Computational Modeling Software and their applications June 21, 2011 Damilola Daramola Center for Electrochemical Engineering Research ABC s of electrochemistry
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
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
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
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
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
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
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
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
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
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
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
Modeling Software Localized Basis Set Programs Gaussian QChem Crystal Plane Wave Programs VASP CASTEP Quantum Espresso (Free) Molecular Mechanics Programs CHARMM Forcite 13
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
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
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
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 9323 9329 17
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
Monoclinic ZrO 2 Available Experimental Values Lattice parameters (use JCPDS or Crystallography Open Database) Bond Lengths and Distances (Literature Search) Vibrational Spectrum 19
Monoclinic ZrO 2 Geometry Optimization and Analysis Frequency Calculation and Analysis Isotopic Substitution and Analysis 20
Monoclinic ZrO 2 (Lattice Parameters) Experiment LDA GGA B3LYP Unit Cell Dimensions (Å) a 5.1488 5.091 5.209 5.232 b 5.2075 5.263 5.304 5.290 c 5.3157 5.206 5.370 5.397 β 99.23 98.386 99.504 99.424 Atom Coordinates Zr x 0.2754 0.2767 0.2765 0.2752 y 0.0390 0.0397 0.0425 0.0415 z 0.2094 0.2130 0.2102 0.2101 Mean Percent Difference LDA 2.85% GGA 1.90% B3LYP 1.35% O 1 x 0.0663 0.0873 0.0721 0.0692 y 0.3278 0.3668 0.3409 0.3324 z 0.3453 0.3189 0.3388 0.3473 O 2 x 0.4570 0.4478 0.4498 0.4526 y 0.7588 0.7601 0.7586 0.7579 z 0.4765 0.4852 0.4812 0.4790 Bondars, B.; Heidemane, G.; Grabis, J.; Laschke, K.; Boysen, H.; Schneider, J.; Frey, F. Journal of Materials Science 1995, 30, 1621 21
Monoclinic ZrO 2 (Bond lengths and angles) Distance (Å) LDA GGA B3LYP Expt Zr - O 1 2.09 2.09 2.08 2.04 Zr - O 2 2.19 2.21 2.20 2.18 Zr - O 3 2.21 2.26 2.28 2.26 Zr - O 4 2.05 2.09 2.09 2.10 Zr - O 5 2.23 2.29 2.30 2.26 Zr - O 6 2.14 2.18 2.19 2.16 Zr - O 7 2.19 2.19 2.18 2.15 Angle ( ) LDA GGA B3LYP Expt 3 O 1 coordination Zr 1 -O-Zr 2 106 109 110 109 Zr 1 -O-Zr 3 142 146 145 145 Zr 2 -O-Zr 3 104 105 105 106 O 2 coordination Zr 1 -O-Zr 2 102 102 102 102 Zr 1 -O-Zr 3 102 103 104 104 Zr 1 -O-Zr 4 106 106 107 107 Zr 2 -O-Zr 3 102 101 100 100 Zr 2 -O-Zr 4 107 108 108 109 Zr 3 -O-Zr 4 133 133 132 132 McCullough, J. D.; Trueblood, K. N. Acta Crystallographica 1959, 12, 507. Experimental Standard Deviations Lengths within 0.05Å Angles within 2 22
Monoclinic ZrO 2 (Numerical Raman Analysis) Expt LDA GGA B3LYP ω (cm -1 ) Δ ω (cm -1 ) Δ ω (cm -1 ) Δ 102 153 51 135 33 131 29 174 159 171 179 187 8 169-10 178 0 190 203 13 182-8 191 0 223 215-7 212-11 219-4 318 317 330 306 333 27 321 15 307 1 334 354 19 325-9 335 1 347 384 37 335-12 338-9 381 395 14 361-20 372-9 413 374 378 476 474-2 455-21 484 9 501 480-21 461-39 486-15 536 562 26 526-10 542 6 558 572 15 546-12 543-15 615 621 6 591-25 605-11 637 638 1 593-43 613-23 721 706 734 Mean Δ 13-12 -3 Max Δ 51 33 29 Min Δ -21-43 -23 Daramola, D., Muthuvel, M. and Botte, G.G., Journal of Physical Chemistry B, 114, pp 9323 9329 23
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 9323 9329 24
Monoclinic ZrO 2 (Isotopic Substitution) Replace 91.22 Zr with 93.40 Zr Replace 16.00 O with 18.00 O Calculate percentage shift in each Raman Peak Daramola, D., Muthuvel, M. and Botte, G.G., Journal of Physical Chemistry B, 114, pp 9323 9329 25
Monoclinic ZrO 2 (Isotopic Substitution) Daramola, D., Muthuvel, M. and Botte, G.G., Journal of Physical Chemistry B, 114, pp 9323 9329 26
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
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