Molecular Physical Chemistry

Molecular Physical Chemistry
 
Author:
José J.C. Teixeira-Dias
Publisher:
Springer
ISBN No: 978-3-319-41093-7
Release at: 2017
Pages: 463
Edition:
First Edition
File Size: 25 MB
File Type: pdf
Language: English



Description of Molecular Physical Chemistry

This book contains chapters on thermodynamics, chemical kinetics, quantum chemistry, molecular symmetry, molecular structure, crystals, and water, and is intended for second-year master’s students in chemistry. It presents the subject through real examples, discussing the results of molecular orbital calculations performed by Gaussian on small molecules, exploring and running Mathematica odes presented at the end of each chapter that enables the student to plot functions, normalize functions, fit data, solve equations, and test physical models; they are accompanied by detailed explanations that provide insight and a suitable environment for active learning. Each chapter contains a glossary of important scientific and technical terms, and the book includes detailed and complete answers to all exercises. Since the molecular orbital calculations presented are standard, packages other than Gaussian can alternatively be used to provide the necessary data. Students who are unfamiliar with Mathematica should watch the set of short videos provided by this software to learn to write and run small programs and follow the explanations to the selected codes at the end of each chapter. Those who are familiar with other computational tools can alternatively use them.

Content of Molecular Physical Chemistry



1 Thermodynamics . 1
1.1 Ideal Gas 2
1.2 Kinetic Model of Gases 3
1.2.1 Pressure and Temperature 4
1.2.2 Distribution of Velocities 6
1.2.3 Mean Free Path9
1.3 Van der Waals Equation13
1.4 Mathematical Tools 16
1.4.1 Exact Differential    17
1.4.2 Fundamental Theorem of Calculus 20
1.4.3 Line Integral. 21
1.5 Thermodynamic Systems   23
1.6 Heat and Work  24
1.6.1 Mechanical Work    25
1.7 First Law   26
1.7.1 Heat Capacities   28
1.7.2 Calorimeter 29
1.7.3 Standard States30
1.8 Reversible Heat Engine  31
1.8.1 Carnot’s Heat Engine   33
1.8.2 Absolute Temperature   33
1.9 Entropy and the Second Law  35
1.10 Irreversible Processes 38
1.10.1 Heat Flow 38
1.10.2 Gas Expansion39
1.10.3 Diffusion of Matter  40
1.10.4 Chemical Reaction  41
1.11 Chemical Potential 42
1.11.1 Gibbs–Duhem Equation  43
1.11.2 Ideal Gas 44
1.11.3 Real Gases45
1.11.4 Liquid Solutions46
1.11.5 Pure Liquids and Solids  47
1.1 Gibbs Energy 47
1.1.1 Chemical Potential and Gibbs Energy
of Formation. 48
1.1. Gibbs–Helmholtz Equation 50
1.13 Chemical Equilibrium 51
1.14 Gibbs Phase Rule. 5
1.15 Helmholtz Energy 54
1.16 Surface Tension  55
1.16.1 Liquid Droplet in Air   55
1.16. Capillary Action56
1.17 Membrane Potential 58
1.18 Electrochemical Cell61
1.18.1 Nernst Equation6
Notes 65
Mathematica Codes  69
Glossary75
Exercises81
References    8
Further Reading  8
 Chemical Kinetics  83
.1 Rate of a Chemical Reaction  84
. Experimental Rate Equation   86
..1 First-Order Reactions   87
.. Second-Order Reactions  88
..3 Zeroth-Order Reactions   89
.3 Effect of Temperature Change   89
.4 Elementary Reactions 91
.5 Complex Reactions9
.6 Extremely Fast Reactions94
.6.1 Neutralization Reaction in Water 96
.7 Chemical Oscillations 96
.7.1 Brusselator97
Notes 10
Mathematica Codes  106
Glossary108
Exercises110
References    111
Further Reading  111
3 The Schrödinger Equation 113
3.1 Operators   114
3.1.1 Eigenvalues and Eigenfunctions 115
3.1. One-Dimensional Schrödinger Equation   115
3.1.3 Hermitian Operators   11
3.1.4 Important Theorems   118
3.1.5 Dirac Notation11
3. Harmonic Oscillator 11
3..1 Reduced Mass1
3.. Classical Treatment  13
3..3 Quantum-Mechanical Treatment 14
3..4 Morse Potential17
3.3 Spherical Coordinates 18
3.4 Angular Momentum 130
3.4.1 Orbital Angular Momentum  131
3.4. Spin  133
3.5 Hydrogen Atom  134
3.6 Antisymmetry Principle  137
3.7 Variational Method141
3.8 Born–Oppenheimer Approximation . 143
3.9 Hartree–Fock Method 146
3.9.1 Slater-Type Orbitals   148
3.9. Hartree–Fock Equations  149
3.9.3 Hartree–Fock–Roothaan Equations 150
3.9.4 Correlation Energy  151
3.10 Density Functional Theory    15
3.10.1 Electron Probability Density 15
3.10. External Potential    15
3.10.3 Functional Derivative   153
3.10.4 Hohenberg–Kohn Theorems  156
3.10.5 Kohn–Sham Method   157
3.10.6 Overview160
3.11 Perturbation Theory 161
3.11.1 Nondegenerate Energy Level  16
3.11. Variational Perturbation Method 164
3.11.3 Degenerate Energy Level 166
3.1 Time-Dependent Perturbation Theory  168
3.1.1 Time-Dependent Schrödinger Equation168
3.1. Time-Dependent Perturbation  169
3.13 Absorption and Emission of Radiation  17
3.13.1 Spontaneous Emission of Radiation    175
3.14 Raman Scattering . 176
3.14.1 Classical Treatment  177
3.14. Quantum-Mechanical Treatment 178
3.15 Molecular Calculations. 181
3.15.1 Computational Methods   181
3.15. Gaussian-Type Functions 18
3.15.3 Standard Basis Sets 185
Notes 186
Mathematica Codes  190
Glossary00
Exercises03
References    05
Further Reading  05
4 Molecular Symmetry  07
4.1 Symmetry Operations 07
4. Point Groups  10
4.3 Matrix Representations. 14
4.4 Character Tables . 18
4.5 Selection Rules  22
4.6 Molecular Vibrations 224
Mathematica Codes  232
Glossary238
Exercises240
Further Reading  241
5 Molecular Structure  243
5.1 Electron Probability Density  244
5.2 Electrostatic Potential 245
5.3 Mulliken Population Analysis   249
5.3.1 Density Matrix249
5.3.2 Minimal Basis Set Calculation for CH4251
5.4 Natural Bond Orbitals 254
5.4.1 Hybrid Atomic Orbitals   254
5.4.2 Natural Bond Orbitals for CH4 . 257
5.4.3 Natural Bond Orbitals for H2C=CH2. 258
5.4.4 Natural Bond Orbitals for HCCH 259
5.4.5 CH Hybrids in CH4, H2C=CH2 and HCCH   260
5.4.6 Molecular Geometries and Electrostatic Potentials 261
5.5 Potential Energy Surfaces262
5.5.1 Intrinsic Reaction Coordinate  264
5.6 Molecular Conformations266
5.6.1 Ethane 266
5.6.2 1,2-Dichloroethane  269
5.6.3 Boltzmann Distribution   270
5.7 Chiral Molecules . 272
Mathematica Codes  277
Glossary281
Exercises284
References    284
Further Reading  285
6 Crystals   287
6.1 Packing Disks and Spheres    287
6.1.1 Disks  287
6.1.2 Spheres . 289
6.1.3 Hexagonal Close Packing  291
6.1.4 Cubic Close Packing   292
6.1.5 Packing Densities    292
6.1.6 Occupying Interstices   295
6.2 Translation Symmetries  297
6.2.1 2D Bravais Lattices 297
6.2.2 3D Bravais Lattices 301
6.3 Crystal Structures . 304
6.3.1 Metals  304
6.3.2 Lattice Energy304
6.3.3 Cesium Chloride and Sodium Chloride305
6.3.4 Diamond and Zinc Blende  306
6.4 X-Ray Diffraction 308
6.5 Electrons in Solids 310
6.6 Semiconductors  312
Mathematica Codes  315
Glossary327
Exercises328
References    329
Further Reading  329
7 Water. 331
7.1 Molecular Geometry 332
7.2 Enthalpy of Formation. 333
7.3 Atomic Charges  333
7.4 Dipole Moment  334
7.4.1 Electric Multipoles  334
7.4.2 Point Dipole    336
7.4.3 Electric Field Streamlines . 337
7.4.4 H2O Dipole and Quadrupole  338
7.5 Molecular Orbitals 339
7.5.1 Natural Bond Orbitals   341
7.6 Molecular Vibrations 342
7.7 Intermolecular Interactions   344
7.7.1 Electrostatic Interaction   344
7.7.2 Induction 346
7.7.3 Dispersion 347
7.8 Hydrogen Bond  349
7.8.1 The Water Dimer    351
7.9 Ice Ih  353
7.9.1 Gas Hydrates. 354
7.10 Liquid Water  355
7.11 Phase Diagram 357
7.12 Water as Solvent . 359
7.12.1 Electric Permittivity   359
7.13 Simple Nonpolar Solutes   361
7.13.1 Ostwald Coefficient 362
7.13.2 Hydrophobic Interaction 365
7.15 Amphipathic Molecules  370
7.15.1 Sodium Decanoate Micelles ..373
7.16 Acids and Bases 375
7.16.1 Autoionization of Water 376
7.16.2 Acid Ionization Constant 377
7.16.3 Lewis Acids and Bases 380
7.17 Standard Electrode Potentials 381
Mathematica Codes  385
Glossary394
Exercises395
References    397
Further Reading  398
Appendix. 399
Answers to Exercises 403
Index 449

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