Advanced Quantum Chemistry III: Part 6
|
|
- Caren Evans
- 5 years ago
- Views:
Transcription
1 Advanced Quantum Chemistry III: Part 6 Norio Yoshida Kyushu University Last updated Winter Term 1
2 Quantum Chemistry for Condensed Phase Liquid phase Solid phase Biological systems 2
3 Divide the system Intermolecular Intramolecular Quantum Classical Biological systems Solute- solvent systems MulL- scale MulL- physics 3
4 Modeling inter- and intra- molecular interaclon 4
5 Intermolecular interaclons Total energy of the system E Total = Ψ AB Energy of isolated system E A 0 = Ψ A 0 Ĥ A Ψ A 0 Ĥ A + Ĥ B + ˆ V AB Ψ AB, E B 0 = Ψ B 0 Ĥ B Ψ B 0 Molecule A Intermolecular interaclon energy Molecule B V A B = E Total (E A 0 + E B 0 ) 5
6 Components of intermolecular interaclon energy V A B = E ES + E PL + E EX + E CT + E MIX E ES : ElectrostaLc energy E PL : PolarizaLon energy E EX : Exchange energy E CT : Charge transfer energy E MIX : Coupling term ( E disp : Dispersion) Kitaura, K. and Morokuma, K., Int. J. Quantum Chem., X, (1976) 6
7 MM force field Nbond MM 1 r V ( R) = k R R 2 bond( ij ) N angle( ijk ) 2 ( 0) ij ij ij angle 1 θ + k 2 dihedral ( ijkl ) n( dihedral ) 2 ( 0 θ θ ) ijk ijk ijk Ndihedral N φn d Vijkl 1 cos( n + ' nφ ) ijkl γ ( ijkl 2 ) * Natom ' Aij B ( LJ ij + δij , i < j + ) Rij Rij,* N atom ' q q ( cl i j + δij +, i < j + ) εrij *, Intramolecular Intermolecular 7
8 Intramolecular force field 1 V k R R Nbond MM r intra ( R) = ij ij ij bond( ij ) 2 N angle( ijk ) 2 ( 0) angle 1 θ + k 2 dihedral ( ijkl ) n( dihedral ) 2 ( 0 θ θ ) ijk ijk ijk i θ ijk R ij j φ ijkl Ndihedral N φn d Vijkl 1 cos( n + % nφ ) ijkl γ & ijkl 2 ' ( k l 8
9 Bond and Angle N bond bond(ij ) 1 2 k ij r ( 0 R ij R ) 2 ij k r ij : spring constant i j R ij R ij 0 N angle angle(ijk ) 1 2 θ k ijk ( 0 θ ijk θ ) 2 ijk k θ ijk : spring constant i k θ ijk j θ ijk 0 9
10 N dihedral N φn V d ijkl dihedral(ijkl) n(dihedral) 2 Dihedral % n & 1 cos nφ ijkl γ ijkl ( ) ' ( n=1 j k l φ ijkl φ ijkl 0 n=2 i φ ijkl 0 10
11 11
12 Intermolecular force field V MM inter ( R) Natom # Aij B $ LJ ij = δij & 12 6 ' i < j &( Rij Rij ') # q q $ Natom cl i j + δij & ' i < j εrij &( ') 12
13 Determine the parameter sets 13
14 Different chemical bonds have different parameters Parameters are assigned typical amino acids, nucleic acids and organic compounds. Famous parameter set OPLS AMBER CHARMM MM3 MM parameter set AMBER force field; JACS 117, (1995)
15 MM parameter set V MM Nbond 1 r (R ) = kij Rij Rij0 bond ( ij ) 2 ( Nangle 2 ) 1 θ + kijk θ ijk θ ijk0 angle ( ijk ) 2 + ( Ndihedral Nd dihedral ( ijkl ) n ( dihedral ) ) φn Vijkl LJ ij ( ) n ( '1 cos nφijkl γ ijkl * 2 ) ' Aij Bij ( + δ , Rij,* i< j +) Rij Natom ' qi q j ( cl + δ ij +, i< j +) ε Rij,* Natom 2
16 Parameter fiang Calculate ab ini7o value of energy Determine the parameters to fit the ab ini7o values i j R ij 16
17 Effective charge on atom: Electrostatic potential (ESP) method Population analysis Mulliken population analysis Löwdin population analysis Natural population analysis Electrostatic potential (ESP) method The electrostatic potential generated by electron density distribution is very different from that by population analysis The effective charges must be determined to reproduce the electrostatic potential around the molecule
18 ESP method Set of the effective charges (q a ) are determined to minimize I. N grid & I = ω ( α u(r α ) u(r α )) 2 N QM ) + 2λ q a Q ( tot + α ' a * u(r α ) = N a Z a r α R a tr(pa(r α )) " q = q n ca 1 + N + e ca 1 1 t % $ ' # $ 1a 1 1 t & a ab = N grid 1 c α r aα r bα N grid α { B} γ = ω α µν ' 1a 1 { } γ = tr(pb γ ) χ * µ (r ')χ ν (r ') r αγ r α r ' dr ' Lagrange multiplier u(r α ) = N a { A(r α )} = µν q n a r α R a + constraint of total charge conservation N a q e a r α R a χ * µ (r')χ ν (r') dr ' r α r'
19 Restrained ESP method Set of the effective charges (q a ) are determined to minimize I. N grid & I RESP = ω ( α u(r α ) u(r α )) 2 N QM + 2λ ( q a Q tot α ' a ) N + + QM g q 2 a a * a Harmonic penalty function 0
20 VDW parameters Adjustable parameter σ (Diameter of Atom of Atom group) ε (EnergeLc parameter) Fit σ and ε to reproduce the density and enthalpy of liquids. ex. sp 2 C and aromalc H Monte Carlo simulalon on benzene liquid and adjuslng the σ and ε to reproduce the density and enthalpy of liquid benzene. 20
21 QM/MM method for liquid phase 21
22 Quantum- Classical Quantum Mechanics/Molecular Mechanics (QM/MM) method a) Solute molecules are described by ab ini7o QM methods. Solvent molecules are treated by MM. Modeling intermolecular interaclons Lennard- Jones potenlal Coulomb interaclon between point charge etc. a) M.J. Field, P.A. Bash, M. Karplus, J. Comput. Chem., 11 (1990)
23 Strategy Solute ( 溶質 ) Quantum mechanics(qm) Solute- solvent interaclon ( 溶質溶媒相互作用 ) Solvent ( 溶媒 ) Molecular Mechanics(MM) 23
24 QM/MM Hamiltonian Ĥ QM /MM = N elec 1 p 2 2 i i N elec N QM A Z A + i r ia N elec 1 + i> j r ij N QM A>B Z A Z B r AB QM N elec N MM q a + i a r ia N QM N MM A a Z A q a r Aa MM +V QM MM QM- MM MM +V MM MM 24
25 QM/MM energy E = Ψ Hˆ Ψ QM / MM QM / MM total E QM / MM el ( D, d) Z q NQM NQM NMM ZAZB A a MM VQM MM + A> B rab A a raa 1 E h D g d NBF NBF NBF NBF NBF NBF QM / MM QM / MM el ( D, d) = µν µν + µνσλ µνσλ µ ν 2 µ ν σ λ h = q ( ) ( ) NMM QM / MM * a µν = hµν + dx1φ µ x1 φν x1 a r1 a V MM MM 25
26 Interaction between QM-MM 1. ElectrostaLc interaclon - InteracLon between QM electron and MM charge 2. PolarizaLon interaclon - QM molecule: Polarized by the electrostalc fields from MM molecule - MM molecule: Fixed 3. Exchange repulsion and dispersion - LJ potenlal (MM Force field) 4. Charge transfer - Not available
27 QM/MM- MD or MC To sample the distribulon of solvent molecule, QM/MM is coupled with MD or MC IniLal structure/distribulon Calculate QM energy Calculate forces aclng on solute molecules Calculate forces aclng on solvent molecules EsLmate new structure/ coordinate 27
28 1st derivalve of energy over atoms coordinates For QM atom QM / MM N dh MM µν dhµν dhµν d * qa = + 1φ µ 1 φν 1 dra dra dra dr dx x A a r x 1a ( ) ( ) For MM atom QM / MM NQM NMM detotal d $ ZAq % a MM MM = & + VQM MM + VMM ' dra dra ( A a raa ) NBF NBF $ * d q + % + & φ ( ) φ ( )' D µ ν & dx x x (. / ') * a 1 µ 1, - ν 1 µν dra r1 a 28
29 Example Intramolecular proton transfer reaclon of glycine N. Okuyama-Yoshida, K. et al. J. Chem. Phys., 113, 3519 (2000). N. Takenaka, et al. Theor. Chem. Acc., 130, 215 (2011). Y. Kitamura, et al. Chem. Phys. Lett., 514, 261 (2011). N. Takenaka, et al. J. Chem. Phys., 137, (2012). 29
30 References コンピュータシミュレーションの基礎 ( 第 2 版 ) 岡崎進 吉井範行化学同人 分子シミュレーション上田顕裳華房 EssenLals of ComputaLonal Chemistry Cramer, WILLEY Understanding Molecular SimulaLon Frenkel and Smit, ACADEMIC PRESS 30
Advanced Quantum Chemistry III: Part 6
Advanced Quantum Chemistry III: Part 6 Norio Yoshida Kyushu University Last updated 16-1-6 2015 Winter Term 1 Quantum Chemistry for Condensed Phase Liquid phase Solid phase Biological systems 2 Divide
More informationCE 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
More informationStructural Bioinformatics (C3210) Molecular Mechanics
Structural Bioinformatics (C3210) Molecular Mechanics How to Calculate Energies Calculation of molecular energies is of key importance in protein folding, molecular modelling etc. There are two main computational
More informationLecture 11: Potential Energy Functions
Lecture 11: Potential Energy Functions Dr. Ronald M. Levy ronlevy@temple.edu Originally contributed by Lauren Wickstrom (2011) Microscopic/Macroscopic Connection The connection between microscopic interactions
More informationAll-atom Molecular Mechanics. Trent E. Balius AMS 535 / CHE /27/2010
All-atom Molecular Mechanics Trent E. Balius AMS 535 / CHE 535 09/27/2010 Outline Molecular models Molecular mechanics Force Fields Potential energy function functional form parameters and parameterization
More informationMolecular mechanics. classical description of molecules. Marcus Elstner and Tomáš Kubař. April 29, 2016
classical description of molecules April 29, 2016 Chemical bond Conceptual and chemical basis quantum effect solution of the SR numerically expensive (only small molecules can be treated) approximations
More informationAdvanced Quantum Chemistry III: Part 8
Advanced Quantum Chemistry III: Part 8 Norio Yoshida Kyushu University Last updated 14-1-30 2013 Winter Term 1 Integral equaeon theory of liquids 2 SolvaEon structure Solvent molecule Move under solute-
More informationk θ (θ θ 0 ) 2 angles r i j r i j
1 Force fields 1.1 Introduction The term force field is slightly misleading, since it refers to the parameters of the potential used to calculate the forces (via gradient) in molecular dynamics simulations.
More informationFragmentation methods
Fragmentation methods Scaling of QM Methods HF, DFT scale as N 4 MP2 scales as N 5 CC methods scale as N 7 What if we could freeze the value of N regardless of the size of the system? Then each method
More information3rd Advanced in silico Drug Design KFC/ADD Molecular mechanics intro Karel Berka, Ph.D. Martin Lepšík, Ph.D. Pavel Polishchuk, Ph.D.
3rd Advanced in silico Drug Design KFC/ADD Molecular mechanics intro Karel Berka, Ph.D. Martin Lepšík, Ph.D. Pavel Polishchuk, Ph.D. Thierry Langer, Ph.D. Jana Vrbková, Ph.D. UP Olomouc, 23.1.-26.1. 2018
More informationBiomolecular modeling I
2016, December 6 Biomolecular structure Structural elements of life Biomolecules proteins, nucleic acids, lipids, carbohydrates... Biomolecular structure Biomolecules biomolecular complexes aggregates...
More informationSpecific Ion Solvtion in Ethylene Carbonate and Propylene Carbonate
Specific Ion Solvtion in Ethylene Carbonate and Propylene Carbonate A. Arslanargin, A. Powers, S. Rick, T. Pollard, T. Beck Univ Cincinnati Chemistry Support: NSF, OSC TSRC 2016 November 2, 2016 A. Arslanargin,
More informationIntermolecular Forces in Density Functional Theory
Intermolecular Forces in Density Functional Theory Problems of DFT Peter Pulay at WATOC2005: There are 3 problems with DFT 1. Accuracy does not converge 2. Spin states of open shell systems often incorrect
More informationDihedral Angles. Homayoun Valafar. Department of Computer Science and Engineering, USC 02/03/10 CSCE 769
Dihedral Angles Homayoun Valafar Department of Computer Science and Engineering, USC The precise definition of a dihedral or torsion angle can be found in spatial geometry Angle between to planes Dihedral
More informationMolecular Modelling. part of Bioinformatik von RNA- und Proteinstrukturen. Sonja Prohaska. Leipzig, SS Computational EvoDevo University Leipzig
part of Bioinformatik von RNA- und Proteinstrukturen Computational EvoDevo University Leipzig Leipzig, SS 2011 Protein Structure levels or organization Primary structure: sequence of amino acids (from
More informationMolecular Dynamics Simulations. Dr. Noelia Faginas Lago Dipartimento di Chimica,Biologia e Biotecnologie Università di Perugia
Molecular Dynamics Simulations Dr. Noelia Faginas Lago Dipartimento di Chimica,Biologia e Biotecnologie Università di Perugia 1 An Introduction to Molecular Dynamics Simulations Macroscopic properties
More informationComputational 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
More informationForce Fields for Classical Molecular Dynamics simulations of Biomolecules. Emad Tajkhorshid
Force Fields for Classical Molecular Dynamics simulations of Biomolecules Emad Tajkhorshid Theoretical and Computational Biophysics Group, Beckman Institute Departments of Biochemistry and Pharmacology,
More informationWhy 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
More informationMolecular Mechanics. Yohann Moreau. November 26, 2015
Molecular Mechanics Yohann Moreau yohann.moreau@ujf-grenoble.fr November 26, 2015 Yohann Moreau (UJF) Molecular Mechanics, Label RFCT 2015 November 26, 2015 1 / 29 Introduction A so-called Force-Field
More informationForce fields in computer simulation of soft nanomaterials
Lecture 2 Part B Force fields in computer simulation of soft nanomaterials Recommended reading: Leach Chapter 4 1 Force Field Methods Force field methods are simulation methods that use classical force
More informationSemi Empirical Force Fields and Their Limitations. Potential Energy Surface (PES)
Semi Empirical Force Fields and Their Limitations Ioan Kosztin Beckman Institute University of Illinois at Urbana-Champaign Potential Energy Surface (PES) Schrödinger equation: H T Ψ( r, = E Ψ( r, H =
More informationThis semester. Books
Models mostly proteins from detailed to more abstract models Some simulation methods This semester Books None necessary for my group and Prof Rarey Molecular Modelling: Principles and Applications Leach,
More information4 th Advanced in silico Drug Design KFC/ADD Molecular Modelling Intro. Karel Berka, Ph.D.
4 th Advanced in silico Drug Design KFC/ADD Molecular Modelling Intro Karel Berka, Ph.D. UP Olomouc, 21.1.-25.1. 2019 Motto A theory is something nobody believes, except the person who made it An experiment
More informationThe Potential Energy Surface (PES) And the Basic Force Field Chem 4021/8021 Video II.iii
The Potential Energy Surface (PES) And the Basic Force Field Chem 4021/8021 Video II.iii Fundamental Points About Which to Be Thinking It s clear the PES is useful, so how can I construct it for an arbitrary
More informationForce Fields for MD simulations
Force Fields for MD simulations Topology/parameter files Where do the numbers an MD code uses come from? ow to make topology files for ligands, cofactors, special amino acids, ow to obtain/develop missing
More informationIntroduction 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.
More informationCARBON 2004 Providence, Rhode Island. Adsorption of Flexible n-butane and n-hexane on Graphitized Thermal Carbon Black and in Slit Pores
CARBON Providence, Rhode Island Adsorption of Flexible n-butane and n-hexane on Graphitized Thermal Carbon Black and in Slit Pores D. D. Do* and H. D. Do, University of Queensland, St. Lucia, Qld 7, Australia
More informationCharge Analysis: Atoms in Molecules
Daubechies Wavelets in Electronic Structure Calculation: BigDFT Code Tutorial CECAM - GRENOBLE : Atoms in Molecules Ali Sadeghi Basel University 21 November 2011 An output of electronic structure calculations
More informationMaterial Science. I. p electron systems. Kanoda. II. d electron systems. Fujimori. Download lecture note
Material Science I. p electron systems Kanoda II. d electron systems Fujimori Download lecture note Download the lecture note prior to each class. Fujimori group home, Department of Physics, School of
More informationQuantum Mechanics - Molecular Mechanics (QM/MM) CHEM 430
Quantum Mechanics - Molecular Mechanics (QM/MM), CHEM 430 Quantum Mechanics In theory, a very accurate treatment of the system Largely ab initio, i.e. parameter-free Very expensive typically scales as
More informationMaterial Science I. p electron systems Kanoda II. d electron systems Fujimori
Material Science I. p electron systems Kanoda II. d electron systems Fujimori Download lecture note Download the lecture note prior to each class. Fujimori group home, Department of Physics, School of
More informationMolecular Mechanics Force Fields
Molecular Mechanics Force Fields Basic Premise If we want to study a protein, piece of DNA, biological membranes, polysaccharide, crystal la;ce, nanomaterials, diffusion in liquids, the number of electrons
More informationBiomolecular modeling I
2015, December 15 Biomolecular simulation Elementary body atom Each atom x, y, z coordinates A protein is a set of coordinates. (Gromacs, A. P. Heiner) Usually one molecule/complex of interest (e.g. protein,
More informationExample questions for Molecular modelling (Level 4) Dr. Adrian Mulholland
Example questions for Molecular modelling (Level 4) Dr. Adrian Mulholland 1) Question. Two methods which are widely used for the optimization of molecular geometies are the Steepest descents and Newton-Raphson
More informationMolecular Mechanics. C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology. January 2001
Molecular Mechanics C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology January 2001 Introduction Molecular Mechanics uses classical type models to predict the energy
More informationarxiv: v1 [cond-mat.stat-mech] 6 Jan 2014
arxiv:1401.1181v1 [cond-mat.stat-mech] 6 Jan 2014 Determination of Forces from a Potential in Molecular Dynamics (note) Bernard Monasse Mines-ParisTech, Cemef bernard.monasse@mines-paristech.fr January
More informationMolecular 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
More informationCoupling the Level-Set Method with Variational Implicit Solvent Modeling of Molecular Solvation
Coupling the Level-Set Method with Variational Implicit Solvent Modeling of Molecular Solvation Bo Li Math Dept & CTBP, UCSD Li-Tien Cheng (Math, UCSD) Zhongming Wang (Math & Biochem, UCSD) Yang Xie (MAE,
More informationDensity Functional Theory: from theory to Applications
Density Functional Theory: from theory to Applications Uni Mainz January 17, 2011 CP-PAW/COSMO Interface Mixed quantum/ classical molecular dynamics (QM/MM) Quantum mechanics is computationally expensive
More informationSubject of the Lecture:
Subject of the Lecture: Conceptual basis for the development of force fields. Implementation/validation Water - a worked example Extensions - combining molecular mechanics and quantum mechanics (QM/MM)
More informationA Nobel Prize for Molecular Dynamics and QM/MM What is Classical Molecular Dynamics? Simulation of explicit particles (atoms, ions,... ) Particles interact via relatively simple analytical potential
More informationPH 548 Atomistic Simulation Techniques
PH 548 Atomistic Simulation Techniques Lectures: Lab: 2-0-2-6 Tuesday 12-1 PM Thursday 12-1 PM Monday 2-5 PM P. K. Padmanabhan PH548: Two Excellent Books How to do it? 1 2 F 12 F 23 3 F i = F ij j i F
More informationCoarse-Grained Models!
Coarse-Grained Models! Large and complex molecules (e.g. long polymers) can not be simulated on the all-atom level! Requires coarse-graining of the model! Coarse-grained models are usually also particles
More informationForce fields, thermo- and barostats. Berk Hess
Force fields, thermo- and barostats Berk Hess What is a force field? A force field usually consists of three parts: a set of functional forms parameters for the functional forms that, usually, depend on
More informationScuola di Chimica Computazionale
Societa Chimica Italiana Gruppo Interdivisionale di Chimica Computazionale Scuola di Chimica Computazionale Introduzione, per Esercizi, all Uso del Calcolatore in Chimica Organica e Biologica Modellistica
More informationMolecular 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,
More informationDeveloping Monovalent Ion Parameters for the Optimal Point Charge (OPC) Water Model. John Dood Hope College
Developing Monovalent Ion Parameters for the Optimal Point Charge (OPC) Water Model John Dood Hope College What are MD simulations? Model and predict the structure and dynamics of large macromolecules.
More informationEnergy functions and their relationship to molecular conformation. CS/CME/BioE/Biophys/BMI 279 Oct. 3 and 5, 2017 Ron Dror
Energy functions and their relationship to molecular conformation CS/CME/BioE/Biophys/BMI 279 Oct. 3 and 5, 2017 Ron Dror Outline Energy functions for proteins (or biomolecular systems more generally)
More informationFree 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
More informationONETEP PB/SA: Application to G-Quadruplex DNA Stability. Danny Cole
ONETEP PB/SA: Application to G-Quadruplex DNA Stability Danny Cole Introduction Historical overview of structure and free energy calculation of complex molecules using molecular mechanics and continuum
More informationWater models in classical simulations
Water models in classical simulations Maria Fyta Institut für Computerphysik, Universität Stuttgart Stuttgart, Germany Water transparent, odorless, tasteless and ubiquitous really simple: two H atoms attached
More informationForce Fields for Classical Molecular Dynamics simulations of Biomolecules. Emad Tajkhorshid
Force Fields for Classical Molecular Dynamics simulations of Biomolecules Emad Tajkhorshid Beckman Institute Departments of Biochemistry Center for Biophysics and Computational Biology University of Illinois
More information1. 3-hour Open book exam. No discussion among yourselves.
Lecture 13 Review 1. 3-hour Open book exam. No discussion among yourselves. 2. Simple calculations. 3. Terminologies. 4. Decriptive questions. 5. Analyze a pulse program using density matrix approach (omonuclear
More informationScientific 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
More informationSoot - Developing anisotropic potentials from first principles for PAH molecules. Tim Totton, Alston Misquitta and Markus Kraft 12/11/2009
Soot - Developing anisotropic potentials from first principles for PAH molecules. Tim Totton, Alston Misquitta and 12/11/2009 HRTEM images of soot Some evidence for different soot structures based on different
More informationICCP 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
More informationSpeeding up path integral simulations
Speeding up path integral simulations Thomas Markland and David Manolopoulos Department of Chemistry University of Oxford Funded by the US Office of Naval Research and the UK EPSRC Outline 1. Ring polymer
More informationMolecular Dynamic Simulation Study of the Volume Transition of PNIPAAm Hydrogels
Molecular Dynamic Simulation Study of the Volume Transition of PNIPAAm Hydrogels Jonathan Walter 1, Jadran Vrabec 2, Hans Hasse 1 1 Laboratory of Engineering, University of Kaiserslautern, Germany 2 and
More informationIntroduction to Molecular Dynamics
Introduction to Molecular Dynamics Dr. Kasra Momeni www.knanosys.com Overview of the MD Classical Dynamics Outline Basics and Terminology Pairwise interacting objects Interatomic potentials (short-range
More informationPolypeptide Folding Using Monte Carlo Sampling, Concerted Rotation, and Continuum Solvation
Polypeptide Folding Using Monte Carlo Sampling, Concerted Rotation, and Continuum Solvation Jakob P. Ulmschneider and William L. Jorgensen J.A.C.S. 2004, 126, 1849-1857 Presented by Laura L. Thomas and
More informationQM/MM Theory and Examples with ORCA
QM/MM Theory and Examples with ORCA Marius Retegan Max Planck Institute for Chemical Energy Conversion Stiftstr. 34-36 Mülheim an der Ruhr QM/MM: an historical overview 1976: Warshell and Levitt Theoretical
More informationMultiscale Materials Modeling
Multiscale Materials Modeling Lecture 09 Quantum Mechanics/Molecular Mechanics (QM/MM) Techniques Fundamentals of Sustainable Technology These notes created by David Keffer, University of Tennessee, Knoxville,
More informationComputational Biology & Computational Medicine
Computational Biology & Computational Medicine Homayoun Valafar Outline Why proteins? What are proteins? How do we compute them? How do we use computational approaches? Why Proteins? Molecular basis of
More informationInteratomic Potentials. The electronic-structure problem
Interatomic Potentials Before we can start a simulation, we need the model! Interaction between atoms and molecules is determined by quantum mechanics: Schrödinger Equation + Born-Oppenheimer approximation
More informationThe Molecular Dynamics Method
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
More informationBiophysics II. Hydrophobic Bio-molecules. Key points to be covered. Molecular Interactions in Bio-molecular Structures - van der Waals Interaction
Biophysics II Key points to be covered By A/Prof. Xiang Yang Liu Biophysics & Micro/nanostructures Lab Department of Physics, NUS 1. van der Waals Interaction 2. Hydrogen bond 3. Hydrophilic vs hydrophobic
More informationThermodynamic behaviour of mixtures containing CO 2. A molecular simulation study
Thermodynamic behaviour of mixtures containing. A molecular simulation study V. Lachet, C. Nieto-Draghi, B. Creton (IFPEN) Å. Ervik, G. Skaugen, Ø. Wilhelmsen, M. Hammer (SINTEF) Introduction quality issues
More informationMultiple time step Monte Carlo
JOURNAL OF CHEMICAL PHYSICS VOLUME 117, NUMBER 18 8 NOVEMBER 2002 Multiple time step Monte Carlo Balázs Hetényi a) Department of Chemistry, Princeton University, Princeton, NJ 08544 and Department of Chemistry
More informationBridging Scales Through Wavefunction Analysis
Bridging Scales Through Wavefunction Analysis Felix Plasser Institute for Theoretical Chemistry, University of Vienna Excited States Bridging Scales Marseille, November 7 10, 2016 F. Plasser Wavefunction
More informationAdvantages of a Finite Extensible Nonlinear Elastic Potential in Lattice Boltzmann Simulations
The Hilltop Review Volume 7 Issue 1 Winter 2014 Article 10 December 2014 Advantages of a Finite Extensible Nonlinear Elastic Potential in Lattice Boltzmann Simulations Tai-Hsien Wu Western Michigan University
More informationThe Effect of Model Internal Flexibility Upon NEMD Simulations of Viscosity
Draft: September 29, 1999 The Effect of Model Internal Flexibility Upon NEMD Simulations of Viscosity N. G. Fuller 1 and R. L. Rowley 1,2 Abstract The influence of model flexibility upon simulated viscosity
More informationStudying complex macromolecules
Studying complex macromolecules M2 SERP-Chem Fabien Cailliez LCP Bât 349 fabien.cailliez@u-psud.fr Outline I. Classical forcefields II. III. IV. Molecular simulations and biomolecules One typical example:
More informationParameterization of a reactive force field using a Monte Carlo algorithm
Parameterization of a reactive force field using a Monte Carlo algorithm Eldhose Iype (e.iype@tue.nl) November 19, 2015 Where innovation starts Thermochemical energy storage 2/1 MgSO 4.xH 2 O+Q MgSO 4
More informationIntermolecular Forces and Monte-Carlo Integration 열역학특수연구
Intermolecular Forces and Monte-Carlo Integration 열역학특수연구 2003.3.28 Source of the lecture note. J.M.Prausnitz and others, Molecular Thermodynamics of Fluid Phase Equiliria Atkins, Physical Chemistry Lecture
More informationSupporting Information
alladium monophosphine d(h 3 ): does it really exist in solution? ietro Vidossich*, Gregori Ujaque,* and Agustí Lledós* Supporting Information Contents: 1. Schemes S1 and S2 2. Computational details 3.
More informationWhy Proteins Fold? (Parts of this presentation are based on work of Ashok Kolaskar) CS490B: Introduction to Bioinformatics Mar.
Why Proteins Fold? (Parts of this presentation are based on work of Ashok Kolaskar) CS490B: Introduction to Bioinformatics Mar. 25, 2002 Molecular Dynamics: Introduction At physiological conditions, the
More informationImperfect Gases. NC State University
Chemistry 431 Lecture 3 Imperfect Gases NC State University The Compression Factor One way to represent the relationship between ideal and real gases is to plot the deviation from ideality as the gas is
More informationChapter 2 Quantum chemistry using auxiliary field Monte Carlo
Chapter 2 Quantum chemistry using auxiliary field Monte Carlo 1. The Hubbard-Stratonovich Transformation 2. Neuhauser s shifted contour 3. Calculation of forces and PESs 4. Multireference AFMC 5. Examples
More informationBiomolecules 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",
More informationReactive 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
More informationMolecular Simulation II
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
More informationLoProp: local property calculations with quantum chemical methods
LoProp: local property calculations with quantum chemical methods Laura Gagliardi Dipartimento di Chimica Fisica F. Accascina Università degli Studi di Palermo Italy Gunnar Karlström, Jesper Krogh, and
More informationIntroduction to DFTB. Marcus Elstner. July 28, 2006
Introduction to DFTB Marcus Elstner July 28, 2006 I. Non-selfconsistent solution of the KS equations DFT can treat up to 100 atoms in routine applications, sometimes even more and about several ps in MD
More informationCrystal Structure Prediction using CRYSTALG program
Crystal Structure Prediction using CRYSTALG program Yelena Arnautova Baker Laboratory of Chemistry and Chemical Biology, Cornell University Problem of crystal structure prediction: - theoretical importance
More informationLecture C2 Microscopic to Macroscopic, Part 2: Intermolecular Interactions. Let's get together.
Lecture C2 Microscopic to Macroscopic, Part 2: Intermolecular Interactions Let's get together. Most gases are NOT ideal except at very low pressures: Z=1 for ideal gases Intermolecular interactions come
More informationMolecular 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
More informationCHEM3023: Spins, Atoms and Molecules
CHEM3023: Spins, Atoms and Molecules Lecture 4 Molecular orbitals C.-K. Skylaris Learning outcomes Be able to manipulate expressions involving spin orbitals and molecular orbitals Be able to write down
More informationIntroduction to Classical Molecular Dynamics. Giovanni Chillemi HPC department, CINECA
Introduction to Classical Molecular Dynamics Giovanni Chillemi g.chillemi@cineca.it HPC department, CINECA MD ingredients Coordinates Velocities Force field Topology MD Trajectories Input parameters Analysis
More informationLiquids as described by quantum and classical mechanics
Liquids as described by quantum and classical mechanics Ph.D. thesis by Thomas Mostrup Nymand Department of Chemistry Denmark 2000 To my family, Rikke, Esben and Gustav Contents List of papers 3 Introduction
More informationElectronic 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
More informationFrom Small Molecules to Biological Molecules: Modelling Interactions. Dr. Antonio Chana Milano, 22 nd April 2008
From Small Molecules to Biological Molecules: Modelling Interactions Dr. Antonio Chana Milano, 22 nd April 2008 Computational Methods & Applicability 2 *Diagram taken from S. C. Glotzer The University
More informationTools for QM studies of large systems
Tools for QM studies of large systems Automated, hessian-free saddle point search & characterization QM/MM implementation for zeolites Shaama Mallikarjun Sharada Advisors: Prof. Alexis T Bell, Prof. Martin
More information3: Many electrons. Orbital symmetries. l =2 1. m l
3: Many electrons Orbital symmetries Atomic orbitals are labelled according to the principal quantum number, n, and the orbital angular momentum quantum number, l. Electrons in a diatomic molecule experience
More informationAppendix: SU(2) spin angular momentum and single spin dynamics
Phys 7 Topics in Particles & Fields Spring 03 Lecture v0 Appendix: SU spin angular momentum and single spin dynamics Jeffrey Yepez Department of Physics and Astronomy University of Hawai i at Manoa Watanabe
More informationChapter 2 Experimental sources of intermolecular potentials
Chapter 2 Experimental sources of intermolecular potentials 2.1 Overview thermodynamical properties: heat of vaporization (Trouton s rule) crystal structures ionic crystals rare gas solids physico-chemical
More information3. Solutions W = N!/(N A!N B!) (3.1) Using Stirling s approximation ln(n!) = NlnN N: ΔS mix = k (N A lnn + N B lnn N A lnn A N B lnn B ) (3.
3. Solutions Many biological processes occur between molecules in aqueous solution. In addition, many protein and nucleic acid molecules adopt three-dimensional structure ( fold ) in aqueous solution.
More informationPost Hartree-Fock: MP2 and RPA in CP2K
Post Hartree-Fock: MP2 and RPA in CP2K A tutorial Jan Wilhelm jan.wilhelm@chem.uzh.ch 4 September 2015 Further reading MP2 and RPA by Mauro Del Ben, Jürg Hutter, Joost VandeVondele Del Ben, M; Hutter,
More informationForce Fields in Molecular Mechanics
Force Fields in Molecular Mechanics Rajarshi Guha (9915607) and Rajesh Sardar (9915610) March 21, 2001 1 Introduction With the advent of computers chemists have realized the utility of carrying out simulations
More informationAdvanced Molecular Dynamics
Advanced Molecular Dynamics Introduction May 2, 2017 Who am I? I am an associate professor at Theoretical Physics Topics I work on: Algorithms for (parallel) molecular simulations including GPU acceleration
More information