Mo:[Kr]5s14d5 Ru:[Kr]5s14d7 Pd:[Kr]4d10 Ag:[Kr]5s14d10 NotethatinthecaseofPdallofthe5selectronshavetransitionedtothed‐orbitals,meaningthateven theunpaired5selectronishigherinenergythanthe4delectrons.InRu,a5selectronis'promoted' eventhoughthisdoesnotresultinahalf‐orfully‐filledshell.Theseobservationsaremerelyevidenceof thecompetitioninenergybetweensanddelectrons. Electronconfigurationsofthetransitionmetalions  Theeffectsnotedherearealsoresponsiblefortheobservedelectronconfigurationsof transitionmetalions.Inallcasestheselectronsarelostfirst,beforeanydelectronsarelost.The reasonforthisisthefirstofthefactorsdiscussedabove.Whenametalisionizedtheeffectivenuclear chargeofeachelectronmustinherentlyincrease(thereislessshielding!)Thiscausessmaller(lowern) orbitalstocompressmorereadilythanlarger(highern)orbitals.Forexample,whenCu([Ar]4s13d10)is ionizedtoCu+1,the'outer'orbitalintheionisinfactthe4sorbital,sincethe3dorbitalsarenowtightly compressed,andarepoorlyshieldedbythe4selectron.ThereforetheelectronconfigurationofCu+is [Ar]3d10.ByexaminingtheelectronconfigurationsaboveitisnowpossibletounderstandwhyCu,Ag, andtoalesserextentAuareuniqueamongthetransitionmetalsintheirabilitytoform+1ions.The predominanceofthe+2oxidationstateacrossmanytransitionmetalsiscausedbythetendencyfor thesemetalstolosebothoftheirselectrons.Thefollowingareexamplesofmetalcationelectron configurations: Cr3+:[Ar]3d3 Mo4+:[Kr]4d2

Zn2+:[Ar]3d10 Unusuallystable+2oxidationstatesareassociatedwithmetalsthathavehalf‐orfully‐filleddsubshells, suchasMnandZn.ZnandCdareonlyfoundinthe+2oxidationstate,muchlikethealkalineearth metals....