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Supported by the "Program for Promoting High-Quality University Education," Department of Chemistry, School of Science started offering "Upgrade Seminar in Chemistry" to the second grade undergraduate students belonging to the Department in 2009. In the seminar, each student selects by himself a theme of the independent study to do self-learning using textbooks, monographs, and internet. The instructor and other students joining the seminar ask questions to the report of the independent study to help the student to prepare his presentation of the independent study. After self-learning of several weeks, each student makes a 10-minute oral presentation, and other students who join the seminar make questions to the presentation, which is a good experience for the student to improve the presentation skill. This seminar is a typical example of the "active learning" recommended for the high-quality university education.

We present the MCSCF version of density functional theory. Two sets of equations, which correspond to the CI and orbital relaxation respectively, are derived. An important feature is that the correlation potential of DFT for CI wavefunction and that for orbitals are different to each other. These relations ensure that a density yielded by a effective MCSCF solution also satisfies the Euler equation of DFT

For studying the group theoretical classification of the solutions of the density functional theory in relativistic framework, we propose quantum electrodynamical density-matrix functional theory (QED-DMFT). QED-DMFT gives the energy as a functional of a local one-body $4\times4$ matrix $Q(x)\equiv -$, where $\psi$ and $\bar{\psi}$ are 4-component Dirac field and its Dirac conjugate, respectively. We examine some characters of QED-DMFT. After these preparations, by using Q(x), we classify the solutions of QED-DMFT under O(3) rotation, time reversal and spatial inversion. The behavior of Q(x) under nonrelativistic and ultrarelativistic limits are also presented. Finally, we give plans for several extensions and applications of QED-DMFT., Comment: 20 pages, 2 figures