This course is designed to provide students the opportunity for learning fundamental aspects of quantum chemistry, with which we can understand all the chemical phenomena in terms of microscopic fundamental laws.
The course is organized to develop students' abilities in the following four subjects:
1) Understanding fundamentals of quantum mechanics and the characteristics of wave functions,
2) Utilizing the quantum-mechanical description of 1D/2D/3D motion of particles.
3) Understanding the motion of electron in atoms in terms of the aforementioned fundamental knowledge in quantum mechanics,
4) Utilizing approximation methods in quantum mechanics to establish the quantum-mechanical description of electronic states and chemical bonding in molecules.
Students will acquire the following two skills by taking this course.
1) Gain an understanding of the basic principles of quantum mechanics, and apply them appropriately to basic problems.
2) Gain a basic understanding of state of motion in atoms and molecules, and chemical bonding based on the knowledge of quantum mechanics.
Wave functions, Quantum numbers, Electronic states, Molecular orbitals, Chemical bonding
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
Towards the end of class, students are given exercise problems related to what is taught on that day to solve.
|Course schedule||Required learning|
|Class 1||The old quantum theory and the wave equation||Describe the hypotheses on photon by Planck and matter waves by de Broglie. Calculate the energy of the hydrogen atom by using the Bohr condition.|
|Class 2||Fundamentals of quantum mechanics||Explain eigenfunctions and eigenvalues. Show that the eigenvalues of Hermitian are real numbers. Show the representation for an averaged value of an observable.|
|Class 3||One-dimensional motion of particles||Derive the eigenfunctions and eigenvalues of a particle in a one-dimensional box. Calculate the expectation values of the position and the momentum of the particle.|
|Class 4||The harmonic oscillator||Show the representation for an eigenvalue of the harmonic oscillator. Draw schematically the wave functions of the harmonic oscillator.|
|Class 5||Rotational motion and the angular momentum||Show the representation for eigenvalues of the angular momentum. Draw schematically the spherical harmonics.|
|Class 6||Motion of the electron in the hydrogen atom||Explain the quantum numbers for the motion of the electron in the hydrogen atom. Draw schematically its radial wave functions for the hydrogen atom.|
|Class 7||Many-electron atoms||Explain the Pauli's exclusion principle. Explain the difference between the energy of a many-electron atom and that of a hydrogen atom. Show the electronic configuration of atoms from the first to forth laws.|
|Class 8||Approximation methods in quantum mechanics 1: Variational method||Explain the variational principle. Calculate energies by using Ritz's variational method.|
|Class 9||Approximation methods in quantum mechanics 2: Perturbation theory||Show the energy correction term by the second-order perturbation theory. Show a perturbed wave function up to first-order.|
|Class 10||The hydrogen molecule ion||Explain the LCAO approximation. Explain the Coulomb and resonance integrals.|
|Class 11||The hydrogen molecule and molecular orbitals||Draw schematically two molecular orbitals of a hydrogen molecule. Explain what the singlet and triplet are.|
|Class 12||Electronic states of diatomic molecules||Show the electronic configuration of homo-nuclear diatomic molecules with atoms in the second law. Show the general trend in the dipole moments of hetero-nuclear diatomic molecules.|
|Class 13||Electronic states of polyatomic molecules||Show the electronic configuration of XH2 molecules with X being a atom in the second law. Explain the relation between photo-electron spectrum and the molecular orbitals.|
|Class 14||Hybrid orbitals and chemical bonding||Show the sp, sp2, sp3 hybrid orbitals in terms of atomic orbitals of the constituent. Explain the aromaticity by using the Huckel approximation.|
|Class 15||Chemical reactivity||Explain the importance of the molecular orbital symmetry in the polymerization reaction of unsaturated hydrocarbons. Estimate the deformation of the molecular orbitals by the substitution effect.|
Physical chemistry: A molecular approach,by D. A. McQuarrie and J. D. Simon, The University Science Books
Quantum chemistry, by K. Ohno, Iwanami Books
Students will be assessed on their understanding of fundamentals of quantum mechanics and their application to atomic/molecular systems.
Students' course scores are based on the final exam (50%) and exercise problems (50%).