Syllabus

Basic Quantum Mechanics unit_01

Syllabus
Structure: Postulates of quantum mechanics. Operators. Time dependent and time independent Schrödinger equations. Born interpretation. Dirac bra-ket notation. Particle in a box: infinite and finite square wells; concept of tunnelling; particle in 1D, 2D and 3D-box; applications. Harmonic oscillator: harmonic and anharmonic potentials; Hermite polynomials. Rotational motion: Angular momentum operators, Rigid rotor. Hydrogen and hydrogen-like atoms: atomic orbitals; radial distribution function.
Core concepts (12)
  • Postulates of Quantum Mechanics
  • Schrödinger Equation
  • Operators and Observable Algebra
  • Wave Function Interpretation
  • Bra-Ket Notation
  • Particle in a Box
  • Tunnelling Phenomenon
  • Quantum Harmonic Oscillator
  • Angular Momentum Operators
  • Rigid Rotor Model
  • Hydrogen Atom Structure
  • Radial Distribution Function
Related concepts (8)
  • Normalisation and Orthogonality
  • Expectation Values
  • Quantum Numbers
  • Nodal Structure
  • Boundary Conditions
  • Hermitian Operators
  • Commutators and Uncertainty
  • Variational Principle

Basic Quantum Mechanics unit_01_concept

Syllabus
Structure: Postulates of quantum mechanics. Operators. Time dependent and time independent Schrödinger equations. Born interpretation. Dirac bra-ket notation. Particle in a box: infinite and finite square wells; concept of tunnelling; particle in 1D, 2D and 3D-box; applications. Harmonic oscillator: harmonic and anharmonic potentials; Hermite polynomials. Rotational motion: Angular momentum operators, Rigid rotor. Hydrogen and hydrogen-like atoms: atomic orbitals; radial distribution function.
Core concepts (12)
  • Postulates of Quantum Mechanics
  • Schrödinger Equation
  • Operators and Observable Algebra
  • Wave Function Interpretation
  • Bra-Ket Notation
  • Particle in a Box
  • Tunnelling Phenomenon
  • Quantum Harmonic Oscillator
  • Angular Momentum Operators
  • Rigid Rotor Model
  • Hydrogen Atom Structure
  • Radial Distribution Function
Related concepts (8)
  • Normalisation and Orthogonality
  • Expectation Values
  • Quantum Numbers
  • Nodal Structure
  • Boundary Conditions
  • Hermitian Operators
  • Commutators and Uncertainty
  • Variational Principle

Approximation Methods of Quantum Mechanics unit_02

Syllabus
Multi-electron atoms: orbital approximation; electron spin; Pauli exclusion principle; Slater determinants. Approximation Methods: Variation method and secular determinants; first order perturbation techniques. Atomic units.
Core concepts (9)
  • Multi-Electron Atoms
  • Orbital Approximation
  • Electron Spin
  • Pauli Exclusion Principle
  • Slater Determinants
  • Variation Method
  • Secular Determinants
  • First-Order Perturbation Theory
  • Atomic Units
Related concepts (8)
  • Effective Nuclear Charge
  • Screening and Shielding
  • Spin-Orbitals
  • Antisymmetry Requirement
  • Hartree–Fock Idea
  • Rayleigh–Ritz Principle
  • Degenerate vs Non-Degenerate Perturbation
  • Unit Conversions in Atomic Units

Approximation Methods of Quantum Mechanics unit_02_concept

Syllabus
Multi-electron atoms: orbital approximation; electron spin; Pauli exclusion principle; Slater determinants. Approximation Methods: Variation method and secular determinants; first order perturbation techniques. Atomic units.
Core concepts (9)
  • Multi-Electron Atoms
  • Orbital Approximation
  • Electron Spin
  • Pauli Exclusion Principle
  • Slater Determinants
  • Variation Method
  • Secular Determinants
  • First-Order Perturbation Theory
  • Atomic Units
Related concepts (8)
  • Effective Nuclear Charge
  • Screening and Shielding
  • Spin-Orbitals
  • Antisymmetry Requirement
  • Hartree–Fock Idea
  • Rayleigh–Ritz Principle
  • Degenerate vs Non-Degenerate Perturbation
  • Unit Conversions in Atomic Units

Structure and Bonding unit_03

Syllabus
Molecular structure and Chemical bonding: Born-Oppenheimer approximation; Valence bond theory and linear combination of atomic orbitals – molecular orbital (LCAO-MO) theory. Hybrid orbitals. Applications of LCAO-MO theory to H2+, H2; orbital theory (MOT) of homo- and heteronuclear diatomic molecules. Hückel approximation and its application to annular π–electron systems.
Core concepts (9)
  • Born-Oppenheimer Approximation
  • Valence Bond Theory
  • LCAO-MO Theory
  • Molecular Orbital Formation
  • Hybrid Orbitals
  • Homonuclear Diatomic Molecules
  • Heteronuclear Diatomic Molecules
  • Hückel Approximation
  • Annular π-Electron Systems
Related concepts (9)
  • Molecular Orbital Diagrams
  • Bond Order
  • Orbital Overlap Integral
  • Σ and π Bonding
  • Aufbau Principle in Molecules
  • Variational Principle in LCAO
  • Electronegativity Differences
  • Aromaticity and Cyclic Conjugation
  • Resonance and Delocalization

Structure and Bonding unit_03_concept

Syllabus
Molecular structure and Chemical bonding: Born-Oppenheimer approximation; Valence bond theory and linear combination of atomic orbitals – molecular orbital (LCAO-MO) theory. Hybrid orbitals. Applications of LCAO-MO theory to H2+, H2; orbital theory (MOT) of homo- and heteronuclear diatomic molecules. Hückel approximation and its application to annular π–electron systems.
Core concepts (9)
  • Born-Oppenheimer Approximation
  • Valence Bond Theory
  • LCAO-MO Theory
  • Molecular Orbital Formation
  • Hybrid Orbitals
  • Homonuclear Diatomic Molecules
  • Heteronuclear Diatomic Molecules
  • Hückel Approximation
  • Annular π-Electron Systems
Related concepts (9)
  • Molecular Orbital Diagrams
  • Bond Order
  • Orbital Overlap Integral
  • Σ and π Bonding
  • Aufbau Principle in Molecules
  • Variational Principle in LCAO
  • Electronegativity Differences
  • Aromaticity and Cyclic Conjugation
  • Resonance and Delocalization

Group Theory and Molecular Symmetry unit_04

Syllabus
Group theory: Symmetry elements and operations; Point groups and character tables; Internal coordinates and vibrational modes; symmetry adapted linear combination of atomic orbitals (LCAO-MO); construction of hybrid orbitals using symmetry aspects.
Core concepts (8)
  • Symmetry Elements and Operations
  • Molecular Point Groups
  • Character Tables
  • Reducible and Irreducible Representations
  • Internal Coordinates and Vibrational Modes
  • Symmetry Adapted Linear Combinations (SALC)
  • Symmetry in LCAO-MO Construction
  • Symmetry-Based Hybrid Orbitals
Related concepts (8)
  • Group Theoretical Terminology
  • Matrix Representations of Operations
  • Mulliken Symbols
  • Projection Operator Method
  • Correlation Tables
  • IR and Raman Activity Criteria
  • Symmetry Labels in MO Diagrams
  • Degeneracy and Symmetry

Group Theory and Molecular Symmetry unit_04_concept

Syllabus
Group theory: Symmetry elements and operations; Point groups and character tables; Internal coordinates and vibrational modes; symmetry adapted linear combination of atomic orbitals (LCAO-MO); construction of hybrid orbitals using symmetry aspects.
Core concepts (8)
  • Symmetry Elements and Operations
  • Molecular Point Groups
  • Character Tables
  • Reducible and Irreducible Representations
  • Internal Coordinates and Vibrational Modes
  • Symmetry Adapted Linear Combinations (SALC)
  • Symmetry in LCAO-MO Construction
  • Symmetry-Based Hybrid Orbitals
Related concepts (8)
  • Group Theoretical Terminology
  • Matrix Representations of Operations
  • Mulliken Symbols
  • Projection Operator Method
  • Correlation Tables
  • IR and Raman Activity Criteria
  • Symmetry Labels in MO Diagrams
  • Degeneracy and Symmetry

Atomic and Molecular Spectroscopy unit_05

Syllabus
Spectroscopy - Atomic spectroscopy; Russell-Saunders coupling; Term symbols and spectral details; origin of selection rules. Rotational, vibrational, electronic and Raman spectroscopy of diatomic and polyatomic molecules. Line broadening. Einstein's coefficients. Relationship of transition moment integral with molar extinction coefficient and oscillator strength. Basic principles of nuclear magnetic resonance - gyromagnetic ratio; chemical shift, nuclear coupling.
Core concepts (12)
  • Atomic Spectroscopy
  • Russell-Saunders Coupling
  • Term Symbols and Selection Rules
  • Rotational Spectroscopy
  • Vibrational Spectroscopy
  • Electronic Spectroscopy
  • Raman Spectroscopy
  • Transition Probabilities and Einstein Coefficients
  • Spectroscopic Parameters
  • Line Broadening Mechanisms
  • Nuclear Magnetic Resonance Fundamentals
  • NMR Chemical Shift and Coupling
Related concepts (5)
  • Quantum Mechanical Foundations
  • Group Theory Applications
  • Boltzmann Distribution
  • Molecular Structure Determination
  • Instrumentation Basics

Atomic and Molecular Spectroscopy unit_05_concept

Syllabus
Spectroscopy - Atomic spectroscopy; Russell-Saunders coupling; Term symbols and spectral details; origin of selection rules. Rotational, vibrational, electronic and Raman spectroscopy of diatomic and polyatomic molecules. Line broadening. Einstein's coefficients. Relationship of transition moment integral with molar extinction coefficient and oscillator strength. Basic principles of nuclear magnetic resonance - gyromagnetic ratio; chemical shift, nuclear coupling.
Core concepts (12)
  • Atomic Spectroscopy
  • Russell-Saunders Coupling
  • Term Symbols and Selection Rules
  • Rotational Spectroscopy
  • Vibrational Spectroscopy
  • Electronic Spectroscopy
  • Raman Spectroscopy
  • Transition Probabilities and Einstein Coefficients
  • Spectroscopic Parameters
  • Line Broadening Mechanisms
  • Nuclear Magnetic Resonance Fundamentals
  • NMR Chemical Shift and Coupling
Related concepts (5)
  • Quantum Mechanical Foundations
  • Group Theory Applications
  • Boltzmann Distribution
  • Molecular Structure Determination
  • Instrumentation Basics

Equilibrium Chemical Thermodynamics I unit_06

Syllabus
Equilibrium - Laws of thermodynamics, Standard states, Thermochemistry, Thermodynamic functions and their relationships, Criteria of spontaneity and equilibrium, Absolute entropy, Partial molar quantities, Thermodynamics of mixing, Chemical potential, Fugacity, activity and activity coefficients, Ideal and Non-ideal solutions, Chemical equilibria, Dependence of equilibrium constant on temperature and pressure
Core concepts (9)
  • Laws of Thermodynamics
  • Thermodynamic Functions and Relations
  • Gibbs-Helmholtz and Maxwell Relations
  • Criteria of Spontaneity and Equilibrium
  • Chemical Potential and Partial Molar Quantities
  • Fugacity and Activity
  • Ideal and Non-ideal Solutions
  • Chemical Equilibrium
  • Temperature and Pressure Dependence of Equilibrium
Related concepts (6)
  • Standard States
  • Thermochemistry
  • Absolute Entropy
  • Gibbs-Duhem Equation
  • Thermodynamics of Mixing
  • Raoult's Law and Henry's Law

Equilibrium Chemical Thermodynamics I unit_06_concept

Syllabus
Equilibrium - Laws of thermodynamics, Standard states, Thermochemistry, Thermodynamic functions and their relationships, Criteria of spontaneity and equilibrium, Absolute entropy, Partial molar quantities, Thermodynamics of mixing, Chemical potential, Fugacity, activity and activity coefficients, Ideal and Non-ideal solutions, Chemical equilibria, Dependence of equilibrium constant on temperature and pressure
Core concepts (9)
  • Laws of Thermodynamics
  • Thermodynamic Functions and Relations
  • Gibbs-Helmholtz and Maxwell Relations
  • Criteria of Spontaneity and Equilibrium
  • Chemical Potential and Partial Molar Quantities
  • Fugacity and Activity
  • Ideal and Non-ideal Solutions
  • Chemical Equilibrium
  • Temperature and Pressure Dependence of Equilibrium
Related concepts (6)
  • Standard States
  • Thermochemistry
  • Absolute Entropy
  • Gibbs-Duhem Equation
  • Thermodynamics of Mixing
  • Raoult's Law and Henry's Law

Phase Rule and Phase Stability unit_07

Syllabus
Phase rule, Clausius-Clapeyron equation, Phase diagram of one component systems (CO2, H2O, S), two component systems (liquid-vapour, liquid-liquid, solid-liquid), Fractional distillation, Azeotropes and eutectics
Core concepts (8)
  • Phase Rule
  • Clausius-Clapeyron Equation
  • One-Component Phase Diagrams
  • Two-Component Liquid-Vapor Systems
  • Two-Component Liquid-Liquid Systems
  • Two-Component Solid-Liquid Systems
  • Azeotropes
  • Eutectics
Related concepts (6)
  • Triple Point and Critical Point
  • Fractional Distillation
  • Vapor Pressure Curves
  • Congruent and Incongruent Melting
  • Lever Rule
  • Degrees of Freedom

Phase Rule and Phase Stability unit_07_concept

Syllabus
Phase rule, Clausius-Clapeyron equation, Phase diagram of one component systems (CO2, H2O, S), two component systems (liquid-vapour, liquid-liquid, solid-liquid), Fractional distillation, Azeotropes and eutectics
Core concepts (8)
  • Phase Rule
  • Clausius-Clapeyron Equation
  • One-Component Phase Diagrams
  • Two-Component Liquid-Vapor Systems
  • Two-Component Liquid-Liquid Systems
  • Two-Component Solid-Liquid Systems
  • Azeotropes
  • Eutectics
Related concepts (6)
  • Triple Point and Critical Point
  • Fractional Distillation
  • Vapor Pressure Curves
  • Congruent and Incongruent Melting
  • Lever Rule
  • Degrees of Freedom

Ionic Equilibrium and Electrochemistry unit_08

Syllabus
Ionic mobility and conductivity. Debye-Hückel limiting law. Debye-Hückel-Onsager equation. Standard electrode potentials and electrochemical cells. Nernst Equation and its application, relationship between Electrode potential and thermodynamic quantities, Potentiometric and conductometric titrations.
Core concepts (10)
  • Ionic mobility
  • Conductivity of electrolyte solutions
  • Debye-Hückel limiting law
  • Debye-Hückel-Onsager equation
  • Standard electrode potentials
  • Electrochemical cells
  • Nernst equation
  • Electrode potential–thermodynamics relationship
  • Potentiometric titrations
  • Conductometric titrations
Related concepts (9)
  • Transport number
  • Kohlrausch’s law of independent migration
  • Ionic strength
  • Activity and activity coefficient
  • Ionic atmosphere
  • Liquid junction potential and salt bridge
  • Reference electrodes
  • pH measurement
  • Cell EMF measurement

Ionic Equilibrium and Electrochemistry unit_08_concept

Syllabus
Ionic mobility and conductivity. Debye-Hückel limiting law. Debye-Hückel-Onsager equation. Standard electrode potentials and electrochemical cells. Nernst Equation and its application, relationship between Electrode potential and thermodynamic quantities, Potentiometric and conductometric titrations.
Core concepts (10)
  • Ionic mobility
  • Conductivity of electrolyte solutions
  • Debye-Hückel limiting law
  • Debye-Hückel-Onsager equation
  • Standard electrode potentials
  • Electrochemical cells
  • Nernst equation
  • Electrode potential–thermodynamics relationship
  • Potentiometric titrations
  • Conductometric titrations
Related concepts (9)
  • Transport number
  • Kohlrausch’s law of independent migration
  • Ionic strength
  • Activity and activity coefficient
  • Ionic atmosphere
  • Liquid junction potential and salt bridge
  • Reference electrodes
  • pH measurement
  • Cell EMF measurement

Statistical Thermodynamics unit_09

Syllabus
Statistical thermodynamics- micro canonical, canonical and grand canonical ensembles, Boltzmann distribution, partition functions and thermodynamic properties.
Core concepts (6)
  • Microcanonical ensemble
  • Canonical ensemble
  • Grand canonical ensemble
  • Boltzmann distribution
  • Partition function
  • Thermodynamic properties from statistics
Related concepts (7)
  • Microstates and macrostates
  • Phase space and density of states
  • Ensemble averages and ergodic hypothesis
  • Statistical definition of entropy
  • Stirling approximation
  • Identical particles and indistinguishability
  • Classical versus quantum statistics

Statistical Thermodynamics unit_09_concept

Syllabus
Statistical thermodynamics- micro canonical, canonical and grand canonical ensembles, Boltzmann distribution, partition functions and thermodynamic properties.
Core concepts (6)
  • Microcanonical ensemble
  • Canonical ensemble
  • Grand canonical ensemble
  • Boltzmann distribution
  • Partition function
  • Thermodynamic properties from statistics
Related concepts (7)
  • Microstates and macrostates
  • Phase space and density of states
  • Ensemble averages and ergodic hypothesis
  • Statistical definition of entropy
  • Stirling approximation
  • Identical particles and indistinguishability
  • Classical versus quantum statistics

Chemical Kinetics unit_10

Syllabus
Kinetics - Elementary, parallel, opposing and consecutive reactions. Steady state approximation. Mechanisms of complex reactions, Kinetics of polymerization. Catalysis concepts and enzyme catalysis. Kinetic isotope effects.
Core concepts (6)
  • Elementary Reactions
  • Complex Reaction Types
  • Steady State Approximation
  • Reaction Mechanisms
  • Catalysis
  • Kinetic Isotope Effects
Related concepts (6)
  • Rate Laws and Order
  • Activation Energy
  • Intermediates and Rate-Determining Steps
  • Polymerization Kinetics
  • Enzyme Kinetics
  • Collision Theory

Chemical Kinetics unit_10_concept

Syllabus
Kinetics - Elementary, parallel, opposing and consecutive reactions. Steady state approximation. Mechanisms of complex reactions, Kinetics of polymerization. Catalysis concepts and enzyme catalysis. Kinetic isotope effects.
Core concepts (6)
  • Elementary Reactions
  • Complex Reaction Types
  • Steady State Approximation
  • Reaction Mechanisms
  • Catalysis
  • Kinetic Isotope Effects
Related concepts (6)
  • Rate Laws and Order
  • Activation Energy
  • Intermediates and Rate-Determining Steps
  • Polymerization Kinetics
  • Enzyme Kinetics
  • Collision Theory

Introduction to Reaction Dynamics unit_11

Syllabus
Unimolecular reactions. Potential energy surfaces and classical trajectories, Concept of Saddle points, Transition state theory - Eyring equation, thermodynamic aspects
Core concepts (5)
  • Unimolecular Reactions
  • Potential Energy Surfaces (PES)
  • Saddle Points
  • Transition State Theory (TST)
  • Thermodynamic Aspects of TST
Related concepts (6)
  • Classical Trajectories
  • Reaction Coordinate
  • Activation Energy
  • Partition Functions
  • First-Order Phase Transitions in Kinetics
  • Comparison of TST to Other Theories

Introduction to Reaction Dynamics unit_11_concept

Syllabus
Unimolecular reactions. Potential energy surfaces and classical trajectories, Concept of Saddle points, Transition state theory - Eyring equation, thermodynamic aspects
Core concepts (5)
  • Unimolecular Reactions
  • Potential Energy Surfaces (PES)
  • Saddle Points
  • Transition State Theory (TST)
  • Thermodynamic Aspects of TST
Related concepts (6)
  • Classical Trajectories
  • Reaction Coordinate
  • Activation Energy
  • Partition Functions
  • First-Order Phase Transitions in Kinetics
  • Comparison of TST to Other Theories

Fast Reaction Kinetics unit_12

Syllabus
Fast reaction kinetics- relaxation and flow methods. Diffusion controlled reactions. Kinetics of photochemical and photo physical processes.
Core concepts (6)
  • Fast Reaction Kinetics
  • Relaxation Methods
  • Flow Methods
  • Diffusion-Controlled Reactions
  • Photochemical Kinetics
  • Photophysical Processes
Related concepts (8)
  • Reaction Timescales and Instrument Response
  • Transient Species and Relaxation to Equilibrium
  • Stopped-Flow Instrumentation
  • Smoluchowski Theory
  • Jablonski Diagram
  • Fluorescence Quenching and Stern–Volmer Analysis
  • Quantum Yield
  • Laser Flash Photolysis

Fast Reaction Kinetics unit_12_concept

Syllabus
Fast reaction kinetics- relaxation and flow methods. Diffusion controlled reactions. Kinetics of photochemical and photo physical processes.
Core concepts (6)
  • Fast Reaction Kinetics
  • Relaxation Methods
  • Flow Methods
  • Diffusion-Controlled Reactions
  • Photochemical Kinetics
  • Photophysical Processes
Related concepts (8)
  • Reaction Timescales and Instrument Response
  • Transient Species and Relaxation to Equilibrium
  • Stopped-Flow Instrumentation
  • Smoluchowski Theory
  • Jablonski Diagram
  • Fluorescence Quenching and Stern–Volmer Analysis
  • Quantum Yield
  • Laser Flash Photolysis

Surfaces and Interfaces unit_13

Syllabus
Surfaces and Interfaces - Physisorption and chemisorption. Langmuir, Freundlich and Brunauer–Emmett–Teller (BET) isotherms. Surface catalysis- Langmuir-Hinshelwood mechanism. Surface tension, viscosity. Self-assembly. Physical chemistry of colloids, micelles and macromolecules
Core concepts (8)
  • Physisorption and Chemisorption
  • Langmuir Isotherm
  • Freundlich Isotherm
  • BET Isotherm
  • Langmuir-Hinshelwood Mechanism
  • Surface Tension
  • Viscosity
  • Self-Assembly
Related concepts (8)
  • Adsorption Thermodynamics
  • Surface Coverage and Kinetics
  • Heterogeneous Surfaces
  • Interfacial Tensions
  • Surfactants and Amphiphiles
  • Colloids and Colloidal Stability
  • Micelle Formation
  • Macromolecular Solutions

Surfaces and Interfaces unit_13_concept

Syllabus
Surfaces and Interfaces - Physisorption and chemisorption. Langmuir, Freundlich and Brunauer–Emmett–Teller (BET) isotherms. Surface catalysis- Langmuir-Hinshelwood mechanism. Surface tension, viscosity. Self-assembly. Physical chemistry of colloids, micelles and macromolecules
Core concepts (8)
  • Physisorption and Chemisorption
  • Langmuir Isotherm
  • Freundlich Isotherm
  • BET Isotherm
  • Langmuir-Hinshelwood Mechanism
  • Surface Tension
  • Viscosity
  • Self-Assembly
Related concepts (8)
  • Adsorption Thermodynamics
  • Surface Coverage and Kinetics
  • Heterogeneous Surfaces
  • Interfacial Tensions
  • Surfactants and Amphiphiles
  • Colloids and Colloidal Stability
  • Micelle Formation
  • Macromolecular Solutions