Applications of High-Performance Computing in Geochemistry Adam F. Wallace ([email protected]) & Kendra J. Lynn ([email protected]) Department of Geological Sciences University of Delaware Kendra J. Lynn Postdoc with Dr. Jessica Warren (left) Lab Members and Affiliates Adam Yifei Ma June Hazewski Chunlei Wang Brianna McEvoy Wallace Ph.D. student M.S. student Ph.D. student M.S. 2017 (Sturchio LaB) Geochemists are interested in processes that occur over a wide variety of time and length scales Atomic Scale Mineral Surfaces Grain Boundary Processes 2.5 x 2.5 µm Whole Rock GloBal Regional Modeling is critical because many locations and conditions of interest are physically inaccessible in the field and in the lab pore-scale whole mineral/rock regional scale nucleation / growth recrystallization Time mineral-water equilibria ion-hydrolysis / polymerization Continuum Ion sorption / desorption Diffusion in solution Coarse Grained gas-water MD ion-ion ion-water Reactive MD (i.e. ReaxFF) QC (ab initio / DFT) Distance Our lab uses experimental and computational tools to investigate mineral-water interactions AFM-based studies of mineral nucleation & growth Theoretical models of mineral stability and reactivity i r i r θ cos 3 i Σ = angle angle ξ 3 2.5 x 2.5 µm ri ri ξbond = r 2 Σ 0 i 7.5 x 7.5 µm Overview of atomistic simulation methods Electronic Structure Methods Classical Molecular Dynamics • Density Functional Theory (DFT), • Based on Newton’s equations of ab initio methods motion. • Based on approximate solutions to Schrodinger’s equation: F = ma HΨ = EΨ • Physics modeled with with less precision. • Physics modeled with “high” • Requires a lot of computer accuracy. power but less than electronic structure methods. • Requires a lot of computer power. • 10-100 ns trajectories typical • 10-20 ps trajectories typical Reactions of geochemical interest are often too slow to be observed with direct simulation methods • Earth’s crust is primarily composed of silicate minerals • At surface conditions most silicates dissolve very slowly (10-6 to 10-14 mol / m2 sec). • Even at 200°C quartz dissolves at ~10-6 mol / m2 sec in salt water solutions. This is equivalent to the release of ~10-4 molecules of 2 H4SiO4° per 100 nm of surface per microsecond. Dove and Nix (2002) GCA, 61:3329-3340. Specialized methods are needed to overcome timescale limitations and enhance sampling Global energy minimization strategies • Minima Hopping (LJ38) • Replica Exchange Molecular Dynamics (CaCO3.nH2O clusters) Exploration of free energy landscapes with biased dynamics • Use of the Colvars Library in LAMMPS • Umbrella Sampling (water exchange on Ca2+) • Metadynamics (Si-O bond hydrolysis) Calculation of reaction rates (water exchange reactions) • Direct methods • Reactive Flux • Forward Flux Sampling Absolute Free Energy methods • 2PT (substitution of CO2 for H2O in sepiolite) Global Energy Minimization Strategies Minima Hopping (Goedecker (2004) J. Chem. Phys., 120:9911) • Hopping is performed by activation-relaxation steps. • During an activation step, a molecular dynamics trajectory is initiated with a given kinetic energy (Ekin) and followed until the potential energy decreases. • During a relaxation step the system energy is minimized to the nearest local minimum. Successful escape Ekin decreases Failed escape • The move to the new minimum is accepted if the Ekin increases energy difference between the new and old minima Potential Energy is less than a parameter (Ediff) that is dynamically adjusted so that ~50% of the moves are accepted. • If the system returns to a minimum it has already Reaction Progress visited Ekin is increased. Minima Hopping (Goedecker (2004) J. Chem. Phys., 120:9911) Implementation Details • Activation steps are performed with LAMMPS • Relaxation steps are performed with LAMMPS or GULP. • A python script controls the setup and execution of LAMMPS/GULP. Energy Minima Visited Parallel Tempering / Replica Exchange Molecular Dynamics Exchange between replicas occurs subject to a conditional probability rule. Replica Exchange Sampling Circumvents High Energy Barriers Potential Energy Landscape Replica Exchange Sampling Can Locate Global Minima Potential Energy Landscape Enhanced sampling of hydrated CaCO3 clusters with Replica Exchange Molecular Dynamics ( ).Wallace et al. (2013) Science, 341:885-889 Exploration of Free Energy Landscapes with Biased Dynamics Use of the Colvars Library in LAMMPS • The Colvars library is included in LAMMPS distributions as an optional package. • The library enables a number of biased sampling methods, including: umbrella sampling, metadynamics and adaptive bias force. • The library is invoked as a “fix” in the LAMMPS input script. Anatomy of a simple COLVARS input file Output and restart frequency. Block that defines the collective variable to apply the bias to. In this case the distance between two groups containing 1 atom each. This block applies a harmonic restraining potential to maintain the value of the collective variable “DIST” centered around 3.1. The energy units are those used by lammps. In this case the force constant is in eV. Sample COLVARS Output MD Step Instantaneous value of “DIST” Obtaining the free energy barrier (Umbrella Sampling) Define reaction progress coordinate Apply a Bias along the 1 2 (often metal-oxygen distance for water reaction coordinate exchange reactions) Obtain Biased proBaBility 3 distributions Convert proBaBilities to free 4 energies for each window and suBtract the Bias potential. ComBine free energy 5 segments Using WHAM utility to Process COLVARS Output We use a utility maintained by Alan Grossfield at U. Rochester to process umbrella sampling output from COLVARS. http://membrane.urmc.rochester.edu/content/wham The utility takes a file ”metadata” as input that specifies the locations of the COLVARS output for all the sampling windows, and writes an output file ”freefile” that contains the free energy with respect to the biases coordinate. Using WHAM utility to Process COLVARS Output Sample metadata file window Path to COLVARS output files center Restraint force constant (kcal/mol) Running WHAM Metadynamics Basics The metadynamics method accelerates the exploration of energy landscapes by the slow buildup of a history dependent bias. The bias encourages the simulation to explore new states and ultimately grows to form the negative image of the energy landscape. Van Speybroeck et al. (2014) Chem. Soc. Rev., 43:7326-7357. Metadynamics Simulation of Si-O Bond Hydrolysis ) br O - max(Si min(Si-OW) Sample LAMMPS and COLVARS input files for 2D Metadynamics File to read group definitions from Definition of collective variable “one” as the minimum Si-OW distance. Definition of collective variable “two” LAMMPS groups written to file as the maximum Si-Obr distance. This to be read by COLVARS uses a custom function that depends on the Lepton library. Settings that control the accumulation of the metadynamics bias function. LAMMPS Input COLVARS Input Calculation Water Exchange Rates + # ∗ ,- # ∗ !I H%O '] + H%O [I H%O '/0 H%O ] + H%O 1 �234 = �38 Richens (2005) Chem. Rev., 105(6):1961-2002. Date:12/1/17Comp. Time:15:36:32 by: DElayaraja Page Number: Stage: 5 Proof Chapter No.: 27 Title Name: ADIOCH copy is the copyright property of the publisher and is confidential until formal publication. formal until confidential is and publisher of the property copyright the is copy proof This print. or in proof online this publish to allowed not is It SPi. typesetter and Elsevier reviewer(s), editor(s), author(s), by the To protect the rights of the author(s) and publisher we inform you that this PDF is an uncorrected proof for internal business use only book. of this versions electronic all in colour in appear will figures colour The planned. been not has These proofs may contain colour figures. Those figures may print black and white in the final printed book if a colour print product Correlation of Water Exchange Rates & Bulk Reactivity Trends (Oxides and Orthosilicates) f0010 Fig. 2 Dissolution rates at pH 2 ofCasey simple (2017) oxide Adv. (A) Inorg and. Chem., orthosilicate 69:91-115. (B and C) minerals containing divalent metals. The abscissa is the rate of 2+ exchange of water from the corresponding metal ion (e.g., Mg (aq)), and the ordinate is the dissolution rate of the mineral (e.g., Mg2SiO4, forsterite) normalized to area. The oxide minerals have the rocksalt structure. The orthosilicate minerals (5) have the stoichiometry: 4 M2SiO4(s) and isolated SiO4 À tetrahedra. The end-member compositions of orthosilicates are shown in red squares in (B), whereas the mixed-metal compositions are shown as blue dots.Forthemixed-metalcompositions,dissolutionratesareplottedagainsttheweighted sum of the logarithm of rates of water exchange for the component ions. Note that the dissolution rates for mixed-metal compositions (blue dots in (B)) fall intermediate between the end-member compositions. The rates of ligand exchange of the aquated ions ( ) and the dissolution rates of the orthosilicate minerals ( ) at pH 2 are plotted as a function of the number of d electrons in (C), illustrating the role of ligand-field stabilization in the rates. Panels (B) and (C) are adapted from Ref. Casey, W.H.; Swaddle, T.W. Reviews of Geophysics 2003, 41 (2), 4/1–4/20. Correlation of Water Exchange Rates & Bulk Reactivity Trends3338 P.M. Dove and C.J. Nix (SiO ) (a) 2 -6.0 [] water, electrolytes not present • 0.01 molal MeC12 ~2 © 0.05 molal MeC12 o -6.5 q o = © _= -7.0 @ 2+ ~3 o © -7.5 [] © Si4+ 200oC -8.0 i I r I i I I I r i i [ i ~ i i i i r 0.00 2.00 4.00 6.00 8.00 10.00 log kex of aqueous ions (s -1) (b) -6.0 [] water,Dove andelectrolytes Nix (2002) not present GCA, 61:3329-3340. -6.5 0 O -7.0 © @ -7.5 [] [] o 200°C -8.0 i K i I i i I I i i i I i i i I i r i 0.00 2.00 4.00 6.00 8.00 10.00 log kex of aqueous ions (s -1) Fig.