The Ab Initio Nanoreactor: Discovering Chemical Reaction Networks Todd J
The Ab Initio Nanoreactor: Discovering Chemical Reaction Networks Todd J. Martínez Department of Chemistry & The PULSE Institute Stanford University 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 Oops! Build kinetic model
Quantum Chemistry is Expensive! 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) Evolution of Videogames
2010
1980 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 GPU Gaming Hardware
GeForce GTX Titan: 2688 cores @ 876 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 TeraChem – first quantum chemistry package designed for stream processors
http://www.petachem.com GPU is fundamentally different from CPU
Reordering 2e integrals by type 1 µν | λσ = χ r χ r χ r χ r dr dr ( ) ∫∫ µ ( 1 ) ν ( 1 ) λ ( 2 ) σ ( 2 ) 1 2 r2 − r1
(SS|SS), (SS|SP), (SS|PP), … , (DD|DD) Coulomb repulsion
Intensive logical operations will hamper performance GPU is fundamentally different from CPU
Reordering 2e integrals by size
1/2 1/2 (µν | λσ ) ≤ (µν | µν ) (λσ | λσ )
Absolutely no screening, N4 instead of N2 integrals GPU is fundamentally different from CPU
Exploiting Finite Precision Only need high accuracy for largest integrals
DP
SP TeraChem/GPU is over 100X faster than GAMESS/CPU
BLYP/6-31G*
http://www.msg.chem.iastate.edu/gamess/ 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 Oops! Build kinetic model Pray you found all the relevant minima! ?
Can we discover minima and reactions? The Nanoreactor
• Spherical reflecting boundary conditions • NVT Molecular Dynamics • High T (1000-1500K) • 100-300 atoms • Up to 1ns of dynamics per realization • Automated analysis • Automated refinement Nanoreactor – Is it feasible?
Spherical Boundary Conditions – H2 and C2H2 at high T/P (1500K) 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) More Complex Reactions?
Te Urey-Miller experiment resulted in the creation of many of the same molecules found in the Murchison meteorite. Event Generation
What if reactions don’t happen fast enough? Use artificial event generation! Confning potential has a variable radius given by a square-wave in time. ⎧ 0 r ≤ r t ⎪m k 0 ( ) V (ri ) = ⎨ i 2 (ri − r0 (t)) r > r t ⎩⎪ 2 0 ( ) 9.5 9 8.5 8 7.5
Radius (Å) 7 6.5 6 0 5 10 15 20 25 Time (ps) Analysis
New molecules are identifed 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 identifed 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. Sampling of “Discovered” Molecules
Commonplace compounds O OH H O CH OH H3C NH2 3 OH O H NH2 OH H H HO methanol ethanol methanamine formaldehyde ethylene glycol hydrogen peroxide aminomethanol OH Biologically relevant OH OH O O O NH2 HO NH 2 O N H2N NH2 OH OH HO H urea carbonic acid 2-aminoacetic acid 2-aminopropane-1,1-diol (hydroxymethyl)carbamic acid
NH2
Exotic molecules O O H HO O N O NH2 N O OH OH N NH NH N N H H O OH 1-hydroxy-3-(hydroxymethyl)urea 3-(((aminooxy)carbonyl)amino)propanenitrile 2-(1-(aminooxy)vinyl)pyrazolidin-3- 3,3-dihydroxyaziridin-2-one one O
HO O
4-hydroxyoxetan-2-one Hundreds more! 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: Refinement
In order to determine the feasibility of a reactive trajectory, we search for the minimum energy path.
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:
⎧ ~ 2 ~ 2 ~ 2 ⎫ min (rij ({x})− rij ) + θijk ({x})−θijk + φijkl ({x})−φijkl {x} ⎨ ∑ ∑( ) ∑( ) ⎬ ⎩all pairs angles dihedrals ⎭ 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. 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 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… Representative Reaction 1 *Please don't take the 2D representations too seriously
• H-atom transfer causes bond orders to shift. • Te carbon on the right is oxidized. 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.) Representative Reaction 3
• Formation of formaldimine from carbene species
wB97X-D singlet; ∆E = -32.9 kcal; Ea = 24.8 kcal wB97X-D triplet; ∆E = +19.7 kcal; Ea = 34.1 kcal Representative Reaction 4
• Bond breaking precedes proton transfer Molecules have momentary formal charge Representative Reaction 5
• Bond formation precedes proton transfer Appearance of a catalytic water or proton wire Representative Reaction 6
• Protons can shuttle across multiple waters Minimum energy path appears to prefer sequential hopping Feasibilty of Discovered Reactions
Wide range of reaction energies and barrier heights Many reactions with barriers < 20 kcal/mol Visualizing the Reaction Space
1) Focus on a molecule of interest (urea (NH2)2CO, 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!
Amino Acids From Urey-Miller Nanoreactor?
∆E = -6.3 O ∆E = -11.6 ∆E = 8.9 Ea = 29.6 Ea = 36.8 Ea = 28.3 CO + H O 2 HO OH H2C O + H -H O NH3 cat. H OH 2 2 NH3 cat. H2O cat. ∆E = 27.7 ∆E = -10.5 +NH3 H2O, NH3 cat. Ea = 32.6 Ea = 10.7 H2O cat.
∆E = 6.2 E = 32.8 C a H2C NH HO NH2 HO OH -H2O, H2O cat.
+H2O, CO HCOOH + H2CNH H2O cat. ∆E = -50.5 ∆E = -26.6 + CO ∆E = 21.4 Ea = 10.5 Ea = 31.6 ∆E = -25.4 E = 38.6 a Ea = 46.1 OH C NH2 NH2 O OH ∆E = -51.9 Ea = 31.6 O • 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? Acetylene Nanoreactor – Less Complex? Acetylene Nanoreactor – Less Complex?
Very large final products – from starting with many triple bonds Coronene dimerization A frst 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) Coronene dimerization Several moderate to high-energy dimer isomers were discovered using the nanoreactor (refned with B3LYP-DFT).
Charge transfer complex +106 kcal/mol "Stone-Wales" dimer "Barrelene" dimer + H2 +89 kcal/mol +90 kcal/mol
T-shaped dimer +69 kcal/mol
van der Waals complex 0 kcal/mol Future Work l 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) l New schemes for event generation – Rule-based approaches – Varying electron number – Electronic excitation – Temperature variation l Faster dynamics using multi-time step algorithms – Reactive empirical potentials – Small basis set approaches l True NPT ensemble with ideal gas barostat l Combustion – Soot formation – Ethylene, propane, butanol l Couple with higher levels of theory for refinement steps – E.g., coupled cluster (CCSD) Acknowledgments
Nathan Luehr Ivan Ufimtsev
Fang Liu
Alexey Titov Lee-Ping Wang