Liquid theory for band structure in a liquid. II.porbitals and phonons

Ab Initio Transient Vibrational Spectral Analysis

Pump probe spectroscopy techniques have enabled the direct observation of a variety of transient molecular species in both ground and excited electronic states. Time-resolved vibrational spectroscopy is becoming an indispensable tool for investigating photoinduced nuclear dynamics of chemical systems of all kinds. On the other hand, a complete picture of the chemical dynamics encoded in these spectra cannot be achieved without a full temporal description of the structural relaxation, including the explicit time-dependence of vibrational coordinates that are substantially displaced from equilibrium by electronic excitation. Here we present a transient vibrational analysis protocol combining ab initio direct molecular dynamics and time-integrated normal modes introduced in this work, relying on the recent development of analytic time-dependent density functional theory (TDDFT) second derivatives for excited states. Prototypical molecules will be used as test cases, showing the evolution of the vibrational signatures that follow electronic excitation. This protocol provides a direct route to assigning the vibrations implicated in the (photo)dynamics of several (photoactive) systems.

Effective numbers of modes applied to analysis of internal dynamics of weakly bound clusters

The dependence of the volume of the chaotic component in the internal dynamics of triatomic van der Waals clusters on the angular momentum is calculated using the Monte Carlo and molecular dynamics methods. It has been found that this dependence is nonmonotonic and that its functional form varies for different values of the total energy. The effective number of rotational modes was used to clarify why a change in the volume of chaotic component of the phase space happens for certain values of the angular momentum. We conclude that a large fraction of regular trajectories in relation to all trajectories appears only when there is a possibility for the regular motion to perform a rotation different from that for a chaotic motion. When such difference is small, the regular motion disappears. The effective number of rotational modes can be used to estimate the difference in the type of rotation and is a convenient parameter which controls changes in the dynamics of the system.

Phase space theory of evaporation in neon clusters: the role of quantum effects

Unimolecular evaporation of neon clusters containing between 14 and 148 atoms is theoretically investigated in the framework of phase space theory. Quantum effects are incorporated in the vibrational densities of states, which include both zero-point and anharmonic contributions, and in the possible tunneling through the centrifugal barrier. The evaporation rates, kinetic energy released, and product angular momentum are calculated as a function of excess energy or temperature in the parent cluster and compared to the classical results. Quantum fluctuations are found to generally increase both the kinetic energy released and the angular momentum of the product, but the effects on the rate constants depend nontrivially on the excess energy. These results are interpreted as due to the very few vibrational states available in the product cluster when described quantum mechanically. Because delocalization also leads to much narrower thermal energy distributions, the variations of evaporation observables as a function of canonical temperature appear much less marked than in the microcanonical ensemble. While quantum effects tend to smooth the caloric curve in the product cluster, the melting phase change clearly keeps a signature on these observables. The microcanonical temperature extracted from fitting the kinetic energy released distribution using an improved Arrhenius form further suggests a backbending in the quantum Ne(13) cluster that is absent in the classical system. Finally, in contrast to delocalization effects, quantum tunneling through the centrifugal barrier does not play any appreciable role on the evaporation kinetics of these rather heavy clusters.

Universality in the vibrational spectra of single-component amorphous clusters

We have numerically investigated the vibrational spectra of amorphous single-component clusters for several types of interactions among the particles. For all the potentials we have studied, we find that the density of states can be described, except at the two ends of the spectrum, by the same functional form to a very good approximation, and that the fluctuation properties of the spectra in this central region converge to those of the Gaussian orthogonal ensemble of random matrices with increasing system size. We conjecture that this scenario is true for a broad class of potentials.

Forces due to dynamic structure in thin liquid films

The long-range surface forces arising due to dynamic structure in thin liquid films are considered. The phonon formalism is applied to analyse the contribution of the collective motions in liquid to the excess free energy and the disjoining pressure of the film. It is shown that both the intermolecular interactions and the interactions between liquid and confining phases essentially have an influence on the sign and the magnitude of the phonon component of disjoining pressure and its temperature dependence. The methods and procedures used to assess the density of vibrational states for real and model liquids are discussed. The description of several spectroscopic experimental methodics specific for investigation of thin liquid interlayers is given concurrently with experimental data revealing the dynamic structuring in the course of film thinning.

Spectral statistics of instantaneous normal modes in liquids and random matrices

We study the statistical properties of eigenvalues of the Hessian matrix H (matrix of second derivatives of the potential energy) for a classical atomic liquid, and compare these properties with predictions for random matrix models. The eigenvalue spectra (the instantaneous normal mode or INM spectra) are evaluated numerically for configurations generated by molecular dynamics simulations. We find that distribution of spacings between nearest-neighbor eigenvalues, s, obeys quite well the Wigner prediction s exp(-s(2)), with the agreement being better for higher densities at fixed temperature. The deviations display a correlation with the number of localized eigenstates (normal modes) in the liquid; there are fewer localized states at higher densities that we quantify by calculating the participation ratios of the normal modes. We confirm this observation by calculating the spacing distribution for parts of the INM spectra with high participation ratios, obtaining greater conformity with the Wigner form. We also calculate the spectral rigidity and find a substantial dependence on the density of the liquid.

Mean-atom-trajectory model for the velocity autocorrelation function of monatomic liquids

We present a model for the motion of an average atom in a liquid or supercooled liquid state and apply it to calculations of the velocity autocorrelation function Z(t) and diffusion coefficient D. The model trajectory consists of oscillations at a distribution of frequencies characteristic of the normal modes of a single potential valley, interspersed with position- and velocity-conserving transits to similar adjacent valleys. The resulting predictions for Z(t) and D agree remarkably well with molecular dynamics simulations of Na at up to almost three times its melting temperature. Two independent processes in the model relax velocity autocorrelations: (a) dephasing due to the presence of many frequency components, which operates at all temperatures but which produces no diffusion, and (b) the transit process, which increases with increasing temperature and which produces diffusion. Because the model provides a single-atom trajectory in real space and time, including transits, it may be used to calculate all single-atom correlation functions.