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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