Quantum Chemistry and Spectroscopy
Teacher
Dr. Ashish Kumar Sahoo
Category
Core Courses
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Course Name : Quantum Chemistry and Spectroscopy
Code(Credit) : CUTM 1480 (3-2-1)
Course Objectives
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To impart knowledge about quantum mechanical principles and understanding as well as predicting different microscopic phenomena.
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To understand the covalent nature of bonding and their theoretical background and correlation to practical aspects.
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To have a sound understanding of different spectroscopic techniques and photochemistry.
Course Outcomes
| COs | Course outcomes | Mapping COs with POs (High-3, Medium-2, Low-1) |
| CO1 | Students will gain knowledge on different aspects of quantum chemistry and its applicability in different bonding behavior of atoms. | PO1 (3) |
| CO3 |
Develop skill to identify, predict and analyze different types of interactions of radiation with matter which is crucial for research purposes. |
PO1(3), PO3 (3). |
|
CO4 |
Gain problem-solving skills from spectroscopic data |
PO3(3) |
Course Syllabus
Module 1
Quantum Chemistry Postulates of quantum mechanics, quantum mechanical operators, Schrödinger equation and its application to free particle and “particle-in-a-box” (rigorous treatment), quantization of energy levels, Heisenberg Uncertainty principle; wavefunctions, probability distribution functions, nodal properties, Extension to two and three dimensional boxes, separation of variables, degeneracy. Qualitative treatment of simple harmonic oscillator model of vibrational motion: Setting up of Schrödinger equation and discussion of solution and wavefunctions. Vibrational energy of diatomic molecules and zero-point energy.
Assignment 1: Discussion of Moorse Potential energy diagram from vibrating molecule
Angular momentum: Commutation rules, quantization of square of total angular momentum and z-component. Rigid rotator model of rotation of diatomic molecule. Schrödinger equation, transformation to spherical polar coordinates. Separation of variables. Spherical harmonics. Discussion of solution. Qualitative treatment of hydrogen atom and hydrogen-like ions: setting up of Schrödinger equation in spherical polar coordinates, radial part, quantization of energy (only final energy expression). Average and most probable distances of electron from nucleus.Setting up of Schrödinger equation for many-electron atoms (He, Li). Need for approximation methods. Statement of variation theorem and application to simple systems(particle-in-a-box, harmonic oscillator, hydrogen atom).
Assignment 2: Determination of energy of Hydrogen atom using Variation principle
Assignment 3: Apply Schrodinger's equation to He+ atom
Practice:
Eigen systems: Geometrical Interpretation (v-lab)
Geometry Optimization using ab-initio quantum calcuations (v-lab)
Module 2
Chemical bonding: Covalent bonding, valence bond and molecular orbital approaches, LCAO-MO treatment of H2+. Bonding and antibonding orbitals. Qualitative extension to H2. Comparison of LCAO-MO and VB treatments of H2 (only wavefunctions, detailed solution not required) and their limitations.
Refinements of the two approaches (Configuration Interaction for MO, ionic terms in VB). Qualitative description of LCAO-MO treatment of homonuclear and heteronuclear diatomic molecules (HF, LiH). Localised and non-localised molecular orbitals treatment of triatomic (BeH2, H2O) molecules. Qualitative MO theory and its application to AH2 type molecules.
Assignment 4: Apply MO theory to AH2 type molecules e.g. CO2.
Module 3
Molecular Spectroscopy:
Interaction of electromagnetic radiation with molecules and various types of spectra; Born-Oppenheimer approximation.
Rotation spectroscopy: Selection rules, intensities of spectral lines, determination of bond lengths of diatomic and linear triatomic molecules, isotopic substitution.
Assignment 5: Determine the isotopic mass of carbon using IR data.
Module 4
Vibrational spectroscopy: Classical equation of vibration, computation of force constant, amplitude of diatomic molecular vibrations, anharmonicity, Morse potential, dissociation energies, fundamental frequencies, overtones, hot bands, degrees of freedom for polyatomic molecules, modes of vibration, the concept of group frequencies. Vibration-rotation spectroscopy: diatomic vibrating rotator, P, Q, R branches.
Assignment 6: Assign group frequencies to different functions groups of molecules
Practice:
Calculation of Vibrational Frequency of Molecules and Visualization of Normal Modes (V-lab)
Instrumentation and working principles of solutions infra red (IR) or (vibrational) spectroscopy (v-lab)
Module 5
Raman and Electronic Spectroscopy
Raman spectroscopy: Qualitative treatment of Rotational Raman effect; Effect of nuclear spin, Vibrational Raman spectra, Stokes and anti-Stokes lines; their intensity difference, rule of mutual exclusion.
Electronic spectroscopy: Franck-Condon principle, electronic transitions, singlet and triplet states, fluorescence and phosphorescence, dissociation and predissociation, calculation of electronic transitions of polyenes using free electron model.
Assignment 7: Explain why the intensity of transition are different in spite of equal probability among energy levels.
Assignment 8:Exemplify the concept of predissociation from Franck-Condon's principle
Practice:
Study the 200-500 nm absorbance spectra of KMnO4 and K2Cr2O7 (in 0.1 M H2SO4) and determine the λmax Calculate the energies of the two transitions in different units (J mol-1, kJ mol-1, cm-1, eV).
Study the pH-dependence of the UV-Vis spectrum (200-500 nm) of K2Cr2O7.
Record the 200-350 nm UV spectra of the given compounds (acetone, acetaldehyde,2-propanol, acetic acid) in water. Comment on the effect of structure on the UVspectra of organic compounds.
Module 6
Nuclear Magnetic Resonance (NMR) spectroscopy: Principles of NMR spectroscopy, Larmor precession, chemical shift and low resolution spectra, different scales, spin-spin coupling and high resolution spectra, interpretation of PMR spectra of organic molecules.
Electron Spin Resonance (ESR) spectroscopy: Its principle, hyperfine structure, ESR of simple radicals.
Assignment 9: Deduce the ESR spectrum of methyl radical
Practice:
Nuclear magnetic resosnace spectrocopy and evaulation of simple 1H NMR spectra of select organic compounds (v-lab)
Module 7
Photochemistry
Characteristics of electromagnetic radiation, Lambert-Beer’s law and its limitations, physicalsignificance of absorption coefficients.
Laws, of photochemistry, quantum yield, actinometry, examples of low and high quantum yields, photochemical equilibrium and the differentialrate of photochemical reactions, photosensitised reactions, quenching. Role of photochemical reactions in biochemical processes, photostationary states, chemiluminescence.
Assignment 10: Deduce the kinetics of photochemical reaction between hydrogen and chlorine
Practice:
Verify Lambert-Beer’s law and determine the concentration of CuSO4/KMnO4/K2Cr2O7 in a solution of unknown concentration
Determine the amount of iron present in a sample using 1,10-phenathroline.
Determine the dissociation constant of an indicator (phenolphthalein).
Study the kinetics of interaction of crystal violet/ phenolphthalein with sodium hydroxide.
Reference Books:
Banwell, C. N. & McCash, E. M. Fundamentals of Molecular Spectroscopy 4th Ed. Tata McGraw-Hill: New Delhi (2006).
Chandra, A. K. Introductory Quantum Chemistry Tata McGraw-Hill (2001).
House, J. E. Fundamentals of Quantum Chemistry 2nd Ed. Elsevier: USA (2004).
Lowe, J. P. & Peterson, K. Quantum Chemistry, Academic Press (2005).
Kakkar, R. Atomic & Molecular Spectroscopy, Cambridge University Press (2015).
Session Plan
Session 1
Postulates of quantum mechanics, quantum mechanical operators,
Session 2
Schrödinger equation and its application to free particle and “particle-in-a-box” (rigorous treatment), quantization of energy levels.
Session 3
Heisenberg Uncertainty principle; wavefunctions,
Heisenberg's unertainity principle
https://www.youtube.com/watch?v=MBnnXbOM5S4
Session 4
probability distribution functions, nodal properties,
Session 5
Extension to two and three dimensional boxes, separation of variables, degeneracy.
Session 6
Qualitative treatment of simple harmonic oscillator model of vibrational motion: Setting up of Schrödinger equation and discussion of solution and wavefunctions.
https://www.youtube.com/watch?v=T7fRGXc9SBI
Session 7
Vibrational energy of diatomic molecules and zero-point energy.
Session 8
Assignment 1: Flip class (1 hour)
Moorse potential energy curve and explanation
Session 9
Angular momentum: Commutation rules, quantization of square of total angular momentum and z-component.
Session 10
Rigid rotator model of rotation of diatomic molecule. Schrödinger equation, transformation to spherical polar coordinates.
Session 11
Separation of variables. Spherical harmonics. Discussion of solution.
Session 12
Qualitative treatment of hydrogen atom and hydrogen-like ions: setting up of Schrödinger equation in spherical polar coordinates, radial part, quantization of energy (only final energy expression). Average and most probable distances of electron from nucleus.
Session 13
Setting up of Schrödinger equation for many-electron atoms (He, Li).
Session 14
Need for approximation methods. Statement of variation theorem and application to simple systems(particle-in-a-box, harmonic oscillator, hydrogen atom).
http://vallance.chem.ox.ac.uk/pdfs/VariationPrincipleNotes.pdf
Session 15 (Assignment 2: Flip Class) 1 hour
Determination of energy of Hydrogen atom using Variation principle
Session 16 (Assignment 3: Flip Class) 1 hour
Apply Schrodinger's equation to He+ atom
Session 17: Practice 1 (2 hours)
Geometry Optimization using ab-initio quantum calcuations (v-lab)
V lab link:
Session 18
Chemical bonding: Covalent bonding, valence bond and molecular orbital approaches.
https://www.youtube.com/watch?v=g-tE6MN-wrE
https://www.youtube.com/watch?v=vHXViZTxLXo
Session 19
Session 20
Session 21
Comparison of LCAO-MO and VB treatments of H2 (only wavefunctions, detailed solution not required) and their limitations.
Session 22
Refinements of the two approaches (Configuration Interaction for MO, ionic terms in VB). Qualitative description of LCAO-MO treatment of homonuclear and heteronuclear diatomic molecules (HF, LiH). Localised and non-localised molecular orbitals treatment of triatomic (BeH2, H2O) molecules.
Session 23:(Assignment 4: Flip Class) (1 hour)
Apply MO theory to AH2 type molecules e.g. CO2.
Session 24
Molecular Spectroscopy:
Interaction of electromagnetic radiation with molecules and various types of spectra; Born-Oppenheimer approximation.
Session 25
Rotation spectroscopy: Selection rules, intensities of spectral lines, determination of bond lengths of diatomic and linear triatomic molecules, isotopic substitution.
Session 26 (Assignment 5: Flip Class) (1 hour)
Determine the isotopic mass of carbon using IR data.
Session 27
Vibrational spectroscopy: Classical equation of vibration, computation of force constant,amplitude of diatomic molecular vibrations, anharmonicity, Morse potential, dissociation energies,
https://ocw.mit.edu/courses/chemistry/5-61-physical-chemistry-fall-2007/lecture-notes/lecture35.pdf
Session 28
fundamental frequencies, overtones, hot bands, degrees of freedom for polyatomic molecules, modes of vibration, concept of group frequencies. Vibration-rotation spectroscopy: diatomic vibrating rotator, P, Q, R branches.
https://ocw.mit.edu/courses/chemistry/5-61-physical-chemistry-fall-2007/lecture-notes/lecture35.pdf
Session 29: (Assignment 6: Flip Class) (1 hour)
Identification the group frequencies of functional groups of given molecules
Session 30 Practice 2 (2 hours)
Calculation of Vibrational Frequency of Molecules and Visualization of Normal Modes
V lab link:
Session 31: Practice 3 (2 hours)
Instrumentation and working principles of solutions infra red (IR) spectroscopy(v-lab)
V lab link:
Session 32
Raman spectroscopy: Qualitative treatment of Rotational Raman effect; Effect of nuclear spin, Vibrational Raman spectra, Stokes and anti-Stokes lines; their intensity difference, rule of mutual exclusion.
Session 33
Electronic spectroscopy: Franck-Condon principle, electronic transitions, singlet and triplet states, fluorescence and phosphorescence, dissociation and predissociation, calculation of electronic transitions of polyenes using free electron model.
Session 34: (Assignment 7: Flip Class) (1 hour)
Explain why the intensity of transition are different in spite of equal probability among energy levels.
Session 35: (Assignment 8: Flip Class) (1 hour)
Exemplify the concept of predissociation from Franck-Condon's principle
Session 36: Practice 4 (2 hours)
Study the 200-500 nm absorbance spectra of KMnO4 and K2Cr2O7 (in 0.1 M H2SO4) and determine the λmax Calculate the energies of the two transitions in different units (J mol-1, kJ mol-1, cm-1, eV).
Session 37: Practice 5 (2 hours)
pH effects on absorption spectra: pKa determination by spectrophotometric method
V Lab link:
Session 38: Practice 6 (2 hours)
Record the 200-350 nm UV spectra of the given compounds (acetone, acetaldehyde,2-propanol, acetic acid) in water. Comment on the effect of structure on the UVspectra of organic compounds.
Session 39
Nuclear Magnetic Resonance (NMR) spectroscopy: Principles of NMR spectroscopy, Larmor precession, chemical shift and low resolution spectra, different scales, spin-spin coupling and high resolution spectra, interpretation of PMR spectra of organic molecules.
https://www.youtube.com/watch?v=ywR6aLpfjl0
Session 40
Electron Spin Resonance (ESR) spectroscopy: Its principle, hyperfine structure, ESR of simple radicals.
Session 41: (Assignment 9: Flip Class) (2 hours)
Deduce the ESR spectrum of methyl radical
Session 42: Practice 7 (2 hours)
Nuclear magnetic resosnace spectrocopy and evaulation of simple 1H NMR spectra of select organic compounds (v-lab)
V lab link:
Session 43
Characteristics of electromagnetic radiation, Lambert-Beer’s law and its limitations, physicalsignificance of absorption coefficients.
Session 44
Laws, of photochemistry, quantum yield, actinometry, examples of low and high quantum yields, photochemical equilibrium and the differential rate of photochemical reactions,
Session 45
photosensitised reactions, quenching. Role of photochemical reactions in biochemical processes, photostationary state.
Session 47 (Assignment 10: Flip Class) (2 hours)
Deduce the kinetics of photochemical reaction between hydrogen and chlorine.
Session 48: Practice 8 (2 hours)
Verify Lambert-Beer’s law and determine the concentration of
CuSO4/KMnO4/K2Cr2O7 in a solution of unknown concentration
Session 49: Practice 9 (2 hours)
Study the kinetics of iodination of propanone in acidic medium.
Session 50: Practice 10 (2 hours)
Determine the amount of iron present in a sample using 1,10-phenathroline.
Session 51: Practice 11 (2 hours)
Determine the dissociation constant of an indicator (phenolphthalein).
Session 52: Practice 12 (2 hours)
Study the kinetics of interaction of crystal violet/ phenolphthalein with sodium hydroxide.
Case Studies
Case Studies
Our Main Teachers
Dr. Ashish Kumar Sahoo has 3 years of teaching experience in undergraduate as well as postgraduate level. His areas of interest are in Advanced Physical Chemistry and Material Chemistry. Dr. Sahoo has a number of international publications. His research interest semiconducting materials in both pure as well as interstitially dopped and making use of simple […]