Molecular Physical Chemistry A Computer-based Approach using Mathematica and Gaussian

This is the physical chemistry textbook for students with an affinity for computers! It offers basic and advanced knowledge for students in the second year of chemistry masters studies and beyond. In seven chapters, the book presents thermodynamics, chemical kinetics, quantum mechanics and molecular...

Full description

Saved in:
Bibliographic Details
Main Author Teixeira-Dias, José J. C
Format eBook Book
LanguageEnglish
Published Cham Springer Nature 2017
Springer
Springer International Publishing AG
Springer International Publishing
Edition1
Subjects
Atomic/Molecular Structure and Spectra
Chemistry
Chemistry and Materials Science
Chemistry, Physical and theoretical
Engineering Thermodynamics, Heat and Mass Transfer
Physical & theoretical chemistry
Physical Chemistry
Spectroscopy/Spectrometry
Thermodynamics
Online AccessGet full text
ISBN3319410938
9783319410937
331941092X
9783319410920
DOI10.1007/978-3-319-41093-7

Cover

Table of Contents:
  • 2.2 Experimental Rate Equation -- 2.2.1 First-Order Reactions -- 2.2.2 Second-Order Reactions -- 2.2.3 Zeroth-Order Reactions -- 2.3 Effect of Temperature Change -- 2.4 Elementary Reactions -- 2.5 Complex Reactions -- 2.6 Extremely Fast Reactions -- 2.6.1 Neutralization Reaction in Water -- 2.7 Chemical Oscillations -- 2.7.1 Brusselator -- Notes -- 1. Matrix Diagonalization -- 2. Systems of First-Order Linear Differential Equations -- Mathematica Codes -- M1. First-Order Chemical Reaction -- M2. Brusselator -- Glossary -- Exercises -- References -- Further Reading -- 3 The Schrödinger Equation -- Abstract -- 3.1 Operators -- 3.1.1 Eigenvalues and Eigenfunctions -- 3.1.2 One-Dimensional Schrödinger Equation -- 3.1.3 Hermitian Operators -- 3.1.4 Important Theorems -- 3.1.5 Dirac Notation -- 3.2 Harmonic Oscillator -- 3.2.1 Reduced Mass -- 3.2.2 Classical Treatment -- 3.2.3 Quantum-Mechanical Treatment -- 3.2.4 Morse Potential -- 3.3 Spherical Coordinates -- 3.4 Angular Momentum -- 3.4.1 Orbital Angular Momentum -- 3.4.2 Spin -- 3.5 Hydrogen Atom -- 3.6 Antisymmetry Principle -- 3.7 Variational Method -- 3.8 Born-Oppenheimer Approximation -- 3.9 Hartree-Fock Method -- 3.9.1 Slater-Type Orbitals -- 3.9.2 Hartree-Fock Equations -- 3.9.3 Hartree-Fock-Roothaan Equations -- 3.9.4 Correlation Energy -- 3.10 Density Functional Theory -- 3.10.1 Electron Probability Density -- 3.10.2 External Potential -- 3.10.3 Functional Derivative -- 3.10.4 Hohenberg-Kohn Theorems -- 3.10.5 Kohn-Sham Method -- 3.10.6 Overview -- 3.11 Perturbation Theory -- 3.11.1 Nondegenerate Energy Level -- 3.11.2 Variational Perturbation Method -- 3.11.3 Degenerate Energy Level -- 3.12 Time-Dependent Perturbation Theory -- 3.12.1 Time-Dependent Schrödinger Equation -- 3.12.2 Time-Dependent Perturbation -- 3.13 Absorption and Emission of Radiation
  • Intro -- Preface -- Contents -- Credits -- 1 Thermodynamics -- Abstract -- 1.1 Ideal Gas -- 1.2 Kinetic Model of Gases -- 1.2.1 Pressure and Temperature -- 1.2.2 Distribution of Velocities -- 1.2.3 Mean Free Path -- 1.3 Van der Waals Equation -- 1.4 Mathematical Tools -- 1.4.1 Exact Differential -- 1.4.2 Fundamental Theorem of Calculus -- 1.4.3 Line Integral -- 1.5 Thermodynamic Systems -- 1.6 Heat and Work -- 1.6.1 Mechanical Work -- 1.7 First Law -- 1.7.1 Heat Capacities -- 1.7.2 Calorimeter -- 1.7.3 Standard States -- 1.8 Reversible Heat Engine -- 1.8.1 Carnot's Heat Engine -- 1.8.2 Absolute Temperature -- 1.9 Entropy and the Second Law -- 1.10 Irreversible Processes -- 1.10.1 Heat Flow -- 1.10.2 Gas Expansion -- 1.10.3 Diffusion of Matter -- 1.10.4 Chemical Reaction -- 1.11 Chemical Potential -- 1.11.1 Gibbs-Duhem Equation -- 1.11.2 Ideal Gas -- 1.11.3 Real Gases -- 1.11.4 Liquid Solutions -- 1.11.5 Pure Liquids and Solids -- 1.12 Gibbs Energy -- 1.12.1 Chemical Potential and Gibbs Energy of Formation -- 1.12.2 Gibbs-Helmholtz Equation -- 1.13 Chemical Equilibrium -- 1.14 Gibbs Phase Rule -- 1.15 Helmholtz Energy -- 1.16 Surface Tension -- 1.16.1 Liquid Droplet in Air -- 1.16.2 Capillary Action -- 1.17 Membrane Potential -- 1.18 Electrochemical Cell -- 1.18.1 Nernst Equation -- Notes -- Mathematica Codes -- M1. Maxwell Distribution of Molecular Speeds -- M2. Critical Point for Van der Waals Fluid -- M3. 3D Plot of the Van der Waals Equation in Reduced Variables -- M4. Absolute and Reduced Temperatures for the Van der Waals Carbon Dioxide -- M5. Isothermal and Adiabatic Transformations on an Ideal Gas Surface -- M6. Efficiency of the Carnot Heat Engine -- M7. Gibbs Energy and Affinity of a Chemical Reaction -- Glossary -- Exercises -- References -- Further Reading -- 2 Chemical Kinetics -- Abstract -- 2.1 Rate of a Chemical Reaction
  • 3.13.1 Spontaneous Emission of Radiation -- 3.14 Raman Scattering -- 3.14.1 Classical Treatment -- 3.14.2 Quantum-Mechanical Treatment -- 3.15 Molecular Calculations -- 3.15.1 Computational Methods -- 3.15.2 Gaussian-Type Functions -- 3.15.3 Standard Basis Sets -- Notes -- 1. Particle in a One-Dimensional Box -- 2. Two-Particle Rigid Rotor -- Mathematica Codes -- M1. Wave Equation -- M2. Helmholtz Equation -- M3. Harmonic Oscillator -- M4. Spherical Harmonics -- M5. Determinants -- M6. Systems of Homogeneous Linear Equations -- M7. Normalization Constants for Slater-Type Orbitals -- M8. Functional Derivative -- M9. STO Versus a Gaussian Function at the Origin -- M10. Fitting Gaussian Functions to a 1s Hydrogen Orbital -- M11. Product of Gaussian Functions -- Glossary -- Exercises -- References -- Further Reading -- 4 Molecular Symmetry -- Abstract -- 4.1 Symmetry Operations -- 4.2 Point Groups -- 4.3 Matrix Representations -- 4.4 Character Tables -- 4.5 Selection Rules -- 4.6 Molecular Vibrations -- Mathematica Codes -- M1. Classes of Symmetry Operations -- M2. Multiplication Table for the C2v Group -- M3. Selection Rule for a Particle in a One-Dimensional Box -- M4. Selection Rule for the Two-Particle Rigid Rotor -- M5. Selection Rule for the Harmonic Oscillator -- Glossary -- Exercises -- Further Reading -- 5 Molecular Structure -- Abstract -- 5.1 Electron Probability Density -- 5.2 Electrostatic Potential -- 5.3 Mulliken Population Analysis -- 5.3.1 Density Matrix -- 5.3.2 Minimal Basis Set Calculation for CH4 -- 5.4 Natural Bond Orbitals -- 5.4.1 Hybrid Atomic Orbitals -- 5.4.2 Natural Bond Orbitals for CH4 -- 5.4.3 Natural Bond Orbitals for H2C=CH2 -- 5.4.4 Natural Bond Orbitals for HC≡CH -- 5.4.5 CH Hybrids in CH4, H2C=CH2 and HC≡CH -- 5.4.6 Molecular Geometries and Electrostatic Potentials -- 5.5 Potential Energy Surfaces
  • 5.5.1 Intrinsic Reaction Coordinate -- 5.6 Molecular Conformations -- 5.6.1 Ethane -- 5.6.2 1,2-Dichloroethane -- 5.6.3 Boltzmann Distribution -- 5.7 Chiral Molecules -- Mathematica Codes -- M1. Natural Bond Orbitals for CH4 -- M2. Potential Energy Surface -- M3. Right- and Left-Handed Helices -- M4. Optical Rotation -- Glossary -- Exercises -- References -- Further Reading -- 6 Crystals -- Abstract -- 6.1 Packing Disks and Spheres -- 6.1.1 Disks -- 6.1.2 Spheres -- 6.1.3 Hexagonal Close Packing -- 6.1.4 Cubic Close Packing -- 6.1.5 Packing Densities -- 6.1.6 Occupying Interstices -- 6.2 Translation Symmetries -- 6.2.1 2D Bravais Lattices -- 6.2.2 3D Bravais Lattices -- 6.3 Crystal Structures -- 6.3.1 Metals -- 6.3.2 Lattice Energy -- 6.3.3 Cesium Chloride and Sodium Chloride -- 6.3.4 Diamond and Zinc Blende -- 6.4 X-Ray Diffraction -- 6.5 Electrons in Solids -- 6.6 Semiconductors -- Mathematica Codes -- M1. Packing of Disks -- M2. Hexagon of Disks -- M3. Disk Layers -- M4. The Third Dimension -- M5. HCP Structure -- M6. 2D Square Point Lattice -- M7. 2D Hexagonal Point Lattice -- M8. 3D Bravais Lattices -- M9. CsCl Structure -- M10. NaCl Structure -- M11. from Energy Levels to Bands -- M12. Fermi-Dirac Distribution -- Glossary -- Exercises -- References -- Further Reading -- 7 Water -- Abstract -- 7.1 Molecular Geometry -- 7.2 Enthalpy of Formation -- 7.3 Atomic Charges -- 7.4 Dipole Moment -- 7.4.1 Electric Multipoles -- 7.4.2 Point Dipole -- 7.4.3 Electric Field Streamlines -- 7.4.4 H2O Dipole and Quadrupole -- 7.5 Molecular Orbitals -- 7.5.1 Natural Bond Orbitals -- 7.6 Molecular Vibrations -- 7.7 Intermolecular Interactions -- 7.7.1 Electrostatic Interaction -- 7.7.2 Induction -- 7.7.3 Dispersion -- 7.8 Hydrogen Bond -- 7.8.1 The Water Dimer -- 7.9 Ice Ih -- 7.9.1 Gas Hydrates -- 7.10 Liquid Water -- 7.11 Phase Diagram -- 7.12 Water as Solvent
  • 7.12.1 Electric Permittivity -- 7.13 Simple Nonpolar Solutes -- 7.13.1 Ostwald Coefficient -- 7.13.2 Hydrophobic Interaction -- 7.14 Ionic Solutions -- 7.15 Amphipathic Molecules -- 7.15.1 Sodium Decanoate Micelles -- 7.16 Acids and Bases -- 7.16.1 Autoionization of Water -- 7.16.2 Acid Ionization Constant -- 7.16.3 Lewis Acids and Bases -- 7.17 Standard Electrode Potentials -- Mathematica Codes -- M1. Representation of the Water Molecule -- M2. Electrostatic Potential Contours for a Dipole -- M3. Interactive Manipulation of Charge -- M4. Vector Field Streamlines -- M5. Luzar's Model -- M6. Micelle-Monomers Equilibrium -- M7. Critical Micelle Concentration -- M8. Weak Acid HA -- Glossary -- Exercises -- References -- Further Reading -- 8 Erratum to: Molecular Physical Chemistry -- Erratum to:&amp -- #6 -- J.J.C. Teixeira-Dias, Molecular Physical Chemistry, DOI 10.1007/978-3-319-41093-7 -- Appendix -- Answers to Exercises -- E1. Mathematica Code and Results -- E2. Mathematica Code and Results -- E3. Mathematica Code and Results -- E4. Mathematica Code and Results -- E5. Mathematica Code and Results -- E6. Mathematica Code and Results -- E7. -- E8. -- E9. -- E10. -- E11. -- E12. -- E13. -- E14. -- E15. -- E16. -- E17. -- E18. -- E19. -- E20. -- E1. Mathematica Code and Results -- E2. -- E3. Mathematica Code and Results -- E4. -- E5. -- E6. -- E1. -- E2. Mathematica Code and Results -- E3. -- E4. -- E5. -- E6. -- E7. -- E8. Mathematica Code and Results -- E9. Mathematica Code and Results -- E10. Mathematica Code and Results -- E11. -- E12. -- E13. -- E14. -- E15. Mathematica Code and Results -- E16. Mathematica Code and Results -- E17. -- E18. -- E19. -- E20. -- E21. -- E22. Mathematica Code and Results -- E23. Mathematica Code and Results -- E24. -- E25. -- E26. Mathematica Code and Results -- E27. -- E28. Mathematica Code and Results
  • E29. Mathematica Code and Results