Understanding Chemical Reactions through Computer Modeling. Tyler R. Josephson University of Delaware 4/21/16

Transcription

1 Understanding Chemical Reactions through Computer Modeling Tyler R. Josephson University of Delaware 4/21/16

2 A little about me B.S. in Chem E from U of M, 2011 Currently, Ph.D. student at University of Delaware, advisor Dion Vlachos Collaborated with Prof. Tsilomelekis Research interests: Fuels and chemicals from biomass Computational tools for studying chemical reactions in solution 2

3 Why is Catalysis Important? 3

4 Opportunities for Computational Experiments Access details about molecular and atomic structure that can be hard to get from experiment Discover trends that aid in catalyst discovery Improve accuracy and reliability in scale-up Process control during plant operation Just about anything can be modeled! Explosive, unstable, toxic, expensive compounds 4

5 Today s Lecture 1. Calculating interactions in molecules 2. Computing reaction energies 3. Finding transition states 4. Modeling complex reaction networks to simulate reactor performance in real systems 5

6 Interactions from Quantum Chemistry 2 protons 2 electrons Infinite separation e - 1+ e - 1+ ΔE f Formation Energy Hydrogen Molecule ΔE f = repulsion of nuclei + repulsion of electrons + attraction of electrons to nuclei + electron exchange energy 6

7 Interactions from Quantum Chemistry 2 protons 2 electrons Infinite separation ΔE f Formation Energy ΔE f = repulsion of nuclei + repulsion of electrons + attraction of electrons to nuclei + electron exchange energy ΔE f = ΔE f (d) Geometry of atoms affects total energy for H 2, this is H-H distance Minimize energy as function of d to get most stable H 2 molecule e - d e - Hydrogen Molecule 7

8 Interactions from Quantum Chemistry 1 carbon nucleus 4 hydrogen nuclei 10 electrons Infinite separation ΔE f Formation Energy Methane ΔE f = repulsion of nuclei + repulsion of electrons + attraction of electrons to nuclei + electron exchange energy 8

9 Interactions from Quantum Chemistry 1 carbon nucleus 4 hydrogen nuclei 10 electrons Infinite separation ΔE f Formation Energy Methane ΔE f = repulsion of nuclei + repulsion of electrons + attraction of electrons to nuclei + electron exchange energy ΔE f = ΔE f (r C,r H1,r H2,r H3,r H4 ) = ΔE f (r) Minimize energy as function of x,y,z coordinates of all atoms to get most stable CH 4 molecule 9

10 A Universal Method 10

11 A Universal Method 1 carbon nucleus 2 oxygen nuclei 22 electrons Infinite separation ΔE f Carbon Dioxide 8 carbon nuclei 4 nitrogen nuclei 2 oxygen nuclei 10 hydrogen nuclei 102 electrons Infinite separation ΔE f Caffeine 1 O nucleus 1 H nucleus 18 Pt nuclei 1413 electrons Infinite separation 5 carbon nuclei 2 nitrogen nuclei 3 oxygen nuclei 10 hydrogen nuclei 78 electrons Infinite separation ΔE f = ΔE f (r) locations of all nuclei ΔE f OH on Platinum nanoparticle ΔE f Glycine/alanine peptide = protein! With more atoms and electrons comes more computational cost and more degrees of freedom 11

12 Challenges Computational cost (CPU hours) increases with system size and level of accuracy Most rigorous, extremely high accuracy methods scale with N 7, where N is # of electrons Less accurate methods scale with ~N 4 or N 2 Supercomputers help, but only so much! Must have well-defined system What does a catalyst look like (crystal structure, active site)? Liquids solvation structure 12 Foresman and Frisch, Exploring Chemistry with Electronic Structure Methods, 122

13 Accuracy? Calculation gives ΔE f (0 K) need ΔH f (298 K) ΔH f (0 K) = ΔE f (0 K) + vibrational correction ΔH f (298 K) = ΔH f (0 K) + thermal correction 454 experimental values of ΔH f (298 K) were compared to calculated values For most molecules, error for gas phase species is 1 kcal/mol (4 kj/mol) More approximate methods are less accurate, but faster to calculate Example Species: CH 4, CH 3 OH, CO 2 SO 2, C 6 F 6, NaF N 2 O 3, AlF, C 12 H J. Chem. Phys. 123, (2005)

14 Today s Lecture 1. Calculating interactions in molecules 2. Computing reaction energies 3. Finding transition states 4. Modeling complex reaction networks to simulate reactor performance in real systems 14

15 Calculating Reaction Thermochemistry CH 4 + 2O 2 CO 2 + 2H 2 O ΔH rxn = ΔH f_co2 + 2*ΔH f_h2o ΔH f_ch4 2*ΔH f_o2 Calculate ΔH f for each species My calculated result: ΔH rxn (298 K) = kcal/mol Lower Heating Value of Methane = kcal/mol 1 C nucleus 4 H nuclei 10 electrons Infinite separation ΔH f = kcal/mol Methane 2 O nuclei 16 electrons Infinite separation ΔH f = kcal/mol Oxygen 2 H nuclei 1 O nucleus 10 electrons Infinite separation ΔH f = kcal/mol Water 1 C nucleus 2 O nuclei 22 electrons Infinite separation ΔH f = kcal/mol Carbon Dioxide 15

16 Calculating Reaction Thermochemistry Glucose 6-member ring ΔH f 6 carbon nuclei 6 oxygen nuclei 12 hydrogen nuclei 96 electrons Infinite separation ΔH f_glu = kcal/mol ΔH rxn? Fructose 5-member ring ΔH f ΔH rxn (298 K) = ΔH f_fru (298 K) - ΔH f_glu (298 K) What s different? Just the change in location of the atoms My calculated result: ΔH rxn = 1.8 kcal/mol Experiment: / kcal/mol Why the error? 6 carbon nuclei 6 oxygen nuclei The difference is too small to 12 hydrogen nuclei quantitatively capture, but 96 electrons it s qualitatively right Infinite separation Calculation is gas phase while ΔH f_fru = kcal/mol experiment is aqueous phase 16

17 Today s Lecture 1. Calculating interactions in molecules 2. Computing reaction energies 3. Finding transition states 4. Modeling complex reaction networks to simulate reactor performance in real systems 17

18 Transition State Theory A + B [AB] P Transition state [AB] is in quasi-equilibrium with reactants K = [AB] A [B] = k BT e ΔG RT hν The rate constant of the reaction, k, is given by k = κ k BT e ΔG RT h And since ΔG = ΔH TΔS, k = κ k BT h eδs R e ΔH RT ln k = ln A E a RT 18

19 Transition State Theory A + B [AB] P Transition state [AB] is in quasi-equilibrium with reactants K = [AB] A [B] = k BT e ΔG RT hν The rate constant of the reaction, k, is given by k = κ k BT e ΔG RT h And since ΔG = ΔH TΔS, k = κ k BT h eδs R e ΔH RT ln k = ln A E a RT ΔH = H - H reactants ΔS = S - S reactants We can calculate these! 19

20 Calculating Transition States + Ethylene Cyclopentadiene Transition State Diels Alder Product Local energy minimum Minimize energy in all but 1 degree of freedom This is the reaction coordinate Local energy minimum Open Gaussview to show path of reaction W.L. Jorgensen, et al. J. Am. Chem. Soc., Vol. 115, No. 7,

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22 Accuracy of TS Calculation + Ethylene Cyclopentadiene Transition State Diels Alder Product Reaction in gas phase Ethylene + Cyclopentadiene Cyclopentadiene + Cyclopentadiene Acrolein + Cyclopentadiene Calculated ΔH (298 K) (kcal/mol) Experiment ΔH (298 K) (kcal/mol) Calculated ΔS (298 K) (cal/mol K) Experiment ΔS (298 K) (cal/mol K) W.L. Jorgensen, et al. J. Am. Chem. Soc., Vol. 115, No. 7,

23 Today s Lecture 1. Calculating interactions in molecules 2. Computing reaction energies 3. Finding transition states 4. Modeling complex reaction networks to simulate reactor performance in real systems 23

24 Ethanol Steam Reforming Sutton, J., et al. J. Phys. Chem. C 2013, 117, CH 3 CHO Pt (111) 24

25 Fitting Data to a Power Law Model Fit data to experiment for apparent rate orders, activation energies, and pre-exponentials r CH3CH2OH = k 1 [CH 3 CH 2 OH] a1 [H 2 O] b1 k 1 = A 1 exp(-e a1 /RT) r CH4 = k 2 [CH 3 CH 2 OH] a2 [H 2 O] b2 k 2 = A 2 exp(-e a2 /RT) r CO = k 3 [CH 3 CH 2 OH] a3 [H 2 O] b3 k 3 = A 3 exp(-e a3 /RT) CH 3 CHO Drawbacks: No molecular understanding of reaction Predictions outside range of experimental data are invalid don t extrapolate! Often fail to predict changes that occur during scale up 25

26 Complexity of Practical Reaction Networks 167 reactions 67 species Everything with < 3 carbons! This is just decomposition! * denotes site on Pt catalyst 26 Sutton, J., et al. J. Phys. Chem. C 2013, 117,

27 Microkinetic Modeling Process 1. Calculate energies and barriers for all species and reactions 2. Use a rate model (usually Transition State Theory) to relate energetics and barriers to reaction rates 3. Bring reaction rates into a system of differential equations to solve 4. Set up an in silico experiment to simulate the course of a reaction over time 5. Compare simulated reaction to experiments, and return to refine your model as necessary 27 Sutton, J., et al. J. Phys. Chem. C 2013, 117,

28 Computing the Rate of Each Elementary Step For example: CH 3 CH 2 OH* + * TS CH 2 CH 2 OH* + H* 1. Break C-H bond and place H on Pt catalyst 2. Calculate energetic barrier and use Transition State Theory to get rate constant k k = k BT e ΔG RT h 3. Rate = k[ch 3 CH 2 OH*][*] 28 Sutton, J., et al. J. Phys. Chem. C 2013, 117,

29 Computing the Rate of Each Elementary Step For example: CH 2 CH 2 OH* + * TS CH 2 CHOH* + H* 1. Break C-H bond and place H on Pt catalyst 2. Calculate energetic barrier and use Transition State Theory to get rate constant k k = k BT e ΔG RT h 3. Rate = k[ch 2 CH 2 OH*][*] 29 Sutton, J., et al. J. Phys. Chem. C 2013, 117,

30 Computing the Rate of Each Elementary Step For example: CH 2 CHOH* + * TS CH 2 * + CHOH* 1. Break C-C bond and place CH 2 on Pt catalyst 2. Calculate energetic barrier and use Transition State Theory to get rate constant k k = k BT e ΔG RT h 3. Rate = k[ch 2 CHOH*][*] 30 Sutton, J., et al. J. Phys. Chem. C 2013, 117,

31 Computing the Rate of Each Elementary Step For example: CHOH* + * TS COH* + H* 1. Break C-H bond and place H on Pt catalyst 2. Calculate energetic barrier and use Transition State Theory to get rate constant k k = k BT e ΔG RT h 3. Rate = k[choh*][*] 31 Sutton, J., et al. J. Phys. Chem. C 2013, 117,

32 Computing the Rate of Each For example: COH* + * TS CO* + H* Elementary Step Produced CO finally a stable product that can desorb! 1. Break O-H bond and place on Pt catalyst 2. Calculate energetic barrier and use Transition State Theory to get rate constant k k = k BT e ΔG RT h 3. Rate = k[coh*][*] 32 Sutton, J., et al. J. Phys. Chem. C 2013, 117,

33 Computing the Rate of Each Elementary Step 167 reactions 67 species Now put together differential equations to describe the rate * denotes site on Pt catalyst 33 Sutton, J., et al. J. Phys. Chem. C 2013, 117,

34 A Mass Balance Problem d[ch 3 CH 2 OH ] dx CH 3 CH 2 OH H 2 O 67 species Plug Flow Reactor T, P, amount of catalyst 167 reactions CH 3 CHO CO 2 CO CH 4 H 2 O H 2 = k ads P EtOH k 1 [CH 3 CH 2 OH*][*] k 2 [CH 3 CH 2 OH*][*] k 3 [CH 3 CH 2 OH*][*] d[ch 3 CH 2 O ] dx = k 1 [CH 3 CH 2 OH*][*] k 4 [CH 3 CH 2 O*][*] k 5 [CH 3 CH 2 O*][*] + d[ch 3 CH 1 OH ] dx d[ch 2 CH 2 OH ] dx = k 2 [CH 3 CH 2 OH*][*] k 6 [CH 3 CH 1 OH*][*] + k 7 [CH 3 CH 1 OH*][*] + = k 3 [CH 3 CH 2 OH*][*] k 8 [CH 3 CH 1 OH*][*] + k 9 [CH 3 CH 1 OH*][*] + Solve the ODEs using numerical methods to simulate reactor performance 34 Sutton, J., et al. J. Phys. Chem. C 2013, 117,

35 Calculations Agree with Experiments Apparent activation energy and apparent reaction orders are close to agreeing with the model 12.5% Ethanol, 37.5% H2O, 50% He, 1 atm total pressure Absolute rate is within 1 order of magnitude Compared to experiment 35 Sutton, J., et al. J. Phys. Chem. C 2013, 117,

36 Calculations Agree with Experiments 12.5% Ethanol, 37.5% H2O, 50% He, 1 atm total pressure Experiment: points; Simulation: lines By tuning a single reactor parameter: the amount of catalyst in the simulated reactor, they achieved quantitative agreement with experimental conversion, and qualitative agreement with 36 the selectivity trends. Sutton, J., et al. J. Phys. Chem. C 2013, 117,

37 Additional Insights from Model What determines the rate? Most important step for total conversion: 1 st dehydrogenation of adsorbed ethanol Catalysts that facilitate this step will give fast reactions What controls the selectivity? Most important intermediate for selectivity: CH 3 CO* If catalyst breaks C-C bond, expect CO and CH 4, but if catalyst doesn t, then expect CH 3 CHO Which species are most abundant on the catalyst surface? Scale-Up Extrapolate outside experimental conditions 37 Sutton, J., et al. J. Phys. Chem. C 2013, 117,

38 Biomass Catalysis Application: Fructose Dehydration Caratzoulas and Vlachos, Carbohydrate Res Use computer to examine 11-step mechanism between fructose and HMF Identify highestbarrier step (ratedetermining step) Isotopic labelling experiments support hypothesis from calculations 38

39 Opportunities for Computational Experiments Just about anything can be modeled! Explosive, unstable, toxic, expensive compounds Access details about molecular and atomic structure that can be hard to get from experiment Discover trends that aid in catalyst discovery Assist in reactor scale-up Process control during plant operation 39

40 Questions?