| Course title | |||||
| 構造化学 [Structural Chemistry] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 2 | |
| Department | Year | 3～4 | Semester | Spring | |
| Course type | Spring | Course code | 023301 | ||
| Instructor(s) | |||||
| 尾﨑 弘行 [OZAKI Hiroyuki] | |||||
| Facility affiliation | Faculty of Engineering | Office | Email address | ||
| Course description |
| It will be shown in this course that knowledge on “group theory” sometimes helps you discuss the properties of molecules without complicated calculation. Next, using perturbation theory a time-dependent Schroedinger equation will be solved approximately to obtain formulae, which serve as a foundation for the interpretation of various spectra arising from rotational, vibrational or electronic transitions. Then the principles of experimentally investigating the detailed structures of molecules (e.g. symmetry, bond length, orbital energy, bonding nature) will be introduced individually. |
| Expected Learning |
|
Learners who successfully complete this course will be able to (1) classify molecules according to the symmetries and, hence, (a) promptly decide if an important integral must be zero upon examining orbital interaction or spectroscopic transition; (b) construct the MOs of polyatomic molecules using symmetry adopted linear combinations; (c) identify the symmetry species of a normal mode, and decide which modes are infrared or Raman active; (2) grasp the concept of perturbation theory and the process of formulating transition moments; (3) understand the theoretical backgrounds of various spectroscopies and obtain information on the geometric and electronic structures of molecules from the spectra. |
| Course schedule |
|
Part 1 Group Theory (Chapter 12) Week 1 Significance of group theory in chemistry; Symmetry operation; Symmetry element; Point group; Symmetry classification of molecules (1). Week 2 Symmetry classification of molecules (2). Learners are encouraged to use all the knowledge they have so far acquired to determine the point groups of various molecules. Week 3 Group properties; Mathematical definition of a group; Representative of operation; Matrix representation; Representation of group multiplication; Trace; Characters and classes. Week 4 Block-diagonal form; Irreducible and reducible representation; Character table; Symmetry species; Symmetry properties of functions and rotations; Transformation of p AOs; reduction of a representation to the direct sum of irreducible representations. Week 5 Criteria for vanishing integrals; Decomposition of a direct product; Allowed or forbidden electric dipole transition of an electron in an MO to another MO; Projection operator; Symmetry-adapted linear combinations (SALC). Week 6 Construction of MOs for various XYn type molecules. Preparation of SALCs for Yn (= MOs of ring-shaped Yn type molecules); Application of orbital interaction rules to the AOs of X and the SALCs spanning the same irreducible representation (belonging to the same symmetry species). Part 2 Perturbation Theory (Chapter 9, Sections 9 and 10; Chapter 13, Section 2) Week 7 Time-independent (non-degenerate) perturbation theory. First-order correction to the energy and wavefunction; Second-order correction to the energy. Week 8 Time-dependent perturbation theory to investigate interaction between the electromagnetic field and the molecule. Variation of constants: Time-dependent linear combination of time-dependent unperturbed states; Transition probability and rate; Fermi’s golden rule. Week 9 Einstein transition probabilities. Einstein coefficient of stimulated absorption, stimulated emission, and spontaneous emission; Transition dipole moment; Population of the upper and the lower state. Part 3 Molecular Spectroscopy (Chapters 13 and 14) Week 10 Electromagnetic spectrum and classification of the spectral regions; Spectral linewidth; Pure rotational transition of diatomic molecules: Moment of inertia, Rotational constant, Rotational term, Selection rules, Appearance of rotational spectra, Line spacing, Determination of bond length. Week 11 Pure rotational transition of symmetric rotators; Stark effect and permanent electric dipole moment; Raman process: Rayleigh scattering and Raman scattering, Stokes lines and anti-Stokes lines, Selection rules and appearance of rotational Raman spectra. Week 12 Vibrations of diatomic molecules. Energy levels; Selection rules for a harmonic oscillator; Anharmonicity; Vibration-rotation spectra: Spectral branches, Determination of bond length; Vibrational Raman spectra and branches. Week 13 Vibrations of polyatomic molecules. Normal modes; Normal coordinates; Vibrational selection rules; Symmetry aspects of molecular vibrations: Identifying the symmetry species of a normal mode, Infrared or Raman active normal modes, Exclusion rule. Week 14 Characteristics of electronic transitions. Selection rules for the electronic spectra; Vibrational structure: Vertical transition, Franck-Condon factor; d-d transition; Vibronic transition; Charge-transfer transition; π*←π and π*←n transition. Week 15 Fates of electronically excited states. Fluorescence and phosphorescence; Vibrational structure. Photoelectron spectroscopy. Analysis of kinetic energy; Koopmans’ theorem; Orbital energy; Vibrational structure; Bonding, antibonding or nonbonding character of an MO; Chemical shift. |
| Prerequisites |
| Inorganic Chemistry I, Quantum Chemistry I, and Quantum Chemistry II |
| Required Text(s) and Materials |
| P. W. Atkins and J. de Paula, “Physical Chemistry” 8th (or 9th) Ed., Oxford, 2006 (2009). |
| References |
| Handouts will be distributed. |
| Assessment/Grading |
| Final examination (70 %); Quizzes, Reports, and Attendance (30 %). |
| Message from instructor(s) |
|
I hope you have a little patience with “mathematics” to marshal and understand important chemical facts. It makes almost no sense to learn the rules or numerical expressions by rote; please enjoy the process in which they are derived. The experience will enable you to approach various problems from the standpoint of structural chemistry. Depending on learners’ comprehension, explanation for certain items may be repeated; in that case the above mentioned schedule will be changed and some items will have to be omitted. |
| Course keywords |
| Molecular symmetry, Irreducible representation, Perturbation theory, Transition probability, Spectroscopy |
| Office hours |
| Friday (School day) 16:30 - 17:30 |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/22/2017 9:12:02 PM |