Quantum Chemistry I (GSC)

Lecture schedule 1st 10/2 lecture 2nd 10/9 lecture 3rd 10/16 lecture 4th 10/23 lecture 5th 10/30 lecture 6th 11/6 lecture 7th 11/20 lecture 8th 12/4 lecture 9th 12/11 lecture 10th 12/18 lecture 11th 12/25 lecture 12th 1/8 lecture 13th 1/15 lecture 14th 1/22 final exam Course syllabus: 1. Introduction - Energy and geometrical structure of molecules 1.1. Absorption and emission of light by dye molecules 1.2. Infrared radiation from the Earth 1.3. Microwave arriving from outer space 1.4. The hierarchical structure of molecular energy levels 1.5. The diffraction of electron beams and molecular structure 1.6. Solving Schrödinger’s equation - One-dimensional problem 1.7. Determination of the size of β-carotene molecule 2. Vibrating molecules 2.1. Quantum theory of molecular vibration 2.2. Morse oscillator 2.3. Schrödinger’s equation of a one-dimensional harmonic oscillator 2.4. Parity of the eigenfunctions of HO 2.5. Eigenfunctions of HO 2.6. Matrix elements 2.7. Selection rule and overtone transitions 2.8. Hermite operators 2.9. Creation and annihilation operators 2.10. First-order perturbation theory 2.11. Example of the first order perturbation theory 2.12. Hamiltonian matrix and its diagonalization 2.13. Inversion motion of ammonia and its double minimum potential 2.14. Far-infrared spectrum of cyclopentene 2.15. Morse oscillator 2.16. Birge-Sponer plot 2.17. Vibrational degrees of freedom 2.18. Normal mode vibration 2.19. Anharmonic couplings 3. Rotating molecules 3.1. Representation of Laplacian in spherical coordinate system 3.2. Rotational energy of diatomic molecules 3.3. Rotational constant 3.4. Determination of the internuclear distance 3.5. Rotational Spectra of diatomic molecules 3.6. Angular momentum operators 3.7. Commutation relations 3.8. Eigenvalues of angular momentum operators 3.9. Eigenfunctions of angular momentum operators 3.10. Determination of the rotational constants of H^35Cl and H^37Cl 3.11. Isotope shift in the fundamental vibrational transition of HCl 4. Electronic structure of a hydrogen atom 4.1. Emission lines of hydrogen atoms 4.2. Radial wave functions of a hydrogen atom 4.3. Another approach for solving the radial Schrödinger equation 4.4. Radial wave functions of a hydrogen atom derived by the lowering operator 4.5. Derivation of the ionization potential of a hydrogen atom 4.6. Angular parts of the wave functions of a hydrogen atom

Lectures will be given using Power point slides. The slides will be distributed through ITC-LMS. Attendees are strongly encourage to participate in the lectures by asking questions or giving comments about the lecture materials. Report assignments will be assigned occasionally. The final exam will be given at the end of the course.

Grading is based on the final exam scores, report assignments, your contributions to the lectures.

Handouts will be distributed in each lecture.

“Quantum Mechanics of Molecular Structures” by K. Yamanouchi (Springer). “Molecular Quantum Mechanics” by P. W. Atkins and R. S. Friedman (Oxford University Press)

None.