J. L. Skinner

VIBRATIONAL SPECTROSCOPY AS A PROBE OF STRUCTURE AND DYNAMICS IN LIQUID WATER

Water is, of course, a fascinating and important substance. For such a simple molecule, its condensed phase properties are surprisingly complex. Here we might mention the many different solid phases, the higher density of the liquid as compared to ice Ih, and the density maximum (as a function of temperature) in the liquid phase. Moreover, for such a light molecule, many of the liquid-state properties are anomalous: the boiling point, freezing point, heat capacity, surface tension, and viscosity are all unusually high. Even so, it is perhaps surprising that we still do not fully understand the properties of the liquid state.1-3 From a theoretical point of view, this can probably be attributed to two features of liquid water: cooperative hydrogen bonding (H-bonding) and nuclear quantum effects. The former refers to the fact that the binding energy of two H-bonded molecules is modified by the presence of a third molecule.4-9 In terms of simulating the liquid, then, it follows that the potential energy cannot be written as a sum of twomolecule terms. This means that simple two-body simulation models cannot completely describe reality, and attempts to capture the effects of these many-body interactions with polarizable models are not fully satisfactory either.8,10 Nuclear quantum effects occur because the hydrogen nucleus is sufficiently light that classical mechanics for the nuclear motion is simply not adequate. Thus, classical mechanics cannot describe such important properties as spatial dispersion of the hydrogen positions, nuclear tunneling, zero-point energy, and quantization of nuclear motions. Much energy has recently been expended toward the simulation of liquid water using ab initio electronic-structure methods (which, in priniciple, will produce the correct Born-Oppenheimer potential surface, including the effects of many-body interactions),11-19 together with methods for quantum dynamics,19-25 but still more work needs to be done before we have a complete and accurate description.

Hydrogen bonding definitions and dynamics in liquid water

X-ray and neutron diffractions, vibrational spectroscopy, and x-ray Raman scattering and absorption experiments on water are often interpreted in terms of hydrogen bonding. To this end a number of geometric definitions of hydrogen bonding in water have been developed. While all definitions of hydrogen bonding are to some extent arbitrary, those involving one distance and one angle for a given water dimer are unnecessarily so. In this paper the authors develop a systematic procedure based on two-dimensional potentials of mean force for defining cutoffs for a given pair of distance and angular coordinates. They also develop an electronic structure-based definition of hydrogen bonding in liquid water, related to the electronic occupancy of the antibonding OH orbitals. This definition turns out to be reasonably compatible with one of the distance-angle geometric definitions. These two definitions lead to an estimate of the number of hydrogen bonds per molecule in liquid simple point charge/extended (SPC/E) water of between 3.2 and 3.4. They also used these and other hydrogen-bond definitions to examine the dynamics of local hydrogen-bond number fluctuations, finding an approximate long-time decay constant for SPC/E water of between 0.8 and 0.9 ps, which corresponds to the time scale for local structural relaxation.

Vibrational spectroscopy of HOD in liquid D2O. III. Spectral diffusion, and hydrogen-bonding and rotational dynamics

Time-resolved infrared spectroscopy has the potential to provide unprecedented information about molecular dynamics in liquids. In the case of water, one of the most exciting techniques being developed is transient hole-burning. From experiments on dilute HOD in D2O one can obtain the transition frequency time-correlation function for the OH stretch vibration, finding that it decays on a time scale of between 0.5 and 1 ps. In this paper we provide a molecular-level interpretation of this spectral diffusion time-correlation function. First, we verify that for hydrogen-bonded HOD molecules the instantaneous OH frequency is highly correlated with the distance to the (hydrogen-bonded) D2O molecule. Second, we show that the instantaneous OH frequency is highly correlated with whether or not the HOD molecule has a hydrogen bond. Finally, we show that the short-time dynamics of the spectral diffusion time-correlation function is due to hydrogen-bond stretching motions, while the longer-time decay observed in the...

IR and Raman spectra of liquid water: Theory and interpretation

IR and Raman (parallel- and perpendicular-polarized) spectra in the OH stretch region for liquid water were measured some years ago, but their interpretation is still controversial. In part, this is because theoretical calculation of such spectra for a neat liquid presents a formidable challenge due to the coupling between vibrational chromophores and the effects of motional narrowing. Recently we proposed an electronic structure/molecular dynamics method for calculating spectra of dilute HOD in liquid D(2)O, which relied on ab initio calculations on clusters to provide a map from nuclear coordinates of the molecules in the liquid to OH stretch frequencies, transition dipoles, and polarizabilities. Here we extend this approach to the calculation of couplings between chromophores. From the trajectories of the fluctuating local-mode frequencies, transition moments, and couplings, we use our recently developed time-averaging approximation to calculate the line shapes. Our results are in good agreement with experiment for the IR and Raman line shapes, and capture the significant differences among them. Our analysis shows that while the coupling between chromophores is relatively modest, it nevertheless produces delocalization of the vibrational eigenstates over up to 12 chromophores, which has a profound effect on the spectroscopy. In particular, our results demonstrate that the peak in the parallel-polarized Raman spectrum at about 3250 wavenumbers is collective in nature.

Relaxation processes and chemical kinetics

The role of relaxation processes in determining the rates of activated events has long been a point of discussion in chemical physics. In this paper, we re‐examine this issue. We idealize the problem as the classical motion of a particle in a one‐dimensional potential coupled to a heat bath. This situation is described by a kinetic equation with a ’’collision operator’’ glc. An expansion in powers of the damping constant g is developed. This expansion is not limited to the case of high activation barriers. We compare results for various choices of the collision operator and provide a new derivation of Slater’s new rate theory. A Pade approximant approach unifies our low g results with those in the high g, i.e., diffusive, regime.

Combined electronic structure/molecular dynamics approach for ultrafast infrared spectroscopy of dilute HOD in liquid H2O and D2O

We present a new approach that combines electronic structure methods and molecular dynamics simulations to investigate the infrared spectroscopy of condensed phase systems. This approach is applied to the OH stretch band of dilute HOD in liquid D2O and the OD stretch band of dilute HOD in liquid H2O for two commonly employed models of water, TIP4P and SPC/E. Ab initio OH and OD anharmonic transition frequencies are calculated for 100 HOD x (D2O)n and HOD x(H2O)n (n = 4-9) clusters randomly selected from liquid water simulations. A linear empirical relationship between the ab initio frequencies and the component of the electric field from the solvent along the bond of interest is developed. This relationship is used in a molecular dynamics simulation to compute frequency fluctuation time-correlation functions and infrared absorption line shapes. The normalized frequency fluctuation time-correlation functions are in good agreement with the results of previous theoretical approaches. Their long-time decay times are 0.5 ps for the TIP4P model and 0.9 ps for the SPC/E model, both of which appear to be somewhat too fast compared to recent experiments. The calculated line shapes are in good agreement with experiment, and improve upon the results of previous theoretical approaches. The methods presented are simple, and transferable to more complicated systems.

Hydrogen bonding at the water surface revealed by isotopic dilution spectroscopy

The air–water interface is perhaps the most common liquid interface. It covers more than 70 per cent of the Earth’s surface and strongly affects atmospheric, aerosol and environmental chemistry. The air–water interface has also attracted much interest as a model system that allows rigorous tests of theory, with one fundamental question being just how thin it is. Theoretical studies have suggested a surprisingly short ‘healing length’ of about 3 ångströms (1 Å = 0.1 nm), with the bulk-phase properties of water recovered within the top few monolayers. However, direct experimental evidence has been elusive owing to the difficulty of depth-profiling the liquid surface on the ångström scale. Most physical, chemical and biological properties of water, such as viscosity, solvation, wetting and the hydrophobic effect, are determined by its hydrogen-bond network. This can be probed by observing the lineshape of the OH-stretch mode, the frequency shift of which is related to the hydrogen-bond strength. Here we report a combined experimental and theoretical study of the air–water interface using surface-selective heterodyne-detected vibrational sum frequency spectroscopy to focus on the ‘free OD’ transition found only in the topmost water layer. By using deuterated water and isotopic dilution to reveal the vibrational coupling mechanism, we find that the free OD stretch is affected only by intramolecular coupling to the stretching of the other OD group on the same molecule. The other OD stretch frequency indicates the strength of one of the first hydrogen bonds encountered at the surface; this is the donor hydrogen bond of the water molecule straddling the interface, which we find to be only slightly weaker than bulk-phase water hydrogen bonds. We infer from this observation a remarkably fast onset of bulk-phase behaviour on crossing from the air into the water phase.

Hydrogen bonding and Raman, IR, and 2D-IR spectroscopy of dilute HOD in liquid D2O

We present improvements on our previous approaches for calculating vibrational spectroscopy observables for the OH stretch region of dilute HOD in liquid D2O. These revised approaches are implemented to calculate IR and isotropic Raman spectra, using the SPC/E simulation model, and the results are in good agreement with experiment. We also calculate observables associated with three-pulse IR echoes: the peak shift and 2D-IR spectrum. The agreement with experiment for the former is improved over our previous calculations, but discrepancies between theory and experiment still exist. Using our proposed definition for hydrogen bonding in liquid water, we decompose the distribution of frequencies in the OH stretch region in terms of subensembles of HOD molecules with different local hydrogen-bonding environments. Such a decomposition allows us to make the connection with experiments and calculations on water clusters and more generally to understand the extent of the relationship between transition frequency and local structure in the liquid.

Ultrafast vibrational spectroscopy of water and aqueous N-methylacetamide: Comparison of different electronic structure/molecular dynamics approaches.

Kwac and Cho [J. Chem. Phys. 119, 2247 (2003)] have recently developed a combined electronic structure/molecular dynamics approach to vibrational spectroscopy in liquids. The method involves fitting ab initio vibrational frequencies for a solute in a cluster of solvent molecules to a linear combination of the electrostatic potentials on the solute atoms due to the charges on the solvent molecules. These authors applied their method to the N-methylacetamide-D/D(2)O system. We (S. A. Corcelli, C. P. Lawrence, and J. L. Skinner, [J. Chem. Phys. 120, 8107 (2004)]) have recently explored a closely related method, where instead of the electrostatic potential, the solute vibrational frequencies are fit to the components of the electric fields on the solute atoms due to the solvent molecules. We applied our method to the HOD/D(2)O and HOD/H(2)O systems. In order to make a direct comparison of these two approaches, in this paper we apply their method to the water system, and our method to the N-methylacetamide system. For the water system we find that the electric field method is superior to the potential approach, as judged by comparison with experiments for the absorption line shape. For the N-methylacetamide system the two methods are comparable.

Vibrational spectroscopy of HOD in liquid D2O. II. Infrared line shapes and vibrational Stokes shift

We present semiclassical calculations of the infrared line shapes for the three intramolecular vibrations of dilute HOD in liquid D2O. In these calculations the vibrations of HOD are treated quantum mechanically, and the rotations and translations of all the molecules are treated classically. The approach and model, which is based on earlier work of Oxtoby and of Rey and Hynes, was discussed in detail in Paper I, on vibrational energy relaxation in the same system, of this series. A novel feature of our approach is a self-consistent renormalization scheme for determining the system and bath Hamiltonians for a given vibrational state of the HOD molecule. Our results for the line shapes are in reasonable agreement with experiment. We also explore the extent to which the frequency fluctuations leading to the line shape are Gaussian. Finally, we calculate the vibrational Stokes shift for the OH stretch fundamental. Our result, which is nonzero only because the specification of the bath Hamiltonian depends on ...