1. Plan for Day 4 Skip ahead to Lesson 5, about Mechanism Construction
I have rearranged and added some slides in Lesson 5….
This will be the focus for the first two lectures
The 3rd lecture this morning will be a Guest Lecture, on Model Reduction, by Prof. Tianfeng Lu of Univ. of Connecticut
Tomorrow we will do Ignition, Soot Formation, and miscellaneous follow ups on earlier lectures.

2. Progress towards Accurate Predictive Gas Kinetics via systematic construction of reaction mechanisms
William H. Green
MIT Dept. of Chemical Engineering
Adapted from a talk presented at the
24th Intl. Symposium on Gas Kinetics
York, July 19, 2016

3. Long-term project: making Gas Kinetics into a Quantitative Predictive Science
Historically: Kinetics has been more Postdictive than Predictive
Do the experiment first, then build a model to interpret/rationalize the known results
Instead: make quantitative predictions first, then do experiments to falsify the predictions
If predictions were this good, they would be very helpful in designing the most informative experiments.
Valuable for public policy decision-making e.g. air pollution
Accurate predictions the key to efficient rational design
Rapidly engineer improved reactive systems

4. Ability to make Accurate Quantitative
Predictions of Gas Kinetics would improve
Decision-making & accelerate Innovation.
But Predictions are Hard:
Chemistry is “much too complicated” Physics
P.A.M. Dirac, Proc. Royal Society A, Vol. 123, No. 792 (Apr. 6, 1929), pp

5. Progress on Predicting Chemistry… a Timeline
1929 Dirac: “equations much too complicated to be soluble”
1935 Transition State Theory & Hartree-Fock method formulated.
1960’s DFT and Coupled-Cluster method for molecules formulated. Microcanonical TST clearly formulated: RRKM
1980’s Supercomputers. Stiff ODE solvers. CHEMKIN software.
1988 Creation of DFT functionals usefully accurate for chemistry
~1990 able to compute molecular spectra, entropies, Cp’s a priori.
1990’s: quantum chemistry goes mainstream. Pople & Kohn Nobel (1998). Methods developed for computing rates of barrierless reactions, esp. by Klippenstein.
By end of 20th century able to predict individual rate coefficients a priori but accuracy limited by errors in computed energies.
By 2010 explicitly correlated CCSD(T)-F12 methods give accurate a priori energies for most fuel molecules and many transition states

6. Quantum Enthalpy Predictions: Highest level calcs
are good to ~1 kcal/mole, but others need BAC
Hcorrected = Hquantum correction for each C-C bond, each C-O bond, etc.
DFT (B3LYP)
CCSD(T)-F12
/TZ
CBS-
QB3
CCSD(T)-F12
/QZ
Error (Expt(ATcT) – Quantum) 2 kcal/tick mark

7. BAC can (mostly) fix enthalpy, but leave discrepancies in computed barrier heights
Slightly
Different
Barrier
Depending
on which
Direction
you compute
the
Reaction
In this case the inconsistency is ~0.6 kcal/mole
= 35% error in rate at 1000 K, factor of

8. Today: typical uncertainty in a priori calculation of k(T,P) ~ factor of 3
CH2OO + CH3CHO
CH2OO + CH3C(O)CH3
Elsamra et al. IJCK (2016) RCCSD(T)-F12a/cc-pVTZ-F12//B3LYP/MG3S

9. Simplified reaction mechanism
Reaction Mechanisms
Simplified reaction mechanism
Detailed mechanisms
𝐶 3 𝐻 𝑂 2 ⟶2 𝐶 𝑂 𝐻 2 𝑂
Let me first sketch the context of this research.
In our group we are mainly studying chemical processes driven by radical chemistry. Combustion, pyrolysis, oxidation. Our main goal is construct a reaction mechanism that can aid in understanding chemical processing, and that can improve the design of new processes or new products.
We aim at building detailed reaction mechanisms that contain only elementary reactions whose parameters can be determined through experimental observation or from the fundamental laws of physics and chemistry. We believe detailed mechanisms are a systematic way of gaining a thorough understanding of the underlying chemistry. They are also the most predictive and robust model of the process.
The challenge witht hti aproach is the explosion in size of these mechanisms as we move forward to more complex systems. This plot shows the exponential relation between the number of carbons in combustion models and the number of reactions or species in the mechanism.
Bulding these models by hand is simply impossible. We need tools that automate the mechansim building process.
====
Dit wordt dan ook een kinetisch model genoemd. Een voorbeeld van een kinetisch model is deze vergelijking hier die aangeeft dat de molecule Dimethylether met zuurstof reageert tot CO2 en water.
Hoewel deze vergelijking aangeeft hoeveel molecules zuurstof nodig zijn om met 1 molecule DME te reageren, toch is ze erg simplistisch en kan dit simpele kinetische model vele phenomenen niet verklaren die belangrijk zijn. Het is immers zo dat de omzetting niet in één stap gebeurt, maar in vele tussen stappen.
Daarom probeert men gedetailleerdere kinetisch modellen te maken die meer detail opnemen en die daardoor betere de werkelijkheid weergeven. De limiet van dit detail is het zogenaamde microkinetisch model die tracht om alle vereenvoudigingen te vermijden en enkel maar zogenaamde elementary reacties op te nemen.

10. Quiz: How would you build a reaction mechanism?
Suppose you need to build a better kinetic model for your favorite system. You are in the normal situation: from the literature you know that a certain set of species and reactions are probably important. Assume you have a variety of ways available to you to estimate or compute the thermochemical and transport parameters for any molecule, and similarly you have a variety of ways to estimate or compute any rate coefficient, even for reactions that no one has discussed in the literature.
How do you proceeed? There are a lot of steps, try to write down as many of these steps as you can; then as a class we’ll try to synthesize them into a systematic approach.

11. Can we predict time-evolution of whole reacting systems? Many Issues…
Often O(103) important molecules, and O(104) important reactions; must select from a much larger list of candidate species and reactions.
Humans are not good at making or checking models this complicated. Use computer to list the reactions
Requires very large number of quantum chemistry calculations. Need supercomputer resources.
Need good Benson-type estimates to identify which reactions are worth computing quantum mechanically
Experiments only test some predictions of the model, often cannot determine any of the parameters.
All the numbers in model have uncertainties: UQ

12. fuel combustion simulation
Chemistry is “Much Too Complicated” for humans: We need to put it in a black box!
Engine design
predicted
emissions
Computer builds
and solves the
fuel combustion simulation
chemistry knowledge
(clearly documented)
engine performance
Fuel Composition
error
bars
operating conditions
This is ultimate goal. Let’s start with an easier case:
0-d or 1-d reactors where the flow field is simple…

13. Chemical Kinetic Modeling Challenges
Identify all important reactions & species
But not unimportant species & reactions: how to distinguish?
Compute all reaction rate coefficients (and properties,
e.g. thermochemistry) to sufficient accuracy.
We use Functional Group extrapolations & Quantum Chemistry
Large models pose numerical and computer problems
Very challenging for humans to handle, interpret, debug…
…SO WE TRY TO AUTOMATE EVERYTHING
We build on many prior efforts by many people, see e.g.
Comprehensive Chemical Kinetics 35 (1997)
Advances in Chemical Engineering 32 (2007)

14. (CHEMKIN, Cantera, KIVA, GTPower)
Commercial software can solve
detailed kinetic simulations for simple flows, geometries…
…if one can supply the full
reaction mechanism.
Simulation
predictions
CHEMKIN
or CANTERA
Diff. Eq. solver
Very long
list of
reactions
with rate
parameters
Interpreter
(CHEMKIN, Cantera, KIVA, GTPower)
Simulation
equations
dY/dt = …

15. Key Ingredients for Mechanism Generation
Chemical species representation
Reactions between species
Thermodynamic and rate parameter estimation
Every approach of automatic network generation deals with the same problems, namely how to represent molecules, in a unique way.
How to build your model, and how not keep on adding reactions for ages.
When building quantitative kinetic models on top of that, you would need thermodynamic properties for species, and kinetic parameters for reactions.
On top of that, when you create such a program, how do you make sure that you are not re-inventing the wheel in terms of code. I saw that a lot of those network generatin codes work fine for the original idea they were designed for. For example many combustion codes allow elements carbon, hydrogen, oxygen. But once you have the idea: hey maybe I want to add nitrogen chemistry as well, or my feedstock contains sulfur that is reactive as well, you check those codes and you see: oh boy, this is gonna be a whole lot of work to add that.
Metric for species inclusion into the model

16. Which species to add to a growing model?
Child Species
(1st generation
byproducts)
All other
Chemical
Species

17. Several alternatives for how to construct network
Human selection: add the reactions and additional species you think are important.
Generational growth: at each iteration add all the child molecules which can be formed in a single elementary step from species currently in the model.
Directed growth: for certain types of species, only allow them to do certain types of reactions. For example, big radicals only allowed to unimolecularly decompose into smaller radicals.
Rate-based algorithm is like directed growth or human selection, but uses a numerical test of importance to decide which species to add to the model, rather than a pre-set rule or human intuition.

18. How we construct large chemistry models
Sensitivity
Analysis
Chemistry knowledge
Unambiguous
documentation
of assumptions
about how
molecules react
Simulation
predictions
High-accuracy quantum calculations on sensitive parameters
Diff. Eq. solver
Very long
list of
reactions
with rate
parameters
Interpreter
(CHEMKIN, Cantera, KIVA, GTPower)
Simulation
equations
dY/dt = …

19. constructs models consisting of elementary reaction
estimates reaction kinetics and thermochemistry
open source
C.W. Gao, J.W. Allen, W.H. Green, R.H. West, Comput. Phys. Commun. 203 (2016) 212–225

20. How RMG works Kinetic model Inlet composition and conditions (T, P)
Kinetic and Thermodynamic libraries
(optional, recommended for small species)
Kinetic model
User specified tolerance
Termination criteria
(time and\or conversion)

21. Rate-Based algorithm: Faster pathways explored further, growing the model
Before:
“Current Model” inside.
RMG decides whether
or not to add species to
this model.
Final model typically
~500 species, 8000 rxns
After:
Open-Source RMG software.
Download from rmg.sourceforge.net

22. Open-Source Reaction Mechanism Generator (RMG) decides which species belong in the model. Iterative refinement of the Model!
Before:
Main RMG algorithm
Generate all possible reactions/intermediates using reaction family templates
Estimate kinetics and thermochemical parameters using group additivity
Choose important intermediates based on highest flux
Compute Sensitivities
Calculate Most Sensitive Parameters with High Level Quantum Chemistry
Repeat.
After:

23. Chemical species representation
In RMG, molecules are described using “adjacency lists”, a graph representation of the atoms and bonds that connect them.

24. Reaction generation through reaction families
RMG generates elementary reactions from chemical species using an extensible set of 45 reaction families.
Few of the reaction families are shown below.

25. Reaction family recipe
Reaction recipe dictates how the bond connectivity changes when the reaction proceeds to products

26. Thermodynamic and rate parameter estimation
Benson-style group additivity is used to estimate thermochemical parameters including enthalpy, 𝐻 𝑓 0 , entropy S0, and heat capacities Cp
Enthalpy and entropy of cyclic and fused cyclic compounds is determined using Quantum Mechanics Thermodynamic Property interface (QMTP)
For most reaction families in RMG, rates are defined in forward direction. Reverse rates are determined from thermochemistry
𝑋+𝑌 ⇌𝑍
𝑟 𝑓
𝑟 𝑏
𝑑 𝑋 𝑑𝑡 =− 𝑟 𝑓 + 𝑟 𝑏
𝑟 𝑓 = 𝑘 𝑓 ∙ 𝑋 ∙ 𝑌
𝑟 𝑏 = 𝑘 𝑏 ∙ 𝑍

27. Mechanism Size Control
𝑅 𝑖,𝑒𝑑𝑔𝑒 = 𝑗 𝑟 𝑖,𝑗 > 𝜀∙𝑅 𝑐ℎ𝑎𝑟 𝜀
user specified error tolerance
Example range: 0.1 – 0.01
𝑅 𝑐ℎ𝑎𝑟 = 𝑗 𝑅 𝑗 ² , 𝑠𝑝𝑒𝑐𝑖𝑒𝑠 𝑗 ∈𝑐𝑜𝑟𝑒
Susnow, Roberta G., et al. The Journal of Physical Chemistry A  (1997):

28. Rate based algorithm as implemented in RMG

29. Example: methane oxycombustion 10% CH4, 20% O2 in CO2 at 1800 K, 1 atm
How RMG works
Example: methane oxycombustion 10% CH4, 20% O2 in CO2 at 1800 K, 1 atm

30. How RMG works
Core
Edge

31. How RMG works

32. How RMG works Core: Core + Edge: 1907 species, 5331 reactions
(tolerance = 0.01, conversion = 90%; overall time = 40 min)

33. Chemical Activation “skips steps”, complicating mechanism generation
Looks like
A+BD+E
but with odd
P-dependent
rate coefficient.
We taught RMG to
recognize these
cases, include the
reactions, and
automatically
compute k(T,P)

34. Quiz
Write down a steady-state equation for the population of C*, one of the vibrationally excited states of C.

35. Real chemically activated systems are complicated: C5H5+C5H5  naphthalene
Many models say C5H5+C5H5  C10H8 + H + H
But C10H10 intermediate
can live long enough to
undergo H-abstraction…
Instead:
C5H5 + C5H5 = C10H10
C10H10 + R  C10H9 +RH
C10H9  C10H8 + H

36. Need to enumerate which isomers are important in k(T,P) calculation… similar to task of identifying which additional species need to be in the RMG model
Reactions forming a single product X, e.g. A+B  X or C  X
X might be formed chemically-activated (i.e. with excess energy, non-Boltzmann), and react further before being thermalized.
When X appears on the Edge, RMG searches for unimolecular reactions of X to form new products, e.g. X  F + G and X  Y
RMG then computes k(T,P) for A+B  F+G and A+B  Y, via energized X.
Note Y might be formed chemically-activated. So the algorithm is recursive.
A flux criterion is applied, similar to that used on the Edge species, to see if these additional channels are significant or negligible.
For details see J.W. Allen et al. Phys. Chem. Chem. Phys. (2012) and rmg.mit.edu

37. Sections in an RMG input file
Detailed description regarding sections in input file at Py/users/rmg/examples.html#commented-input-file

38. The RMG output
Mechanism files are in chemkin folder in the directory: chem.inp chem_annotated.inp species_dictionary.txt tran.dat

39. Scripts Using RMG’s scripts you could: Merge models Compare models
Generate a flux diagram
Run Sensitivity Analysis
Standardize species names
Estimate thermo data
Generate reactions
Create an RMG library
… and much more!

40. RMG Website Tools
See

41. Troubleshooting on GitHub
See

42. How to install RMG on your computer?
See: > Documentation > User’s Guide > Installation

43. Does this really work. We compared with hundreds of data on butanols
Does this really work? We compared with hundreds of data on butanols. All the predictions are accurate above ~900 K.
isomers
RMG built model:
372 species
8,723 reactions
All sensitive rxns
computed.
Ignition Delays
Flame speeds
P= atm
Merchant et al.,
Hansen et al.,
Combust. Flame
(2013).
Pyrolysis Byproducts

44. RMG model quantitatively predicted dozens of species profiles in Adv Light Source flame expts.
Isobutanol/H2/O2in Ar, H2:O2 1:1, f=1.4, 15 torr
Data measured by Nils Hansen
Funded by DOE Combustion Energy Frontier Research Center, ALS, & CRF
Hansen et al. Combust. Flame 2013

45. Not just C4 fuels; RMG can also predict C10 chemistry
JP-10 Pyrolysis T~1000 K, P~2 bar
C3H6
cycloC5H6
cycloC5H8
C2H4
CH4 H2
Similar level of agreement for many other species
See Vandewiele et al. Energy & Fuels (2014).
For model & expts with JP-10 + O2, see Gao et al. Combust. Flame (2015)

46. RMG can now handle some Heteroatoms, e.g. N… CH3CH2NH2 + O2OH
500 ppm EA ppm O2 in Ar at 1399 K and 1.96 bar
2000 ppm EA ppm O2 in Ar at 1441 K and 2.13 bar
Experimental data of S. Li, D.F. Davidson, R.K. Hanson,
Combustion and Flame 161 (2014) 2512–2518

47. Detailed Models Tell a Lot about the Process
Dashed arrows – pre-ignition
Note the first major radical generation in the system is from the C–C bond scission 47
A. Grinberg Dana, B. Buesser, S.S. Merchant, W.H. Green, 2017, In Progress

48. And Sulfur too: tBu-S-tBu With Cyclohexene Cyclohexene
inhibitor significantly alters products…
but
consumption of tBu-S-tBu
almost
unchanged
Class et al.
PCCP (2016)
653 K
200 torr

49. Most t-butyl sulfide reacts unimolecularly,
but initial product thiol lives long enough to react
with radicals (giving different products)

50. Quiz
To add a new element, we need to teach the computer any completely new types of reactions that are done only by that element. We also need to add new functional groups involving that element, with their thermochemical group values, and also how the presence of that functional group changes the rate estimates.
Most of the functional groups used for thermochemistry are of the type
C/W/X/Y/Z
i.e. the thermochemistry of a tetrahedral Carbon atom surrounded 4 other atoms. For hydrocarbons there are only 5 of these (for carbon touching 0,1,2,3, or 4 H atoms). How many of these tetrahedral Carbon groups are there for systems which include C,H,N,O,&S atoms?

51. End of 2nd Lecture, Day 4

52. Day 5 Agenda
Some Issues with Mechanism Construction / Reduction (finish Lesson 5)
What chemistry matters for fuel performance?
Some more requirements a good fuel should meet, and some fuels issues you should be aware of
NOx chemistry
Ignition Chemistry (first batch of Lesson 4 slides)
Soot Chemistry (Lesson 7 slides)

53. Wow, That Looks Great! Really Can Predict Kinetics, sometimes to close to experimental accuracy
What is the catch?

54. Predictive Chemical Kinetics: The Downside
Need pretty good estimates (to decide which reactions are important) and also high-accuracy rate & thermo calculations (to achieve quantitative predictions)
Problems with either estimates or quantum calcs can lead to poor predictions
Very quick to get a rough prediction based on estimates, much slower to get an accurate prediction: dozens of quantum calcs required in the best case.
Many Limitations of present methods, e.g.:
High T only (> 600 K)
Troubles modeling MW growth (e.g. polycyclic aromatics)
Estimates based on 2-d representation, unaware of 3-d effects
Mostly neutral gas phase species (a little bit of liquid phase)
Mostly limited to C/H/O molecules (some S, Si, Cl examples)

55. Issues with Rate-Based Selection
If you have an error in a rate estimate, it will change which model is constructed.
Worst rate estimates are for the reactions humans think are least important; sometimes they are estimated too high and get included in model
Rate is important, but it is not the same as sensitivity: some low-rate reactions are important, must be included in the model.
There is a proof that for a very tight tolerance rate-based algorithm converges, but in practice we often cannot achieve a tight enough tolerance because of computer/programming limitations.
This is particularly problematic for low-T ignition

56. Valid Range of a kinetic model
Chemistry changes a lot with composition and reaction conditions (especially temperature).
Models are always a truncated expression of reality, leave out some reactions.
If you change composition or temperature enough, some reaction left out of the model will become important.
“Valid range” defines how far the conditions could change before an additional species or reaction would need to be added. See Jing Song et al., Chemical Engineering Science 57, 4475 (2002).
Unfortunately, today the valid ranges of many models are unknown or at least unstated, so models are frequently applied at reaction conditions where they are not valid.

57. Accuracy much worse at lower Temperatures
Rates and Keq’s scale as exp(-E/RT).
Estimated E’s can be off by several kcal/mole.
Even with expensive quantum calc we could be off by more than 1 kcal/mole.
So all the numbers in the model could be off by factors of exp(±1 kcal/mole / RT). Small at high T, but order of magnitude errors at room T.
To go to low T, need more accurate Ea’s….

58. Predictions not perfect yet: iso-butanol model that worked so well completely misses [O2] sensitivity of low-T ignition delay!
Const. [Fuel]
Model:
No [O2]
dependence
In Air
Model predicts
[fuel] dependence
reasonably well
Expts:
τ ~ [O2]-1.5
Data measured by B. Weber and C.J. Sung (UConn) 58

59. Why is Low T ignition/oxidation hard to predict accurately?
Errors in Ea amplified at low T:
exp(-(EaE)/RT) so errors in k(T) scale as exp(E/RT)
At low T, addition reactions (e.g. of O2) occur, creating many larger species. (At high T molecules get smaller not larger)
Often many reactions omitted during model construction (tolerance not tight enough)
Quantum more expensive for bigger molecules
Bigger molecules usually have more floppy modes
Quantum often less accurate for peroxy species
Peroxy and oxy radicals have two electronic states…
We are still learning peroxy chemistry, maybe missing some reaction templates
And at low T, need to worry about condensed phase, not just Gas Kinetics

60. Why is predictive kinetics slow?
Even relatively simple high T systems can involve >100 kinetically significant species, and >500 important reactions.
Number of “edge” species grows exponentially.
Systems with molecular weight growth can have orders of magnitude more species & reactions
Usually we have to compute most of the thermo & rate parameters… but accurate quantum chemistry calculations are slow and difficult for large molecules.
Automated transition state (saddle point) search is not yet robust. Saddle point search often needs human assistance.

61. Pruning the Edge of the Growing Reaction Network Keeps Memory Usage Under Control
“Erase Negligible Reactions
As Soon As You Can” allows
us to model very complicated
systems
Han & Green, Comput. Chem. Eng.
100, 1-8 (2017)
Funded by this program

62. 2-d vs 3-d molecules and transition states
Most thermo & rate estimates depend on local functional group, implicitly a 2-d representation of the molecules, do not consider 3-d effects
Fused ring strain, Steric crowding
Importance of planarity for aromaticity & resonance
Stereoelectronics, Intramolecular H-bonding
Conformers (e.g. coupled hindered rotors)
These effects are huge for polycyclic molecules, and for many reactions through cyclic TS’s (e.g. intramolecular H-abstractions)
If the estimates are way off, RMG will omit important species and reactions. No easy way to recover.

63. Summary Predictive Kinetics would be great for Combustion problems.
Now practical to make fairly accurate predictions of thermo & kinetic parameters (~1 kcal/mole, factor of 3).
We can automatically build predictive kinetic models for CHNOS species up to about C10…guided by Benson methods.
Sensitive numbers can/should be refined using quantum chemistry.
Often the model predictions are quantitative at high T.
Real Predictions and Experimental Tests, not fits to a training set, needed to quantify errors of the prediction methodology
many accurate quantum calculations will be needed to extend to new chemistry, lower temperatures
Predictive Chemistry looks a lot more promising now than it did in 1929… 63

64. Acknowledgements
RMG was developed by a large number of students & postdocs over the last 15 years; I am very grateful to all of them. I particularly acknowledge the 3 recent Lead Developers of RMG: Joshua Allen, Connie Gao, and Kehang Han. Also Prof. Richard West of Northeastern University, who inspired a major revamp of the software, and continues to inspire my students and his to tackle hard problems with professional software development approaches. The biggest and most continuous funding source for the creation & improvement of RMG has been the DOE GPCP program.
JP-10 pyrolysis: Nick Vandewiele, K. Van Geem, G. Marin, FWO, Navy
Isobutanol Flames: Shamel Merchant, Michael Harper, Nils Hansen, DOE Combustion EFRC
Ethylamine, N in RMG: Alon G. Dana, Beat Buesser, Shamel Merchant, DOE GPCP