Spectroscopic interpretation: the high vibrations of CDBrClF

We extract the dynamics implicit in an algebraic fitted model Hamiltonian for the deuterium chromophore's vibrational motion in the molecule CDBrClF. The original model has four degrees of freedom, three positions and one representing interbond couplings. A conserved polyad allows in a semiclassical approach the reduction to three degrees of freedom. For most quantum states we can identify the underlying motion that when quantized gives the said state. Most of the classifications, identifications, and assignments are done by visual inspection of the already available wave function semiclassically transformed from the number representation to a representation on the reduced dimension toroidal configuration space corresponding to the classical action and angle variables. The concentration of the wave function density to lower dimensional subsets centered on idealized simple lower dimensional organizing structures and the behavior of the phase along such organizing centers already reveals the atomic motion. Extremely little computational work is needed.     

Inelastic neutron scattering study of hydrogen in d(8)-THFD(2)O ice clathrate

In situ neutron inelastic scattering experiments on hydrogen adsorbed into a fully deutrated tetrahydrofuran-water ice clathrate show that the adsorbed hydrogen has three rotational excitations (transitions between J=0 and 1 states) at approximately 14 meV in both energy gain and loss. These transitions could be unequivocally assigned since there was residual orthohydrogen at low temperatures (slow conversion to the ground state) resulting in an observable J=1-->0 transition at 5 K (kT=0.48 meV). A doublet in neutron energy loss at approximately 28.5 meV is interpreted as J=1-->2 transitions. In addition to the transitions between rotational states, there are a series of peaks that arise from transitions between center-of-mass translational quantum states of the confined hydrogen molecule. A band at approximately 9 meV can be unequivocally interpreted as a transition between translational states, while broad features at 20, 25, 35, and 50-60 meV are also interpreted to as transitions between translational quantum states. A detailed comparison is made with a recent five-dimensional quantum treatment of hydrogen in the smaller dodecahedral cage in the SII ice-clathrate structure. Although there is broad agreement regarding the features such as the splitting of the J=1 degeneracy, the magnitude of the external potential is overestimated. The numerous transitions between translational states predicted by this model are in poor agreement with the experimental data. Comparisons are also made with three simple exactly solved models, namely, a particle in a box, a particle in a sphere, and a particle on the surface of a sphere. Again, there are too many predicted features by the first two models, but there is reasonable agreement with the particle on a sphere model. This is consistent with published quantum chemistry results for hydrogen in the dodecahedral 5(12) cage, where the center of the cage is found to be energetically unfavorable, resulting in a shell-like confinement for the hydrogen molecule wave function. These results demonstrate that translational quantum effects are very significant and a classical treatment of the hydrogen molecule dynamics is inappropriate under such conditions.     

Ultrafast dynamics of halogens in rare gas solids

We perform time resolved pump-probe spectroscopy on small halogen molecules ClF, Cl2, Br2, and I2 embedded in rare gas solids (RGS). We find that dissociation, angular depolarization, and the decoherence of the molecule is strongly influenced by the cage structure. The well ordered crystalline environment facilitates the modelling of the experimental angular distribution of the molecular axis after the collision with the rare gas cage. The observation of many subsequent vibrational wave packet oscillations allows the construction of anharmonic potentials and indicate a long vibrational coherence time. We control the vibrational wave packet revivals, thereby gaining information about the vibrational decoherence. The coherence times are remarkable larger when compared to the liquid or high pressure gas phase. This fact is attributed to the highly symmetric molecular environment of the RGS. The decoherence and energy relaxation data agree well with a perturbative model for moderate vibrational excitation and follow a classical model in the strong excitation limit. Furthermore, a wave packet interferometry scheme is applied to deduce electronic coherence times. The positions of those cage atoms, excited by the molecular electronic transitions are modulated by long living coherent phonons of the RGS, which we can probe via the molecular charge transfer states.     

Bistable stochastic biochemical networks: highly specific systems with few chemicals

In this paper we describe a class of stochastic biochemical systems exhibiting bistable behavior, in the sense that the invariant measure associated to the system is concentrated near two different classes of states of the system. We develop methods that allow us to describe the behavior of the invariant measure in some suitable asymptotic limits, as well as the switching times for the transitions between the states close to each of the states with high probability. Due to the discrete character of the problem, switching times cannot be computed using the classical Kramers’ formula, and alternative methods are required.     

Theory of the statistics of kinetic transitions with application to single-molecule enzyme catalysis

Single-molecule spectroscopy can monitor transitions between two microscopic states when these transitions are associated with the emission of photons. A general formalism is developed for obtaining the statistics of such transitions from a microscopic model when the dynamics is described by master or rate equations or their continuum analog, multidimensional reaction-diffusion equations. The focus is on the distribution of the number of transitions during a fixed observation time, the distribution of times between transitions, and the corresponding correlation functions. It is shown how these quantities are related to each other and how they can be explicitly calculated in a straightforward way for both immobile and diffusing molecules. Our formalism reduces to renewal theory when the monitored transitions either go to or originate from a single state. The influence of dynamics slow compared with the time between monitored transitions is treated in a simple way, and the probability distributions are expressed in terms of Mandel-type formulas. The formalism is illustrated by a detailed analysis of the statistics of catalytic turnovers of enzymes. When the rates of conformational changes are slower than the catalytic rates which are in turn slower than the binding relaxation rate, (1) the mean number of turnovers is shown to have the classical Michaelis-Menten form, (2) the correlation function of the number of turnovers is a direct measure of the time scale of catalytic rate fluctuations, and (3) the distribution of the time between consecutive turnovers is determined by the steady-state distribution.     

A six-dimensional H(2)-H(2) potential energy surface for bound state spectroscopy

We present a six-dimensional potential energy surface for the (H(2))(2) dimer based on coupled-cluster electronic structure calculations employing large atom-centered Gaussian basis sets and a small set of midbond functions at the dimer's center of mass. The surface is intended to describe accurately the bound and quasibound states of the dimers (H(2))(2), (D(2))(2), and H(2)-D(2) that correlate with H(2) or D(2) monomers in the rovibrational levels (v,j)=(0,0), (0,2), (1,0), and (1,2). We employ a close-coupled approach to compute the energies of these bound and quasibound dimer states using our potential energy surface, and compare the computed energies for infrared and Raman transitions involving these states with experimentally measured transition energies. We use four of the experimentally measured dimer transition energies to make two empirical adjustments to the ab initio potential energy surface; the adjusted surface gives computed transition energies for 56 experimentally observed transitions that agree with experiment to within 0.036 cm(-1). For 26 of the 56 transitions, the agreement between the computed and measured transition energies is within the quoted experimental uncertainty. Finally, we use our potential energy surface to predict the energies of another 34 not-yet-observed infrared and Raman transitions for the three dimers.     

Freezing and folding behavior in simple off-lattice heteropolymers

We have performed parallel tempering Monte Carlo simulations using a simple continuum heteropolymer model for proteins. All 10 heteropolymer sequences which we have studied have shown first-order transitions at low temperature to ordered states dominated by single chain conformations. These results are in contrast with the theoretical predictions of the random energy model for heteropolymers, from which we would expect continuous transitions to glassy behavior at low temperatures.     

The performance of time-dependent density functional theory based on a noncollinear exchange-correlation potential in the calculations of excitation energies

In the present work we have studied the accuracy of excitation energies calculated from spin-flip transitions with a formulation of time-dependent density functional theory based on a noncollinear exchange-correlation potential proposed in a previous study. We compared the doublet-doublet excitation energies from spin-flip transitions and ordinary transitions, calculated the multiplets splitting of some atoms, the singlet-triplet gaps of some diradicals, the energies of excited quartet states with a doublet ground state. In addition, we attempted to calculate transition energies with excited states as reference. We compared the triplet excitation energies and singlet-triplet separations of the excited state from spin-flip and ordinary transitions. As an application, we show that using excited quartet state as reference can help us fully resolve excited states spin multiplets. In total the obtained excitation energies calculated from spin-flip transitions agree quite well with other theoretical results or experimental data.     

Potential-energy surfaces of local excited states from subsystem- and selective Kohn-Sham-TDDFT

Calculating excited-state potential-energy surfaces for systems with a large number of close-lying excited states requires the identification of the relevant electronic transitions for several geometric structures. Time-dependent density functional theory (TDDFT) is very efficient in such calculations, but the assignment of local excited states of the active molecule can be difficult. We compare the results of the frozen-density embedding (FDE) method with those of standard Kohn-Sham density-functional theory (KS-DFT) and simpler QM/MM-type methods. The FDE results are found to be more accurate for the geometry dependence of excitation energies than classical models. We also discuss how selective iterative diagonalization schemes can be exploited to directly target specific excitations for different structures. Problems due to strongly interacting orbital transitions and possible solutions are discussed. Finally, we apply FDE and the selective KS-TDDFT to investigate the potential energy surface of a high-lying π → π^∗ excitation in a pyridine molecule approaching a silver cluster.     

Cornucopian cylindrical aggregate morphologies from self-assembly of amphiphilic triblock copolymer in selective media

We have investigated, both experimentally and theoretically, the aggregation of ABA amphiphilic triblock copolymers in dilute solution. We observed a number of complex architectures having toroidal and network structures, including some novel ones. The computational analyses of these systems offer some insight into the origins of the self-assembly of these amphiphiles. The results we obtained using real-space self-consistent field theory reveal that the formation of network and toroidal structures from the block copolymers occurs as the result of the breaking of "inhomogeneous vesicles"; the observed polymorphism results from the existence of multiple metastable states.     

High resolution rotational spectroscopy on D2O up to 2.7 THz in its ground and first excited vibrational bending states

We present highly accurate laboratory measurements on the pure rotational spectrum of doubly deuterated water, D2O, in selected frequency regions from 10 GHz up to 2.7 THz. Around 140 rotational transitions in both the vibrational ground and first excited bending states (upsilon2=0,1) were measured in total, involving energy levels with unexcelled high J and Ka rotational quantum numbers. The data give valuable information for the spectroscopic analysis of this molecule. In the case of the light and non-rigid water molecule, standard methods for its analysis are limited due to large centrifugal distortion interactions. Here, we present a global analysis of rotational and rovibrational data of the upsilon2=0 and 1 states of D2O by means of an Euler expansion of the Hamiltonian. In addition to the newly measured pure rotational transitions, around 4000 rotational and rovibrational lines have been included from previous work. It was possible to reproduce the extensive dataset to nearly its experimental uncertainty. The improved predictive capability of the model compared to previous work will be demonstrated.     

Classical theory of collisional entropy production

A classical dynamical theory of elementary collision processes is formulated in analogy to the quantum theory of the dynamical scattering matrix, which can be defined for a pure quantum stationary scattering state. The elements of this matrix are probability amplitudes for transitions between internal states defined for given values of a reaction coordinate. The squared magnitudes of these amplitudes, modeled in the proposed classical theory, define normalized internal state population distributions suitable for information theoretical analysis. Statistical entropy and surprisal are defined as dynamical functions of a reaction coordinate. This formalism differs fundamentally from concepts based on the classical Liouville equation.     

Parity-dependent rotational rainbows in D2-NO and He-NO differential collision cross sections

The (j', Omega', epsilon') dependent differential collision cross sections of D2 with fully state selected (j = 12, Omega = 12, epsilon = -1) NO have been determined at a collision energy of about 550 cm(-1). The collisionally excited NO molecules are detected by (1+1') resonance enhanced multiphoton ionization combined using velocity-mapped ion-imaging. The results are compared to He-NO scattering results and tend to be more forward scattered for the same final rotational state. Both for collisions of the atomic He and the molecular D2 with NO, scattering into pairs of rotational states with the same value of n = j' - epsilon epsilon'2 yields the same angular dependence of the cross section. This "parity propensity rule" remains present both for spin-orbit conserving and spin-orbit changing transitions. The maxima in the differential cross sections-that reflect rotational rainbows-have been extracted from the D2-NO and the He-NO differential cross sections. These maxima are found to be distinct for odd and even parity pair number n. Rainbow positions of parity changing transitions (n is odd) occur at larger scattering angles than those of parity conserving transitions (n is even). Parity conserving transitions exhibit-from a classical point of view-a larger effective eccentricity of the shell. No rainbow doubling due to collisions onto either the N-end or the O-end was observed. From a classical point of view the presence of a double rainbow is expected. Rotational excitation of the D2 molecules has not been observed.     

Characterization of rough surfaces with vibrated drops

Wetting transitions were studied with vertically-vibrated drops on various artificial and natural rough substrates. Alternative pathways of wetting transitions were observed. The model of wetting transition is presented. Multiple minima of the Gibbs free energy of a drop deposited on a rough surface explain alternative pathways of wetting transitions. We demonstrate that a wetting transition occurs when the constant force resulting from vibrations, Laplace and hydrostatic pressure acts on the triple line. It is shown that the final wetting states are mainly the Cassie impregnating wetting state with water penetrating the pores in the outer vicinity of the droplet or the Wenzel state with water inside the pores under the droplet whereas the substrate ahead the drop is dry.