In non-relativistic fermionic systems, spin is a vital property. Approximate ground state wave functions can often violate spin-symmetry by relaxing spin constraints to provide additional electron correlation effects essential for describing multi-determinant systems such as transition metal complexes. Symmetry breaking, however, comes at the price of losing good quantum numbers and deteriorating molecular properties. We describe the projection technique to restore the lost symmetry, which can be combined with traditional electronic structure theories, delivering higher accuracy in the treatment of dynamical and static electron correlations.

Heterogeneous systems consisting with nanomaterials (hereafter referred to as nanointerface systems) are extensively investigated in relation to interests in batteries, photo-and electro-catalysts, solar cells, and optoelectronic devices. To efficiently design these functional materials, it is required to obtain atomic-scale insights into the response mechanism to light and voltage bias. However, first-principles theoretical studies on nanointerface systems under light and voltage bias have been scarcely performed because of two problems. Firstly, a huge computational cost is needed to calculate a nanointerface system with a first-principles computational method. Secondly, it is difficult to theoretically describe electronic structure explicitly considering light and voltage bias. In this review, we report the recent progress in our theoretical and computational studies on nanointerface systems. The optical response of various systems such as a gold-thiolate nanocluster and a MoS₂-graphene heterostructure has been simulated using a first-principles computational method for carrying out massively parallel calculations of photoexcited electron dynamics. The computational results have been analyzed with theoretical formulas for revealing the role of the interface region in the optical response. We have also developed an original theoretical method for investigating electrode systems. The developed method has been used to elucidate the mechanism of the electronic structure change inherent in nanointerface systems by applying bias voltage, which causes the electronic charging and generates the electric field from a gate electrode.

Chiral vibrational sum frequency generation (VSFG) spectroscopy has attracted much attention as a new tool for studying chirality with high sensitivity. Recently, we have developed heterodyne-detected chiral VSFG (HD-chiral VSFG) spectroscopy for the first time, which enables us to determine the phase of the electric field of a chiral VSFG signal. We show that HD-chiral VSFG spectroscopy is capable of the detection and distinction of chirality even from monolayers. In addition, we have studied fundamental aspects of chiral VSFG such as electronic resonance effects and the spatial origin of the signals by using HD-chiral VSFG spectroscopy. This review introduces the principle of chiral VSFG, HD-chiral VSFG spectrometer we have constructed, and its applications to not only bulk samples but also interfaces including monolayers and thin films.

Interfacial phenomena, in which water molecules are deeply involved, are critical subjects in basic and applied research in a wide range of fields, including physics, chemistry, and biology. In the symmetry-breaking interfacial systems, molecular orientation is key structural parameter that determines the functional properties of water molecules. However, orientation of water molecules, i.e. configuration of hydrogens, in the interfacial hydrogen-bond network has been extremely difficult to be investigated by traditional structure-analysis techniques such as electron diffraction, grazing X-ray scattering and even scanning probe microscopy, because hydrogen has only a single electron and responds extremely weakly to the probes of these techniques; thus, the determination of molecular orientation of interfacial water systems has been an experimental challenge. We have recently tackled the challenges of elucidating the orientational structures of water molecules on metal surfaces by using cutting-edge nonlinear optical spectroscopy, i.e. heterodyne-detected sum-frequency generation (HD-SFG) spectroscopy. In this review article, brief descriptions of the basic concept of SFG spectroscopy as a hydrogen-configuration sensitive probe are followed by overviews of our current understanding of the adsorption geometry and rotational ordering of water molecules on representative metal surfaces and ice-film surfaces.

In the graph theory, it is known that the line graphs of the K₄ and diamond lattices are the hyper-kagome and pyrochlore lattices, respectively. The hyper-kagome and pyrochlore lattices are possible frustration lattices, because they consist of a triangular or tetrahedral component. In the present article, we describe the crystal structures and physical properties of a molecule-based K₄, (–)-NDI-Δ, and a molecule-based diamond, bpBDTDA. The line graph transformation reveals a spin frustration in (–)-NDI-Δ, which results in a spin liquid ground state, and a bond frustrations in bpBDTDA, which induces a stepwise and inhomogeneous lattice dimerization.

In recent years molecular spectroscopy of condensed phase has made remarkable progress partly due to the advances in its instrumentation and partly due to the development of quantum chemistry. This review paper aims at outlining how quantum chemistry has contributed to the progress in molecular spectroscop for the last 15 years or so. This review covers a wide range of molecular spectroscopy from far-ultraviolet to far-infrared/terahertz spectroscopy and Raman spectroscopy. Thus, the recent development of both electronic spectroscopy and vibrational spectroscopy are involved in this review. This review puts some particular emphasis on anharmonic calculations and Cartesian coordinte tensor transfer (CCT) method. The latter is useful for calculating vibrational spectra of large molecules such as proteins and polymers with intemolecular interactions. In this review infrared spectroscopy and near-infrared spectroscopy offer good examples for demonstrating the usefulness of anharmoc calculations. Far-infrared/terafertz/low-frequency Raman spectroscopy and Raman optical activity provide interesting examples of application of CCT method.