安藤 耕司

A semiquantal analysis of condensed phase chemical dynamics, outlined recently for a double-well linearly coupled to dissipative harmonic bath [K. Ando, Chem. Phys. Lett. 376, 532 (2003)], is formulated in detail to clarify its general features as well as the specifics of the linear and quadratic coupling cases. The theory may be called a "semiquantal time-dependent Hartree (SQTDH)" approach, as it assumes a factorized product of the squeezed coherent state wave packets for the variational subspace of the many-dimensional time-dependent wave function. Due to this assumption, it straightforwardly satisfies the canonicity condition introduced by Marumori [Prog. Theor. Phys. 64, 1294 (1980)] and is described by a set of Hamilton equations of motion in an extended phase space that includes auxiliary coordinates representing the wave packet widths. The potential in the extended phase space provides a pictorial understanding of the quantum effects affected due to the bath coupling, e.g., suppression of the wave packet spreading in terms of the potential wall developing along the auxiliary coordinates. The idea is illustrated by prototypical models of quartic double-well and cubic metastable potentials linearly and quadratically coupled to the bath. Further applications and extensions, where the SQTDH method will offer a practical approach for introducing quantum effects into realistic molecular dynamics simulations, are also discussed. (C) 2004 American Institute of Physics.

The ground and excited state potentials and force field of the copper ion site of plastocyanin in the oxidized state is studied by ab initio electronic structure calculations, with the aim to explore the mechanism of its photodynamics. It is shown that the potential energy surface of the ligand-to-metal charge-transfer (LMCT) state, which corresponds to the intense similar to600 nm absorption, is repulsive along the Cu-S(Cys) distance, where S(Cys) denotes the sulfur atom of the cystein ligand, and crosses with the d --> d ligand field excited states at the Cu-S(Cys) length of similar to2.7 Angstrom or longer. The crossing distance varies depending on the Cu-N(His) distance of the two histidine ligands, indicating that the Cu-His ligand vibrational motions, in addition to the Cu-S(Cys) stretch, constitute a major component of the reaction coordinate for the nonradiative transitions. This feature is explained in terms of the different charge distributions and the resulting electrostatic interactions in these states. The influence from the methionine ligand is seen to be minor, although the possible dynamical coupling via the dispersion interactions is not ruled out. A shorter Cu-S(Met) equilibrium distance (2.4 Angstrom) than in the crystal structure (2.9 Angstrom) is found, suggesting that the structural constraint from the surrounding protein may be playing some role.

A semiquantal theory is applied to a double-well potential coupled to dissipative bath. The analysis demonstrates in a comprehensive way how the quantum effect, e.g., the spreading of the wave packet width, is suppressed along the bath coupling strength. A quasi-classical approximation is introduced to derive a compact analytical formula, by which the kinetic isotope effects are briefly discussed. The coupled generalized Langevin equations indicate that the auxiliary semiquantal coordinates modulate the effective barrier frequency along the system coordinate, basically to reduce the frequency and thus to enhance the dynamical friction effect. (C) 2003 Elsevier B.V. All rights reserved.

An alternative Liouville formulation of mixed quantum- classical dynamics outlined recently [K. Ando, Chem. Phys. Lett. 360, 240 (2002)] is expanded in detail by taking an explicit account of the parametric dependence of the electronic (adiabatic) basis on the nuclear coordinates. As a consequence of the different operational order of the partial Wigner transformation for the nuclear coordinates and the calculation of the matrix elements in the adiabatic electronic basis, the present formula differs from the previously proposed one, slightly in the appearance but significantly in the treatment of nonadiabatic transitions in the trajectory implementation in that the former does not contain the " off- diagonal Hellmann - Feynman forces'' representing the so- called " momentum- jump'' associated with the nonadiabatic transitions. Because of this, the present formula is free from the numerical instability intrinsically coming from the momentum- jump operation at around the classical turning points of the nuclear motion. It is also shown that the density matrices from the two approaches coincide when the electronic basis is independent of the nuclear coordinates ( R), and hence the momentum- jump approximation stems from the R- dependence of the adiabatic electronic basis. Improved stability and comparable to better reproduction of the quantum reference calculations are demonstrated by applications to one and three dimensional spin- boson models and a two- state three- mode model of the S-2 --> S-1 internal conversion of pyrazine. Also discussed is the importance of electronic coherence for the proper treatment of nonadiabatic transition rates which is naturally described by the Liouville methods compared to the conventional independent trajectory approaches. (C) 2003 American Institute of Physics.

Path-integral formulation and Monte Carlo calculations of the reaction-diffusion equation of condensed phase chemical reactions are presented. Numerical calculations are demonstrated for the Sumi-Marcus model of electron transfer reactions, which include the slow and intermediate diffusion regimes, ultrafast photoinduced electron transfers, and nonequilibrium initial distributions. (C) 2003 American Institute of Physics.

An alternative Liouville formulation of mixed quantum-classical dynamics is presented, placing a particular focus on the non-adiabatic couplings in the adiabatic basis. Our formulation does not contain the 'momentum jump' operation which has played a vital role in the previous formulation by Kapral and Ciccotti [J, Chem. Phys. 110 (1999) 8919] in its trajectory implementation but has caused instability problem around the classical turning points. (C) 2002 Elsevier Science B.V. All rights reserved.

A stable and efficient variant of the dynamical fluctuating charge (fluc-q) model for electronically polarizable molecular dynamics (MD) simulation is developed and applied to electron transfer (ET) reactions in water. The energy divergence problem often encountered with the original form of the fluc-q model is essentially removed by introducing an alternative functional form for the electronic self-energy term of hydrogen atoms without any additional parameters. In the application to the aqueous ET problem we find the following: For the present donor-acceptor (DA) model of moderate size, the induced dipole is slightly smaller in the first solvation shell than in the outer region even under the electrostatic field from the ion pair state of the DA, which suggests that the induced dipole is enhanced more in the solvent-solvent hydrogen-bonding structure. The structural aspects are also examined via radial distribution functions. The solvent reorganization energy is demonstrated to be renormalized, both in the magnitude and in the slope along the inverse DA distance, due to coupling with electronic polarization. In the time correlation and spectral density functions of the solvent reaction coordinate, the frequency of the librational coupling motion is slightly blue-shifted and its intensity is suppressed due to inclusion of the solvent electronic polarization. The impact of the electronic polarization on the scaled quantum energy gap law of the ET rate is found to be modest. (C) 2001 American Institute of Physics.

The role of polarization has been systematically studied for the methylchloromethane family ((CH3)(4-n)CCln) of organic liquids. Special attention has been paid to dynamical properties (translational diffusion and rotational relaxation) for which good agreement with experiment is obtained, although structural and electrostatic effects have been addressed as well. Molecular dynamics simulations have been performed, with and without the inclusion of polarization, over a substantial range of temperatures. Polarizability has been handled with the chemical potential equalization (fluctuating charge) method, with a transferable set of parameters having been developed for the methyl group. As a general rule, the inclusion of polarization does not affect structure and slightly slows down the dynamics at all temperatures. The overall muted influence of polarization contrasts with the substantial induced dipole moments obtained, exceeding what had been found in other organic (albeit hydrogen-bonding) liquids.

Solvent nuclear quantum effects in redox electron transfer (ET) reactions between metal ions in aqueous solution are studied via a molecular dynamics simulation analysis. The impacts of the solute size and charge variations together with the solvent ligand effects are examined by comparing with our previous study on a moderate size donor-acceptor system that assumed typical organic fluorescer-quencher molecules [J. Chem. Phys. 106, 116 (1997)]. It is shown that the spectral density function of the solvent coupling to ET, and consequently the quantum ET rate and its energy gap law, are strongly dependent on these variations of the system parameters. Two kinds of decomposition analysis, one into spatial contributions from inner- and outer-sphere solvations, and the other into motional frequency contributions from solvent intramolecular vibrations and intermolecular collective modes, are presented. (C) 2001 American Institute of Physics.

Solvent nuclear quantum effects in outer-sphere electron transfer (ET) reactions in methanol solution are examined via a molecular dynamics simulation analysis. The energy gap law of the quantum mechanical ET rate constant is decomposed into contributions from solvent intramolecular vibrations and other low-frequency intermolecular (collective) modes. It is shown that the high-frequency stretching and bending vibrations from the hydroxyl part of the solvent methanol exhibit marked quantum effects on the ET rate despite of their fractional contributions to the reorganization energy (computed to be <4%). A scaling property of the quantum energy gap law is proposed, which would be useful to coordinate data from variety of donor-acceptor systems where the solvent spectral density may have similar profile but the other parameters such as the reaction distance and the reorganization energy may vary. The results are compared with our previous study on aqueous ETs [K. Ando, J. Chem. Phys. 106, 116 (1997)]. (C) 2001 American Institute of Physics.

We have studied liquid structure for a whole family of methylchloromethane compounds ((CH3)(4-n)CCln), exploiting the interplay of x-ray diffraction measurements and molecular dynamics (MD) computations. To this end we report for the first time x-ray spectra for 1,1,1-trichloroethane (n=3), and 2,2-dichloropropane (n=2), together with a new determination for carbon tetrachloride (n=4). A consistent set of molecular models for MD simulation has also been developed for the full family, providing excellent accord with thermodynamic properties (vaporization enthalpy and density over the full liquid phase), and with diffraction data alike. The theoretical results have allowed the interpretation of the salient features in the experimental spectra and of the trends peculiar to this family of compounds, basically characterized by the suppression of one of the two main peaks in the spectrum as the number of chlorines is diminished. A numerical method that constructs radial correlation functions for ideal dimer geometries has served to explore the most probable structures between nearest neighbors. We have concluded that structure at short intermolecular distances cannot be assigned to any clear-cut geometry. Instead, it can be explained by a combination of corner-to-face and interlocked configurations, with a contribution (dependent on the compound) of face-to-face configurations. (C) 2000 American Institute of Physics. [S0021-9606(00)51417-2].

The results of a theoretical study of the acid ionization to form first a contact ion pair and then a solvent-separated ion pair are presented for HF in water. The ionization reaction to produce the contact ion pair is found to involve adiabatic quantum proton transfer (PT) and has an activation barrier in a collective solvent reaction coordinate of 2.9 kcal/mol, with a positive reaction free energy estimated as 2.2 kcal/mol. This result identifies the weakness of HF acid in aqueous solution as arising from this intrinsic acid ionization step, rather than from the thermodynamic difficulty of separating the ions so produced. The calculated charge distributions for the first step are in support of the unconventional Mulliken picture for PT. The second step to produce a solvent-separated ion pair is found to be sequential in connection with the first step, rather than concerted, and is also a quantum adiabatic PT. This reaction step proceeds via a solvent reaction coordinate and is slightly activated. The two step sequence in reverse order is discussed in connection with the Eigen picture of acid-base recombination in aqueous solution.

A theory to describe nonequilibrium electronic surface crossing during vibrational relaxation induced by ultrafast photoexcitation is developed and applied to the primary electron transfer (ET) in bacterial photosynthetic reaction centers. As a key concept, we define on a microscopic basis the angle between two reaction coordinates each representing the environmental nuclear displacements coupled to the initial photoexcitation (to the P* state) and to the subsequent ET processes, respectively. The "cross-spectral" density function, whose integral intensity gives the cosine of this angle, is also defined to give a consistent (nonphenomenological) description of the vibrational coherence and its dephasing. In the application to the primary ET in bacterial photosynthesis, we find (1) the time-dependent ET rate exhibits marked oscillation at low temperatures due to the nonequilibrium vibrational coherence in the P* state. However, it does not contribute very much to accelerate the primary ET rate with respect to the total population decay of the P* state. (2) The static energetics (that give a small barrier for the ET) and the nuclear quantum tunneling effect at low temperatures, rather than the dynamical nuclear coherence, are the main origins that reasonably reproduce the ultrafast ET and its anomalous temperature dependence (accelerated as the temperature decreases). From the calculations on alternative parameter regimes, we also examine the conditions in which the nonequilibrium nuclear vibrations may accelerate the photoinduced ET. We further propose that detailed experimental analysis of the transient behavior of the oscillating time-dependent reaction rate may provide useful information on the interplay between the vibrational dephasing and the surface crossing dynamics of ultrafast reactions as well as on the underlying static energetics of the system.

The acid ionization of HCl in water is examined via a combination of electronic structure calculations with ab initio molecular orbital methods and Monte Carlo computer simulations, The following key features are taken into account in the modeling: the polarization of the electronic structure of the solute reaction system by the solvent, the quantum character of the proton nuclear motion, the solvent fluctuation and reorganization along with the solvent polarization effects on the proton potential, and a Grotthuss mechanism of the aqueous proton transfer, The mechanism is found to involve the following: first, a nearly activationless motion in a solvent coordinate, which is adiabatically followed by the quantum proton rather than tunneling, to produce a contact ion pair Cl--H3O+, which is stabilized by similar to 7 kcal/mol; second, motion in the sol vent with a small activation barrier, as a second adiabatic proton transfer produces a solvent-separated ion pair from the contact ion pair in a nearly thermoneutral process, Motion of a neighboring water molecule-to accommodate the change of the primary coordination number from 4 for H2O to 3 for H3O+ of a proton-accepting water molecule-is indicated as a key feature in the necessary solvent reorganizations. It is estimated, via a separate argument, that the remainder of the process to produce the completely separated ions involves a free energy change of less than 1 kcal/mol. It is argued that the reorganization of the heavy atoms between which the proton transfers plays an essential role in assisting the adiabatic (nontunneling) and stepwise transfer mechanism and that the concerted pathway of the multiple proton transfers in water is unfavorable.

Electronic structure evolution of an organic dye coumarin 120 coupled to polar solvation dynamics is examined by combining ab initio electronic structure calculations and molecular dynamics (MD) simulations. Sets of nonorthogonal Hartree-Fock molecular orbitals optimized in vacuo and in dielectric continuum are utilized for a quantum mechanical description of the solute electronic polarization coupled to the solvent fluctuation. The adiabatic MD simulation for methanol solution is performed to evaluate the equilibrium and nonequilibrium dynamics of the (S-0-S-1) energy gap coordinate and the dipole moments. The absorption and fluorescence spectra are computed via the spectral density functions obtained from the simulation analysis. The results for the quantum polarizable (Q-Pol) model of the solute probe are compared with those for a nonpolarizable fixed-charge (Fix-Z) model. It is shown :hat the solute electronic polarization notably affects the solvent-induced key quantities such as the reorganization energy, the spectral linewidth, and the Stokes shift (which are mutually related): For example, the computed Stokes shifts are similar to 2500 and similar to 4000 cm(-1) for Fix-Z and Q-Pol, respectively. On the other hand, the solute polarization tends to slightly slow down the methanol solvation, which is not necessarily attributed to reduction of the ''solvent force constant'' because the effective mass of the coordinate is reduced as well. (C) 1997 American Institute of Physics.

The quantum energy gap law for electron transfer (ET) reactions in water is examined. Molecular dynamics (MD) simulation analysis is carried out to obtain the solvent reorganization energies, time correlation functions (TCF), spectral density functions, and quantum rate constants. Their dependence on the reaction free energy and on the donor-acceptor distance is explored along with the solvent isotope effects. Properties of the imaginary-time saddle-point for the TCF expression of the ET rate formula are also examined. The high-frequency intramolecular vibrational modes of the solvent water are found to present marked quantum effects on the ET rate, while their contribution to the static reorganization energy is small (less than 6%). The energy gap dependence of the quantum activation free energy is shown to become nearly independent of the donor-acceptor distance when renormalized by the reorganization energy. Approximations to compute quantum rate constants from MD simulation data are briefly discussed in light of of the present results. (C) 1997 American Institute of Physics.

The results of a theoretical study of the first acid-ionization step to produce a contact-ion pair are presented for HF in water. The reaction is found to be an adiabatic quantum proton transfer, and has an activation barrier in a collective solvent reaction coordinate of ca. 3 kcal mol(-1).

The reaction dynamics of twisted intramolecular charge-transfer (TICT) state formation of 4-(N,N-dimethylamino)benzonitrile (DMABN) in methanol solvent has been studied theoretically. Molecular dynamics calculations were carried out for the St state of DMABN, and the reaction free energy surfaces were constructed as a function of solvation coordinate and torsional angle of the dimethylamino group. The solvation coordinate was defined by the potential energy difference between the S-1 and S-2 states. It was found that the potential barrier for the TICT state formation exists and the free energy along the solvation coordinate was well represented by the harmonic curves, To investigate the dynamics of reaction, the equations of motions for the solvation coordinate and the torsional angle were derived and stochastic trajectory calculations were carried out. The results were that (a) the reaction rate is significantly slower than the time scale of relaxation in the solvation coordinate, (b) the rate is about half of the transition-state theory prediction, and (c) the coupling between the motions along the torsional angle and the solvation coordinate is relatively small.

The photoinduced intermolecular electron transfer (ET) reaction between N,N-dimethylaniline and excited state anthracene in acetonitrile solution is studied theoretically. A solvation coordinate s which represents stochastic one-dimensional dynamics of the solution phase reaction is defined and a Hamiltonian in terms of s and perpendicular bath modes is derived from the spin-boson Hamiltonian. This has an advantage that the dynamics of the transferring electron is influenced by the bath only through coupling with the coordinate s. Intra- and intermolecular potentials are constructed by using ab initio molecular orbital methods, and a series of molecular dynamics simulation analysis is performed. Mean force potentials as a function of the donor-acceptor distance R are computed and the bimolecular encounter dynamics is investigated. Diabatic free energy curves for the coordinate s are computed and shown to be well approximated by parabolas, indicating that the dielectric saturation effect is negligible. The dependence of the free energy relationships on R is examined. It is shown that the present system corresponds to the increasing region of the rate constant, in contrast with the conventional picture. The electronic coupling of the ET is evaluated by the method of corresponding orbitals. The R dependence of the ET rate is evaluated and the reaction adiabaticity and mechanism are discussed. Dynamical solvent effects are taken into consideration in terms of the generalized Langevin equation formalism.

The Kim-Hynes theory for electronic structure for reaction systems in solution is applied to the reaction class of the title, focusing on the I-+I-->I2- reaction in acetonitrile solvent from a valence bond perspective. The transition between a delocalized electronic structure at small internuclear separations r to localized structures at large r is described in terms of a two-dimensional nonequilibrium free energy surface; the second coordinate is a solvent coordinate gauging the state of the solvent orientational polarization. The reaction path on this surface is described, and is contrasted with an equilibrium solvation perspective. An important focus is the polarization force, defined as the force on the diatomic ion coordinate r due to the solvent, which arises from the charge shifting, or electronic structure change, in the solute system along the reaction coordinate. It is argued that this force should play a significant role in the vibrational relaxation of the I2- ion.

The solvation dynamics associated with the ionization of N,N-dimethylaniline (DMA) in water and methanol solutions has been studied theoretically. Potential energy surfaces of DMA and DMA + were computed by ab initio molecular orbital (MO) methods. Intermolecular pair potential functions between DMA and H2O were developed with the aid of the electron distributions of DMA and H2O and the results of MO calculations for the DMA-H2O system. Potential functions between DMA and MeOH were also determined empirically using the parameters for DMA-H2O interaction. Equilibrium and nonequilibrium molecular dynamics calculations were carried out for the DMA-water and DMA-methanol solutions. The simulation results were analyzed comparing two solvents in order to obtain a realistic molecular model for the solvation dynamics of DMA in polar solvents. The solvation coordinate was defined by the potential energy difference between neutral and cation states and free energy curves along it were constructed using the umbrella sampling method. They were found to be well described by parabolas and nonlinear effects such as the dielectric saturation were not observed. The fluctuation-dissipation relation was also examined. It was found that the present systems follow the linear response to a reasonable approximation. In order to provide a kinematic foundation for the choice of the solvation coordinate, the generalized Langevin equation (GLE) for the motion along the solvation coordinate is derived utilizing the reaction path model originally developed to describe photochemical processes in the gas phase. The mechanism of the dielectric relaxation dynamics was discussed on the basis of the quantities in the GLE deduced from the molecular dynamics (MD) calculations.