Vibrational frequency fluctuation of ions in aqueous solutions studied by three-pulse infrared photon echo method

In liquid water, hydrogen bonds form three-dimensional network structures, which have been modeled in various molecular dynamics simulations. Locally, the hydrogen bonds continuously form and break, and the network structure continuously fluctuates. In aqueous solutions, the water molecules perturb the solute molecules, resulting in fluctuations of the electronic and vibrational states. These thermal fluctuations are fundamental to understanding the activation processes in chemical reactions and the function of biopolymers. In this Account, we review studies of the vibrational frequency fluctuations of solute molecules in aqueous solutions using three-pulse infrared photon echo experiments. For comparison, we also briefly describe dynamic fluorescence Stokes shift experiments for investigating solvation dynamics in water. The Stokes shift technique gives a response function, which describes the energy relaxation in the nonequilibrium state and corresponds to the transition energy fluctuation of the electronic state at thermal equilibrium in linear response theorem. The dielectric response of water in the megahertz to terahertz frequency region is a key physical quantity for understanding both of these frequency fluctuations because of the influence of electrostatic interactions between the solute and solvent. We focus on the temperature dependence of the three experiments to discuss the molecular mechanisms of both the frequency fluctuations in aqueous solutions. We used a biexponential function with sub-picosecond and picosecond time constants to characterize the time-correlation functions of both the vibrational and electronic frequency fluctuations. We focus on the slower component, with time constants of 1-2 ps for both the frequency fluctuations at room temperature. However, the temperature dependence and isotope effect for the time constants differ for these two types of fluctuations. The dielectric interactions generally describe the solvation dynamics of polar solvents, and hydrodynamic theory can describe the slow component for the electronic states. Compared with the slow component of the solvation dynamics, however, the picosecond component for the vibrational frequency fluctuations is less sensitive to temperature. Therefore, the slow component of the vibrational frequency fluctuation is determined by different underlying dynamics, which are important for the solvation dynamics of the electronic state. The time constant for the picosecond component for the vibrational frequency fluctuation does not significantly depend on the solute. We propose that the vibrational frequency fluctuates because of the constant structural changes in the hydrogen-bonding network of water molecules around the solute.

Temperature dependence of vibrational frequency fluctuation of N(3) (-) in D(2)O

We have studied the temperature dependence of the vibrational frequency fluctuation of the antisymmetric stretching mode of N(3) (-) in D(2)O by three-pulse infrared (IR) photon echo experiments. IR pump-probe measurements were also carried out to investigate the population relaxation and the orientational relaxation of the same band. It was found that the time-correlation function (TCF) of the frequency fluctuation of this mode is well described by a biexponential function with a quasistatic term. The faster decay component has a time constant of about 0.1 ps, and the slower component varies from 1.4 to 1.1 ps in the temperature range from 283 to 353 K. This result indicates that liquid dynamics related to the frequency fluctuation are not highly sensitive to temperature. We discuss the relationship between the temperature dependence of the vibrational frequency fluctuation and that of the molecular motion of the system to investigate the molecular origin of the frequency fluctuation of the solute. We compare the temperature dependence of the frequency fluctuation with that of other dynamics such as dielectric relaxation of water. In contrast to the Debye dielectric relaxation time of D(2)O, the two time constants of the TCF of the frequency fluctuation do not exhibit strong temperature dependence. We propose a simple theoretical model for the frequency fluctuation in solutions based on perturbation theory and the dipole-dipole interaction between the vibrational mode of the solute and the solvent molecules. This model suggests that the neighboring solvent molecules in the vicinity of the solute play an important role in the frequency fluctuation. We suggest that the picosecond component of the frequency fluctuation results from structural fluctuation of the hydrogen-bonding network in water.

TIGER2: an improved algorithm for temperature intervals with global exchange of replicas

An empirical sampling method for molecular simulation based on "temperature intervals with global exchange of replicas" (TIGER2) has been developed to reduce the high demand for computational resources and the low computational efficiency of the conventional replica-exchange molecular dynamics (REMD) method. This new method overcomes the limitation of its previous version, called TIGER, which requires the assumption of constant heat capacity during quenching of replicas from elevated temperatures to the baseline temperature. The robustness of the TIGER2 method is examined by comparing it against a Metropolis Monte Carlo simulation for sampling the conformational distribution of a single butane molecule in vacuum, a REMD simulation for sampling the behavior of alanine dipeptide in explicit solvent, and REMD simulations for sampling the folding behavior of two peptides, (AAQAA)(3) and chignolin, in implicit solvent. The agreement between the results from these conventional sampling methods and the TIGER2 simulations indicates that the TIGER2 algorithm is able to closely approximate a Boltzmann-weighted ensemble of states for these systems but without the limiting assumptions that were required for the original TIGER algorithm. TIGER2 is an efficient replica-exchange sampling method that enables the number of replicas that are used for a replica-exchange simulation to be substantially reduced compared to the conventional REMD method.

An improved replica-exchange sampling method: temperature intervals with global energy reassignment

In a molecular dynamics (MD) simulation, representative sampling over the entire phase space is desired to obtain an accurate canonical distribution at a given temperature. For large molecules, such as proteins, this is problematic because systems tend to become trapped in local energy minima. The extensively used replica-exchange molecular dynamics (REMD) simulation technique overcomes this kinetic-trapping problem by allowing Boltzmann-weighted configuration exchange processes to occur between numerous thermally adjacent and compositionally identical simulations that are thermostated at sequentially higher temperatures. While the REMD method provides much better sampling than conventional MD, there are two substantial difficulties that are inherent in its application: (1) the large number of replicas that must be used to span a designated temperature range and (2) the subsequent long time required for configurations sampled at high temperatures to exchange down for potential inclusion within the low-temperature ensemble of interest. In this work, a new method based on temperature intervals with global energy reassignment (TIGER) is presented that overcomes both of these problems. A TIGER simulation is conducted as a series of short heating-sampling-quenching cycles. At the end of each cycle, the potential energies of all replicas are simultaneously compared at the same temperature using a Metropolis sampling method and then globally reassigned to the designated temperature levels. TIGER is compared with regular MD and REMD methods for the alanine dipeptide in water. The results indicate that TIGER increases sampling efficiency while substantially reducing the number of central processing units required for a comparable conventional REMD simulation.

Dynamics of a Multimode System Coupled to Multiple Heat Baths Probed by Two-Dimensional Infrared Spectroscopy

Reduced equation of motion for a multimode system coupled to multiple heat baths is constructed by extending the quantum Fokker-Planck equation with low-temperature correction terms (J. Phys. Soc. Jpn. 2005, 74, 3131). Unlike such common approaches used to describe intramolecular multimode vibration as a Bloch-Redfield theory and a stochastic theory, the present formalism is defined by the molecular coordinates. To explore the correlation among different modes through baths, we consider two cases of system-bath couplings. One is a correlated case in which two modes are coupled to a single bath, and the other is an uncorrelated case in which each mode is coupled to a different bath. We further classify the correlated case into two cases, the plus- and minus-correlated cases, according to distinct correlation manners. For these, one-dimensional and two-dimensional infrared (2D-IR) spectra are calculated numerically by solving the equation of motion. It is demonstrated that 2D-IR spectroscopy has the ability to analyze the correlation of fluctuation-dissipation processes among different modes.

Intra- and intermolecular vibrational energy transfer in tungsten carbonyl complexes W(CO)5(X) (X=CO, CS, CH3CN, and CD3CN)

Vibrational energy relaxation of degenerate CO stretches of four tungsten carbonyl complexes, W(CO)6, W(CO)5(CS), W(CO)5(CH3CN), and W(CO)5(CD3CN), is observed in nine alkane solutions by subpicosecond time-resolved infrared (IR) pump-probe spectroscopy. Between 0 and 10 ps after the vibrational excitation, the bleaching signal of the ground-state IR absorption band shows anisotropy. Decay of the anisotropic component corresponds either to the rotational diffusion of the molecule or to the intramolecular vibrational energy transfer among the degenerate CO stretch modes. The time constant of the anisotropy decay, tauaniso, shows distinct solvent dependence. By comparing the results for the T1u CO stretch of W(CO)6 and the A1 CO stretch of W(CO)5(CS), the time constant of the rotational diffusion, taur, and the time constant of the intramolecular energy transfer among the three degenerate vibrational modes, taue, are determined as 12 and 8 ps, respectively. The tauaniso value increases as the number of carbon atoms in the alkane solvent increases. After 10 ps, the recovery of the bleaching becomes isotropic. The isotropic decay represents the vibrational population relaxation, from v=1 to v=0. In heptane, the time constant for the isotropic decay, tau1, for W(CO)5(CS) and W(CO)6 was 140 ps. The tau1 for the two acetonitrile-substituted complexes, however, shows a smaller value of 80 ps. The vibrational energy relaxation of W(CO)5(CH3CN) and W(CO)5(CD3CN) is accelerated by the intramolecular energy redistribution from the CO ligand to the acetonitrile ligand. In the nine alkane solutions, the tau1 value of W(CO)6 ranges between 124 and 158 ps, showing the apparent V-shaped solvent dependence with its minimum in decane, while the tau1 value shows little solvent dependence for W(CO)5(CH3CN) and W(CO)5(CD3CN).