1435323589716.542 ProblemSet1Answers

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Chemistry8003:ComputationalChemistry

WinterQuarter1997

(Due1/27/97)

UsingPCModel,answerthethreequestionsbelow.

1.Theprogramwillhappilybuildpolypeptidesforyouifproperlyinstructed.WhatisthedifferenceinenergybetweenthehelicalformofAla5andit'sfullyextended(i.e.,[[beta]]sheet)form?WhatisthesamedifferenceforGly5?Areyourresultsconsistentwiththeexperimentalobservationthatpolyalanineformshelicesinwaterwhilepolyglycinedoesnot?Oneargumentthatmightbeleveledagainstcomparingthiscalculationtoexperimentisthatitisagasphasecalculation.Recalculatetheenergydifferencesusingadielectricconstantof78.3(water).Howdothingschange?[Note:Onecouldinprincipleworryagreatdealaboutwhetheroneshouldusethezwitterionicformofthepolypeptide,whetheroneshouldtrytooptimizethetorsionsoftheaminoandcarboxyltermini,etc.Don't.JuststartfromwhateverPCModeldraws(forgoodnesssakedon'ttrytodrawthesebyhandfindthepolypeptideconstructionmenu!)andbeginyourminimizationsfromthere.]

Heatsofformation(kcal/mol)ofvariouspolypeptideconformers.dielectric=1.5(default) dielectric=78.3helix sheet helix sheet

Gly5 293.8 294.8 265.8 261.1Ala5 331.2 328.2 302.5 295.3

So,inthedefaultdielectricof1.5,polyalanineprefersthehelixtotheextendedform,butpolyglycinedoesnotthisisentirelyconsistentwithexperimentalobservations.Raisingthedielectricconstantmakestheheatofformationlessnegativeineverycase(becausethedielectricisscreeningfavorableinteractionsbetweencharges)andnowbothpolypeptidespreferhelixoverextended,althoughpolyalaninedoessotoalargerextent(7.2vs4.7kcal/mol).Thisillustratesthedangersofattemptingtoaccountforsolvationwithsimplyabulkdielectricconstant.ThequalitativecomparisonbetweenAlaandGlyisprobablyinterpretable,butitisdoubtfulthattheequilibriumconstantbetweenthetwoformswouldbeaccuratelycalculatedinanyoneoftheseinstances.Averyinterestingquestion,however,istheaccuracyofthequalitativeobservationthatthepreferenceforhelixoverextendedconformationincreaseswithincreasingdielectricinthesecases.Thisisprobablycorrect,sinceahelixhasalargenetdipole,whiletheextendedconformationdoesnot.

2.Minimizeandreporttheheatsofformationforstructures1and2.Theformerismethylterminatedquartz,ifyoulike,whilethelatterisamildlyunusualtetraorthoester.Oneofthesemoleculeshassignificantlymorebendingstrainenergythantheother.Whatlinkagecontributesmosttothisdifference,thatis,whatanglehasalotmorestraininonemoleculecomparedtotheanalogousangleintheothermolecule?Youwillneedtosupportyouranswereitherbycomparingcalculatedanglestothetabulatedequilibriumvaluesintheforcefield(gottafindthose,inthatcase)orbycomparingtoostensiblystrainfreemoleculeshavingthesamelinkage.Tomakelifeabitsimpler,let'sassumeallangleshavethesameforceconstant(i.e.,onlydisplacementfromequilibriummattershere).

1435323589961.542 ProblemSet1Answers

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Hf(kcal/mol)38.0226.7

Thelargestdifferenceinanglestrain(total28.8and1.3kcal/molfor1and2,respectively)occursfortheXOXangle(whereX=CorSi).In1thisangleis116.6oandin2thisangleis106.1o.Inprinciple,theacyclicmoleculesH3SiOSiH3andH3COCH3arerelativelyunstrainedandserveasusefulmodelstoexaminethe"preferred"XOXangleitis128.9oinH3SiOSiH3and111.8oinH3COCH3.Thus,thisangleisdistorted12.3oin1andonly5.7oin2.Sincetheanglebendingenergyisquadraticindisplacement,thiswouldbearoughlyfourfoldenergydifferencegivenidenticalforceconstants.

3.Cyclohexaneiswellknowntohavetwominimumenergyconformations,achairandatwistboat.PCModelpredictsthesetohaveheatsofformationof29.5and24.2kcal/mol,respectively.Thisagreescloselywithexperiment(itwaspartoftheparameterizationoftheforcefield,sothatneednotbesurprising).ChaircyclohexanehasD3hsymmetry,thetwistboathasD2symmetrythisimpliesthatthereisasingleuniqueringatomintheformer,butinthelattertherearetwokindsofringatoms.TabulatetheheatsofformationforallpossiblestereoisomersthatarisefromsubstitutingN,O,Si,P,orSforC(thatis,doacompleteconformationalanalysisforpiperidine,tetrahydropyran,silacyclohexane,phosphorinane,andpentamethylenesulfide).Notethatforthepnictogens,theremaybeissuesassociatedwithstereochemistryatthatatom.Inadditiontothetabulation,commentonanyparticularlynoteworthytrendsintheenergydifferences(limityourselfto100wordsorlessonyourcommentary).

Byvirtueofthesymmetriesofthespeciesinvolved,thereisonlyonechairformforallsubstitutionsbutNandP,wherethepnictogenHbondmaybeeitheraxialorequatorial.Thesameistrueofthetwistboatswithsubstitutionofaheteroatomatoneofthefourfoldequivalentpositions.Substitutionatthetwofoldequivalentpositiondeliversonlyonestereoisomerforanysubstitutionsincethehydrogenatomsonthispositionarechemicallyequivalent.

Heatsofformation(kcal/mol)ofvarioussixmemberedrings.

X

[Hequatorial] [Haxial] [Hequatorial] [Haxial]

C 29.5 (24.2)

N 12.1 11.8 7.0 7.2 7.1

1435323590342.542 ProblemSet1Answers

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O 53.7 50.5 48.9

Si 24.3 20.2 18.9

P 20.8 22.6 17.3 (notstationary) 17.0

S 16.2 11.9 10.9

Therelativeenergiesoftwistboatsvschairsremainsremarkablyconstantoverallofthesesubstitutionsabout5kcal/mol.Formostoftheheterotwistboats,itismorefavorabletoputtheheteroatomatthetwofoldsymmetricpositionthanthefourfoldsymmetricone.Theconservationofrelativeenergiesiseitherwrong(badforcefield?)or,ifcorrect,isacoincidentalcancellationofvariouseffects(e.g.,withO,therearenobad"flagpole"interactionsacrossthetwistboatwithoxygen,buttheCObondsareshorterthanCC,sotheremaininginteractionsareworsethanincyclohexane).