Quantum Chemistry I (GSC)

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 5. Electron scattering and electron diffraction and determination of geometrical structure of molecules 5.1. Two methods for determining geometrical structures of molecules 5.2. Quantum theory of electron scattering by atoms 5.3. Born approximation 5.4. Electron scattering by diatomic molecules 5.5. Effect of molecular vibration 5.6. Electron diffraction by polyatomic molecules 5.7. Molecular structural determination from a molecular scattering curve 5.8. Damping of sM(s) by the phase shifts in the scattering and by the molecular vibration 5.9. The shrinkage effect

Lecture

Attendance and examination at the end of the course.

“Quantum Mechanics of Molecular Structures” by K. Yamanouchi (Springer).

“Molecular Quantum Mechanics” by P. W. Atkins and R. S. Friedman (Oxford University Press)

None.