| Course title | |||||
| 量子化学Ⅱ [Quantum ChemistryⅡ] | |||||
| Course category | technology speciality courses | Requirement | Credit | 2 | |
| Department | Year | 2～4 | Semester | 3rd | |
| Course type | 3rd | Course code | 022383 | ||
| Instructor(s) | |||||
| 尾﨑 弘行 [OZAKI Hiroyuki] | |||||
| Facility affiliation | Faculty of Engineering | Office | Email address | ||
| Course description |
| Atomic structure and chemical bonding, which were qualitatively treated without derivation of formulae in Inorganic Chemistry I, are discussed in this course on the basis of quantum theory. Following Quantum Chemistry I, learners accustom themselves to rules in the microscopic world, become familiar with the behavior of electrons in atoms, and then experience the usefulness of an important methodology to apply the quantum theory to molecules, i.e., molecular orbital approximation. |
| Expected Learning |
|
Learners who successfully complete this course will be able to (1) solve the Schroedinger equation of hydrogenic atoms; (2) understand the meaning of the orbital approximation for many-electron atoms; (3) classify the electronic states of an atom using term symbols; (4) extend orbital approximation to molecules; (5) derive rules for orbital interaction using the variation principle; (6) discuss molecular properties based on the Hueckel approximation. As for corresponding criteria in the diploma policy, refer to the curriculum maps. |
| Course schedule |
|
Part 1 Atomic Structure and Atomic Spectra (Chapter 9) (A) Preparation Week 1 Spectrum of atomic hydrogen; Schroedinger equation of a hydrogenic atom. (Some items studied in Quantum Chemistry I will be reviewed if necessary.) (B) How do we solve the Schroedinger equation for a hydrogenic atom? Week 2 Separation of the relative motion of the electron and the nucleus from the motion of the atom as a whole; Separation of angular and radial motion. Week 3 Transformation of the radial wave equation into associated Laguerre differential equation; Solutions (associated Laguerre polynomials) and quantization; Normalization of radial wavefunctions; Energy eigenvalues. Week 4 General expressions of radial functions; Atomic orbital (AO) obtained as the product of a radial function and a spherical harmonic; Real linear combinations and drawings of AOs (review); Mean radius and the most probable radius of an AO; Ionization energy; Spectroscopic transitions. (C) We cannot obtain the exact solutions of the Schroedinger equation for a many-electron atom. Week 5 Orbital approximation; Pauli principle and Slater determinant; Penetration and shielding; Hund’s maximum multiplicity rule and spin correlation; Self-consistent field procedure. (D) Energy levels in ordinary atoms are not given solely by the energies of the AOs; the electrons interact with one another in various ways. Week 6 Singlet and triplet state of helium metastable atoms; Splitting of the sodium D lines; Angular momentum and magnetic moment; Spin-orbit coupling; Clebsch-Gordan series. (E) A term symbol gives a detailed description of an electron configuration. Week 7 Schroedinger equation without spin-orbit interaction energy; LS term classifying the states by the total orbital angular and the total spin angular momentum quantum number (QN); Consideration of spin-orbit interactions by total angular momentum QN (Russell-Saunders coupling scheme). (F) Let’s derive term symbols for various configurations of atoms. Week 8 Complete set of microstates; Ground and excited state of carbon; Hund’s rules and the relative energies of terms; j-j coupling scheme; Selection rules. Week 9 Summary of atomic structure. Midterm Examination (90 minutes) Part 2 Electronic Structures of Molecules (Chapter 10) (G) Hydrogen molecular ion is the prototypical species of molecular orbital (MO) theory. Week 10 Born-Oppenheimer approximation; Schroedinger equation; Exact solution using spheroidal coordinates (will be mentioned briefly); Linear combination of AOs approximation; Variation principle; Derivation process of the energies and wavefunctions for the bonding and the antibonding MO. (H) Rules to construct MOs from two AOs of the same or different type(s) can be obtained by a slight modification. Week 11 One-to-one orbital interaction: Changes in orbital energies, Phase and ratio of orbital mixing; Two-to-one orbital interaction (will be mentioned briefly). (I) We can now resolve an issue left pending in Inorganic Chemistry I. Week 12 Homonuclear diatomic molecules of period 2 elements. Two-to-two interactions of 2s and 2p AOs; Inverted order of a π and a σ MO energy for N2 and O2; Term symbols classifying the electronic states. (J) The MOs of a larger molecule are obtained by solving the secular determinant. Week 13 Hueckel approximation; π-conjugated systems (1): MO energy and wavefunction, Total π-electron binding energy, Delocalization energy. Week 14 π-conjugated systems (2): π electron density and bond order; Transition and ionization energy. σ electronic systems comprising s or p AOs. (K) We can also construct MOs from those of the parts of the molecule. Week 15 π MOs of allyl radical and butadiene obtained without calculation; Infinite liner chain and band formation. |
| Prerequisites |
|
Related courses: Inorganic Chemistry I and Quantum Chemistry I In addition to 30 hours in the class, students are recommended to prepare for and revise the lectures, spending the standard amount of time as specified by the university and using the lecture handouts as well as the references. |
| Required Text(s) and Materials |
| P. W. Atkins and J. de Paula, “Physical Chemistry” 10th Ed., Oxford, 2014. |
| References |
| Handouts will be distributed. |
| Assessment/Grading |
|
Final examination (45 %); Midterm examination (45 %); Quizzes and Reports (10 %). (Questions are designed to assess the understanding of and the ability to explain the topics dealt in the lectures.） Grade distribution (FY2021): S 13 %, A 37 %, B 17 %, C 13 %, D 20 % Grade distribution (FY2020): S 9 %, A 31 %, B 40 %, C 9 %, D 11 % |
| Message from instructor(s) |
|
It is indispensable for you to have a discipline of this field explaining the structures and properties of chemical substances at the atomic or molecular level. Though you must get familiar with somewhat complicated equations to avoid hocus-pocus, I hope you will not reject quantum theory out of hand. It would be nice if you can check all the derivation of formulae with paper and pen, but please do not forget to examine the physical or chemical meanings of the results. 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 |
| Schroedinger equation, Wavefunction and energy, Atomic orbital, Molecular orbital, Variation principle. |
| Office hours |
| Friday (School day) 12:00 - 13:00 |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/3/2022 9:13:43 PM |