We have applied the fully variational molecular orbital (FVMO) method to systematically improve the values of energy-components, that is, the kinetic energy of electron and potential energy, as with that of total energy. The FVMO method enables us to describe accurate values of energy-components, since the quantum-mechanical Virial and Hellmann-Feynman theorems are completely satisfied due to the optimization of the exponents and centers in Gaussian-type functions (GTFs) basis sets. In the calculation of H₂ molecule, we have found that the energy components and total energy with FVMO method using only [6s] GTFs are actually improved more than those with the conventional MO using a much larger basis set including the multiple polarization functions of [6s3p2d1f]. Additionally, drastic improvement of virial ratios for several hydride molecules with the FVMO method is demonstrated in the current work. The energy-component analysis using the FVMO method would be a powerful tool to elucidate various chemical problems.

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Unpublished trial calculations for 2p state (²P) and 3d state (²D) using the fully variational molecular orbital (FVMO) method with only 1s-type Gaussian type functions (GTFs) as the basis set are reported. All calculations in this study have been performed by the FVMO program GAMERA augmented by ROHF part and C_2v symmetry consideration. Antisymmetric pairs of 1s-type GTFs have been optimized for the orbital exponents and the position of the orbital center simultaneously and it is found that the optimized exponents are approximately the same as but slightly larger than those in standard 2p-type GTF expansions in all cases (Table 3). Total energies (orbital energies) with both types of GTF expansions are nearly the same but those with antisymmetric pairs of 1s-type GTFs are slightly higher (Table 2). The trial for 3d orbital with the expansion of quadruple 1s-type GTFs was not successful. However, the present study implies that the FVMO method with only 1s-type GTFs as the basis set will be promising if the possibility, the advantage, and the implementation of the program are investigated.

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To elucidate the adequate molecular exponents for sp³-, sp²-, and sp-hybrid characters, we have performed the optimization for both geometry and Gaussian-type function (GTF) exponents using various hydrocarbon molecules. We have found that the scale factor 1.2 is significant for the p-type GTFs in sp³-carbon, as well as hydrogen. The optimized molecular exponents give a flexible description of σ and π bonds in C-C chemical bonds induced by the difference of hybrid states. We also confirmed the efficiency of our calculation concerning the total energy and geometrical parameters in comparison with the results using the high quality basis sets.

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The geometric isotope effect (GIE) on low barrier hydrogen-bonded systems of acetic acid dimer, formic acid dimer, and their anion clusters is analyzed by HF and hybrid DFT levels of the multi-component molecular orbital (MC_MO) method, which directly includes nuclear quantum effect of proton/deuteron. Our optimized geometries for both neutral and anionic species with HF level of MC_MO method have reproduced the overall tendency of the GIE of the corresponding experimental ones. On the other hand, the results for anionic clusters with hybrid BHandHLYP functional of MC_MO method give poor agreement due to the underestimation of the barrier height of hydrogen-bonding. Our multi-component analysis clearly demonstrates that the hydrogen-bonding interaction energy is strongly affected by the distribution of nuclear wavefunction.

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A model of catalytic reaction center on TiO₂ surface is proposed. The model cluster contains two active titanium atoms and an active oxygen atom. It is shown that the HOMO of the model consists of the atomic orbitals of active titanium and oxygen. The HOMO also contributes to the interlayer bond. This fact shows that the structure change of TiO₂ is essential to explain the catalytic behavior.
A dissociation reaction of water molecule from the model surface is examined. The reaction path is calculated and the reaction mechanism is investigated. The reaction consists of two processes. In the first step, a hydrogen atom of the water molecule dissociates and approaches an oxygen atom in the TiO₂ active center. In the second step, a dissociated hydrogen gets an electron from the HOMO of TiO₂ and approaches another titanium atom in the active center. In this process, the hydrogen atom becomes neutral from ionic state, i.e., the hydrogen atom is reduced by this reaction.

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Previously, our research group carried out molecular orbital studies of the interaction between MgATP and the myosin motor domain using the PM3 method of MOPAC97. In this study, we present recalculation results obtained using the PM6 method of MOPAC2009 and discuss the problems that may be encountered in further studies. Previous research carried out by our group in this field is introduced briefly. Furthermore, it is proposed that the increase in the distance between P_γ and the bridging O atom bound to P_β initiates the dissociation of γ-phosphate from ATP. Our results demonstrate that semi-empirical molecular orbital methods are useful in studying the chemical reactions underlying the initial step of ATP hydrolysis in the myosin motor domain.

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The development of functional liposomes using phospholipid liposomes has been performed for some time; however, from the perspectives of efficiency and safety, it is important that the fusion or aggregation of liposomes be controlled and regulated. Phospholipids are ubiquitous in biological membranes; among them, phosphatidylcholines (PC) are commonly used in studies on bilayer membranes and functional liposomes. In addition, the aggregation/disaggregation phenomena of PC liposomes are thought to be caused by heat fluctuations in the membrane during gel-liquid crystal transition. Moreover, a dipole is present in the hydrophilic moiety of PC molecules. Therefore, it is considered that the aggregation phenomenon of phospholipid liposomes might be due to heat fluctuations in the membranes and also the effect of local electric forces caused by the dipole. Therefore, in order to examine the three-dimensional conformation of phospholipid molecules, we calculated the total energy of PC molecules using the molecular orbital method, and 3 optimized structures were found. These structures correlated well with those obtained from other experiments. This shows that the analysis of the molecular structure of phospholipids using the molecular orbital method can be an effective tool to elucidate the interactions between membranes and the properties and functions of phospholipid liposomes.

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The correlation between the elongation of the bond length and the onset temperature of the self-decomposing reaction was evaluated. The substitution products of nitrobenzene were chosen as the samples. The dispersion of the bond length calculated by quantum-chemistry theory with the harmonic oscillator approximation was used for evaluating the elongation. They were used for the calculation of the vibration frequencies and the unitary conversion coefficients which convert Cartesian coordinates to the standard vibration coordinates. Temperature influence was included in the partition function. The influence of the quantum-chemical calculation method was checked by the partition function. Even with the PM3 method of the semi-empirical molecular orbital theory, the partition function was agreed well with the experimental results. The results of the PM3 calculation of the non-conjugative substituent showed that the elongation was longer when the substance had a lower onset temperature.

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Molecular dynamics calculations with constant-temperature and constant-pressure scheme are used to investigate the rotational properties, especially the molecular orientational transition between stable and metastable molecular orientations (rotation-jump), of C₆₀molecules in solid state. The analysis of the event probability of rotation-jumps induced at around the structural phase transition temperature suggests the existence of two different processes of the molecular rotation-jump in solid C₆₀. One is the rotational motion with gear mechanics, in which the rotation-jump of neighboring C₆₀'s are induced at almost the same time. The other is the propagation of rotation-jump with the velocity of ∼ 3 Å/ps through solid C₆₀.

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We here show some examples of our approaches to molecular design using computational science. Firstly, we explain the conical intersection (CI), which plays an important role in nonadiabatic transitions in photophysical and photochemical processes. Next, we show some of our researches on photochromic molecules, diarylethenes; non-destructive readout by infrared spectroscopy, electrochromism, and its reactions in polymers. Finally, we discuss the computation of NMR chemical shifts of large bio-molecules using the FMO method, which is targeted for drug design.

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