Slow hydrogen-bond switching dynamics at the water surface revealed by theoretical two-dimensional sum-frequency spectroscopy.

Using our newly developed explicit three-body (E3B) water model, we simulate the surface of liquid water. We find that the timescale for hydrogen-bond switching dynamics at the surface is about three times slower than that in the bulk. In contrast, with this model rotational dynamics are slightly faster at the surface than in the bulk. We consider vibrational two-dimensional (2D) sum-frequency generation (2DSFG) spectroscopy as a technique for observing hydrogen-bond rearrangement dynamics at the water surface. We calculate the nonlinear susceptibility for this spectroscopy for two different polarization conditions, and in each case we see the appearance of cross-peaks on the timescale of a few picoseconds, signaling hydrogen-bond rearrangement on this timescale. We thus conclude that this 2D spectroscopy will be an excellent experimental technique for observing slow hydrogen-bond switching dynamics at the water surface.

Vibrational spectroscopy of water in hydrated lipid multi-bilayers. II. Two-dimensional infrared and peak shift observables within different theoretical approximations.

In a previous report, we calculated the infrared absorption spectrum and both the isotropic and anisotropic pump-probe signals for the OD stretch of isotopically dilute water in dilauroylphosphatidylcholine (DLPC) multi-bilayers as a function of the lipid hydration level. These results were then compared to recent experimental measurements and are in generally good agreement. In this paper, we will further investigate the structure and dynamics of hydration water using molecular dynamics simulations and calculations of the two-dimensional infrared and vibrational echo peak shift observables for hydration water in DLPC membranes. These observables have not yet been measured experimentally, but future comparisons may provide insight into spectral diffusion processes and hydration water heterogeneity. We find that at low hydration levels the motion of water molecules inside the lipid membrane is significantly arrested, resulting in very slow spectral diffusion. At higher hydration levels, spectral diffusion is more rapid, but still slower than in bulk water. We also investigate the effects of several common approximations on the calculation of spectroscopic observables by computing these observables within multiple levels of theory. The impact of these approximations on the resulting spectra affects our interpretation of these measurements and reveals that, for example, the cumulant approximation, which may be valid for certain systems, is not a good approximation for a highly heterogeneous environment such as hydration water in lipid multi-bilayers.

Semiclassical quantization in Liouville space for vibrational dynamics.

Semiclassical approximations to quantum mechanics can include quantum coherence effects in dynamical calculations based on classical mechanics. The Herman-Kluk (HK) semiclassical propagator has been demonstrated to reproduce quantum effects in nonlinear vibrational response functions of anharmonic oscillators but does not provide a practical numerical route to calculations for multiple degrees of freedom. In an HK calculation of a response function, quantum coherence effects enter through interference between pairs of classical trajectories. We have previously elucidated the mechanism by which the HK approximation reproduces quantum effects in response functions in the regime of quasiperiodic dynamics. We have applied this understanding to significantly simplify the semiclassical calculation of response functions in this dynamical regime. The phase space difference between trajectories is treated perturbatively in anharmonicity, allowing integration over these differences to be performed analytically and leaving integration over mean trajectories to be performed numerically. This mean-trajectory (MT) approximation has been applied to linear and nonlinear vibrational response functions for isolated and coupled anharmonic motions. Here, we derive an MT approximation for the Liouville space time evolution operator or superoperator that propagates the density operator. This analysis provides a form of the MT approximation that is readily applicable to other dynamical quantities besides response functions and clarifies the connection between semiclassical quantization of propagators for the wave function and for the density operator.

Semiclassical nonlinear response functions for coupled anharmonic vibrations.

Observables in linear and nonlinear infrared spectroscopy may be computed from vibrational response functions describing nuclear dynamics on a single electronic surface. We demonstrate that the Herman-Kluk (HK) semiclassical approximation to the quantum propagator yields an accurate representation of quantum coherence effects in linear and nonlinear response functions for coupled anharmonic oscillators. A considerable numerical price is paid for this accuracy; the calculation requires a multidimensional integral over a highly oscillatory integrand that also grows without bound as a function of evolution times. The interference among classical trajectories in the HK approximation produces quantization of good action variables. By treating this interference analytically, we develop a mean-trajectory (MT) approximation that requires only the propagation of classical trajectories linked by transitions in action. The MT approximation accurately reproduces coherence effects in response functions of coupled anharmonic oscillators in a regime in which the observables are strongly influenced by these interactions among vibrations.

Semiclassical mean-trajectory approximation for nonlinear spectroscopic response functions.

Observables in nonlinear and multidimensional infrared spectroscopy may be calculated from nonlinear response functions. Numerical challenges associated with the fully quantum-mechanical calculation of these dynamical response functions motivate the development of semiclassical methods based on the numerical propagation of classical trajectories. The Herman-Kluk frozen Gaussian approximation to the quantum propagator has been demonstrated to produce accurate linear and third-order spectroscopic response functions for thermal ensembles of anharmonic oscillators. However, the direct application of this propagator to spectroscopic response functions is numerically impractical. We analyze here the third-order response function with Herman-Kluk dynamics with the two related goals of understanding the origins of the success of the approximation and developing a simplified representation that is more readily implemented numerically. The result is a semiclassical approximation to the nth-order spectroscopic response function in which an integration over n pairs of classical trajectories connected by distributions of discontinuous transitions is collapsed to a single phase-space integration, in which n continuous trajectories are linked by deterministic transitions. This significant simplification is shown to retain a full description of quantum effects.

Interference and quantization in semiclassical response functions.

Application of the Herman-Kluk semiclassical propagator to the calculation of spectroscopic response functions for anharmonic oscillators has demonstrated the quantitative accuracy of these approximate dynamics. In this approach, spectroscopic response functions are expressed as multiple phase-space integrals over pairs of classical trajectories and their associated stability matrices. Here we analyze the Herman-Kluk semiclassical approximation to a linear response function and determine the origin of the capacity of this method to reproduce quantum effects in a response function from classical dynamical information. Our analysis identifies those classical trajectories that contribute most significantly to the response function on different time scales. This finding motivates a procedure for computing the linear response function in which the interference between pairs of classical trajectories is treated approximately, resulting in an integral over a single average trajectory, as in a purely classical calculation.

Surface-enhanced Raman spectroscopic study of 1,4-phenylene diisocyanide adsorbed on gold and platinum-group transition metal electrodes.

Self-assembled monolayers of 1, 4-phenylene diisocyanide (PDI) were formed on Au and Pt-group transition metals and examined by surface-enhanced Raman spectroscopy under controlled applied potential. On all of the metals examined, PDI adsorbs in an edge-on manner, with one NC group bound to the surface and the other pointing away from the surface. The N-C stretching frequency (nu(NC)) suggests that depending on the metal, PDI adsorbs on different binding sites: terminal sites on Au, both terminal and bridging on Rh and Pt, and predominantly 3-fold hollow sites for Pd. This binding site preference can be understood in terms of the difference in d-band center energy and d-orbital filling among the metals. The applied potential affects the N-C bonding differently as inferred from the potential dependence of nu(NC). On Au, Rh, and Pd, the nu(NC) increases linearly with the applied potential, yielding a Stark tuning slope, dnu(NC)/dE, of 25, 12, and 10 cm(-1)/V, respectively. On Pt, the nu(NC) is nearly independent of the applied potential. On all of the metals studied, the frequencies of benzene ring vibration modes are not dependent on the applied potential, consistent with the edge-on orientation in which the ring does not directly interact with the surface. Several ring vibrations are, however, sensitive to the nature of metal substrate due to different binding sites involved. The ability of the free NC group to function as an anchoring point is demonstrated by the attachment of gold nanoparticles on PDI-covered Au and Pd. The study provides useful NC-metal bonding information for isocyanide-based molecular electronic developments.