This book discusses major developments of quantum mechanics from classical to computational chemistry. The book is student and user friendly and includes exhaustive derivations, mathematical proofs, and theorems. A series of solved numerical have been added after each topic to have a better understanding of the subject. It will be helpful to Chemistry students at undergraduate and postgraduate level, as well for those appearing in various competitive examinations. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan)

lgli/Dua A. Quantum Chemistry. Classical to Computational_2025.pdf

lgrsnf/Dua A. Quantum Chemistry. Classical to Computational_2025.pdf

zlib/no-category/Dua, Amita, Singh, Chayannika/Quantum Chemistry: Classical to Computational_28106033.pdf

Amita Dua, Chayannika Singh

Taylor & Francis Ltd

United Kingdom and Ireland, United Kingdom

CRC Press (Unlimited), [S.l.], 2024

2025

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Cover
Half Title
Quantum Chemistry: Classical to Computational
Copyright
Detailed Contents
Preface
1. Classical Mechanics
1.1 Dalton’s Atomic Theory
1.2 What are Classical Mechanics and Quantum Mechanics?
1.3 J.J. Thomson Model of Atom
1.4 Rutherford’s Nuclear Model of Atom—Discovery of Nucleus
1.5 Developments Leading to the Bohr Model of Atom
1.5.1 Dual Nature of Electromagnetic Radiation
1.5.2 Emission and Absorption Spectra
1.6 Bohr Model of Atom
1.7 Sommerfeld Theory
2. Towards Quantum Mechanics
2.1 Reasons for the Failure of Classical Model of Atom or Bohr Model of Atom
2.2 Developments Leading to Quantum Mechanical Model of Atom
2.3 de-Broglie’s Dual Nature of Matter
2.4 Heisenberg’s Uncertainty Principle
3. Introduction to Quantum Mechanics
3.1 Necessity of Quantum Mechanics
3.2 Schrodinger Wave Equation
3.3 Derivation of Time Independent Schrodinger Wave Equation
3.4 Physical Significance of Wavefunction (ψ) and Probability Density (ψ2)
3.5 Concept of Atomic Orbital
3.6 Quantum Mechanical Model of Atom
3.7 Eigen Value and Eigen Wavefunction
3.8 Normalised, Orthogonal and Orthonormal Wavefunction
3.9 Operators
3.10 Postulates of Quantum Mechanics
3.11 Derivation of Time Independent Schrodinger Wave Equation on the Basis of Postulates of Quantum Mechanics
3.12 Steady State Schrodinger Wave Equation
4. Particle in a Box: Quantisation of Translational Energy
4.1 Application of Postulates of Quantum Mechanics to Simple System
4.2 Operation of Quantum Mechanics
4.3 Introduction to Translational Motion of a Particle
4.4 Particle in One Dimensional Box: Quantisation of Translational Energy
4.4.1 Solution of Schrodinger Wave Equation
4.4.2 Conclusions from the Study of a Particle in One-dimensional Box
4.4.3 Solution of Properties in One Dimensional Box
4.4.4 Application of Particle in a One-dimensional Box
4.5 Particle in Two-dimensional Box
4.5.1 Two Dimensional Rectangular Box
4.5.2 Two Dimensional Square Box (Concept of Degeneracy)
4.6 Particle in Three Dimensional Box
4.6.1 Three Dimensional Cuboidal Box
4.6.2 Three dimensional Cubical Box (Concept of Degeneracy)
4.7 Free Particle
4.7.1 Solution of Schrodinger Wave Equation
4.7.2 Quantisation of Energy Levels: Difference between Particle in Free State and Under Bound State
5. Rigid Rotator: Quantisation of Rotational Energy
5.1 Introduction
5.2 Classical Treatment of Rigid Rotator
5.2.1 Kinetic Energy of Rigid Rotator
5.3 Quantum Mechanical Treatment: Schrodinger Wave Equation for Rigid Rotator
5.3.1 Deriving Schrodinger Equation by Reducing Angular Momentum of Kinetic Energy Operator in Polar Co-ordinates
5.3.2 Deriving Schrodinger Equation by Reducing Laplacian of Kinetic Energy Operator in Polar Coordinates
5.4 Wavefunction of Rigid Rotator
5.4.1 Solving the Φ Part of Wavefunction
5.4.2 Solving the Θ Part of Wavefunction
5.4.3 Spherical Harmonics, Y(θ, φ)
5.5 Rotational Energy of the Rigid Rotator
5.6 Rotational spectra
6. Linear Harmonic Oscillator: Quantisation of Vibrational Energy
6.1 Introduction
6.2 Classical Treatment of Linear Harmonic Oscillator
6.2.1 Frequency of Linear Harmonic Oscillator
6.2.2 Potential Energy of Linear Harmonic Oscillator
6.2.3 Total Energy of the Linear Harmonic Oscillator
6.3 Quantum Mechanical Treatment: Schrodinger Wave Equation for Linear Harmonic Oscillator
6.4 Solution of Schrodinger Wave Equation
6.4.1 Factorization Method
6.4.2 Power Series Method
6.5 Vibrational Energy Levels for Linear Harmonic Oscillator
6.6 Wavefunction Plots for Linear Harmonic Oscillator
6.7 Probability Plots for Linear Harmonic Oscillator
6.8 Symmetry of the Vibrational Wavefunction
6.9 Calculation of Properties of Linear Harmonic Oscillator
6.10 Orthonormal Sets of Wavefunction
6.11 Virial Theorem
6.12 Vibrational Spectra
7. “Hydrogen Atom”: Quantisation of Electronic Energy
7.1 Necessity of Replacing Bohr Theory
7.2 Setting of Schrodinger Equation for Hydrogen Atom
7.2.1 Solving the Φ Part of Wavefunction
7.2.2 Solving the Θ Part of Wavefunction
7.2.3 Solving the Radial Part, R, of Wavefunction
7.3 Quantum Numbers
7.3.1 Significance of Quantum Numbers
7.3.2 Importance of Quantum Numbers in Explaining Hydrogen Spectrum
7.4 Degenerate and Non-Degenerate Orbitals
7.5 Degeneracy of Energy Levels
7.6 Wavefunction of the Hydrogen Atom
7.6.1 Radial Wavefunction and Radial Plots
7.6.2 Angular Wavefunction and Shape of Orbitals
7.6.3 Contour Diagram or Contour maps
7.6.4 Total Wavefunction of Hydrogen Atom
7.7 Calculation of Properties of Hydrogen Atom
7.7.1 Probability density (ψ2)
7.7.2 Most Probable Distance (r) or Position of Maximum Probability Using Radial Probability Density Function
7.7.3 Average Value of Position or Expectation Value of Position or Mean Radius
7.7.4 Expectation value of Energy
7.8 Magnetic Properties: Angular Momentum and Magnetic Moment
7.8.1 Classical Expression of Magnetic Moment due to Orbital Motion of Electron
7.8.2 Quantum Mechanical Expression of Magnetic Moment Due to Orbital Motion of Electron
7.8.3 Potential Energy Due to Orbital Motion of an Electron in a Magnetic Field: Larmor Precession
7.8.4 Zeeman Effect
7.8.5 Anomalous Zeeman Effect
7.8.6 Explanation of Anomalous Zeeman Effect: Spin Quantum Number
7.8.7 Magnetic Moment Due to Spinning Motion of Electron
7.8.8 Potential Energy Due to Spinning Motion of Electron in a Magnetic Field
7.8.9 Experimental Demonstration of Electron Spin: Stern-Gerlach Experiment
7.9 Spin Orbit Coupling and Term Symbols
8. Multielectron System and Approximate Methods
8.1 Introduction
8.2 Pertubation Method
8.2.1 Solution of Pertubation Method
8.2.2 Application of Pertubation Method on Helium Atom
8.3 Variation Method
8.3.1 Solution of Variation Method
8.3.2 Application of Variation Method on Helium Atom
8.3.3 Application of Variation Method for Various Other Systems
8.4 Self-Consistent Field Method
9. Chemical Bonding
9.1 Introduction
9.2 Born-Oppenheimer Approximation
9.3 Approximate Methods to Solve Schrodinger Equation of a Molecule: Valence Bond Approach and Molecular Orbital Approach
9.3.1 Valence Bond (VB) Approach
9.3.2 Molecular Orbital (MO) Approach
9.4 Approximation of Linear Combination of Atomic Orbitals: LCAO–MO Treatment
9.5 LCAO–MO Treatment of Hydrogen Molecule Ion (H2+)
9.6 Hydrogen Molecule: Qualitative Treatment
9.6.1 Pauli’s Exclusion Principle w.r.t. Hydrogen Molecule
9.6.2 Hund’s Rule of Maximum Multiplicity w.r.t. Hydrogen Molecule
9.6.3 Aufbau’s Principle w.r.t. Hydrogen Molecule
9.7 LCAO–MO Treatment of Hydrogen Molecule
9.7.1 Configuration Interaction
9.8 Valence Bond Treatment (VBT) of Hydrogen Molecule
9.9 Comparison of VBT and MOT
9.10 LCAO–MO Treatment of Homonuclear Diatomic Molecules
9.11 LCAO–MO Treatment of Heteronuclear Diatomic Molecules
9.12 LCAO–MO Treatment of Triatomic Molecules
10. Hückel Molecular Orbital Theory
10.1 Introduction
10.2 Application of HMO Theory of Conjugated Systems
10.2.1 Ethylene
10.2.2 1,3-Butadiene
10.2.3 Cyclobutadiene
10.2.4 Cyclopropene
10.2.5 Benzene
10.3 Delocalization Energy
11. Basics of Computational Chemistry
11.1 Introduction
11.2 Potential Energy Surface (PES)
11.3 Stationary Point
11.4 Geometry Optimization
11.5 Molecular Mechanics (MM) Method
11.5.1 Applications of MM Method
11.6 Ab-initio Method
11.6.1 Applications of ab-initio Method
11.7 Semi-Empirical Method
11.7.1 Applications of Semi-Empirical Method
11.8 Density Functional Theory (DFT) Method
11.8.1 Applications of Density Functional Theory Method
11.9 Basis Set
Appendices
Appendix A1: Fundamental Physical Constants
Appendix A2: Standard Integrals
Appendix A3: Important Mathematical Formulae
Appendix A4: Selected Derived Units
Appendix A5: Energy Conversion Factors
Appendix A6: Unit Prefixes
Appendix A7: Logarithms Table
Appendix A8: Antilogarithms Table
Appendix A9: How to Take Log and Antilog
Index

2024-03-17