Tight TST for Reactions with Barriers

1. Additions2. Abstractions3. CH3OH Ignition at High Pressure4. Isomerizations5. Programs

AdditionsTransition State Determination is TrivialStart with low-level determination; e.g., B3LYP/6-31G* in Gaussian

(i) Setup z-matrix with internal coordinates(ii) Set atom-atom separation for forming bond to 2.2 Å(iii) opt=(ts,calcfc,noeigentest,internal)

If this fails(i) do set of constrained optimizations at R=1.8 to 3.0 Å on 0.2 Å grid(ii) Find maximum in Eopt (R)(iii) Use geometry from maximum in Eopt (R) as starting geometry for(iv) opt=(ts,calcfc,noeigentest,internal)

B3LYP underestimates barriers and so barriers may be incorrectly absentFor radical+molecule CASPT2(1e,1o) in MOLPRO is good alternative to

DFTProceed to higher level method

QCISD(T) or CASPT2 with larger active spacelarger basis sets - CBS extrapolation

H + C2H2

H + C2H4

H + C2H2 H + C2H4

H + C2H2

H + C2H4

H + C4H2

H + C4H2

C2H3 + C4H8G3/B3PW91Goldsmith, Ismail, Green,JPCA, 13357, 2009

CO + HO2 → CO2 + OH

0

CO+HO 2•

TS1 (trans) 17.9

trans -HOOC •OTS2 (trans)

12.7

–61.8

TS3 (cis) 18.9

TS4Internal rotation

(trans _ cis)15.8

cis -HOOC•O(no stationery geometry found)

6.5

CO 2+•OH

TS5 22.8

HCO 3•

32.8

HC•O+O2

TS6 35.1 TS7 35.7

-1.1 0

CO+HO 2•

TS1 (trans) 17.9

trans -HOOC •OTS2 (trans)

12.7

–61.8

TS3 (cis) 18.9

TS4Internal rotation

(trans _ cis)15.8

cis -HOOC•O(no stationery geometry found)

6.5

CO 2+•OH

TS5 22.8

HCO 3•

32.8

HC•O+O2

TS6 35.1 TS7 35.7

-1.1

•High Level Electronic Structure Theory•Careful treatment of torsional modes

CO + HO2 → CO2 + OH Energetics

Cr i tical energy (kcal/mol) Geom. Opt.

(Active Space )

Species PT2/CBSa CI/CBSa CI+QC/CBSa

PT2(5e,5o ) CO+HO2 TS1 17.1 25.9 21.3

PT2(9e,8o ) CO+HO2

TS1 18.2 25.7 21.4

PT2(11e,10o ) CO+HO2

TS1 18.4

Products/ transition

state

G3B3 CCSD(T)/ cc-pVTZ

CCSD(T)/ cc-pVQZa

CCSD(T)/ CBS

FCC/CBS Literature value

CO2+OH -63.3 -59.9 -61.0 -61.8 -61.7 -61.6±0.1

HOO C•O 6.3 8.1 7.2 6.5 6.0

TS1 18.3 18.8 18.3 17.9 17.3

TS2 12.0 14.4 13.4 12.7 11.8

TS3 19.3 19.9 19.3 18.9 18.2

TS4 15.5 17.2 16.4 15.8 15.3

HCO+O2 33.3 33.1 33.7 34.1 34.0 33.6±0.1

T1 Diagnostic for TS1 = 0.028

CO + HO2 → CO2 + OH Modeling

AbstractionsTransition State Determination is StraightforwardConsider from Higher Energy Side

(i) do constrained optimization at R=2.6 Å(ii) repeat with gradually decreasing (e.g., by 0.2 or 0.1 or0.05 Å) separation until maximum in Eopt is reached(iii) Use geometry from maximum in Eopt (R) as startinggeometry for(iv) opt=(ts,calcfc,noeigentest,internal) (Gaussian)

optg,root=2 (Molpro)Will be some difficulties at short R related to transferring atomProceed to higher level method

QCISD(T) or CASPT2 with larger active spacelarger basis sets

C2H4 + OH → C2H3 + H2O

NH2 + OH = 3NH + H2O NH3 + 3O = NH2 + OH

Approach to Improving Mechanisms

The MET Paradigm: Integration of Modeling, Experiment, andTheory through feedback loops at all levels of chemicalcomplexity

Competition Between• Dissociation

– CH3OH → CH3 + OH Two Radicals– CH3OH → 1CH2 + H2O

• Abstraction– CH3OH + O2 → CH2OH + HO2 High Temperature– CH3OH + O2 → CH3O + HO2– CH3OH + HO2 → CH2OH + H2O2 High Pressure– CH3OH + HO2 → CH3O + H2O2– CH3OH + OH → CH2OH + H2O Rich; Low Pressure– CH3OH + OH → CH3O + H2O– CH3OH + O → CH2OH + OH Lean– CH3OH + O → CH3O + OH– CH3OH + H → CH2OH + H2 Rich– CH3OH + H → CH3O + H2

Fuel Conversion Methanol

Ignition of MethanolMechanism of Zhao, Kazakov, Chaos, Dryer, and

Scire, Jr.: IJCK , 2007– 21 species, 93 reversible reactions– Developed to treat moderate pressure dilute

conditions of flow reactorWant to use this mechanism to model CH3OH

combustion in an engine?• Michael J. Davis• Rex T. Skodje• Stephen J. Klippenstein• Lawrence B. Harding• Alison S. Tomlin

Global Variance AnalysisIgnition Delay for Flow Reactor

CH3OH + HO2

CH3OH + OH

CH3OH + H

CH2O + OHOH + HO2

H + O2

Variance Analysis Engine Conditions

CH3OH + HO2

H2O2HO2 + HO2 CH3OH + O2

Rate Constant for CH3OH + HO2

TST

UCCSD(T)/CBS//CASPT2/atz

Uncertainty ~ Factor of 2

Variance Analysis: Updated Rate Constant

CH3OH + O2

HO2 + HO2CH3OH + HO2

Rate Constant for CH3OH + O2

TST

UCCSD(T)/CBS//CASPT2/atz

Uncertainty ~ Factor of 2

Change in ignition characteristics

• P = 5 bar• Ignition occurs at much longer times with new rate

constant

Ignition Delay vs Temperature

High Pressure Flow Reactor Glarborg

P=100 bar

IsomerizationsTransition State Determination More Complicated

Provide starting and ending structuresMake sure atoms match from start to finishOpt=qst2 in Gaussian

Often can just guess at structure through geometryE.g., H atom transfers - make a ring with transferring

H equidistant from beginning and ending atoms

Many other approaches - but I’m not knowledgeableabout them

1,4 H-transfers in 1-pentyl and 1-hexyl

Isomerizations

• Source code: ~ 83,000 lines (Fortran)• Installation: Perl script• Manual: 590 pages• Test runs: 106• Parallelization: MPI• Version 2010 available as of June 1, 2010 at

http://comp.chem.umn.edu/truhlar/

POLYRATE Program

Simple barrier reactions: RP-VTSTReaction-path variational transition state theory

Cartesian dividing surfaces from Garrett & Truhlar 1979Curvilinear dividing surfaces from Jackels, Gu & Truhlar 1995

Barrierless association reactions: VRC-VTSTVariable-reaction-coordinate variational transition state theory

Multi-faceted dividing surfaces from Georgievskii & Klippenstein 2003Potential Energy Surface (PES)

Defined by energies, gradients, and Hessians calculated by an electronicstructure program "on the fly” - direct dynamics

POLYRATEElectronic Structure Interfaces

GAUSSRATE JAGUARATE

POLYRATE

GAMESSPLUSRATE NWCHEMRATE ….

GAUSSIAN JAGUAR GAMESSPLUS NWCHEM ….

Available without license fee from Truhlar group web site:http://comp.chem.umn.edu/truhlar

Hooks subroutines

Other Programs (Mostly Master Equation Codes)VariFlex KlippensteinResearch Code - Not usable without personal training

MESMER Pilling (Leeds)http://sourceforge.net/projects/mesmer/

Multiwell Barker (Michigan)http://esse.engin.umich.edu/multiwell/MultiWell/MultiWell%20H

ome/MultiWell%20Home.html

ChemRate Tsang (NIST)http://www.mokrushin.com/ChemRate/chemrate.html

TheRate Truong (Utah)http://www.cse-online.net/twiki/bin/view/Main/KineticsWiki

SummaryIf barrier is greater than ~2 kcal/mol don’t bother with variational

Exception: In Ring formation entropy is changing very rapidly so maywant to consider variations to ring formation side

Could ignore tunneling for T beyond ~ 1000 KHowever asymmetric Eckart tunneling calculations are essentially trivialand so might as well be includedIf tunneling is significant the most important thing (for the tunnelingestimate) is to do a high level calculation of the imaginary frequency

Each of you should be able to write your own variational RRHO TST codewith Eckart tunneling in just a few hours -- it really is that easy

Including hindered rotors is a little more complicated, but can probably doneat the separable level with less than a day of effort

Common error: Often there are two saddle points corresponding to cis andtrans reaction. Often people think of these as two distinct reactions.Better perspective is as a single reaction with a hindered rotor mode thatconnects the two saddle points.

Be careful with symmetry numbers

TST for Radical-RadicalReactions

1. Variable Reaction Coordinate Approach2. Potential Energy for Larger Molecules3. 1-Dimensional Corrections4. Direct Coupling to Electronic Structure

Theory5. Dynamical Correction6. Geometric Mean Rule7. Oxygen Centered Radicals8. Resonantly Stabilized Radicals

Where is the Transition State?Calculate Q(T,R) or N(E,R) as function of RTransition State is at position of minimum in Q or N

Radical - MoleculeSaddle PointExp (-βE) dominates

Radical - RadicalNo Saddle PointWith Decreasing R

Entropy DecreasesExp (-βVmin) Increases

CH3 + H

Variable Reaction CoordinateTransition State Theory

• Approximate Separation of Modes– Conserved Modes – Vibrations of Fragments– Transitional Modes – Fragment Rotations, Orbital

Motion, and Reaction Coordinate• Conserved Modes

– Quantum Harmonic Vibrators– Independent of Reaction Coordinate– Direct Sums

• Transitional Modes– Classical Phase Space Integrals– Fully Coupled and Full Anharmonicity– Monte Carlo Integration

Variable Reaction CoordinateCH3 + H

Fixed Distance BetweenPivot Points

Hd

R

Pivot PointC

HH

H

Multiple Pivot Points on EachFragment

Multi-Faceted Dividing Surface

Optimize Both d and R

Active Space Test

(2e,2o) (8e,8o) (8e,8o) - (2e,2o)

CAS+1+2+QC

Contour Increments: Attractive: 0.1, 1.0, 10Repulsive: 0.1, 1.0, 10

kcal/mol

CAS+1+2+QC vs Full CI

Basis Set Dependence

0

1

2

3

4

5

0 500 1000 1500 2000

ciqc/dzciqc/tzciqc/qzciqc/adzciqc/atzciqc/aqz

k (1

0-10 c

m3 m

olec

ule-1

s-1

)

Temperature (K)

-15

-10

-5

0

4.5 5 5.5 6 6.5 7 7.5 8

Rel

ativ

e E

ner

gy (

kca

l/m

ole)

RCH

(atomic units)

cc-pvdz

aug-cc-pvtz

aug-cc-pvdz

cc-pvqz

cc-pvtz

aug-cc-pvqz

H+CH3 VRC-TST kinetics

0

1

2

3

4

5

6

0 500 1000 1500 2000 2500

CH3 + H : High Pressure

Temperature (°K)

VRC-TST

Su and Michael

Brouard et al

Seakins et alk (1

0-10 c

m3

mol

ecul

e-1 s

-1)

H+CH3 Trajectory Results

0

1

2

3

4

5

6

0 500 1000 1500 2000 2500

CH3 + H : High Pressure

Temperature (°K)

VRC-TST

Su and Michael

Brouard et al

Seakins et alk (1

0-10 c

m3

mol

ecul

e-1 s

-1)

Trajectory

Potential Energy Surfacesfor Larger Molecules

CAS+1+2+QC; accurate but too slowWhat else?o DFTo MP2o CCSD(T); Spin Flipo CASSCFo CASPT2Aug-cc-pvtz; accurate but too slow

Small basis set calculations for orientationdependenceLarge basis set along MEPAdd 1d correction to small basis set

Difference Potentials

B3LYP

UHF MP2 CCSD(T)

BH&HLYP MPW1K CAS

CASPT2

h+ch3 potential surfacecomparison

CAS and CASPT2 vs CAS+1+2+QC

Test of MEP Correction

0

0.5

1

1.5

2

2.5

3

3.5

0 500 1000 1500 2000

CAS+1+2+QC/atzCASPT2/dz + CorrectionSillesen et al (1993)Pimentel et al (2004)

k(10

-10 c

m3 m

olec

ule-1

sec-1

)

Temperature (K)

0

0.5

1

1.5

2

2.5

3

3.5

0 500 1000 1500 2000

CAS+1+2+QC/atzCASPT2/dz + CorrectionFahr,Laufer,Klein,Braun,1991Monks et al 1995Fahr, 1995Heinemann et al 1988Kowari et al 1981

k(10

-10 c

m3 m

olec

ule-1

sec-1

)

Temperature (K)

H + C2H3 → C2H4 H + C2H5 → C2H6

H + Alkyl RadicalPotential Energy Surface

Blue = attractive contoursRed = repulsive contours

H + C6H5 → C6H6

0

1

2

3

4

5

6

0 500 1000 1500 2000

k (1

0-10 c

m3 m

olec

ule-1

sec

-1 )

Temperature

Ackermann, Hippler, Pagsberg, Reihls and Troe

1990

Davis,Wang,

Brezinsky andLaw1996

Braun-Unkhoff, Frank, Just 1989

Muller-Markgraf and Troe 1988

VRC-TST k(E,J)

Kumaranand

Michael1997

H• + R• Unsaturated Radicals

Direct Variable Reaction Cooordinate TST– Evaluate configurational integrals [ xp (-βV) dq]– Arbitrary separation and orientations (6 dimensional)– Direct Potential Evaluations -- low level - CASPT2/dz– One dimensional corrections based on high level

evaluations along the minimum energy path– First implemented for 1CH2 + CO– Alkyl + H; Alkyl + Alkyl’;– Saturated and Unsaturated– Oxygen and Nitrogen Centered Radicals– Resonantly Stabilized Radicals– R + O2

Test of C-C MEP Correction CH3 + CH3

1

2

3

4

5

6

7

8

0 500 1000 1500 2000

Wang et al (2003)CAS+1+2+QC/atz

Slagle et al (1988)

Hippler et al (1984)

Walter et al (1990)

CASPT2/dz + Corr

Anastasi and Arthur (1987)

Wagner & Wardlaw (1988)k

(10-1

1 cm

3 mol

ecul

e-1 s

-1)

Temperature (K)

Direct Dynamics CH3 + CH3

• CASPT2 - no analytic gradients at the time• Use B3LYP - Absolute rate ~ two times too low• Rigid body dynamics• Propagate forward and backward from TS• κ = Trajectory capture rate / VRC-TST capture rate

Temp κ300 0.77500 0.84730 0.811000 0.851500 0.882000 0.93

CH3 + CH3 CH3 + C2H5

0

5

10

15

0 500 1000 1500 2000

Temperature (K)

Zhu, Xu and Lin (2004)

Knyazev and Slagle (2001)

Sillesen, Ratajczakand

Pagsberg (1993)

Garland and Bayes (1990)

Anastasi and Arthur(1987)

k ∞ (

10-1

1 cm

3 mol

ecul

e-1 s

-1)

2

3

4

5

6

7

8

0 500 1000 1500 2000

CASPT2 + Dyn. Corr.CASPT2Hippler et al (1984)Anastasi and Arthur (1987)Slagle et al (1988)Walter et al (1990)

Temperature (K)

k (1

0-11 c

m3 m

olec

ule-1

s-1

)

Comparison with Experiment

0

1

2

3

4

5

0 500 1000 1500 2000

k(10

-11 c

m3 m

olec

ule-1

s-1)

Temperature (K)

Present Work

Baulch (1992)

Dobis and Benson(1991)

Tsang and Hampson(1986)Anastasi and Arthur

(1987)

Sillesen et al (1986)

Arthur (1986)

Pacey (1984)

Shaffir, Slagle and Knyazev(2003)

0

5

10

15

20

0 500 1000 1500 2000

Temperature (K)

Tsang (1988)

Warnatz (1984)

Arrowsmith and Kirsch (1978)

Adachi and Basco (1981)

Golden et al (1974)

Anastasi and Arthur (1987)

Parkes and Quinn (1976)

Hiatt and Benson (1972)

k ∞ (

10-1

2 cm

3 mol

ecul

e-1 s

-1)

Present Work

C2H5 + C2H5 iC3H7 + iC3H7

Kinetics of Alkyl Radical + Alkyl Radical AdditionPotential Energy SurfaceCH3 + R

Red = RepulsiveBlue = Attractive

High Pressure Addition Rate Coefficient

Geometric Mean RulekAB = 2.0 sqrt( kAA x kBB )

10-12

10-11

10-10

0 500 1000 1500 2000

k (c

m3 m

olec

ule-1

s-1

)

Temperature (K)

CH3 + CH

3

i-C3H

7 + i-C

3H

7

CH3 + i-C

3H

7

CH3 + i-C

3H

7

from Geometric Mean Rule

10-11

10-10

0 500 1000 1500 2000

k (c

m3 m

olec

ule-1

s-1

)

Temperature (K)

CH3 + CH

3

C2H

5 + C

2H

5

CH3 + C

2H

5

C2H

5 + C

2H

5

from Geometric Mean Rule

10-12

10-11

10-10

0 500 1000 1500 2000

k (c

m3 m

olec

ule-1

s-1

)

Temperature (K)

CH3 + CH

3

t-C4H

9 + t-C

4H

9

CH3 + t-C

4H

9

CH3 + t-C

4H

9

from Geometric Mean Rule

10-12

10-11

10-10

0 500 1000 1500 2000

k (c

m3 m

olec

ule-1

s-1

)

Temperature (K)

C2H

5 + C

2H

5

i-C3H

7 + i-C

3H

7

C2H

5 + i-C

3H

7

C2H

5 + i-C

3H

7

from Geometric Mean Rule

10-12

10-11

10-10

0 500 1000 1500 2000

k (c

m3 m

olec

ule-1

s-1

)

Temperature (K)

C2H

5 + C

2H

5

t-C4H

9 + t-C

4H

9

C2H

5 + t-C

4H

9

C2H

5 + t-C

4H

9

from Geometric Mean Rule10-12

10-11

10-10

0 500 1000 1500 2000

k (c

m3 m

olec

ule-1

s-1

)

Temperature (K)

i-C3H

7 + i-C

3H

7

t-C4H

9 + t-C

4H

9

i-C3H

7 + t-C

4H

9

i-C3H

7 + t-C

4H

9

Geometric Mean Rule

C2H5 + CH3 → C2H4 + CH4

10-13

10-12

10-11

0 500 1000 1500 2000

E=-0.77 kcal/molE=-1.39 kcal/molE=-2.01 kcal/molE=-2.65 kcal/molAnastasi et al (1987)Thynne 1962Grotewold et al, Terry et al.

k (c

m3 m

olec

ule-1

s-1

)

Temperature (K)

E(CAS+1+2+QC/atz) = -1.09 kcal/mol E(CASPT2/atz) = -2.18 kcal/mol

Orientation-dependent basis set effectscc-pVDZaug-cc-pVTZ

C OH H

H'

HC

O

H H

H'

HC−O = 4 ÅThick line = -1 kcal/molSpacing = 0.2 kcal/mol

Oxygen-containingsystemsrequirelargerbasis sets!

Correction Potentials

E = EPT2/DZ + ECP(RCO ;MEP)ECP = EPT2/ATZ− EPT2/DZ

Applied successfully toCF3 + OHC2H5 + OHCH3 + HO2

(4e,3o) Active SpaceState Averaged CAS

CH3 RadicalOH Radical and Lone Pair

CH3 + OH →CH3OH

CH3 + OH: High Pressure Addition

Soot Formation & Resonantly Stabilized Radicals• C3 through C5; key radicals in soot formation

– C3H3 (CH2CCH)– C3H5 (CH2CHCH2)– C4H3 (CH2CCCH)– C4H5 (CH2CHCCH2, CH3CCCH2, CH3CHCCH, cyc-

CHCHCHCH2- )– C5H3 (CHCCHCCH, CH2CCCCH)– cyc-C5H5

• New Questions– Mutliple Addition Channels / Multifaceted Dividing

Surfaces– How many active orbitals are needed?– Is dz basis still good enough for treating orientation

dependence?– Is CH3 + H correction from dz to atz along minimum

energy path still appropriate?

H + HCCCH → C3H3

H + HCCCH → C3H3

Resonant Stabilization Test

Allyl + H Active Space Test 3 Different 2e,2o CAS Solutions

ECAS + 116.

-0.95266

-0.95265

-0.95250

-10

-8

-6

-4

-2

0

4 4.5 5 5.5 6 6.5 7 7.5 8

(2e,2o)-CASPT2(2e,2o)-CASPT2'(4e,4o)-CASPT2

V (

kcal

/mol

)

RCH

(au)

Resonant + H Comparison with Experiment

1E-10

2E-10

3E-10

4E-10

5E-10

0 500 1000 1500 2000 2500

dzdz + CH3-H (atz-dz) Corr.adzadz + CH3-H (atz-adz) Corr.Hanning-Lee & Pilling (1992)

k (c

m3 m

olec

ule-1

s-1

)

Temperature (K)

1E-10

2E-10

3E-10

4E-10

5E-10

0 500 1000 1500 2000 2500

CH3CCHCH2CCH2TotalAtkinson et al. (1999)

k (c

m3 m

olec

ule-1

s-1

)

Temperature (K)

Allyl + H Propargyl + H

Cyclopentadienyl + H

Benzyl + H

6x10-11

8x10-11

1x10-10

3x10-10

5x10-10

7x10-10

9x10-10

400 800 1200 1600 2000

TotalTolueneParaOrtho

Bartels et al.Ackerman et al. aAckerman et al. bAckerman et al. c

k (c

m3 m

ole

cule

-1 s

-1)

Temperature (K)

CH3 + C6H5 → C7H8

2x10-11

3x10-11

4x10-11

5x10-11

6x10-11

7x10-118x10-119x10-111x10-10

400 800 1200 1600 2000

TheoryPark et al. (1997)Tokmakov et al. (1999)Park et al. (1999)

k (c

m3 m

ole

cule

-1 s

-1)

Temperature (K)

CH3 + C3H3

Rate and Branching Ratio

0

5

10

15

20

0 500 1000 1500 2000

k ∞ (

10-1

1 cm

3 mol

ecul

e-1 s

-1)

Temperature

Fahr & Nayak (2000)

Knyazev & Slagle(2001)

1

2

3

4

5

6

0 500 1000 1500 2000 2500

CH

3-CH

2CC

H /

CH

2CC

H-C

H3

Temperature

Fahr & Nayak (2000)

VRC-TST

C3H3 + C3H3 High Pressure Recombination

C3H3 + C3H3

C3H5 + C3H5 High Pressure Recombination

C2H3 + O2

-6

-5

-4

-3

-2

-1

0

1

2 2.5 3 3.5 4 4.5 5

C2H

3 + O

2

PT2(3,3)PT2(7,5);LSPT2(9,7)PT2(11,9)CI+QC(3,3)CI+QC(7,5)CI+QC(9,7)

V (

Kca

l/mol

)

RCO

(Ang)

How many active orbitals are required? Is PT2 or CI+QC better for minimum energy path?

2E-12

3E-12

4E-12

5E-12

6E-12

7E-12

8E-129E-121E-11

2E-11

400 800 1200 1600 2000

Park et al. (1984)Slagle et al. (1984)Fahr & Laufer (1988)Krueger and Weitz (1988)Knyazev and Slagle (1995)Eskola and Timonen (2003)PT2CI

k (c

m3 m

olec

ule-1

s-1

)

Temperature (K)

1CH2 + C2H2

Procedures for Direct VRC-TSTProgram - VaReCoF (Variable Reaction Coordinate Flux)• Choose reference method for orientational sampling -

e.g., CASPT2(2e,2o)/dz• Evaluate E(∞) for reference method• Evaluate 1-D correction along MEP and write subroutine

for evaluating it• Choose sets of dividing surfaces to sample

– Center-of-mass at long-range (9 to 20 Å)– Orbital centered at short range (4 to 8 Å)

• Choose desired accuracy and maximum sampling points• Run, checking to make sure orbitals don’t switch and

energies are consistent with expectationsPOLYRATE also has Direct VRC-TST module

Multiple Transition States, DirectDynamics, and Roaming Radicals

1. Two Transition States for Radical-Molecule Reactions

2. Direct Dynamics as a Complement to TST3. Roaming Radical Reactions

Two Transition StatesSchematic Potential Energy Surface for Radical Molecule Addition

Two Transition States

• Inner TS– Entropic Barrier– Covalent Bond Formation– Rigid Rotor Harmonic Oscillator

• Outer TS– Long Range TST

• Effective TS1/Neff = 1/Ninner + 1/Nouter

C2H6 + CN → C2H5 + HCN CASPT2(7e,6o)/ADZ Potential Energy Surface

Radical Molecule Kinetics C2H6 + CN

O(3P)•three degenerate orbitals•split by spin-orbitinteraction

O(3P) + alkene•2 attractive•1 repulsive

Schematic Potential for O(3P) + alkene

O(3P) + alkene

-20

-15

-10

-5

0

5

10

1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4

C2H4+O(X)C2H4+O(A)trans-butene+O(X)trans-butene+O(A)

V (

kJ/m

ol)

RCO

(Å)

2D Graph 1

T (K)1 10 100 1000

(

)

10-12

10-11

10-10

iso- butene

trans- butenecis- butene

1- butene

propene

ethene

C2H4 + OH High P Limit

C2H4 + OH High P Limit

C2H4 + OH Pressure Dependence

Two transition statesOuter: 1CH2 + H2O → vdWInner: vdW → SP→ CH3OH

1CH2 + H2O

1CH2 + H2O

vdW

SP

Two Transion State Summary

Outer Transition State usually no longer important atcombustion temperatures

However, fitting barrier at room temperature employing onlyinner transition state will yield overestimated barrier height

An overestimate for the barrier height will yield anunderestimate for the high temperature rate constant

For a few rare cases like 1CH2 + H2O the inner saddle point isso low (e.g, -7 kcal/mol) that outer transition state still hasa significant effect at 1000 K

Exothermic Reactions: What are the Products?

Direct DynamicsComplements TST

Direct Dynamics

B3LYP/6-31G*• Initiate in reactants• Terminate when any atom-atom separation is

larger than some cutoff• Time Step = 1 fs• Maximum time = 2.4 ps• Careful about spin conservation and about finding

adiabatic state

When is direct dynamics useful?When chemically activated dissociation occurs sorapidly that process is not statistialI.e., when RRKM estimated dissociation lifetime is~ 1 ns or less.

C2H3 + O2: Initiated in the Entrance ChannelProduct E=31 E=38 E=47 E=63 Total HCO+CH2O 0.5 0.41 0.31 0.15 0.33 CH2CHO+O 0.5 0.34 0.55 0.62 0.50 C2H2+HO2 0.07 0.03 0.08 0.05 CH2CO+OH 0.03 0.03 0.03 OCHCHO+H 0.07 0.02 CH2OCO+H (COC Ring)

0.15 0.02

CO+CH2OH 0.07 0.02 CH3+CO2 0.03 0.02 HCCO+H2O 0.01 0.01 CHOO+CH2 0.01 0.01 # of Reactive Trajectories

2 29 67 13 111

C2H3 + O2: Initiated at OO Fission TransitionState

Product E=6 E=12 E=25 Total HCO+CH2O 0.92 0.98 0.82 0.92 OCHCHO+H 0.03 0.08 0.03 CH3+CO2 0.02 0.02 0.02 0.02 CH2CO+OH 0.01 0.04 0.01 CH2OCO+H COC Ring

0.01 0.02 0.01

CH2OH +CO 0.02 0.005 # of Reactive Trajectories

90 61 50 201

HCO Internal Energy Distribution

Much of theHCO willdissociatewithout furthercollisions

C2H5+O → C2H5O → CH3 … CH2O → CH4+HCO

HCCO + O2 The Mystery of Prompt CO2

CO and CO2 are observed on same timescale in C2H2 oxidation

How?

Speculation:C2H2 + O = HCCO + HHCCO + O2 = H + CO + CO2

Does HCCO + O2 really make both CO and CO2?

HCCO + O2 Potential Energy Surface

HCCO + O2 Product Branching from Dynamics

E kcal

J Total #

HCO+CO2 HCO2+CO OCHCO+O CO+HOCO Non

Reactive 22 0 9 4(1.0) 5 25 0 37 17(0.77) 1(0.05) 2(0.09) 2(0.09) 15 25 20 53 18(0.67) 2(0.07) 4(0.15) 3(0.11) 26 25 50 53 14(0.82) 1(0.06) 2(0.12) 36 31 0 57 13(0.65) 2(0.10) 4(0.20) 1(0.05) 37 Total 209 66(0.73) 5(0.06) 11(0.12) 8(0.09) 119

H2NOOH → H2NO ··· OH → HNO + H2O

Roaming Radical Mechanisms are UbiquitousAny molecule for which weakest bond fission produces two

radicals that can participate in a barrierless abstraction oraddition reaction

H2CO → H ⋅⋅⋅ HCO → H2 + COCH3CHO → CH3 ⋅⋅⋅ HCO → CH4 + CO(CH3)2CO → CH3 ⋅⋅⋅ CH3CO → CH4 + CH2=CO

C3H8 → CH3 ⋅⋅⋅ C2H5 → CH4 + CH2=CH2

(CH3)4C → CH3 ⋅⋅⋅ (CH3)3C → CH4 + (CH3)2C=CH2

C2H4 → H ⋅⋅⋅ C2H3 → H2 + C2H2

CH3OOH → CH3O ⋅⋅⋅ OH → CH2O + H2O

How Much Do They Contribute?

Roaming radical mechanism dominates over simple bondfission in low T limit

TSR(C1) TST(Cs)

RCC=3.4Å RCC=2.1Å

Energy Relative to CH3+HCO

-1.1 (kcal/mol) -0.2 (kcal/mol)

Roaming TightSaddle Point Structures

Are the Tight and Roaming Mechanisms Distinct?

Minimum Energy Path for Tight TS

Minimum Energy Path for RoamingMechanism

CH3 + HCO CASPT2/aug-cc-pvdz Interaction Potential

R= 5.9 6.0 6.5 au

R= 6.8(~TS) 7.5 8.0 8.5 au

Is the Branching to Roaming Still Large atCombustion Temperatures?

Kiefer - A roaming branching of 70% should have had majoreffects in our Laser Schlieren shock tube experiments

Shepler, Braams, BowmanJ Phys Chem A, 112, 9344(2008)

Full-DimensionalQuasiclassicalTrajectory Simulations

Reduced Dimensional Dynamics• Important Dynamics occurs at large separations -- van der Waals region

• Separation into Conserved Modes (Vibrations of Fragments) andTransitional Modes (Rotations and Translations of Fragments)

• Internal degrees of freedom of the radical fragments are kept fixed

• Analogous to our Variable Reaction Coordinate TST1)Simplifies surface fitting

• Atom + Linear: 2D (O+OCN)

• Atom + Nonlinear Polyatomic: 3D (H+HCO)

• Linear + Linear: 4D (OH+OH)

• Linear + Nolinear Polyatomic: 5D (OH+CH3O)

• 2 Nonlinear Polyatomics: 6D (CH3+HCO)

2)Simplifies electronic structure calculations

• Allows very small active spaces (2E,2O)

3)Simplifies Dynamics

• Eliminates problems with zero point conservation for conservedvibrational modes

Six Dimensional CH3 + HCO Surface

(i) Internal degrees of freedom of CH3 and HCO fixed

(ii) Eight, 12D, multinomial Morse fits (each containing 533 terms)cover different (but overlapping) ranges of inter-fragmentseparation.

(iii) Individual fits connected by switching functions.

(iv) ~100,000 (2E,2O)-CASPT2/aug-cc-pvdz calculations(permutation symmetry expands this to ~300,000 points).

(v) For the ~50,000 points within ±5 kcal/mol of the CH3+HCOasymptote the final fit yields an RMS deviation of <0.5 kcal/mol.

(vi) 1D corrections for basis set, active space, geometry relaxationand changes in conserved mode zero point energy.

Six Dimensional CH3 + HCO Surface:Ab Initio vs Fit

CH3 + HCO Bimolecular Rates: Ab Initio vs Fit

1x10-11

2x10-11

3x10-11

4x10-11

5x10-11

6x10-11

7x10-118x10-11

0 500 1000 1500 2000

CH3CHO;FitCH3CHO;DirectCH4+CO;FitCH4+CO;Direct

k (c

m3 m

olec

ule-1

s-1

)

Temperature (K)

Dividing Surface for Initiating Trajectories

1-Dimensional Corrections

CH3CHO Side CH4 + CO Side

Energy Dependent BranchingTransitional Modes Only

Energy Dependent Branching All Modes

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30

Bra

nchi

ng

E (kcal/mol)

Shepler, Braams, Bowman JPCA, 112, 9344 (2008)

6D Trajectories

CH4 + CO Branching Ratios:Roaming/Total Molecular

Experiments:Heazlewood,Jordan, Kable,Selby, Osborn,Shepler, Braams,BowmanPNAS, 105, 12719(2008)

Shock Tube Experiments Acetaldehyde

H Atom Time Trace H Atom Sensitivity

HCO Decays “Instantaneously” to H + CO

Theory - Experiment Comparison

}}

Experiment

6D trajectories

0

0.2

0.4

0.6

0.8

1

5 6 7 8 9 10

P~200P~350P~500P~1000P=200P=350P=500P=1000

Bra

nchi

ng

10000 K/T

Iso-Octane Modeling (Bill Pitz)

Roaming Radicals Summary• Roaming branching fraction decreases with

temperature, but only slowly• Branching to Roaming will generally be 10 ± 10 % at

combustion temperatures• Roaming in CH3OOH appears to have a modest

effect on ignition of iso-octane• Expect similar effects for other fuels and for otherflame properties

• Would be interesting to see what happens if oneassumes 10% roaming branching for all molecularfissions in some mechanism