CanTherm Refresher/OverviewEnochDames

RMGStudyGroupMeetingJan.12,2015

OnlineResources:http://cheme.scripts.mit.edu/green-group/cantherm/http://greengroup.github.io/RMG-Py/theory/measure/index.htmlhttp://cccbdb.nist.gov/ - tablesofforceconstantscalingfactors,lotsofexplanationsandtutorials

UserGuide:http://greengroup.github.io/RMG-Py/users/cantherm/index.html

•WhatisCanTherm?Howisitused?

•Theworld’smostcompactoverviewofthetheorybehindratetheorypackages(withemphasisonkinetics)

•RunningCanTherm

•ComplexPdep ExampleCalculation,I/Ocomponents

OutlineofthisRMGStudyGroup

ObjectiveofthisRMGStudyGroup

ProvidebasicinformationandconductabriefoverviewoftopicsnecessaryforcomputingpressuredependentratesusingCanTherm

WhatisCanTherm?CanTherm isanopensourcepythonpackageofutilitiesforthecomputationofthefollowing:1. Thermodynamicpropertiesofstablemolecules(H298,S ,Cp(T))

(seeShamel’s studygrouppresentation#5formore)2. Highpressurelimitratecoefficients,k¥3. Pressuredependentratecoefficients,k(T,P), forarbitrarilylarge

multiple-wellreactionnetworksusingeitherModifiedStrongCollision,ReservoirStateorChemicallySignificantEigenvalue(CSE)approximations

Notes:• CanTherm doesnothaveaGUI• Therearenumerousothersimilarcodesoutthere,butCanTherm hasthenicefeaturethatmanymolecularpropertiescanbeautomaticallyreadinfromoutputsofquantumchemistryjobs

• IfyouforkedoveracopyofRMG-Py fromGithub,youhaveCanTherm

HowCanTherm IsUsed

CanTherm

QuantumChemistryApplication:Gaussian,QChemMolpro,Mopac

MoleculeEditor

RateCoefficients,ThermodynamicProperties

Preparejobsvia GaussView,WebMO,Avagadro(opensource),etc.See:http://en.wikipedia.org/wiki/Molecule_editor

Runjobstoobtainenergies,frequencies

Computek(T,P),thermoparameters

Usek(T,P),thermoparametersforscience

ElectronicStructureandRates:varyinglevelsoftheory

Zador etal2010Prog.Energy.Combust.Sci.

11elec

T tN

=

Bestpractices:alwaysmakeanattempttovalidateorverifytheaccuracyofyourmethods,eitherthroughcomparisonwithexperimentsorbenchmarkcalculations

ElectronicStructureandRates:varyinglevelsoftheory

Zador etal2010Prog.Energy.Combust.Sci.

11elec

T tN

=

Q:Whichmodelchemistryisrightforyou?A:dependsonthelevelofaccuracyyourequire,computationalresources(time)

Sub-orbitalspaceview:differencesbetweenHF,post-HF,andDFT

• Hartree Fock (HF)theoryisawaytovariationallyestimatetheenergyofasystemofelectronsandnuclei,butneglectselectroncorrelation(meanfieldapprx).

• postHFmethodsareadvancementsofHFthataddelectroncorrelationasopposedtosimplyaveragingitout

• DensityFunctionalTheory(DFT):• Computationallyfaster,scalesbetterwithsize• Focusisonelectrondensityratherthanwavefunction• Molecularenergyisafunctionofelectrondensityisafunctionofspacialcoordinates(position),hencethenameDFT

• ManyDFTmethodsaresemi-empirical(i.e.,trainedagainstaexperimentallyderiveddataset)

• HybridorCompositemethods:modelchemistriesinvolvingbothHFandDFTcomponents,designedtoyieldaccurateenergiesatreducedcomputationalcosts(e.g.,CBS-QB3)

H EY = Y

Electronicstructurecalculationsonlyprovidegeometries,relative energies,forceconstants,andsometimes,correctpointgroupsnecessaryforcalculationofratesandthermo

properties

SymmetryNumbers,PointGroups:ImportantforA-factorsandthermoThingstoknow:1. Symmetryoperations2. Howtoidentifypointgroups3. Therotationalsymmetry

correspondingtovariouspointgroups

Tips:• Flowchartshelp.Ifyoucanperform

basicsymmetryoperations,youcanuseaflowchart.

• Manyonlineresources/tutorials

Rotationalsymmetryreducesamolecule'sentropybyafactorofRln(s),where s istherotationalsymmetrynumberandR thegasconstant.Example:aC60 BuckminsterfullerenebelongstotheIh pointgroupandhasarotationalsymmetryof60.Neglectingtherotationalcontributiontoentropyresultsinanerrorofover8cal/mol-Kinanestimationofitsstandardstateentropy.

Question.Howdoestherotationalsymmetryofcyclohexane changewithtemperature?

PointGroup s

C1 1

Ci 1

Cs 1

C2v 2

C¥v 1

D¥h 2

Sm m/2

Cn n

Cnv n

Dn 2n

Dnh 2n

Dnd 2n

T 12

Td 12

Oh 24

Ih 60

m =2,4,6,...n =2,3,4,...

Aneffortinfutility:statisticalmechanicsinoneslide( )

( ),, ,

iB

E N Vk T

iQ N V T e

-

=å

( ),iB

Ek T

toti

q V T e-

=å

Thecanonicalpartitionfunction(e.g.,macroscopic),Q,issummedoverallenergylevelsofa‘system’

Wetypicallyassumethatmoleculardegreesoffreedommaybeuncoupled:

( ) ( ) ( ) ( ) ( ), ,tot elec trans rot vibq V T q T q V T q T q T=

( ) ( ),, ,

!

Nq V T

Q N V TN

é ùë û= Undertheidealgasassumption,wecanrewritethecanonicalPartitionfunctionasafunctionofthemolecularpartitionfunction

( )2

1 2B

Ek T

elecq T g g e-

= + + ×××

( )3/ 2

2

2, Btrans

Mk Tq V T Vh

pæ ö= ç ÷è ø

( )2

21

B

B

hvk T

vib hvk T

eq Te-=

-

( )1 2

,3 , B B Brot D

x y z

k T k T k Tq V TB B B

ps

=

2

,

lnB

N V

QU k TT

¶æ ö= ç ÷¶è ø ,

lnln BN V

QS Q k TT

¶æ ö= + ç ÷¶è ø

Weusetheserelationstoderivestandardthermodynamicproperties:

( )†

0exptotB

Btot

Qk T Ek T k Th Qk¥

-æ ö= ç ÷è ø

l

Transitionstatetheorygivesonlythehigh-pressurelimitrate,formostreactions

ConventionalTSTfailsforsomesystems:• Barrierless reactions.Mustusevariationalorothermethods• Systemswithmanypossibletransitionstates

( )0

expB

EQ E dEk Tr¥

æ ö-= ç ÷è øò

0.1

10

1000

105

107

10 100 1000 104

2mpbenzyl

r(E)

, sta

tes/

cm-1

Energy (cm-1)

DEgrain = 10 cm-1

RRKMtheoryisusedinthecontextofthemasterequationforenergytransfertocomputepressuredependence

CanTherm countsthedensityofstatesusingthemethodofsteepestdecents,whichhasbeenshowntobeaccurateandfasterthandirectcounting.

RRKMrate:

( ) ( )dN EE dEr =

( ) ( )ii

N E E E= ¶ -å

( ) ( )( )

†N Ek E

h Er=

PressureDependence– aunimolecularperspective

ReadJoshAllen’sPdep paperforanindepthdiscussion:

*fkA M A M+ ¾¾® +* bkA M A M+ ¾¾® +

2* kA products¾¾®

The unimolecular dissociation process is captured by the well-known Lindemann-Hinshelwood mechanism:

( )id A Edt

é ùë û =rate loss of Ai

due to reactionrate of collisional production

of A at energy level jcollisional rate loss of A at energy level i- -

( ) [ ] ( ) ( ){ } ( ) ( )iij j ji i m i i

j m

d A EZ M P A E P A E k E A E

dté ùë û é ù= - -é ù é ùë û ë ûë ûå å

2 (2,2) 3 1 18 Bij ij a

k TZ N cm mol ssµ

- -= W

Collisionrateandfrequency: Microcanonicalrateconstant:

( ) ( )( )

' ††, 1

,

r ina

r in

W EQk E l s

Q h Er-=

Themasterequation• Themasterequationinchemicalkineticsdescribesthetimeevolutionofareaction

network• Considerareactant,A,with3Ndegreesoffreedom,dependingonthesurrounding

Tandbathgas• AismoreaccuratelyenvisionedasA(Ei)

Themasterequation(2)

• Theprobabilityofenergytransferisrelatedtotheenergytransferuponcollisionwithbathgas

• Theaveragedownwardenergytransferredisbathgas(andreactant)dependentandtypicallyafunctionoftemperature

Sources:• Empiricallyderived• Computed• Tuned

dP Ea D

( ) 1300 300

n

d dTE E cm-D = D

( ) [ ],2 18 l sBij ij

k T M sw sµ

-= W

CollisionFrequency,Lennard JonesParameters

Thereducedcollisionintegralcapturesthenon-ideality ofrealcollidingmoleculesbyincorporatingaspectsoftheinteractionpotentialbetweentwospecies.

Gas-Kinetictheoryisusedtocomputethecollisionfrequency.Species’6-12Lennard-Jonesparametersareneededtocomputethereducedcollisionintegral.

OnlineRMGresourcesmakelifeeasier

TheJoback methodisoneofcorrespondingstatesthatrelatesthecriticaltemperatureandpressureofmoleculestotheirLJ-parameters

C2H3+1,3C4H6

n-C6H9

-44.9

c6-C6H9

c5a-C6H9

-54.3

C6H8c5+H

-16.6endo exo

01.9

-22.6 -23.41,4-cC6H8+H

1,3-cC6H8 +H

-21.1

-64.3

-20.9 -17.3

-0.9

-11.8

-48.0

RelativeEnergy(kcal/m

ol)

+H

••

•

•

+•

n-C6H8 +H

-17.4

•

+CH3

+H

cC5H6 +CH3

-25.7

-20.5

-31.9

-6.6

-12.7

-19.8

-56.2

H+

H+

-23.3

-14.9

c5b-C6H9

c5c-C6H9

Example– largemulti-wellsystem:vinyl+butadiene

5wells,6productchannels,12transitionstates® 47+separateinputandGaussian/Qchem filesneeded(notinlcuding HRs)!

Reactants

#!/usr/bin/env python#-*- coding:utf-8-*-

modelChemistry ="M08SO/MG3S*“frequencyScaleFactor =0.985useHinderedRotors =TrueuseBondCorrections =False

Cantherm inputfilecomponents– piecebypiece

Thefirstfewlines:

Cantherm inputfilecomponents– speciescardslabel speciesfilenameandlocation

bimolecularproductsdon’tneedenergytransfercomponents

Lennard-Jones6-12parameters

Don’trelyonyourmemory– usecomments

Cantherm inputfilecomponents– transitionstates

Label IDandlocation ofTSfiles.Note:nocollisionalinformationneeded.

Reactioncardsareneededforeachreactionyouwanttocomputethekinetics(oneforeachTSinyoursystem):

kinetics(‘reactionlabel’):IndicatestoCanTherm thatyouwanttocomputek¥ foreachofthesereactions,whichareidentifiedaccordingtolabelsinthecorrespondingreaction cards

ForPdep reactions,thissectionisnecessaryanddefinesthemultiplewellreactionnetwork.Includeallrelevantisomers/wells.

Thereactant[s]andbathmustbeincluded.

networklabel

Energydomaindiscretization

rateparametrization:PLOGorChebyshev

Masterequationsolutionmethod

Cantherm inputfilecomponents– pdep

IncludeExternal1Drotorasanactivedegreeoffreedom.SpecifictoassumingthatthemoleculeisasymmetrictopwithIa ¹ Ib ~ IcBytreatingitasactive,itexchangesenergywithothermoleculardegreesoffreedom,convolutedintodensityofstates

Cantherm inputfilecomponents– speciesfiles

1DHinderedRotorinformation,tofollow

Ok,thereshouldbe3N-6DOFOnlynecessaryforthermocalcs

Useflowchartandtablepresentedearliermoleculartotalelectronicspinmultiplicity(seeShamel’s talk)molecularopticalisomers(seeShamel’s talk)

LocationofGaussian/QChem outputfile,andmodelchemistryused.

Ifallyourinputparametersarecorrect,andifCanThermcanaccepttheleveloftheoryyoucomputedyoursystemat:

Lookatoutputfiles:• pdf ofreactionnetwork• anyFileName.out• chem.inp• pdfs of1Drotorpotentialsand.txts ofdihedralanglevs potentialenergy

RunCantherm.Forexample,atlinux commandline:python~edames/RMG-Py/cantherm.pyanyFileName.py

Cantherm generatesapdf ofyournetwork,whichcanserveasagoodsanitycheck

Makesureyournetworklooksgood:• Nounreasonablylargeabsoluteenergyvalues(defaultunitsarekJ/mol)• Allwellsareconnectedasyouexpectandcomparewellwithyourindependentlycreatedpotentialenergysurface

• Allbarriersandrelativeenergieslookreasonablecomparedtoyourindependentlyperformedcalculations

Cantherm outputfilecomponents– chem.inp

Fittedhigh-Plimitratesrequestedinkinetics cardsof

input

Cantherm outputfilecomponents– chem.inp

Pdep rates:• eitherPLOGorChebyshev(seedocumentationfordefinitions)

• always lookatfittingerrorsinanyFileName.out

Cantherm outputfilecomponents– anyFileName.out1.Containsallnecessaryspecies,ts,informationforthesupportinginformationofamanuscript:• Geometry• Energy• MW• Externalmomentsofinertia• Forceconstants• 1DHRinformation,ifany

Cantherm outputfilecomponents– anyFileName.out2.Tabulatedk¥ forallreactionsspecifiedin‘kinetics’cardsofinputfile:• 3-parameterArrheniusfits• fittingerrors• units• tunnelingcorrectionfactors

Cantherm outputfilecomponents– anyFileName.out3.Tabulatedk(T,P) forallpossibledirectandwell-skippingreactionsinyourreactionnetwork:• tabulatedvaluesarerawMEsoln.output• PLOG/Chebyshev fittingerrors• units

• fittedtosameno.ofpointsastemperaturesdesired(increasefordecreasedfittingerror)

106

107

108

109

1010

1011

1012

0.50 1.00 1.50 2.00 2.50 3.00 3.501000 K / T

P = 25 Torr Hektotal

nC6H9

nC6H8 + H

c5a-C6H9

c6-C6H9

1,3-cC6H8 + H

1,4-cC6H8 + H

cC5H6 + CH3

fulvene+ H

measured

Cantherm outputfilecomponents– overallplottedrates

n-butoxy decomp./isom.comparisons(k¥):HRvsRRHO

105

106

107

108

109

1010

1011

1012

0.50 1.00 1.50 2.00 2.50 3.00

nC4H9O-1=nC4H9O-5nC4H9O-1=CH2O+n-propyl

1000 K / T

rate

, s-

1

Solidlines:HinderedrotortreatmentDashedlines:RRHOtreatment•

12

3

45

Whatthe1,5H-shifttransitionstate‘looks’like:

Considerationofhinderedrotorsimportantwhentheyaretiedupintransitionstates

Hinderedrotors• Typicallycanbeidentifiedbyavibrationalfrequencieslessthan150cm-1

• Knowtherearemanywaystoaccountfor1-Dinternalrotors.Cantherm projectsoutthedegreeoffreedomcorrespondingtotherotorfromtheforceconstantmatrix– agoodcompromisebetweenaccuracyandspeed.

• 1-DpotentialscanstypicallyperformedinGaussianorQChem• Caremustbetakenwhenpreparingcantherm inputfiles• IfV(q=0°)¹ 0,fourier fitwillbeinaccurate,\ usermay‘shift’potentialtofixthis,

ratherthanrecompute scanfromdifferentstartinggeometry

Hinderedrotors

notperformingthermocalcs sothissectionisnotrelevant

externalrotationalsymmetrymoleculartotalelectronicspinmultiplicity(seeShamel’s talk)molecularopticalisomers(seeShamel’s talk)

LocationofGaussian/QChem outputfile,andmodelchemistryused.

pivots:twoatomsdefiningaxisofrotationtop:atomscontaininginoneoftwoportionsofrotatingmoietysymmetry:3(•CH3),2(•CH2),1(potato)fit:typically,use‘best’Note:atomindicesshouldcorrespondtothoseinthegeometryfilereadinbycantherm

Inthiscase,Ipointcantherm toa.txtfileforthepotential(ScanLog asopposedtoGaussianLog orQchemLog)

1. Definethereactionnetworkandexplorepathways– thiscanbedoneusingRMG(e.g.,viageneratereactions);performaliteraturesearch

2. Knowwhatyouwanttocalculate(i.e.,relevantT,P)andwhatyouaredoing.3. Conductquantumchemistrycalculations(Gaussian,Qchem,Molpro forCC)ata

desired/appropriateleveloftheory4. Confirmthatyourgeometrieshavebeenoptimizedproperly

- lookateachstructureandaskyourselfiftheenergyisataminimum- doeseachsaddlepoint(TS)haveoneandonlyoneimaginaryfrequency?- visualinspectionviaamoleculeeditor(therearemany:GaussView,Avagadro,etc.Seehttp://en.wikipedia.org/wiki/Molecule_editor)Note:avagadro isnicebecauseitcanperformisomersearchesforyou.

5. [Verycarefully]prepareyourCanTherm inputfiles,triplecheckeverything6. RunCanTherm.7. Inspectoutputpdfs:network,1DHRs8. Beforeyouusetheparametrized ratecoefficientsinkineticmechanisms,makesure

thefittingerrorsareacceptabletoyou,orelseconsiderotheroptions(increasenTemps,userawoutput,otherfittingmethods)

RecipeforReliableRateTheoryCalculations

Questions?