# Quantum Chemistry and Spectroscopy

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# Code(Credit) : CUTM 1480 (3-2-1)

## Learning Outcomes

After completion of the course, the students will able to

## 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 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://ocw.mit.edu/courses/physics/8-03sc-physics-iii-vibrations-and-waves-fall-2016/syllabus/MIT8_03SCF16_Text_Ch1.pdf

## 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.

https://ocw.mit.edu/courses/physics/8-01sc-classical-mechanics-fall-2016/week-11-angular-momentum/32.2-calculating-angular-momentum

## Session 10

Rigid rotator model of rotation of diatomic molecule. Schrödinger equation, transformation to spherical polar coordinates.

https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec05.pdf

## 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.

https://ocw.mit.edu/courses/chemistry/5-112-principles-of-chemical-science-fall-2005/video-lectures/lecture-6-schroedinger-equation-for-h-atom/

## 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 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.

linearcombinationoftomicorbitals

## 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.

https://ocw.mit.edu/courses/chemistry/5-80-small-molecule-spectroscopy-and-dynamics-fall-2008/lecture-notes/08s_elecconfigs.pdf

## Session 25

Rotation spectroscopy: Selection rules, intensities of spectral lines, determination of bond lengths of diatomic and linear triatomic molecules, isotopic substitution.

Rotational spectra

## 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

http://ccnsb04-iiith.vlabs.ac.in/exp5/Introduction.html?domain=Computer%20Science&lab=Computer%20Systems%20Organization%20lab

## Session 31: Practice 3 (2 hours)

Instrumentation and working principles of solutions infra red (IR) spectroscopy(v-lab)

http://ccnsb06-iiith.vlabs.ac.in/exp7/Introduction.html?domain=%20Chemical%20Sciences&lab=Physical%20Chemistry%20Lab

## 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.

Raman spectroscopy 1

Raman spectroscopy 2

## 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.

https://ocw.mit.edu/courses/chemistry/5-61-physical-chemistry-fall-2017/lecture-notes/MIT5_61F17_lec30_lec31.pdf

## 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

http://mas-iiith.vlabs.ac.in/exp9/Introduction.html?domain=%20Chemical%20Sciences&lab=ABSORPTION%20SPECTROSCOPY%20VIRTUAL%20LAB

## 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://ocw.mit.edu/courses/chemistry/5-61-physical-chemistry-fall-2017/lecture-notes/MIT5_61F17_lec30_lec31.pdf

## 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)

http://ccnsb06-iiith.vlabs.ac.in/exp5/Introduction.html?domain=%20Chemical%20Sciences&lab=Physical%20Chemistry%20Lab

## Session 43

Characteristics of electromagnetic radiation, Lambert-Beer’s law and its limitations, physicalsignificance of absorption coefficients.

Beer-Lamberts law

https://ocw.mit.edu/courses/chemistry/5-61-physical-chemistry-fall-2017/lecture-videos/electronic-spectroscopy-and-photochemistry/

## Session 44

Laws, of photochemistry, quantum yield, actinometry, examples of low and high quantum yields, photochemical equilibrium and the differential rate of photochemical reactions,

photochemistry 1

photochemistry 2

actinometry

Kinetics_of_photochemical_reactions

## Session 45

photosensitised reactions, quenching.  Role of photochemical reactions in biochemical processes, photostationary state.

photosensitized

Kinetics_of_photochemical_reactions

https://ocw.mit.edu/courses/chemistry/5-61-physical-chemistry-fall-2017/lecture-videos/electronic-spectroscopy-and-photochemistry/

## 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 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.