Molecular dynamics with quantum transitions study of the vibrational relaxation of the HOD bend fundamental in liquid D2O

The molecular dynamics with quantum transitions method is used to study the vibrational relaxation of the HOD bend fundamental in liquid D(2)O. All of the vibrational bending degrees of freedom of the HOD and D(2)O molecules are described by quantum mechanics, while the remaining translational and rotational degrees of freedom are described classically. The effect of the coupling between the rotational and vibrational degrees of freedom of the deuterated water molecules is analyzed. A kinetic mechanism based on three steps is proposed in order to interpret the dynamics of the system. It is shown that intermolecular vibrational energy transfer plays an important role in the relaxation process and also that the transfer of energy into the rotational degrees of freedom is favored over the transfer of energy into the translational motions. The thermalization of the system after the relaxation is reached in a shorter time scale than that of the recovery of the hydrogen bond network. The relaxation and equilibration times obtained compare well with experimental and previous theoretical results.     

Laser diagnostics of elementary processes in molecular beam scattering on surfaces

We survey the main aspects of the laser techniques to study the elementary processes that take place in the scattering of molecules from crystallographic surfaces. We discuss the salient features of the accommodation of the translational, rotational and vibrational degrees of freedom of the scattered molecules and we summarize the main results of a recent comparative study of molecular beam scattering on graphite and diamond.     

State-resolved velocity map imaging of surface-scattered molecular flux

This work describes a novel surface-scattering technique which combines resonance enhanced multiphoton ionization (REMPI) with velocity-map imaging (VMI) to yield quantum-state and 2D velocity component resolved distributions in the scattered molecular flux. As an initial test system, we explore hyperthermal scattering (E(inc) = 21(5) kcal mol(-1)) of jet cooled HCl from Au(111) on atomically flat mica surfaces at 500 K. The resulting images reveal 2D (v(in-plane) and v(out-of-plane)) velocity distributions dominated by two primary features: trapping/thermal-desorption (TD) and a hyperthermal, impulsively scattering (IS) distribution. In particular, the IS component is strongly forward scattered and largely resolved in the velocity map images, which allows us to probe correlations between rotational and translational degrees of freedom in the IS flux without any model dependent deconvolution from the TD fraction. These correlations reveal that HCl molecules which have undergone a large decrease in velocity parallel to scattering plane have actually gained the most rotational energy, reminiscent of a dynamical energy constraint between these two degrees of freedom. The data are reduced to a rotational energy map that correlates with velocity along and normal to the scattering plane, revealing that exchange occurs primarily between rotation and the in-plane kinetic energy component, with v(out-of-plane) playing a relatively minor role.     

Effects of classical nonlinear resonances in grazing diatom-surface collisions

Energy transfer between vibrational, rotational, and translational degrees of freedom of a molecule during a collision process is enhanced when the classical frequencies associated with the initial state are in the proximity of nonlinear resonance conditions. We present an analysis of the classical resonant effects in the collisions of light diatoms with periodic surfaces, and discuss the initial conditions in which these effects can be observed. In particular, we find that for grazing incidence and resonant initial values of the classical frequencies, corresponding to specific vibro-rotational molecular states and translational energies, an efficient energy transfer between the intramolecular vibro-rotational degrees of freedom and the translational degree of freedom along a symmetry direction on the surface can be found. This efficient energy transfer manifests itself in the emergence of specific peaks in the molecular diffraction patterns. The predictions of the resonance analysis are contrasted with the results of classical trajectory calculations obtained in a diatom-rigid surface collision model.     

Dynamic arrest in a liquid of symmetric dumbbells: reorientational hopping for small molecular elongations

We present extensive equilibrium and out-of-equilibrium molecular-dynamics simulations of a liquid of symmetric dumbbell molecules, for constant packing fraction, as a function of temperature and molecular elongation. We compute diffusion constants as well as odd and even orientational correlators. The notations odd and even refer to the parity of the order l of the corresponding Legendre l polynomial, evaluated for the orientation of the molecular axis relative to its initial position. Rotational degrees of freedom of order l are arrested if, in the long-time limit, the corresponding orientational l correlator does not decay to zero. It is found that for large elongations translational and rotational degrees of freedom freeze at the same temperature. For small elongations only the even rotational degrees of freedom remain coupled to translational motions and arrest at a finite common temperature. On the contrary, the odd rotational degrees of freedom remain ergodic at all investigated temperatures. Hence, in the translationally arrested state, each molecule remains trapped in the cage formed by its neighboring molecules, but is able to perform 180 degrees rotations, which lead to relaxation only for the odd orientational correlators. The temperature dependence of the characteristic time of these residual rotations is well described by an Arrhenius law. Finally, we discuss the evidence in favor of the presence of the type-A transition for the odd rotational degrees of freedom, as predicted by mode-coupling theory for small molecular elongations. This transition is distinct from the type-B transition, associated with the arrest of the translational and even rotational degrees of freedom for small elongations, and with all degrees of freedom for large elongations. Odd orientational correlators are computed for small elongations at very low temperatures in the translationally arrested state. The obtained results suggest that hopping events restore the ergodicity of the odd rotational degrees of freedom at temperatures far below the A transition.     

Steering and ro-vibrational effects on dissociative adsorption and associative desorption of H2/Pd(100)

The interaction of hydrogen with many transition metal surfaces is characterized by a coexistence of activated with non-activated paths to adsorption with a broad distribution of barrier heights. By performing six-dimensional quantum dynamical calculations using a potential energy surface derived from ab initio calculations for the system H₂/Pd(100) we show that these features of the potential energy surface lead to strong steering effects in the dissociative adsorption and associative desorption dynamics.

In particular, we focus on the coupling of the translational, rotational and vibrational degrees of freedom of the hydrogen molecule in the reaction dynamics.     

Aging in a free-energy landscape model for glassy relaxation

The aging properties of a simple free-energy landscape model for the primary relaxation in supercooled liquids are investigated. The intermediate scattering function and the rotational correlation functions are calculated for the generic situation of a quench from a high temperature to below the glass transition temperature. It is found that the reequilibration of molecular orientations takes longer than for translational degrees of freedom. The time scale for reequilibration is determined by that of the primary relaxation as an intrinsic property of the model.     

Energy controlled insertion of polar molecules in dense fluids

We present a method to search low energy configurations of polar molecules in the complex potential energy surfaces associated with dense fluids. The search is done in the configurational space of the translational and rotational degrees of freedom of the molecule, combining steepest-descent and Newton-Raphson steps which embed information on the average sizes of the potential energy wells obtained from prior inspection of the liquid structure. We perform a molecular dynamics simulation of a liquid water shell which demonstrates that the method enables fast and energy-controlled water molecule insertion in aqueous environments. The algorithm finds low energy configurations of incoming water molecules around three orders of magnitude faster than direct random insertion. This method represents an important step towards dynamic simulations of open systems and it may also prove useful for energy-biased ensemble average calculations of the chemical potential.     

Product energy distribution for exothermic reactive collisions

A statistical-dynamic model for calculating product state distributions for reactive collisions is presented. For the vibrational-translational coupling Franck-Condon type approximations are adopted which lead to very good agreement with exact quantum calculations in the limit of the collinear arrangement. The rotational degrees of freedom are treated statistically. The energy distribution among vibrational translational and rotational degrees of freedom is discussed as a function of the masses and the attractive part of the potential. Extension from triatomic to polyatomic exchange reactions are considered. A detailed comparison with other simple models is made.     

State-to-state dynamics at the gas-liquid metal interface: rotationally and electronically inelastic scattering of NO[2Π(1/2)(0.5)] from molten gallium

Jet cooled NO molecules are scattered at 45° with respect to the surface normal from a liquid gallium surface at E(inc) from 1.0(3) to 20(6) kcal/mol to probe rotationally and electronically inelastic scattering from a gas-molten metal interface (numbers in parenthesis represent 1σ uncertainty in the corresponding final digits). Scattered populations are detected at 45° by confocal laser induced fluorescence (LIF) on the γ(0-0) and γ(1-1) A(2)Σ ← X(2)Π(Ω) bands, yielding rotational, spin-orbit, and λ-doublet population distributions. Scattering of low speed NO molecules results in Boltzmann distributions with effective temperatures considerably lower than that of the surface, in respectable agreement with the Bowman-Gossage rotational cooling model [J. M. Bowman and J. L. Gossage, Chem. Phys. Lett. 96, 481 (1983)] for desorption from a restricted surface rotor state. Increasing collision energy results in a stronger increase in scattered NO rotational energy than spin-orbit excitation, with an opposite trend noted for changes in surface temperature. The difference between electronic and rotational dynamics is discussed in terms of the possible influence of electron hole pair excitations in the conducting metal. While such electronically non-adiabatic processes can also influence vibrational dynamics, the γ(1-1) band indicates <2.6 × 10(-4) probability for collisional formation of NO(v = 1) at surface temperatures up to 580 K. Average translational to rotational energy transfer is compared from a hard cube model perspective with previous studies of NO scattering from single crystal solid surfaces. Despite a lighter atomic mass (70 amu), the liquid Ga surface is found to promote translational to rotational excitation more efficiently than Ag(111) (108 amu) and nearly as effectively as Au(111) (197 amu). The enhanced propensity for Ga(l) to transform incident translational energy into rotation is discussed in terms of temperature-dependent capillary wave excitation of the gas-liquid metal interface.     

Packing density and structure effects on energy-transfer dynamics in argon collisions with organic monolayers

A combined experimental and molecular-dynamics simulation study has been used to investigate energy-transfer dynamics of argon atoms when they collide with n-alkanethiols adsorbed to gold and silver substrates. These surfaces provide the opportunity to explore how surface structure and packing density of alkane chains affect energy transfer in gas-surface collisions while maintaining the chemical nature of the surface. The chains pack standing up with 12 degrees and 30 degrees tilt angles relative to the surface normal and number densities of 18.9 and 21.5 A(2)molecule on the silver and gold substrates, respectively. For 7-kJmol argon scattering, the two surfaces behave equivalently, fully thermalizing all impinging argon atoms. In contrast, these self-assembled monolayers (SAMs) are not equally efficient at absorbing the excess translational energy from high-energy, 35 and 80 kJmol, argon collisions. When high-energy argon atoms are scattered from a SAM on silver, the fraction of atoms that reach thermal equilibrium with the surface and the average energy transferred to the surface are lower than for analogous SAMs on gold. In the case of argon atoms with 80 kJmol of translational energy scattering from long-chain SAMs, 60% and 45% of the atoms detected have reached thermal equilibrium with the monolayers on gold and silver surfaces, respectively. The differences in the scattering characteristics are attributed to excitation efficiencies of different types of surface modes. The high packing density of alkyl chains on silver restricts certain low-energy degrees of freedom from absorbing energy as efficiently as the lower-density monolayers. In addition, molecular-dynamics simulations reveal that the extent to which argon penetrates into the monolayer is related to packing density. For argon atoms with 80-kJmol incident energy, we find 16% and 7% of the atoms penetrate below the terminal methyl groups of C(10) SAMs on gold and silver, respectively.     

Rotational correlation and dynamic heterogeneity in a kinetically constrained lattice gas

We study the dynamical heterogeneity and glassy dynamics in a kinetically constrained lattice-gas model which has both translational and rotational degrees of freedom. We find that the rotational relaxation time tracks the structural relaxation time as density is increased whereas the translational diffusion constant exhibits a strong decoupling. We investigate distributions of exchange and persistence times for both the rotational and translational degrees of freedom and compare our results on the distributions of rotational exchange times to recent single molecule studies.     

Structural relaxation and glass transition behavior of binary hard-ellipse mixtures

Structural relaxation and glass transition in binary hard-spherical particle mixtures have been reported to exhibit unusual features depending on the size disparity and composition. However, the mechanism by which the mixing effects lead to these features and whether these features are universal for particles with anisotropic geometries remains unclear. Here, we employ event-driven molecular dynamics simulation to investigate the dynamical and structural properties of binary two-dimensional hard-ellipse mixtures. We find that the relaxation dynamics for translational degrees of freedom exhibit equivalent trends as those observed in binary hard-spherical mixtures. However, the glass transition densities for translational and rotational degrees of freedom present different dependencies on size disparity and composition. Furthermore, we propose a mechanism based on structural properties that explain the observed mixing effects and decoupling behavior between translational and rotational motions in binary hard-ellipse systems.     

Classical model for electronically non-adiabatic collision processes resonance effects in electronic-vibrational energy transfer

A classical model for electronically non-adiabatic collision processes is applied to E → V energy transfer in a collinear system, A + BC (v = 1) → A¹ + BC (v = 0), resembling Br-H₂.The model, which treats electronic as well as translational, rotational, and vibrational degrees of freedom by classical mechanics, describes the resonance features in this process reasonably well.     

Reactive and nonreactive scattering of N2 from Ru(0001): a six-dimensional adiabatic study

We have studied the dissociative chemisorption and scattering of N(2) on and from Ru(0001), using a six-dimensional quasiclassical trajectory method. The potential energy surface, which depends on all the molecular degrees of freedom, has been built applying a modified Shepard interpolation method to a data set of results from density functional theory, employing the RPBE generalized gradient approximation. The frozen surface and Born-Oppenheimer [Ann. Phys. (Leipzig) 84, 457 (1927)] approximations were used, neglecting phonons and electron-hole pair excitations. Dissociative chemisorption probabilities are found to be very small even for translational energies much higher than the minimum reaction barrier, in good agreement with experiment. A comparison to previous low dimensional calculations shows the importance of taking into account the multidimensional effects of N(2) rotation and translation parallel to the surface. The new calculations strongly suggest a much smaller role of nonadiabatic effects than previously assumed on the basis of a comparison between low dimensional results and experiments [J. Chem. Phys. 115, 9028 (2001)]. Also in agreement with experiment, our theoretical results show a strong dependence of reaction on the initial vibrational state. Computed angular scattering distributions and parallel translation energy distributions are in good agreement with experiments on scattering, but the theory overestimates vibrational and rotational excitations in scattering.     

On the degeneracy of the Hessian matrix

A widespread notion in the computational chemistry literature about the Hessian matrix has been revisited, namely, that the Hessian matrix over Cartesian space is sixfold degenerate due to the three translational and three rotational degrees of freedom. It has been shown that this is true only at critical points on the potential energy hypersurface, otherwise the Hessian matrix is only threefold degenerate. The rotational degrees of freedom generally do not cause degeneracy in the Hessian matrix away from critical points.On leave until January 1993 from the Department of General and Analytical Chemistry, Technical University Budapest, Szt. Gellért 4, H-1111 Budapest, Hungary.     

Single-particle colloid tracking in four dimensions

Coating a close-packed fluorescent colloid monolayer with a nanometer-thick metal film followed by sonication in liquid produces modulated optical nanoprobes. The metal coating modulates the fluorescence as these structures rotate in suspension, enabling the use of these particles as probes to monitor both rotational and center-of-mass (translational) dynamics in complex environments. Here, we demonstrate methods to simultaneously measure two translational and two rotational degrees of freedom, with excellent agreement to theory. The capability to determine two angles of rotation opens several new avenues of future research.     

Calculation of rotational partition functions by an efficient Monte Carlo importance sampling technique

The evaluation of the classical rotational partition function represented by a configuration integral over all external and internal rotational degrees of freedom of nonrigid chain polyatomic molecules is described. The method of Pitzer and Gwinn is used to correct the classical partition function for quantum mechanical effects at low temperatures. The internal rotor hindrance and all coupling arising from the external and internal rotational degrees of freedom are explicitly taken into account. Importance sampling Monte Carlo based on the adaptive VEGAS algorithm to perform multidimensional integration is implemented within the TINKER program package. A multidimensional potential energy hypersurface is calculated with the MM3(2000) molecular mechanics force field. Numerical tests are performed on a number of small n-alkanes (from ethane to octane), for which the absolute entropies calculated at three different temperatures are compared both with the experimental values and with the previous theoretical results. The application of a more efficient importance sampling technique developed here results in a substantial reduction of statistical errors in the evaluation of the configuration integral for a given number of Monte Carlo steps. Error estimates for the calculated entropies are given, and possible sources of systematic errors, and their importance for a reliable prediction of the absolute entropy, are discussed.     

Hydrogen molecule in the small dodecahedral cage of a clathrate hydrate: quantum five-dimensional calculations of the coupled translation-rotation eigenstates

We report quantum five-dimensional (5D) calculations of the energy levels and wave functions of the hydrogen molecule, para-H2 and ortho-H2, confined inside the small dodecahedral (H2O)20 cage of the sII clathrate hydrate. All three translational and the two rotational degrees of freedom of H2 are included explicitly, as fully coupled, while the cage is treated as rigid. The 5D potential energy surface (PES) of the H2-cage system is pairwise additive, based on the high-quality ab initio 5D (rigid monomer) PES for the H2-H2O complex. The bound state calculations involve no dynamical approximations and provide an accurate picture of the quantum 5D translation-rotation dynamics of H2 inside the cage. The energy levels are assigned with translational (Cartesian) and rotational quantum numbers, based on calculated root-mean-square displacements and probability density plots. The translational modes exhibit negative anharmonicity. It is found that j is a good rotational quantum number, while the threefold degeneracy of the j = 1 level is lifted completely. There is considerable translation-rotation coupling, particularly for excited translational states.