Parameterization of a reactive force field using a Monte Carlo algorithm
|
|
|
- Roderick Jefferson
- 6 years ago
- Views:
Transcription
1 Parameterization of a reactive force field using a Monte Carlo algorithm Eldhose Iype (e.iype@tue.nl) November 19, 2015 Where innovation starts
2 Thermochemical energy storage 2/1 MgSO 4.xH 2 O+Q MgSO 4 +xh 2 O MgSO 4 +xh 2 O MgSO 4.xH 2 O +Q Energy storage density of thermochemical materials is about 10 times higher than that of water.
3 Thermochemical energy storage 2/1 Problem: Changes in the crystallinity of the material, Slow kinetics, Reusability etc. Dehydration Hydration MgSO 4.xH 2 O+Q MgSO 4 +xh 2 O MgSO 4 +xh 2 O MgSO 4.xH 2 O +Q
4 Thermochemical energy storage 2/1 Dehydration Hydration MgSO 4.xH 2 O+Q MgSO 4 +xh 2 O MgSO 4 +xh 2 O MgSO 4.xH 2 O +Q Aim: To study hydration and dehydration reactions To characterize the structural changes To understand the mechanism of water release during dehydration
5 Molecular dynamics Atoms are assumed to be point mass particles which obey Newton s laws of motion All particles interact with each other through some potential, U(r 1,r2, r N ) Force acting on any particle at any time is calculated as, F = U(r 1,r2, r N ) Positions are updated by integrating the equation of motion, F = ma Force Field Energy,E = E(r 1,r 2, r N ) 3/1 Force,F = E(r 1,r 2, r N )
6 Condensed water between two Pt slabs 4/1 Details: NVT ensemble, ρ water = kg/m 3
7 Condensed water between two Pt slabs 4/1 Details: NVT ensemble, ρ water = kg/m 3
8 Two phase water between platinum slabs 5/1 Details: NVT ensemble, ρ water = kg/m 3
9 Two phase water between platinum slabs 5/1 Details: NVT ensemble, ρ water = kg/m 3
10 ReaxFF force field 6/1 E system =E vdwaals + E Coulomb + E bond + E val + E tors Characteristics of ReaxFF + E over + E under + E H bond + E lp + E conj + E pen + E coa + E C2 + E triple Dynamic charges are calculated using EEM van Der Waal s interaction is calculated using a Morse-type potential Energy surface is made continuous Connected interactions include Bonded interaction (two body) Valence angle interaction (three body) Torsion interaction (four body) Hydrogen bond interaction
11 ReaxFF force field 6/1 E system =E vdwaals + E Coulomb + E bond + E val + E tors Characteristics of ReaxFF + E over + E under + E H bond + E lp + E conj + E pen + E coa + E C2 + E triple Dynamic charges are calculated using EEM van Der Waal s interaction is calculated using a Morse-type potential Energy surface is made continuous Connected interactions include Bonded interaction (two body) Valence angle interaction (three body) Torsion interaction (four body) Hydrogen bond interaction
12 What makes ReaxFF reactive? ReaxFF calculates bond order between every pair of atoms Bond order is a function of distance of separation Every connected interaction is made a function of this bond order Thus all the bonds become dynamic 7/1 BO ij =BO σ ij + BO π ij + BO ππ ij [ ) ] Pbo2 =exp + exp P bo1 [ P bo5 ( rij r σ o ( rij r ππ o + exp ) Pbo6 ] [ P bo3 ( rij r π o ) Pbo4 ]
13 Bond energy in Reax force field 8/1 Bond energy E system =E vdwaals + E Coulomb + E bond + E val + E tors + E over + E under + E H bond + E lp + E conj + E pen + E coa + E C2 + E triple [ E bond = D σ e BOσ ij exp P be1 (1 ( BO σ ) )] Pbe2 ij D π e BO π ij D ππ e BO ππ ij
14 E conj and E coa in ReaxFF 9/1
15 E pen for valence angle in ReaxFF 10/1
16 E C2 for valence angle in ReaxFF 11/1
17 DFT introduction First Hohenberg-Kohn Theorem 12/1 v ext (r) Ψ 0 n 0 (r) = Ψ 0 ˆn(r) Ψ 0 The theorem states that, one has a one-to-one correspondence between the external potential V ext in the Hamiltonian, the (non-degenerate) ground state Ψ 0 resulting from the Schrödinger equation and the associated ground state (electron) density n 0.
18 DFT introduction First Hohenberg-Kohn Theorem 12/1 v ext (r) Ψ 0 n 0 (r) = Ψ 0 ˆn(r) Ψ 0 The theorem states that, one has a one-to-one correspondence between the external potential V ext in the Hamiltonian, the (non-degenerate) ground state Ψ 0 resulting from the Schrödinger equation and the associated ground state (electron) density n 0.
19 DFT introduction 13/1 E[n] = Ψ[n] Ĥ Ψ[n] Thus, the many-body problem of N electrons with 3N spatial coordinates is reduced to a problem involving only 3 spatial coordinates. The second theorem states that the ground state correponds to the density which minimizes the total energy of the system. E 0 < E[n]
![DFT introduction 13/1 E[n] = Ψ[n] Ĥ Ψ[n] Thus, the many-body problem of N electrons with 3N spatial coordinates is reduced to a problem involving only 3](/docs-images/77/75264287/images/20-0.jpg "spatial coordinates. The second theorem states that the ground state correponds to the density which minimizes the total energy of the system.")
20 DFT introduction 13/1 E[n] = Ψ[n] Ĥ Ψ[n] Thus, the many-body problem of N electrons with 3N spatial coordinates is reduced to a problem involving only 3 spatial coordinates. The second theorem states that the ground state correponds to the density which minimizes the total energy of the system. E 0 < E[n]
21 Parameterization of ReaxFF force field Quantum Chemical (DFT) data is used to parameterize the force field A training data set is prepared which contains the following informations Atomic charges (Mulliken) Equilibrium bond lengths Equilibrium bond angles Torsion angles Energies of the DFT optimized geometries Heat of formation Error in the force field is then calculated n [ xi,qm x i,reaxff Err(p 1,p 2, p n ) = i=1 σ i ] 2 14/1
22 Parameterization of ReaxFF force field Quantum Chemical (DFT) data is used to parameterize the force field A training data set is prepared which contains the following informations Atomic charges (Mulliken) Equilibrium bond lengths Equilibrium bond angles Torsion angles Energies of the DFT optimized geometries Heat of formation Error in the force field is then calculated n [ xi,qm x i,reaxff Err(p 1,p 2, p n ) = i=1 σ i ] 2 14/1
23 Parameterization of ReaxFF force field Quantum Chemical (DFT) data is used to parameterize the force field A training data set is prepared which contains the following informations Atomic charges (Mulliken) Equilibrium bond lengths Equilibrium bond angles Torsion angles Energies of the DFT optimized geometries Heat of formation Error in the force field is then calculated n [ xi,qm x i,reaxff Err(p 1,p 2, p n ) = i=1 σ i ] 2 14/1
24 Parabolic search algorithm 15/1 Err(p 1,p 2, p n ) = n [ xi,qm x i,reaxff σ i i=1 ] Error 1178 Error in the force field Trial values for a paramter
25 Drawbacks of parabolic search algorithm Only one parameter is searched at a time The procedure has to repeated over several rounds It will only find a local minimum Needs a good starting point Shapes of typical ReaxFF Error surface 16/1 Error Error vs σ-bond radius Error Error vs EEM hardness σ-bond radius of S-atom EEM hardness for Mg-atom 1e+07 9e+06 Error vs vdw parameter Error vs r vdw 8e Error 7e+06 6e+06 5e+06 4e+06 3e+06 2e+06 1e vdw parameter for S-O interaction Error vdw radius of Mg-atom (r vdw )
26 A double well potential with a linear term 17/1 U(x) = x x x
27 Equilibrium distribution of states The distribution has a global maximum near the left well. 17/
28 Metropolis Monte Carlo (MMC) method 18/1 Calculate the error of the starting force field, Errold Make a new proposition (move) for the parameters Calculate the error of the new force field, Errnew Calculate the difference in the Error, i.e. Err = Err new Err old Accept the move with a probability given by, Repeat the algorithm P = min[1,exp( β Error)],where,β = 1 k B T
29 Error vs β for a Simulated Annealing run 19/1 7e+06 Error vs β =1/(K B T) 6e+06 5e+06 Error 4e+06 3e+06 2e+06 1e e β
30 Comparison between MMC and ParSearch 19/1 For five random starting force fields Error ratio (Error MMC /Error ParSearch ) Trial 1 Trial 2 Trial 3 Trial 4 Trial Iteration
31 Comparison of the error values 20/1 Table : Initial and final errors of the five simulations. The average < Error > and the coefficient of variation, std(sigma) <Error>, of the final errors are shown. Trial Error initial 1E 6 Error final 1E 6 ParSearch MMC < Error > std(error) <Error>
32 Energies of the hydrates of MgSO 4.xH 2 O 21/1 x ranging from 0 to DFT ReaxFF Err rms : 9.8 kcal/mol Energy (kcal/mol) Geometry number
33 Equation of state for MgSO 4 21/1 Energy (kcal/mol) DFT ReaxFF ReaxFF (100 * σ i ) Err rms ReaxFF (100 * σ i ): 4.5 kcal/mol Err rms ReaxFF: 4.8 kcal/mol Volume
34 Equation of state for MgSO 4.7H 2 O 21/1 Energy (kcal/mol) DFT ReaxFF ReaxFF (100 * σ i ) Err rms ReaxFF: 3.4 kcal/mol Err rms ReaxFF (100 * σ i ) : 7.0 kcal/mol Volume
35 Binding energy 21/1 Binding energy of one water molecule on the (100) surface of MgSO 4 Binding Energy with one water molecule MgSO 4 Energy (kcal/mol) DFT ReaxFF ReaxFF (100 * σ i ) Err rms ReaxFF: 18.0 kcal/mol Err rms ReaxFF (100 * σ i ): 10.7 kcal/mol Distance
36 Hydrogen bonds in MgSO 4 hydrates 22/1 Number of escaped water molecules mbar-noHB 19.5mbar-noHB 39mbar-noHB 9.75mbar 19.5mbar 39mbar Time (ns) The hydrogen bonds slows down the kinetics of dehydration as can be seen from the two sets of dehydration curves (one with hydrogen bonds and the other without hydrogen bonds) in the figure.
37 Dissaperance of step-edge sites 23/1 The movement of step-edge sites in Co-nanoparticles are studied using ReaxFF.
38 Conclusion Metropolis MC algorithm is used to parameterize the ReaxFF force field. The method shows good improvement over the traditional optimization scheme. The stochastic nature of the method allows one to arrive at the global minima in the parameter space. 24/1
39 Thank You!! 25/1
Electrochemistry project, Chemistry Department, November Ab-initio Molecular Dynamics Simulation
Electrochemistry project, Chemistry Department, November 2006 Ab-initio Molecular Dynamics Simulation Outline Introduction Ab-initio concepts Total energy concepts Adsorption energy calculation Project
Reactive potentials and applications
1.021, 3.021, 10.333, 22.00 Introduction to Modeling and Simulation Spring 2011 Part I Continuum and particle methods Reactive potentials and applications Lecture 8 Markus J. Buehler Laboratory for Atomistic
Session 1. Introduction to Computational Chemistry. Computational (chemistry education) and/or (Computational chemistry) education
Session 1 Introduction to Computational Chemistry 1 Introduction to Computational Chemistry Computational (chemistry education) and/or (Computational chemistry) education First one: Use computational tools
Supplementary Materials
Supplementary Materials Atomistic Origin of Brittle Failure of Boron Carbide from Large Scale Reactive Dynamics Simulations; Suggestions toward Improved Ductility Qi An and William A. Goddard III * Materials
The Pennsylvania State University. The Graduate School. College of Engineering DEVELOPMENT AND APPLICATION OF THE REAXFF POTENTIAL FOR
The Pennsylvania State University The Graduate School College of Engineering DEVELOPMENT AND APPLICATION OF THE REAXFF POTENTIAL FOR HETEROGENEOUS CATALYSIS AND METAL OXIDATION: TOWARD THE DYNAMIC SAMPLING
Computational Methods. Chem 561
Computational Methods Chem 561 Lecture Outline 1. Ab initio methods a) HF SCF b) Post-HF methods 2. Density Functional Theory 3. Semiempirical methods 4. Molecular Mechanics Computational Chemistry " Computational
CE 530 Molecular Simulation
1 CE 530 Molecular Simulation Lecture 14 Molecular Models David A. Kofke Department of Chemical Engineering SUNY Buffalo kofke@eng.buffalo.edu 2 Review Monte Carlo ensemble averaging, no dynamics easy
Hyeyoung Shin a, Tod A. Pascal ab, William A. Goddard III abc*, and Hyungjun Kim a* Korea
The Scaled Effective Solvent Method for Predicting the Equilibrium Ensemble of Structures with Analysis of Thermodynamic Properties of Amorphous Polyethylene Glycol-Water Mixtures Hyeyoung Shin a, Tod
Charge equilibration
Charge equilibration Taylor expansion of energy of atom A @E E A (Q) =E A0 + Q A + 1 @Q A 0 2 Q2 A @ 2 E @Q 2 A 0 +... The corresponding energy of cation/anion and neutral atom E A (+1) = E A0 + @E @Q
Reactive Force Field & Molecular Dynamics Simulations (Theory & Applications)
Reactive Force Field & Molecular Dynamics Simulations (Theory & Applications) Ying Li Collaboratory for Advanced Computing & Simulations Department of Chemical Engineering & Materials Science Department
Quantum Mechanical Simulations
Quantum Mechanical Simulations Prof. Yan Wang Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332, U.S.A. yan.wang@me.gatech.edu Topics Quantum Monte Carlo Hartree-Fock
1 Density functional theory (DFT)
1 Density functional theory (DFT) 1.1 Introduction Density functional theory is an alternative to ab initio methods for solving the nonrelativistic, time-independent Schrödinger equation H Φ = E Φ. The
Material Surfaces, Grain Boundaries and Interfaces: Structure-Property Relationship Predictions
Material Surfaces, Grain Boundaries and Interfaces: Structure-Property Relationship Predictions Susan B. Sinnott Department of Materials Science and Engineering Penn State University September 16, 2016
Structure of Cement Phases from ab initio Modeling Crystalline C-S-HC
Structure of Cement Phases from ab initio Modeling Crystalline C-S-HC Sergey V. Churakov sergey.churakov@psi.ch Paul Scherrer Institute Switzerland Cement Phase Composition C-S-H H Solid Solution Model
Introduction to ReaxFF: Reactive Molecular Dynamics
Introduction to ReaxFF: Reactive Molecular Dynamics Ole Carstensen carstensen@scm.com TCCM ADF Tutorial April 21 Amsterdam Outline ReaxFF - general aspects Molecular Dynamics Intro 200 DFT 100 ReaxFF Harmonic
Density Functional Theory
Chemistry 380.37 Fall 2015 Dr. Jean M. Standard October 28, 2015 Density Functional Theory What is a Functional? A functional is a general mathematical quantity that represents a rule to convert a function
Why study protein dynamics?
Why study protein dynamics? Protein flexibility is crucial for function. One average structure is not enough. Proteins constantly sample configurational space. Transport - binding and moving molecules
Supplementary Figure 1. Schematic of rapid thermal annealing process: (a) indicates schematics and SEM cross-section of the initial layer-by-layer
Supplementary Figure 1. Schematic of rapid thermal annealing process: (a) indicates schematics and SEM cross-section of the initial layer-by-layer film configuration, (b) demonstrates schematic and cross-section
Computational Chemistry. An Introduction to Molecular Dynamic Simulations
Computational Chemistry An Introduction to Molecular Dynamic Simulations Computational chemistry simulates chemical structures and reactions numerically, based in full or in part on the fundamental laws
Molecular Mechanics: The Ab Initio Foundation
Molecular Mechanics: The Ab Initio Foundation Ju Li GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7 18, 2006, MIT, Cambridge, MA, USA 2 Outline Why are electrons quantum? Born-Oppenheimer
The Projector Augmented Wave method
The Projector Augmented Wave method Advantages of PAW. The theory. Approximations. Convergence. 1 The PAW method is... What is PAW? A technique for doing DFT calculations efficiently and accurately. An
Lecture 8: Introduction to Density Functional Theory
Lecture 8: Introduction to Density Functional Theory Marie Curie Tutorial Series: Modeling Biomolecules December 6-11, 2004 Mark Tuckerman Dept. of Chemistry and Courant Institute of Mathematical Science
ReaxFF MgH Reactive Force Field for Magnesium Hydride Systems
J. Phys. Chem. A 2005, 109, 851-859 851 ReaxFF MgH Reactive Force Field for Magnesium Hydride Systems Sam Cheung, Wei-Qiao Deng, Adri C. T. van Duin, and William A. Goddard III* Materials and Process Simulation
Monte Carlo (MC) Simulation Methods. Elisa Fadda
Monte Carlo (MC) Simulation Methods Elisa Fadda 1011-CH328, Molecular Modelling & Drug Design 2011 Experimental Observables A system observable is a property of the system state. The system state i is
Dept of Mechanical Engineering MIT Nanoengineering group
1 Dept of Mechanical Engineering MIT Nanoengineering group » To calculate all the properties of a molecule or crystalline system knowing its atomic information: Atomic species Their coordinates The Symmetry
Methods of Computer Simulation. Molecular Dynamics and Monte Carlo
Molecular Dynamics Time is of the essence in biological processes therefore how do we understand time-dependent processes at the molecular level? How do we do this experimentally? How do we do this computationally?
Introduction to molecular dynamics
1 Introduction to molecular dynamics Yves Lansac Université François Rabelais, Tours, France Visiting MSE, GIST for the summer Molecular Simulation 2 Molecular simulation is a computational experiment.
Reactivity and Organocatalysis. (Adalgisa Sinicropi and Massimo Olivucci)
Reactivity and Organocatalysis (Adalgisa Sinicropi and Massimo Olivucci) The Aldol Reaction - O R 1 O R 1 + - O O OH * * H R 2 R 1 R 2 The (1957) Zimmerman-Traxler Transition State Counterion (e.g. Li
Teoría del Funcional de la Densidad (Density Functional Theory)
Teoría del Funcional de la Densidad (Density Functional Theory) Motivation: limitations of the standard approach based on the wave function. The electronic density n(r) as the key variable: Functionals
Electronic Structure Calculations and Density Functional Theory
Electronic Structure Calculations and Density Functional Theory Rodolphe Vuilleumier Pôle de chimie théorique Département de chimie de l ENS CNRS Ecole normale supérieure UPMC Formation ModPhyChem Lyon,
Fixed-Node quantum Monte Carlo for Chemistry
Fixed-Node quantum Monte Carlo for Chemistry Michel Caffarel Lab. Physique et Chimie Quantiques, CNRS-IRSAMC, Université de Toulouse e-mail : caffarel@irsamc.ups-tlse.fr. p.1/29 The N-body problem of Chemistry
Introduction to Computational Chemistry
Introduction to Computational Chemistry Vesa Hänninen Laboratory of Physical Chemistry Chemicum 4th floor vesa.hanninen@helsinki.fi September 10, 2013 Lecture 3. Electron correlation methods September
Exchange Correlation Functional Investigation of RT-TDDFT on a Sodium Chloride. Dimer. Philip Straughn
Exchange Correlation Functional Investigation of RT-TDDFT on a Sodium Chloride Dimer Philip Straughn Abstract Charge transfer between Na and Cl ions is an important problem in physical chemistry. However,
GEM4 Summer School OpenCourseWare
GEM4 Summer School OpenCourseWare http://gem4.educommons.net/ http://www.gem4.org/ Lecture: Molecular Mechanics by Ju Li. Given August 9, 2006 during the GEM4 session at MIT in Cambridge, MA. Please use
T6.2 Molecular Mechanics
T6.2 Molecular Mechanics We have seen that Benson group additivities are capable of giving heats of formation of molecules with accuracies comparable to those of the best ab initio procedures. However,
Molecular Dynamics, Monte Carlo and Docking. Lecture 21. Introduction to Bioinformatics MNW2
Molecular Dynamics, Monte Carlo and Docking Lecture 21 Introduction to Bioinformatics MNW2 If you throw up a stone, it is Physics. If you throw up a stone, it is Physics. If it lands on your head, it is
The Schrödinger equation for many-electron systems
The Schrödinger equation for many-electron systems Ĥ!( x,, x ) = E!( x,, x ) 1 N 1 1 Z 1 Ĥ = " $ # " $ + $ 2 r 2 A j j A, j RAj i, j < i a linear differential equation in 4N variables (atomic units) (3
Key concepts in Density Functional Theory (I) Silvana Botti
From the many body problem to the Kohn-Sham scheme European Theoretical Spectroscopy Facility (ETSF) CNRS - Laboratoire des Solides Irradiés Ecole Polytechnique, Palaiseau - France Temporary Address: Centre
VALENCE Hilary Term 2018
VALENCE Hilary Term 2018 8 Lectures Prof M. Brouard Valence is the theory of the chemical bond Outline plan 1. The Born-Oppenheimer approximation 2. Bonding in H + 2 the LCAO approximation 3. Many electron
Molecular Mechanics / ReaxFF
Molecular Dynamics simulations Lecture 09: Molecular Mechanics / ReaxFF Dr. Olli Pakarinen University of Helsinki Fall 2012 Lecture notes based on notes by Dr. Jani Kotakoski, 2010 CONTENTS Molecular mechanics
Electronic structure theory: Fundamentals to frontiers. 2. Density functional theory
Electronic structure theory: Fundamentals to frontiers. 2. Density functional theory MARTIN HEAD-GORDON, Department of Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley
Introduction to Computational Chemistry Computational (chemistry education) and/or. (Computational chemistry) education
Introduction to Computational Chemistry Computational (chemistry education) and/or (Computational chemistry) education First one: Use computational tools to help increase student understanding of material
Supporting Information
Electronic Supplementary Material (ESI) for Nanoscale. This journal is The Royal Society of Chemistry 207 Supporting Information Carbon Nanoscroll- Silk Crystallite Hybrid Structure with Controllable Hydration
Quantum Monte Carlo simulation of spin-polarized tritium
Higher-order actions and their applications in many-body, few-body, classical problems Quantum Monte Carlo simulation of spin-polarized tritium I. Bešlić, L. Vranješ Markić, University of Split, Croatia
74 these states cannot be reliably obtained from experiments. In addition, the barriers between the local minima can also not be obtained reliably fro
73 Chapter 5 Development of Adiabatic Force Field for Polyvinyl Chloride (PVC) and Chlorinated PVC (CPVC) 5.1 Introduction Chlorinated polyvinyl chloride has become an important specialty polymer due to
Density Functional Theory. Martin Lüders Daresbury Laboratory
Density Functional Theory Martin Lüders Daresbury Laboratory Ab initio Calculations Hamiltonian: (without external fields, non-relativistic) impossible to solve exactly!! Electrons Nuclei Electron-Nuclei
Quantum Chemical Simulations and Descriptors. Dr. Antonio Chana, Dr. Mosè Casalegno
Quantum Chemical Simulations and Descriptors Dr. Antonio Chana, Dr. Mosè Casalegno Classical Mechanics: basics It models real-world objects as point particles, objects with negligible size. The motion
Ideal Gas Behavior. NC State University
Chemistry 331 Lecture 6 Ideal Gas Behavior NC State University Macroscopic variables P, T Pressure is a force per unit area (P= F/A) The force arises from the change in momentum as particles hit an object
Chemistry 3502/4502. Final Exam Part I. May 14, 2005
Chemistry 3502/4502 Final Exam Part I May 14, 2005 1. For which of the below systems is = where H is the Hamiltonian operator and T is the kinetic-energy operator? (a) The free particle (e) The
Computational Chemistry I
Computational Chemistry I Text book Cramer: Essentials of Quantum Chemistry, Wiley (2 ed.) Chapter 3. Post Hartree-Fock methods (Cramer: chapter 7) There are many ways to improve the HF method. Most of
Biomolecules are dynamic no single structure is a perfect model
Molecular Dynamics Simulations of Biomolecules References: A. R. Leach Molecular Modeling Principles and Applications Prentice Hall, 2001. M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids",
ICCP Project 2 - Advanced Monte Carlo Methods Choose one of the three options below
ICCP Project 2 - Advanced Monte Carlo Methods Choose one of the three options below Introduction In statistical physics Monte Carlo methods are considered to have started in the Manhattan project (1940
Density Functional Theory
Density Functional Theory March 26, 2009 ? DENSITY FUNCTIONAL THEORY is a method to successfully describe the behavior of atomic and molecular systems and is used for instance for: structural prediction
Molecular modeling and simulation in chemistry
Molecular modeling and simulation in chemistry 1/20 Elements of modeling: Nuclei + electrons + photons: QED Nuclei + electrons: Schrödinger equation Auxiliary interaction centers (sites) Atoms classical
Introduction to density-functional theory. Emmanuel Fromager
Institut de Chimie, Strasbourg, France Page 1 Emmanuel Fromager Institut de Chimie de Strasbourg - Laboratoire de Chimie Quantique - Université de Strasbourg /CNRS M2 lecture, Strasbourg, France. Institut
Dominant Paths in Protein Folding
Dominant Paths in Protein Folding Henri Orland SPhT, CEA-Saclay France work in collaboration with P. Faccioli, F. Pederiva, M. Sega University of Trento Henri Orland Annecy meeting 2006 Outline Basic notions
Computational Physics Lectures: Variational Monte Carlo methods
Computational Physics Lectures: Variational Monte Carlo methods Morten Hjorth-Jensen 1,2 Department of Physics, University of Oslo 1 Department of Physics and Astronomy and National Superconducting Cyclotron
Molecular Dynamics, Monte Carlo and Docking. Lecture 21. Introduction to Bioinformatics MNW2
Molecular Dynamics, Monte Carlo and Docking Lecture 21 Introduction to Bioinformatics MNW2 Allowed phi-psi angles Red areas are preferred, yellow areas are allowed, and white is avoided 2.3a Hamiltonian
AN AB INITIO INVESTIGATION OF VAN DER WAALS-RICH SYSTEMS AND A MACHINE LEARNING APPROACH TO FINDING ANALYTICAL FUNCTIONS DESCRIBING TABULATED DATA
AN AB INITIO INVESTIGATION OF VAN DER WAALS-RICH SYSTEMS AND A MACHINE LEARNING APPROACH TO FINDING ANALYTICAL FUNCTIONS DESCRIBING TABULATED DATA BY BRIAN KOLB A Dissertation Submitted to the Graduate
COSMO-RS Theory. The Basics
Theory The Basics From µ to properties Property µ 1 µ 2 activity coefficient vapor pressure Infinite dilution Gas phase Pure compound Pure bulk compound Partition coefficient Phase 1 Phase 2 Liquid-liquid
Fundamentals and applications of Density Functional Theory Astrid Marthinsen PhD candidate, Department of Materials Science and Engineering
Fundamentals and applications of Density Functional Theory Astrid Marthinsen PhD candidate, Department of Materials Science and Engineering Outline PART 1: Fundamentals of Density functional theory (DFT)
Scientific Computing II
Scientific Computing II Molecular Dynamics Simulation Michael Bader SCCS Summer Term 2015 Molecular Dynamics Simulation, Summer Term 2015 1 Continuum Mechanics for Fluid Mechanics? Molecular Dynamics the
The Pennsylvania State University. School of Engineering. Department of Mechanical & Nuclear Engineering
The Pennsylvania State University School of Engineering Department of Mechanical & Nuclear Engineering DEVELOPMENT OF A REAXFF REACTIVE FORCE FIELD FOR SILICON/OXYGEN/HYDROGEN/FLUORIDE INTERACTIONS AND
Anion-π and π-π cooperative interactions
Chapter 5 Anion-π and π-π cooperative interactions 5.1 Introduction The design of selective receptors of anionic species is a very active area of research within supramolecular chemistry due to the potential
Markov Processes. Stochastic process. Markov process
Markov Processes Stochastic process movement through a series of well-defined states in a way that involves some element of randomness for our purposes, states are microstates in the governing ensemble
Molecular Simulation II. Classical Mechanical Treatment
Molecular Simulation II Quantum Chemistry Classical Mechanics E = Ψ H Ψ ΨΨ U = E bond +E angle +E torsion +E non-bond Jeffry D. Madura Department of Chemistry & Biochemistry Center for Computational Sciences
Reactive molecular dynamics simulations of plasma treatment of emerging pollutants in water
Reactive molecular dynamics simulations of plasma treatment of emerging pollutants in water Pascal Brault GREMI, UMR7344 CNRS Université d Orléans, Orléans, France Outline Plasma- liquid interactions Reactive
An Introduction to Quantum Chemistry and Potential Energy Surfaces. Benjamin G. Levine
An Introduction to Quantum Chemistry and Potential Energy Surfaces Benjamin G. Levine This Week s Lecture Potential energy surfaces What are they? What are they good for? How do we use them to solve chemical
Computational Nanoscience
Computational Nanoscience Applications for Molecules, Clusters, and Solids KALMÄN VARGA AND JOSEPH A. DRISCOLL Vanderbilt University, Tennessee Щ CAMBRIDGE HP UNIVERSITY PRESS Preface Part I One-dimensional
Introduction to model potential Molecular Dynamics A3hourcourseatICTP
Introduction to model potential Molecular Dynamics A3hourcourseatICTP Alessandro Mattoni 1 1 Istituto Officina dei Materiali CNR-IOM Unità di Cagliari SLACS ICTP School on numerical methods for energy,
The chemical bond The topological approach
The chemical bond The topological approach Julia Contreras-García 1. Why and how studying chemical bonds? 2. Topology a) critical points b) topological partitions 3. Chemical functions a) electron density
Phase Equilibria and Molecular Solutions Jan G. Korvink and Evgenii Rudnyi IMTEK Albert Ludwig University Freiburg, Germany
Phase Equilibria and Molecular Solutions Jan G. Korvink and Evgenii Rudnyi IMTEK Albert Ludwig University Freiburg, Germany Preliminaries Learning Goals Phase Equilibria Phase diagrams and classical thermodynamics
Pseudopotentials for hybrid density functionals and SCAN
Pseudopotentials for hybrid density functionals and SCAN Jing Yang, Liang Z. Tan, Julian Gebhardt, and Andrew M. Rappe Department of Chemistry University of Pennsylvania Why do we need pseudopotentials?
Multiscale Materials Modeling
Multiscale Materials Modeling Lecture 02 Capabilities of Classical Molecular Simulation These notes created by David Keffer, University of Tennessee, Knoxville, 2009. Outline Capabilities of Classical
Density functional theory
Density functional theory Seminar Ib - 1. letnik, II. stopnja Author: Matic Pečovnik Mentor: Doc. Dr. Tomaž Rejec Faculty of Mathematics and Physics, University in Ljubljana Abstract Many-body problems
Free Energy Simulation Methods
Free Energy Simulation Methods Free energy simulation methods Many methods have been developed to compute (relative) free energies on the basis of statistical mechanics Free energy perturbation Thermodynamic
Electronic structure theory: Fundamentals to frontiers. 1. Hartree-Fock theory
Electronic structure theory: Fundamentals to frontiers. 1. Hartree-Fock theory MARTIN HEAD-GORDON, Department of Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley National
Development of a ReaxFF Reactive Force Field for Glycine and Application to Solvent Effect and Tautomerization
J. Phys. Chem. B 2011, 115, 249 261 249 Development of a ReaxFF Reactive Force Field for Glycine and Application to Solvent Effect and Tautomerization Obaidur Rahaman, Adri C. T. van Duin, William A. Goddard
Electron Correlation
Electron Correlation Levels of QM Theory HΨ=EΨ Born-Oppenheimer approximation Nuclear equation: H n Ψ n =E n Ψ n Electronic equation: H e Ψ e =E e Ψ e Single determinant SCF Semi-empirical methods Correlation
Reactive Force Fields in Particular ReaxFF and Application Possibilities
Reactive Force Fields in Particular ReaxFF and Application Possibilities Thomas Schönfelder 07/01/2010 Chemnitz Part I: General Concepts and Comparison to other Simulation Methods Part II: ReaxFF as Reactive
Understanding Molecular Simulation 2009 Monte Carlo and Molecular Dynamics in different ensembles. Srikanth Sastry
JNCASR August 20, 21 2009 Understanding Molecular Simulation 2009 Monte Carlo and Molecular Dynamics in different ensembles Srikanth Sastry Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Molecular Mechanics. I. Quantum mechanical treatment of molecular systems
Molecular Mechanics I. Quantum mechanical treatment of molecular systems The first principle approach for describing the properties of molecules, including proteins, involves quantum mechanics. For example,
Molecular dynamics simulation. CS/CME/BioE/Biophys/BMI 279 Oct. 5 and 10, 2017 Ron Dror
Molecular dynamics simulation CS/CME/BioE/Biophys/BMI 279 Oct. 5 and 10, 2017 Ron Dror 1 Outline Molecular dynamics (MD): The basic idea Equations of motion Key properties of MD simulations Sample applications
DFT in practice. Sergey V. Levchenko. Fritz-Haber-Institut der MPG, Berlin, DE
DFT in practice Sergey V. Levchenko Fritz-Haber-Institut der MPG, Berlin, DE Outline From fundamental theory to practical solutions General concepts: - basis sets - integrals and grids, electrostatics,
Block Iterative Eigensolvers for Sequences of Dense Correlated Eigenvalue Problems
Mitglied der Helmholtz-Gemeinschaft Block Iterative Eigensolvers for Sequences of Dense Correlated Eigenvalue Problems Birkbeck University, London, June the 29th 2012 Edoardo Di Napoli Motivation and Goals
Electron States of Diatomic Molecules
IISER Pune March 2018 Hamiltonian for a Diatomic Molecule The hamiltonian for a diatomic molecule can be considered to be made up of three terms Ĥ = ˆT N + ˆT el + ˆV where ˆT N is the kinetic energy operator
CHEM6085: Density Functional Theory
Lecture 5 CHEM6085: Density Functional Theory Orbital-free (or pure ) DFT C.-K. Skylaris 1 Consists of three terms The electronic Hamiltonian operator Electronic kinetic energy operator Electron-Electron
Molecular Dynamic Simulations in JavaScript
Molecular Dynamic Simulations in JavaScript Daniel Kunin Abstract Using a Newtonian mechanical model for potential energy and a forcebased layout scheme for graph drawing I investigated the viability and
DENSITY FUNCTIONAL THEORY FOR NON-THEORISTS JOHN P. PERDEW DEPARTMENTS OF PHYSICS AND CHEMISTRY TEMPLE UNIVERSITY
DENSITY FUNCTIONAL THEORY FOR NON-THEORISTS JOHN P. PERDEW DEPARTMENTS OF PHYSICS AND CHEMISTRY TEMPLE UNIVERSITY A TUTORIAL FOR PHYSICAL SCIENTISTS WHO MAY OR MAY NOT HATE EQUATIONS AND PROOFS REFERENCES
High-order Chin actions in path integral Monte Carlo
High-order Chin actions in path integral Monte Carlo High-order actions and their applications, Barcelona 2009 Jordi Boronat Departament de Física i Enginyeria Nuclear Universitat Politècnica de Catalunya
Electronic structure calculations: fundamentals George C. Schatz Northwestern University
Electronic structure calculations: fundamentals George C. Schatz Northwestern University Electronic Structure (often called Quantum Chemistry) calculations use quantum mechanics to determine the wavefunctions
5.1 Classical Harmonic Oscillator
Chapter 5 Harmonic Oscillator 5.1 Classical Harmonic Oscillator m l o l Hooke s Law give the force exerting on the mass as: f = k(l l o ) where l o is the equilibrium length of the spring and k is the
ReaxFF force fields. Development of a transferable empirical method for atomic-scale simulations of chemical reactions
ReaxFF force fields Development of a transferable empirical method for atomic-scale simulations of chemical reactions Adri van Duin, Kimberley Chenoweth 2 and Bill Goddard 2 : Department of Mechanical
Potential Energy (hyper)surface
The Molecular Dynamics Method Thermal motion of a lipid bilayer Water permeation through channels Selective sugar transport Potential Energy (hyper)surface What is Force? Energy U(x) F = " d dx U(x) Conformation
Density Functional Theory for Electrons in Materials
Density Functional Theory for Electrons in Materials Richard M. Martin Department of Physics and Materials Research Laboratory University of Illinois at Urbana-Champaign 1 Density Functional Theory for
Low-dimensional Material: Structure-property Relationship and. Applications in Energy and Environmental Engineering
Low-dimensional Material: Structure-property Relationship and Applications in Energy and Environmental Engineering Hang Xiao Submitted in partial fulfillment of the requirements for the degree of Doctor
Advanced Quantum Chemistry III: Part 3. Haruyuki Nakano. Kyushu University
Advanced Quantum Chemistry III: Part 3 Haruyuki Nakano Kyushu University 2013 Winter Term 1. Hartree-Fock theory Density Functional Theory 2. Hohenberg-Kohn theorem 3. Kohn-Sham method 4. Exchange-correlation
The Pennsylvania State University. The Graduate School. Department of Mechanical and Nuclear Engineering
The Pennsylvania State University The Graduate School Department of Mechanical and Nuclear Engineering DEVELOPMENT AND APPLICATION OF A REAXFF REACTIVE FORCE FIELD FOR HYDROGEN COMBUSTION A Thesis in Mechanical
Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802, USA
Atomistic-Scale Simulations of Defect Formation in Graphene Under Noble Gas Ion Irradiation Kichul Yoon a, Ali Rahnamoun a, Jacob L. Swett b, Vighter Iberi c, d, David A. Cullen e, Ivan V. Vlassiouk f,
CE 530 Molecular Simulation
1 CE 530 Molecular Simulation Lecture 1 David A. Kofke Department of Chemical Engineering SUNY Buffalo kofke@eng.buffalo.edu 2 Time/s Multi-Scale Modeling Based on SDSC Blue Horizon (SP3) 1.728 Tflops