Information on solvent-solute interaction is necessary in order to fully understand chemical processes in solution. This is because the environment around the solute molecule varies time to time with the motion of the solvent molecules and the fluctuation induced by the solvent motion either accelerates or decelerates chemical processes. The present study aims at understanding these dynamic environments around molecules by analyzing bandshapes of probe molecule solvated in various solvents. Carbon dioxide has been chosen to be the probe molecule for two reasons. One of the reasons is that the molecule has simple structure having well separated three vibrational bands. The other is that the molecule does not have permanent dipole moment, and thus soluble in both polar and non-polar solvents. The infrared bandshape of its antisymmetric stretch mode is precisely analyzed. This mode had been chosen because it has large absorption coefficient while absorption of the solvents are generally small in this region.

Infrared bandshape includes vibrational bandshape and rotational bandshape. Vibrational bandshape is determined by vibrational dephasing due to frequency modulation of the probe molecule. Rotational bandshape is determined by reorientational motion of the probe. Total bandshape is therefore obtained by Fourier transforming total correlation function; the product of vibrational correlation function and rotational correlation function. Therefore environment around solute molecule can be studied as follows. First, correlation functions are created for a model system. Second, corresponding spectrum for the correlation functions are calculated and compared to the observed spectrum. Finally rationality of the model system is evaluated and, if necessary, feedback is given to the model system and the bandshape is calculated again.

For infrared measurement, sample chamber has been evacuated to 0.5-2 Torr (measured by a thermistor attached to the spectrograph) in order to reduce the concentration of carbon dioxide inside the spectrograph. Sealed cell has been constructed to prevent sample solution from evaporation. S/N ratio of the infrared spectrum has improved, and infrared spectra of carbon dioxide in various solvents have been successfully obtained. The solvents include polar solvents (water, alcohols, acetonitrile, acetone, and dimethyl sulfoxide), and non-polar solvents (alkanes and cycloalkanes).

Temperature controlled infrared spectra of carbon dioxide in hexane, dodecane and ethanol has also been measured. A new temperature-tunable sealed cell has been constructed since sample is more likely to evaporate during temperature-controlled measurements compared to usual infrared measurements. There are few improved features to overcome this problem. Temperature can be controlled by circulating constant-temperature water from a chille. Temperature has been controlled from 5 to 70 °C. A new side lid for the sample chamber has been constructed to introduce constant-temperature water, sample and thermocouple inside the evacuated sample chamber.

Polarized Raman scattering spectra in acetonitrile have been measured in order to estimate contribution of rotational broadening to the bandshape. Spectra have been measured on a Raman spectroscopic system build by Okajima et al.

Sub-picosecond time-resolved infrared spectroscopy has also been carried out in order to estimate rotational correlation. Measurements have been done on laboratory-build Time-resolved infrared spectroscopic system. Signal is hardly seen with natural-abundant 12CO2 sample, since atmospheric carbon dioxide absorbs most of the infrared light. Isotope-selected 13CO2 is used for probe. The solvent is ethanol.

The observed bandshape of the antisymmetric stretch band of carbon dioxide is slightly asymmetric due to a small band located at lower frequency region. This small band is proved to be a hot band by temperature-controlled measurements. It is neglected in the analysis. The observed bandshape is not reproduced by a single Lorentzian, indicating that the vibrational dephasing of the mode is not represented by a single exponential decay. In fact, the bandshape is well reproduced by the sum of two Lorentzians with identical center frequency. In all these solvents, the observed bandshapes are fitted only with two Lorentzians. The narrower components have the widths of 2.5-5.5 cm-1 and the broader components have the widths of 7.9-20cm-1. In temperature controlled measurements, the two components have been found to show different behaviors on increasing temperature.

In general, correlation of stochastic processes decay as an exponential function in the long time range. Therefore double-Lorentzian bandshape may due to two dephasing processes. Exchange model which argues multiple dephasing processes is used to analyze the bandshape. Obtained exchange rates (~ 100 ps) are large compared to dephasing time (~ ps and ~ 100 fs), indicating that there is no exchange between the two states during the dephasing process. In other words, the two states are independent, so that the two components can be treated as two Lorentzians. The obtained two center frequencies are very similar for all the solvents studied. It is highly unlikely that the two states having different dephasing times (ps and 100 fs) always have very similar center frequencies. This discussion has another weakness that infrared bandshape is directly analyzed without separating contributions of vibrational and rotational dephasing which assumes single exponential decay for both correlation functions. Raman and TRIR measurements are carried out to separate rotational distribution to the bandshape.

By polarized Raman spectroscopy, isotropic and anisotropic bandwidth is estimated to be 1.29 and 7.9 cm-1, respectively (Lorentzian fit). Therefore the rotational bandwidth is estimated to be 7.9-1.29=5.9 cm-1. This bandwidth exceeds the width of narrower Lorentzian component, 3.2 cm-1 in acetonitrile. Therefore the observed infrared bandshape is suggested to be almost pure rotational.

Anisotropy r has been calculated from the parallel signal and perpendicular signal. Anisotropy shows exponential decay with a time constant of 0.95 ps, which means, in frequency domain, rotational band is a Lorentzian with 5.6 cm-1, which corresponds to the result of Raman measurement.

Computational method has been carried out in order to directly calculate time-dependent frequency and to obtain bandshape. A combination method of classical molecular dynamics (MD) simulation and quantum chemical calculation is used. First classical MD simulation is done. Next field parameters are calculated at each snapshot along the trajectory, which characterize the environment around the probe molecule. At the same time, instantaneous frequency is parameterized by the field parameter by quantum chemical calculation. Time-dependent frequency can be then obtained by substituting field parameters at each time step. Using this method, ab initio computations of time-dependent frequency can be done at low computational cost, without repeated ab initio computation as in quantum chemical simulations.

Instantaneous frequency is parameterized in terms of electric field and Van der Waals field. As for electric field, frequency fluctuation by coulomb interaction is expanded in terms of electric field on carbon atom up to second order. The first term vanishes due to the symmetry of the carbon dioxide molecule; frequency should be the same with an applied electric field of E or -E. Therefore only the second term is evaluated. Coefficients have been obtained with Gaussian 09 program. As for the LJ field, frequency fluctuation caused by Van der Waals interaction is expanded in terms of generalized LJ force up to second order using semi-classical perturbation theory. The first term again vanishes because there is no bond anharmonicity in carbon dioxide molecule. Therefore only the second term is evaluated. Vibrational correlation function is calculated by summing these two correlations. However, the correlation does not decay in the time range of picosecond, and the corresponding power spectrum has no bandwidth. This is due to the amplitude of the fluctuation is too small to give dephasing to the correlation.

Rotational correlation function is calculated directly from the trajectory of the simulation. Molecule-fixed unit vector is set along the molecular axis of carbon dioxide. Correlation function is calculated as an autocorrelation of the unit vector. It seem to be a exponential decay within a few picoseconds. Corresponding power spectrum indicates that the rotational broadening is about 3 cm-1.

Apodization is necessary for Fourier transformation of correlation function into frequency domain. Hamming apodization which gives the same instrument function as FT-IR measurement is used, so that the calculated spectra can be compared to observed infrared spectrum without any convolution or deconvolution.

Total calculated bandshape agrees well with the observed bandshape. The result indicates that the observed bandshape is almost pure rotational, which agrees with the experimental results of Raman (§4.5) and TR-IR (§4.6) measurements. Similar results have been shown for dodecane solution as well.

Rotational motion is often described using diffusion equations, which give exponential decay in correlation function. However, this method assumes "small angular steps", which may not applicable to small molecules. Gordon has shown more generalized rotational diffusion models called m-diffusion model and J-diffusion model, which can treat both small angular steps and large angular steps over 1/2π. Basically the models are rotors with angular frequency changing stochastically. The orientation of the rotors is not changed by the change in angular frequency.

FORTRAN 90 programs have been written to simulate rotational correlation function, instead of solving recursive equations as Gordon has done. A rotor rotates freely with a constant angular frequency. The direction of the moment of inertia is stochastically changed with a certain probability. Correlation functions are calculated for 50 different angular frequencies, and they are summed up according to Maxwell-Boltzmann distribution.

As a result, free rotor (τ=∞) shows negative correlation, which means molecule rotates over 1/2π. With increasing probability of diffusion, negative peak disappears, whereas rapid decrease in first few 100 fs remains as dumped oscillation. This feature resembles the correlation function obtained in MD simulation.

To conclude, double-Lorentzian bandshape seem to correspond to the dumped oscillatory rotation. This is due to carbon dioxide being small, which rotates in large angle steps during diffusion. Also, the rotational dephasing process is able to be observed in vibrational spectra because the molecule is symmetric (non-polar) so that vibrational bandwidth is negligible.

本論文は、各種溶媒中に溶解させた二酸化炭素分子の振動バンド形について、3種の分光測定手法および理論計算・シミュレーション計算を用いて解析を行い、溶液中の動的環境について総合的に考察したものであり、全6章から構成される。

第1章では導入として、本研究の目的が溶液環境の分子レベルにおける理解にあり、それには従来溶媒効果の解析に用いられてきた巨視的・静的な物理量では不十分であることが述べられている。振動バンド形は注目する分子が周囲から受ける揺動の様子を色濃く反映しているため、これを解析することで溶液中の環境をより微視的・動的に理解することができるということが説明されている。また、プローブ分子として用いた二酸化炭素分子が、その振動モードの分離のよさ、極性を問わず様々な溶媒に溶解する汎用性、吸光係数の大きさなどの観点から、本手法に適した選択であることが述べられている。

第2章では、振動バンド形解析の理論について述べられている。振動バンド形は振動数の揺ぎによって引き起こされる振動位相緩和によって決定されるが、実測の振動スペクトルにはそのほかに回転緩和による寄与も含んでいること、赤外スペクトルでは振動と回転の寄与を分離できないが、ラマンスペクトルでは偏光測定を用いて分離可能であること、赤外とラマンでは回転相関関数の形式が異なること、時間分解赤外吸収測定から得られるアニソトロピーの時間変化は、ラマン回転相関関数と同形であること、などが数式を用いて示されている。

第3章では、実際に行った分光測定の手法について述べられている。赤外測定は、炭素数の異なる直鎖およびシクロアルカン類、いくつかの非プロトン性極性溶媒、水及びアルコール類と、多岐にわたる溶媒を用いて行われた。そのうちいくつかの溶媒中においては自作の装置を用いて温度変化測定も行われた。大気中の二酸化炭素の妨害を避けるため真空分光器を用いるなど、測定上工夫した点について示されている。そのほか、偏光ラマン散乱測定と偏光時間分解赤外吸収測定の詳細についても述べられている。

第4章では、得られた測定結果の振動バンド形解析について述べられている。赤外バンド形は測定したすべての溶媒・温度条件において中心波数が等しい2個のローレンツ関数で非常によく近似できた。実測のバンド形をほぼ振動バンド形に等しいと仮定すれば、振動位相緩和過程には時定数の異なる2個の過程が存在することになる。しかし理論モデルを用いた考察から、このような過程は物理的には考えにくいことが示されている。ラマンや時間分解測定の結果も踏まえ、回転による寄与が無視できない可能性が述べられている。

第5章では、MDシミュレーションと量子化学計算を組み合わせ、バンド形を理論的に予測した結果が示されている。計算結果は赤外およびラマンの測定結果を非常によく再現するものであった。この結果から、溶液中の二酸化炭素の振動数の揺らぎは非常に小さくバンド幅にほとんど影響を与えないこと、逆に回転によるバンドの広がりが実測のバンド幅のほとんどを占めることが示された。また、回転の相関関数の最初の数100fsに急激な減少が見られ、これが2個のローレンツ型のバンド形の起源ではないかと考察している。単純な剛体回転子を用いたシミュレーションにより、この減少は小さな分子である二酸化炭素が大きな角度で回転していることに由来することが確認された。

第6章は以上の研究成果のまとめである。

本研究は幅広い測定手法及び計算機を用いた理論予測により振動スペクトルのバンド形について包括的な議論を行った、非常に基礎的かつ重要な研究である。このような研究は溶液中の高速化学過程を理解する上でより実際に即した指標となることが期待され、その意義は大きい。このような新規の知見を提示しその信憑性を多角度から議論した本論文の内容は高く評価できる。

本論文第3, 5章の内容は、Journal of Chemical Physics誌にて公表済み(岡島元、加藤拓也、〓口宏夫との共著)である。論文提出者が主体となって実験および解析を行なっており、その寄与が十分であるので、この論文を学位論文の一部とすることに何ら問題はないと判断する。

以上の理由から、論文提出者渡邉香に博士(理学)の学位を授与することが適当であると認める。