Shigeki Kato

Conical intersections of free energy surfaces in solution: Effect of electron correlation on a protonated Schiff base in methanol solution

The minimum energy conical intersection (MECI) optimization method with taking account of the dynamic electron correlation effect [T. Mori and S. Kato, Chem. Phys. Lett. 476, 97 (2009)] is extended to locate the MECI of nonequilibrium free energy surfaces in solution. A multistate electronic perturbation theory is introduced into the nonequilibrium free energy formula, which is defined as a function of solute and solvation coordinates. The analytical free energy gradient and interstate coupling vectors are derived, and are applied to locate MECIs in solution. The present method is applied to study the cis-trans photoisomerization reaction of a protonated Schiff base molecule (PSB3) in methanol (MeOH) solution. It is found that the effect of dynamic electron correlation largely lowers the energy of S(1) state. We also show that the solvation effect strongly stabilizes the MECI obtained by twisting the terminal C=N bond to become accessible in MeOH solution, whereas the conical intersection is found to be unstable in gas phase. The present study indicates that both electron correlation and solvation effects are important in the photoisomerization reaction of PSB3. The effect of counterion is also examined, and seems to be rather small in solution. The structures of free energy surfaces around MECIs are also discussed.

Geometry optimization based on linear response free energy with quantum mechanical/molecular mechanical method : Applications to Menshutkin-type and Claisen rearrangement reactions in aqueous solution

The authors present a method based on a linear response theory that allows one to optimize the geometries of quantum mechanical/molecular mechanical (QM/MM) systems on the free energy surfaces. Two different forms of linear response free energy functionals are introduced, and electronic wave functions of the QM region, as well as the responses of electrostatic and Lennard-Jones potentials between QM and MM regions, are self-consistently determined. The covariant matrix relating the QM charge distribution to the MM response is evaluated by molecular dynamics (MD) simulation of the MM system. The free energy gradients with respect to the QM atomic coordinates are also calculated using the MD trajectory results. They apply the present method to calculate the free energy profiles of Menshutkin-type reaction of NH3 with CH3Cl and Claisen rearrangement of allyl vinyl ether in aqueous solution. For the Menshutkin reaction, the free energy profile calculated with the modified linear response free energy functional is in good agreement with that by the free energy perturbation calculations. They examine the nonequilibrium solvation effect on the transmission coefficient and the kinetic isotope effect for the Claisen rearrangement.

A wave-function based approach for polarizable charge model: Systematic comparison of polarization effects on protic, aprotic, and ionic liquids

We first describe a wave-function based formalism of polarizable charge model by starting from the Hartree product ansatz for the total wave function and making the second-order expansion of individual molecular energies with the use of partial charge operators. The resulting model is shown to be formally equivalent to the charge response kernel model that starts from the linear-response approximation to partial charges, and also closely related to a family of fluctuating charge models that are based on the electronegativity equalization principle. We then apply the above model to a systematic comparison of polarization effects on qualitatively different liquids, namely, protic solvents (water and methanol), an aprotic polar solvent (acetonitrile), and imidazolium-based ionic liquids. Electronic polarization is known to decelerate molecular motions in conventional solvents while it accelerates them in ionic liquids. To obtain more insights into these phenomena, we consider an effective decomposition of total polarization energy into molecular contributions, and show that their statistical distribution is well-correlated with the acceleration/deceleration of molecular motions. In addition, we perform effective nonpolarizable simulations based on mean polarized charges, and compare them with fully polarizable simulations. The result shows that the former can reproduce structural properties of conventional solvents rather accurately, while they fail qualitatively to reproduce acceleration of molecular motions in ionic liquids.

Grignard Reagents in Solution: Theoretical Study of the Equilibria and the Reaction with a Carbonyl Compound in Diethyl Ether Solvent

The equilibria of Grignard reagents, CH3MgCl and CH3MgBr, in diethyl ether (Et2O) solvent as well as the reaction of the reagents with acetone are studied theoretically. To describe the equilibria and reactions in Et2O solvent, we employ the reference interaction site model self-consistent field method with the second-order Møller-Plesset perturbation (RISM-MP2) free energy gradient method. Since the solvent molecules strongly coordinate to the Grignard reagents, we construct a cluster model by including several Et2O molecules into the quantum mechanical region and embed it into the bulk solvent. We propose that, instead of the traditionally accepted cyclic dimer, the linear form of dimer is as stable as the monomer pair and participates in the equilibria. For the reaction with acetone, two important reaction paths (i.e., monomeric and linear dimeric paths) are studied. It is found that the barrier height for the monomeric path is much higher than that for the linear dimeric path, indicating that the reaction of the Grignard reagent with acetone proceeds through the linear dimeric reaction path. The change of solvation structure during the reaction is examined. On the basis of the calculated free energy profiles, the entire reaction mechanisms of the Grignard reagents with aliphatic ketones in Et2O solvent are discussed.

Protein Collective Motions Coupled to Ligand Migration in Myoglobin

Ligand migration processes inside myoglobin and protein dynamics coupled to the migration were theoretically investigated with molecular dynamics simulations. Based on a linear response theory, we identified protein motions coupled to the transient migration of ligand, carbon monoxide (CO), through channels. The result indicates that the coupled protein motions involve collective motions extended over the entire protein correlated with local gating motions at the channels. Protein motions, coupled to opening of a channel from the distal pocket to a neighboring xenon site, were found to share the collective motion with experimentally observed protein motions coupled to a doming motion of the heme Fe atom upon photodissociation of the ligand. Analysis based on generalized Langevin dynamics elucidated slow and diffusive features of the protein response motions. Remarkably small transmission coefficients for rates of the CO migrations through myoglobin were found, suggesting that the CO migration dynamics are characterized as motions governed by the protein dynamics involving the collective motions, rather than as thermally activated transitions across energy barriers of well-structured channels.

Efficient implementation of three-dimensional reference interaction site model self-consistent-field method: application to solvatochromic shift calculations.

The authors present an implementation of the three-dimensional reference interaction site model self-consistent-field (3D-RISM-SCF) method. First, they introduce a robust and efficient algorithm for solving the 3D-RISM equation. The algorithm is a hybrid of the Newton-Raphson and Picard methods. The Jacobian matrix is analytically expressed in a computationally useful form. Second, they discuss the solute-solvent electrostatic interaction. For the solute to solvent route, the electrostatic potential (ESP) map on a 3D grid is constructed directly from the electron density. The charge fitting procedure is not required to determine the ESP. For the solvent to solute route, the ESP acting on the solute molecule is derived from the solvent charge distribution obtained by solving the 3D-RISM equation. Matrix elements of the solute-solvent interaction are evaluated by the direct numerical integration. A remarkable reduction in the computational time is observed in both routes. Finally, the authors implement the first derivatives of the free energy with respect to the solute nuclear coordinates. They apply the present method to solute water and formaldehyde in aqueous solvent using the simple point charge model, and the results are compared with those from other methods: the six-dimensional molecular Ornstein-Zernike SCF, the one-dimensional site-site RISM-SCF, and the polarizable continuum model. The authors also calculate the solvatochromic shifts of acetone, benzonitrile, and nitrobenzene using the present method and compare them with the experimental and other theoretical results.

Proton-coupled electron transfer of the phenoxyl/phenol couple: effect of Hartree-Fock exchange on transition structures.

Proton‐coupled electron transfer (PCET) and hydrogen atom transfer (HAT) reactions of the phenoxyl/phenol couple are studied theoretically by using wave function theory (WFT) as well as DFT methods. At the complete active space self‐consistent field (CASSCF) level, geometry optimization is found to give two transition states (TSs); one is the PCET type with two benzene rings being nearly coplanar, and the other is the HAT type with two benzene rings taking a stacking structure. Geometry optimization at the (semilocal) DFT level, on the other hand, is found to give only one transition state (i.e., the PCET‐type one) and fail to obtain the stacking TS structure. By comparing various levels of theories (including long‐range corrected DFT functionals), we demonstrate that the Hartree‐Fock exchange at long range plays a critical role in obtaining the sufficient stacking stabilization of the present open‐shell system, and that the sole addition of empirical dispersion correction to semilocal DFT functionals may not be adequate for describing such a stacking interaction. Next, we investigate the solvent effect on the PCET and HAT TS thus obtained using the reference interaction site model self‐consistent field (RISM‐SCF) method. The results suggest that the free energy barrier increases with increasing polarity of the solvent, and that the solvent effects are stronger for the PCET TS than the stacking HAT TS pathway. The reason for this is discussed based on the dipole moment of different TS structures in solution. Copyright for JCC Journal:

An Accurate Calculation of Electronic Contribution to Static Permittivity Tensor for Organic Molecular Crystals on the Basis of the Charge Response Kernel Theory

We have developed a new method to calculate the static permittivity tensors of organic molecular crystals by applying the charge response kernel theory (Morita, A.; Kato, S. J. Am. Chem. Soc. 1997, 119, 4021) in which all the parameters were obtained with the density functional theory. The accuracy together with the requirements of the computation was discussed in terms of positions of the charge response sites and choice of a basis set. The calculated permittivities of typical organic compounds turned out to agree with the experimentally obtained values in the deviation of about 7% when a reasonable computational cost was maintained.

Polarizable Force Field for Protein with Charge Response Kernel.

We present a molecular mechanical force field for polypeptides and proteins involving the electronic polarization effect described with the charge response kernel. All of the electrostatic parameters for 20 amino acids are obtained by ab initio electronic structure calculations and combined with the AMBER99 force field. The refittings of dihedral angle parameters in the torsional potentials are performed so as to reproduce the ab initio optimized geometries and relative energies for the conformers of dipeptides. The present force field is applied to molecular dynamics simulation calculations of the extended alanine tetra and cyclic pentapeptides in aqueous solution. The infrared spectra are calculated in order to analyze the charge polarization effect on the spectral profiles.

Proton transfer in phenol-amine complexes: phenol electronic effects on free energy profile in solution.

Free energy profiles for the proton transfer reactions in hydrogen‐bonded complex of phenol with trimethylamine in methyl chloride solvent are studied with the reference interaction site model self‐consistent field method. The reactions in both the electronic ground and excited states are considered. The second‐order Møller‐Plesset perturbation (MP) theory or the second‐order multireference MP theory is used to evaluate the effect of the dynamical electron correlation on the free energy profiles. The free energy surface in the ground state shows a discrepancy with the experimental results for the related hydrogen‐bonded complexes. To resolve this discrepancy, the effects of chloro‐substitutions in phenol are examined, and its importance in stabilizing the ionic form is discussed. The temperature effect is also studied. In contrast to the ground state, the ππ* excited state of phenol–trimethylamine complex exhibits the proton transfer reaction with a low barrier. The reaction is almost thermoneutral. This is attributed to the reduction of proton affinity of phenol by the ππ* electronic excitation. We further examine the possibility of the electron–proton–coupled transfer in the ππ* state through the surface crossing with the charge transfer type πσ* state.