Computational Modeling Software and their applications
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1 Computational Modeling Software and their applications June 21, 2011 Damilola Daramola Center for Electrochemical Engineering Research ABC s of electrochemistry
2 Introduction Computational Modeling the study and simulation of chemical structures and reactions based on fundamental physics laws. Broadly divided into 2 parts 1. Molecular Mechanics 2. Electronic Structure Methods 2
3 History Classical Mechanics (Newtonian Mechanics) F = m d2 x dt 2 Works well for macroscopic particles Not for microscopic particles due to wave and particle nature Heisenberg s Uncertainty Principle x p x h Levine, I.N.; Quantum Chemistry (Volume 1: Quantum Mechanics and Molecular Electronic Structure) 3
4 History Quantum Mechanics (Wave mechanics) Schrodinger s equation (time independent) HΨ = EΨ Full time equation (one dimension) h2 d 2 ψ x 8π 2 m dx 2 + V x ψ x = Eψ(x) Kinetic Energy Potential Energy 4
5 Molecular Mechanics Use the laws of classical mechanics as the basis of their computations i.e. attempt to solve Newton s second law Smallest physical unit is the atom i.e. electrons and nuclei are taken as a single unit 5
6 Electronic Stucture Methods Use the laws of quantum mechanics as the basis of their computations i.e. attempt to solve Schrodinger equation Electrons are treated explicitly and therefore calculations are more intensive than in the previous method 6
7 Comparison SYSTEMS Molecular Mechanics Works best for larger systems where atomic interactions dominate e.g. Diffusion Electronic Structure Methods Works best for systems where electronic interactions dominate e.g. bond formation COMPUTATIONAL DEMAND GENERALIZATION Relatively inexpensive due to simplified system Is not easily transferable from system to system as atoms are described within a specific context Relatively expensive for systems of relevant size due to the large amount of electrons to be accounted for Better transferability since atoms are modeled as electrons and nuclei and are accounted for seperately 7
8 Electronic Structure Methods Broadly divided into Ab initio (first principles) methods: based solely on quantum mechanics with no experimental parameters used. The most basic form is Hartree- Fock. Semi-empirical methods: use experimental data to simplify calculations, hence less general method but quicker calculations. Density functional theory methods: similar to ab initio but only as computationally demanding as HF with better results due to inclusion of electronic correlation. 8
9 Density Functional Theory Calculations are based on electron density Reduces a 3N system to N Calculations are characterized by Level of theory Basis Set 9
10 Level of Theory Local Density Approximation (LDA) Based on uniform electron gas Works best for metals Generalized Gradient Approximation (GGA) Improved on LDA Hybrid Functions Mixed with Hartree-Fock and Pure DFT approximations 10
11 Basis Set This is the mathematical representation of the molecular orbital. Also known as the space to which the electrons are confined. Choice depends on accuracy required and computational resources available Libraries of basis set are widely available online Types Localized Basis Sets Plane Wave Basis Sets 11
12 Basis Set (Continued) Localized Basis Sets (Chemistry) Plane Wave Basis Sets (Physics) Poster by Damian G. Allis (Solid State DFT Methods and the Property Prediction of High-Symmetry Molecular Crystals) 12
13 Modeling Software Localized Basis Set Programs Gaussian QChem Crystal Plane Wave Programs VASP CASTEP Quantum Espresso (Free) Molecular Mechanics Programs CHARMM Forcite 13
14 Gaussian Most useful for molecules and metallic clusters (nonperiodic) Periodic systems (solids) require high computational resources Possible Calculations Energy Geometry Optimization Frequency and thermochemical analysis Internal Reaction Coordinates 14
15 Crystal Useful for both molecules, surfaces and solid state systems i.e. 1D, 2D and 3D structures Possible Calculations Energy Geometry Optimization Frequency and thermochemical analysis Internal Reaction Coordinates Surface Energies 15
16 Solving a Chemical Problem Determine properties to be investigated (choice of classical or quantum mechanics) Determine system being solved i.e. number of dimensions required (choice of program) Determine elements involved in the system (choice of basis set) Determine accuracy required (choice of level of theory) 16
17 Sample Problems What atoms are causing the vibrations in the raman spectrum of monoclinic ZrO 2? Daramola, D., Muthuvel, M. and Botte, G.G., Journal of Physical Chemistry B, 114, pp
18 Monoclinic ZrO 2 Property to be calculated Frequency (Use Quantum Mechanics) Number of dimensions Three (Use Crystal) Elements involved Zirconium 40 Zr (Use a Pseudopotential based basis set) Oxygen 8 O (Use a large basis set) Accuracy required Match up with experimental measurements 18
19 Monoclinic ZrO 2 Available Experimental Values Lattice parameters (use JCPDS or Crystallography Open Database) Bond Lengths and Distances (Literature Search) Vibrational Spectrum 19
20 Monoclinic ZrO 2 Geometry Optimization and Analysis Frequency Calculation and Analysis Isotopic Substitution and Analysis 20
21 Monoclinic ZrO 2 (Lattice Parameters) Experiment LDA GGA B3LYP Unit Cell Dimensions (Å) a b c β Atom Coordinates Zr x y z Mean Percent Difference LDA 2.85% GGA 1.90% B3LYP 1.35% O 1 x y z O 2 x y z Bondars, B.; Heidemane, G.; Grabis, J.; Laschke, K.; Boysen, H.; Schneider, J.; Frey, F. Journal of Materials Science 1995, 30,
22 Monoclinic ZrO 2 (Bond lengths and angles) Distance (Å) LDA GGA B3LYP Expt Zr - O Zr - O Zr - O Zr - O Zr - O Zr - O Zr - O Angle ( ) LDA GGA B3LYP Expt 3 O 1 coordination Zr 1 -O-Zr Zr 1 -O-Zr Zr 2 -O-Zr O 2 coordination Zr 1 -O-Zr Zr 1 -O-Zr Zr 1 -O-Zr Zr 2 -O-Zr Zr 2 -O-Zr Zr 3 -O-Zr McCullough, J. D.; Trueblood, K. N. Acta Crystallographica 1959, 12, 507. Experimental Standard Deviations Lengths within 0.05Å Angles within 2 22
23 Monoclinic ZrO 2 (Numerical Raman Analysis) Expt LDA GGA B3LYP ω (cm -1 ) Δ ω (cm -1 ) Δ ω (cm -1 ) Δ Mean Δ Max Δ Min Δ Daramola, D., Muthuvel, M. and Botte, G.G., Journal of Physical Chemistry B, 114, pp
24 Monoclinic ZrO 2 (Graphical Raman Analysis) Shifts expected due to zero temperature calculation Daramola, D., Muthuvel, M. and Botte, G.G., Journal of Physical Chemistry B, 114, pp
25 Monoclinic ZrO 2 (Isotopic Substitution) Replace Zr with Zr Replace O with O Calculate percentage shift in each Raman Peak Daramola, D., Muthuvel, M. and Botte, G.G., Journal of Physical Chemistry B, 114, pp
26 Monoclinic ZrO 2 (Isotopic Substitution) Daramola, D., Muthuvel, M. and Botte, G.G., Journal of Physical Chemistry B, 114, pp
27 Further Reading Foresman, J.B. & Frisch, Æ; Exploring Chemistry with Electronic Structure Methods (2 nd Edition) Young, D; Computational Chemistry: A Practical Guide for Applying Techniques to Real World Problems Kohanoff, J.; Electronic Structure Calculations for Solids and Molecules: Theory and Computational Methods Levine, I.N.; Quantum Chemistry (Volume 1: Quantum Mechanics and Molecular Electronic Structure) 27
28 Questions 28
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