The Ab Initio Nanoreactor: Discovering Chemical Reaction Networks Todd J. Martínez Department of Chemistry & The PULSE Institute Stanford University

Transcription

1 The Ab Initio Nanoreactor: Discovering Chemical Reaction Networks Todd J. Martínez Department of Chemistry & The PULSE Institute Stanford University

2 Traditional Approach to Reaction Mechanisms Traditional Approach Guess reactant and product geometries Optimize to refine energy minima Use nudged elastic band to find barriers Compute rates using harmonic TST Build kinetic model Oops! Quantum Chemistry is Expensive!

3 How to Proceed? Quantum chemical methods are very computationally intensive! Example: solvated Rubredoxin protein, 2825 atoms 2 hours on 8,196 processor cores for single energy! Guidon M. et al., JCTC 5, 3010 (2009)

4 Evolution of Videogames Economy of scale - over 1M videogame units sold per year! Games are physics simulations - expect good overlap between demands of video games and chemical simulation Large memory bandwidth to get pixels on screen Closed and programmer-unfriendly architectures

5 GPU Gaming Hardware GeForce GTX Titan: MHz 6 GB on-board memory 1.3 DP TFLOPS, 288 GB/s, peak 8 GPUs in a single box 10.4 DP TFLOPS!! 36 SP TFLOPS!! P-threads, MPI, etc

6 TeraChem first quantum chemistry package designed for stream processors

7 GPU is fundamentally different from CPU Reordering 2e integrals by type ( µν λσ ) = χ µ ( r 1 )χ ν r 1 ( ) 1 χ λ ( r 2 )χ σ ( r 2 )dr 1 dr 2 r 2 r 1 Coulomb repulsion (SS SS), (SS SP), (SS PP),, (DD DD) Intensive logical operations will hamper performance

8 GPU is fundamentally different from CPU Reordering 2e integrals by size ( µν λσ ) ( µν µν ) 1/2 ( λσ λσ ) 1/2 Absolutely no screening, N 4 instead of N 2 integrals

9 GPU is fundamentally different from CPU Exploiting Finite Precision Only need high accuracy for largest integrals DP SP

10 TeraChem/GPU is over 100X faster than GAMESS/CPU BLYP/6-31G*

11 New Opportunities? Traditional Approach Guess reactant and product geometries Optimize to refine energy minima Use nudged elastic band to find barriers Compute rates using harmonic TST Build kinetic model Pray you found all the relevant minima! Oops!? Can we discover minima and reactions?

12 The Nanoreactor Spherical reflecting boundary conditions NVT Molecular Dynamics High T ( K) atoms Up to 1ns of dynamics per realization Automated analysis Automated refinement

13 Nanoreactor Is it feasible? Spherical Boundary Conditions H 2 and C 2 H 2 at high T/P (1500K)

14 Analyzing the Products Hard to tell what is happening get the computer to do the work Early analysis of AIMD trajectory (HF / 3-21G, 120 atoms, 1500 K, 27 ps) Red = Transient species Gray = Hydrogen Blue = Acetylene Gold = Ethane Violet = Ethylene Green = Y-wing (Vinylidene)

15 More Complex Reactions? The Urey-Miller experiment resulted in the creation of many of the same molecules found in the Murchison meteorite.

16 V ( r ) i ( r r ( t) ) i Event Generation What if reactions don t happen fast enough? Use artificial event generation! Confining potential has a variable radius given by a square-wave in time. Radius (Å)" = mik r r > Time (ps)" r r 0 0 ( t) ( t)

17 Analysis New molecules are identified and labeled using graphs. For each frame in the simulation: Use covalent radii to determine whether two atoms are bonded Construct graphs: Nodes = atoms, edges = bonds Connected subgraphs correspond to individual molecules Graph isomorphism used to identify new molecules For each identified molecule in the simulation: Existence of molecule in simulation denoted using true/false time series Use a two-state Hidden Markov Model to reduce noise Extraction of chemical reactions: Chemical reactions correspond to atom and time subsets of the trajectory which correspond to complete and distinct graphs.

18 Sampling of Discovered Molecules Commonplace compounds CH 3 OH H OH 3 C NH 2 methanol ethanol methanamine O H H formaldehyde HO OH ethylene glycol H O O H NH 2 OH hydrogen peroxide aminomethanol Biologically relevant O H 2 N NH 2 OH O OH HO O NH 2 HO OH NH 2 O OH N H OH urea carbonic acid 2-aminoacetic acid 2-aminopropane-1,1-diol (hydroxymethyl)carbamic acid Exotic molecules OH OH O NH 3,3-dihydroxyaziridin-2-one HO N H O O N H OH 1-hydroxy-3-(hydroxymethyl)urea N H N 3-(((aminooxy)carbonyl)amino)propanenitrile O O NH 2 NH N NH 2 2-(1-(aminooxy)vinyl)pyrazolidin-3- one O O HO 4-hydroxyoxetan-2-one O Hundreds more!

19 Refinement Have identified molecules at each time point Automatically get list of reactions which occurred Extract atoms involved in bond rearrangements and solve for minimal energy pathways Few atoms - do this at a higher level of theory Nanoreactor samples and discovers Not required to be accurate physical simulation (but can be) Determining reaction paths:

20 Refinement In order to determine the feasibility of a reactive trajectory, we search for the minimum energy path. min { x} Reactant and product optimizations: Many apparent reactions do not have separate basins of attraction for reactant and product; both optimizations go to the same end point. Internal coordinate interpolation: Remove fast vibrational motion from the reaction; Cartesian coordinate interpolation results in unphysical geometries Perform interpolation in redundant internal coordinates and obtain smoothed Cartesian coordinates by nonlinear least squares optimization: all pairs ~ 2 ~ ~ ijk ijk ijkl ijkl angles dihedrals ( r ({ x} ) r ) + θ ({ x} ) ij ij ( ) 2 θ + ( φ ({ x} ) φ ) 2

21 Refinement In order to determine the feasibility of a reactive trajectory, we search for the minimum energy path. String method (similar to nudged elastic band): Starting from the interpolated coordinates, minimize the perpendicular component of the gradient along the path: Transition state optimization: Start from the highest energy point on the string Find a stationary point on the potential energy surface with one imaginary mode. Intrinsic reaction coordinate: Starting from the transition state, perform geometry optimization along imaginary mode to recover reactants and products.

22 Refinement In order to determine the feasibility of a reactive trajectory, we search for the minimum energy path. Raw data from MD trajectory Final intrinsic reaction coordinate

23 Urey-Miller Experiment Hundreds of compounds were found, including (few) amino acids Reaction 1: Water + aldehyde à diol form of alanine Reaction 2: Formic acid + ethylidene radical + ammonia à aldehyde + water (water cat.) Reaction 3: Water + carbon monoxide à formic acid (ammonia cat.) Reaction 4: Ethylidene radical from a big collision

24 Representative Reaction 1 *Please don't take the 2D representations too seriously H-atom transfer causes bond orders to shift. The carbon on the right is oxidized.

25 Representative Reaction 2 *Please don't take the 2D representations too seriously Cracking into two carbenes occurs with a 56 kcal/mol barrier (Hartree-Fock singlet.)

26 Representative Reaction 3 Formation of formaldimine from carbene species wb97x-d singlet; E = kcal; E a = 24.8 kcal wb97x-d triplet; E = kcal; E a = 34.1 kcal

27 Representative Reaction 4 Bond breaking precedes proton transfer Molecules have momentary formal charge

28 Representative Reaction 5 Bond formation precedes proton transfer Appearance of a catalytic water or proton wire

29 Representative Reaction 6 Protons can shuttle across multiple waters Minimum energy path appears to prefer sequential hopping

30 Feasibilty of Discovered Reactions Wide range of reaction energies and barrier heights Many reactions with barriers < 20 kcal/mol

31 Visualizing the Reaction Space 1) Focus on a molecule of interest (urea (NH 2 ) 2 CO, red sphere) 2) Find all reactions that involve this molecule (colored arrows) 3) Draw all molecules that react with the molecule of interest 4) Too many second-degree connections to count!

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33 Amino Acids From Urey-Miller Nanoreactor? CO + H 2 O E = -6.3 E a = 29.6 NH 3 cat. H O OH E = E a = 36.8 HO OH + H 2 -H 2 O NH 3 cat. E = 8.9 E a = 28.3 H 2 O cat. H 2 C O H 2 O, NH 3 cat. E = 27.7 E a = 32.6 E = E a = NH 3 H 2 O cat. HO C OH H 2 C NH E = 6.2 E a = H 2 O, H 2 O cat. HO NH 2 HCOOH + H 2 CNH E = 21.4 E a = 38.6 NH 2 O C OH E = E a = 10.5 E = E a = 31.6 NH 2 +H 2 O, CO H 2 O cat. E = E a = 31.6 Glycine is formed through nonconventional pathways Pathways have moderate energy barriers (30-50 kcal/mol) Many reactions involve formaldimine, aminomethanol Possible ways for glycine to have formed on early Earth? O OH + CO E = E a = 46.1

34 Acetylene Nanoreactor Less Complex?

35 Acetylene Nanoreactor Less Complex? Very large final products from starting with many triple bonds

36 Coronene dimerization A first step towards combustion: PAH dimerization relevant to soot formation (with H. Wang) Analysis of trajectory (HF / 3-21G, 72 atoms, 1600 K) starting with two coronene molecules Red = Transient species Blue = Anion Gold = Cation (H + in middle) Violet = Cation (H + migrating) Green = Cation (H + on edge) Pink = Covalent dimer Pyrene Dimerization/MNDO: Frenklach (2002)

37 Coronene dimerization Several moderate to high-energy dimer isomers were discovered using the nanoreactor (refined with B3LYP-DFT). Charge transfer complex +106 kcal/mol "Stone-Wales" dimer +89 kcal/mol "Barrelene" dimer + H kcal/mol T-shaped dimer +69 kcal/mol van der Waals complex 0 kcal/mol

38 l l l l l l Future Work Couple nanoreactor to kinetic models Realizations at different concentrations predicted by kinetic models Automated sensitivity analysis to refine rates for relevant reactions l Higher levels of theory l Post-transition state theory (dynamical and/or tunnelling corrections) New schemes for event generation Rule-based approaches Varying electron number Electronic excitation Temperature variation Faster dynamics using multi-time step algorithms Reactive empirical potentials Small basis set approaches True NPT ensemble with ideal gas barostat Combustion Soot formation Ethylene, propane, butanol Couple with higher levels of theory for refinement steps E.g., coupled cluster (CCSD)

39 Acknowledgments Nathan Luehr Ivan Ufimtsev Fang Liu Alexey Titov Lee-Ping Wang