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At least 343 records · Page 19Linked to original sources
PubMed2004

Photodissociation of benzene under collision-free conditions: an ab initio/Rice-Ramsperger-Kassel-Marcus study.

The ab initio/Rice-Ramsperger-Kassel-Marcus (RRKM) approach has been applied to investigate the photodissociation mechanism of benzene at various wavelengths upon absorption of one or two UV photons followed by internal conversion into the ground electronic state. Reaction pathways leading to various decomposition products have been mapped out at the G2M level and then the RRKM and microcanonical variational transition state theories have been applied to compute rate constants for individual reaction steps. Relative product yields (branching ratios) for C(6)H(5)+H, C(6)H(4)+H(2), C(4)H(4)+C(2)H(2), C(4)H(2)+C(2)H(4), C(3)H(3)+C(3)H(3), C(5)H(3)+CH(3), and C(4)H(3)+C(2)H(3) have been calculated subsequently using both numerical integration of kinetic master equations and the steady-state approach. The results show that upon absorption of a 248 nm photon dissociation is too slow to be observable in molecular beam experiments. In photodissociation at 193 nm, the dominant dissociation channel is H atom elimination (99.6%) and the minor reaction channel is H(2) elimination, with the branching ratio of only 0.4%. The calculated lifetime of benzene at 193 nm is about 11 micros, in excellent agreement with the experimental value of 10 micros. At 157 nm, the H loss remains the dominant channel but its branching ratio decreases to 97.5%, while that for H(2) elimination increases to 2.1%. The other channels leading to C(3)H(3)+C(3)H(3), C(5)H(3)+CH(3), C(4)H(4)+C(2)H(2), and C(4)H(3)+C(2)H(3) play insignificant role but might be observed. For photodissociation upon absorption of two UV photons occurring through the neutral "hot" benzene mechanism excluding dissociative ionization, we predict that the C(6)H(5)+H channel should be less dominant, while the contribution of C(6)H(4)+H(2) and the C(3)H(3)+C(3)H(3), CH(3)+C(5)H(3), and C(4)H(3)+C(2)H(3) radical channels should significantly increase.

Journal Article↗
PubMed2004

State-to-state rotational relaxation rate constants for CO+Ne from IR-IR double-resonance experiments: comparing theory to experiment.

IR-IR double-resonance experiments were used to study the state-to-state rotational relaxation of CO with Ne as a collision partner. Rotational levels in the range Ji=2-9 were excited and collisional energy transfer of population to the levels Jf=2-8 was monitored. The resulting data set was analyzed by fitting to numerical solutions of the master equation. State-to-state rate constant matrices were generated using fitting law functions. Fitting laws based on the modified exponential gap (MEG) and statistical power exponential gap (SPEG) models were used; the MEG model performed better than the SPEG model. A rate constant matrix was also generated from scattering calculations that employed the ab initio potential energy surface of McBane and Cybulski [J. Chem. Phys. 110, 11 734 (1999)]. This theoretical rate constant matrix yielded kinetic simulations that agreed with the data nearly as well as the fitted MEG model and was unique in its ability to reproduce both the rotational energy transfer and pressure broadening data for Ne-CO. The theoretical rate coefficients varied more slowly with the energy gap than coefficients from either of the fitting laws.

Journal Article↗
PubMed2004

Fluctuation theorem for nonequilibrium reactions.

A fluctuation theorem is derived for stochastic nonequilibrium reactions ruled by the chemical master equation. The theorem is expressed in terms of the generating and large-deviation functions characterizing the fluctuations of a quantity which measures the loss of detailed balance out of thermodynamic equilibrium. The relationship to entropy production is established and discussed. The fluctuation theorem is verified in the Schlögl model of far-from-equilibrium bistability.

Journal Article↗
PubMed2004

Density and energy relaxation in an open one-dimensional system.

A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically. In this model, the random walkers interact through excluded volume interaction (single-file system); and the total number of walkers in the lattice can fluctuate because of exchange with a bath. In addition, the movement of the random walkers is biased by an external perturbation. Two models for the latter are considered: (1) an inverse potential (V proportional, variant 1/r), where r is the distance between the center of the perturbation and the random walker and (2) an inverse of sixth power potential (V proportional, 1/r6). The calculated density of the walkers and the total energy show interesting dynamics. When the size of the system is comparable to the range of the perturbing field, the energy relaxation is found to be highly nonexponential. In this range, the system can show stretched exponential (e-(t/taus)beta) and even logarithmic time dependence of energy relaxation over a limited range of time. Introduction of density exchange in the lattice markedly weakens this nonexponentiality of the relaxation function, irrespective of the nature of perturbation.

Journal Article↗
PubMed2004

Folding of the GB1 hairpin peptide from discrete path sampling.

The discrete path sampling technique is used to calculate folding pathways of the 16-amino acid beta hairpin-forming sequence from residues 41-56 of the B1 domain of protein G. The folding time is obtained using master equation dynamics and kinetic Monte Carlo simulations, and the time evolution of different order parameters and occupation probabilities of groups of minima are calculated and used to characterize intermediates on the folding pathway.

Binding Sites↗
PubMed2004

Non-Markovian theories based on a decomposition of the spectral density.

For the description of dynamical effects in quantum mechanical systems on ultrashort time scales, memory effects play an important role. Meier and Tannor [J. Chem. Phys. 111, 3365 (1999)] developed an approach which is based on a time-nonlocal scheme employing a numerical decomposition of the spectral density. Here we propose two different approaches which are based on a partial time-ordering prescription, i.e., a time-local formalism and also on a numerical decomposition of the spectral density. In special cases such as the Debye spectral density the present scheme can be employed even without the numerical decomposition of the spectral density. One of the proposed schemes is valid for time-independent Hamiltonians and can be given in a compact quantum master equation. In the case of time-dependent Hamiltonians one has to introduce auxiliary operators which have to be propagated in time along with the density matrix. For the example of a damped harmonic oscillator these non-Markovian theories are compared among each other, to the Markovian limit neglecting memory effects and time dependencies, and to exact path integral calculations. Good agreement between the exact calculations and the non-Markovian results is obtained. Some of the non-Markovian theories mentioned above treat the time dependence in the system Hamiltonians nonperturbatively. Therefore these methods can be used for the simulation of experiments with arbitrary large laser fields.

Journal Article↗
PubMed2004

Fluctuation theorem and Onsager reciprocity relations.

The Onsager and higher-order reciprocity relations are derived from a fluctuation theorem for nonequilibrium reactions ruled by the chemical master equation. The fluctuation theorem is obtained for the generating function of the macroscopic fluxes between chemiostats maintaining the system in a nonequilibrium steady state. The macroscopic affinities associated with the fluxes are identified by graph theory. The Yamamoto-Zwanzig formulas for the reaction constants are also derived from the fluctuation theorem.

Journal Article↗
PubMed2004

Stochastic dynamics of adhesion clusters under shared constant force and with rebinding.

Single receptor-ligand bonds have finite lifetimes, so that biological systems can dynamically react to changes in their environment. In cell adhesion, adhesion bonds usually act cooperatively in adhesion clusters. Outside the cellular context, adhesion clusters can be probed quantitatively by attaching receptors and ligands to opposing surfaces. Here we present a detailed theoretical analysis of the stochastic dynamics of a cluster of parallel bonds under shared constant loading and with rebinding. Analytical solutions for the appropriate one-step master equation are presented for special cases, while the general case is treated with exact stochastic simulations. If the completely dissociated state is modeled as an absorbing boundary, mean cluster lifetime is finite and can be calculated exactly. We also present a detailed analysis of fluctuation effects and discuss various approximations to the full stochastic description.

Journal Article↗
PubMed2004

Nuclear magnetic resonance proton dipolar order relaxation in thermotropic liquid crystals: a quantum theoretical approach.

By means of the Jeener-Broekaert nuclear magnetic resonance pulse sequence, the proton spin system of a liquid crystal can be prepared in quasiequilibrium states of high dipolar order, which relax to thermal equilibrium with the molecular environment with a characteristic time (T1D). Previous studies of the Larmor frequency and temperature dependence of T1D in thermotropic liquid crystals, that included field cycling and conventional high-field experiments, showed that the slow hydrodynamic modes dominate the behavior of T1D, even at high Larmor frequencies. This noticeable predominance of the cooperative fluctuations (known as order fluctuations of the director, OFD) could not be explained by standard models based on the spin-lattice relaxation theory in the limit of high temperature (weak order). This fact points out the necessity of investigating the role of the quantum terms neglected in the usual high temperature theory of dipolar order relaxation. In this work, we present a generalization of the proton dipolar order relaxation theory for highly correlated systems, which considers all the spins belonging to correlated domains as an open quantum system interacting with quantum bath. As starting point, we deduce a formulation of the Markovian master equation of relaxation for the statistical spin operator, valid for all temperatures, which is suitable for introducing a dipolar spin temperature in the quantum regime, without further assumptions about the form of the spin-lattice Hamiltonian. In order to reflect the slow dynamics occurring in correlated systems, we lift the usual short-correlation-time assumption by including the average over the motion of the dipolar Hamiltonian together with the Zeeman Hamiltonian into the time evolution operator. In this way, we calculate the time dependence of the spin operators in the interaction picture in a closed form, valid for high magnetic fields, bringing into play the spin-spin interactions within the microscopic time scale. Then, by adopting the spin-temperature density operator to represent the collective state of the spin system, and removing the traditional hypothesis of high temperature, we deduce an expression for the first order quantum contribution to T1D (-1), in terms of spectral densities, with coefficients in form of spin traces. The properties that distinguish our result from the high-temperature T1D (-1) are as follows. (a) It is exclusively associated to cooperative fluctuations. (b) Because of its quantum character, it relies on both considering the lattice degrees of freedom quantum mechanically and including the spin-spin interactions in the microscopic time scale. With regard to the average dipolar Hamiltonian, only the nonsecular part plays a relevant role. (c) Associated with the structure of the spin operator involved in the quantum contribution, a term arises which is proportional to the number of spins in the correlated molecular domains, showing that the quantum contribution may be of macroscopic size in highly correlated systems. When applied to nematic liquid crystals, the new term exhibits the typical nu(-1/2) Larmor frequency dependence through the spectral density of the OFD, in consistence with the experimental results.

Journal Article↗
PubMed2005

Dissipative quantum phase space dynamics on dynamically adapting grids.

A moving grid approach to a dynamical study of dissipative systems is described. The dynamics are studied in phase space for the Caldeira-Leggett master equation. The grid movement is based on the principle of equidistribution and, by using a grid smoothing technique, the grid points trace a path that continuously adapts to reflect the dynamics of a phase-space distribution function. The technique is robust and allows accurate computations to be obtained for long propagation times. The effects of dissipation on the dynamics are studied and results are presented for systems subject to both periodic and nonperiodic multiminimum potential functions.

Journal Article↗
PubMed2005

Inelastic collisions in para-H2: translation-rotation state-to-state rate coefficients and cross sections at low temperature and energy.

We report an experimental determination of the k(00-->02) rate coefficient for inelastic H(2):H(2) collisions in the temperature range from 2 to 110 K based on Raman spectroscopy data in supersonic expansions of para-H(2). For this purpose a more accurate method for inverting the master equation of rotational populations is presented. The procedure permits us to reduce the measured k(00-->02) rate coefficient to the corresponding sigma(00-->02) cross section in the range of precollisional energy from 360 to 600 cm(-1). Numerical calculations of sigma(00-->02) carried out in the frame of the coupled channel method are also reported for different intermolecular potentials of H(2). A good agreement is found between the experimental cross section and the numerical one derived from Diep and Johnson's potential [J. Chem. Phys. 112, 4465 (2000)].

Journal Article↗
PubMed2005

Ozonolysis of alpha-pinene and beta-pinene: kinetics and mechanism.

A combined quantum-chemical and RRKM/ME (ME--master equation) approach is employed to investigate the structures, energetics, and kinetics of intermediate and stable species, and the yields of stabilized carbonyl oxides and OH radicals from the alpha-pinene and beta-pinene ozonolysis reactions. The cycloaddition of O(3) is highly exothermic, with the reaction energies of 55.1 and 51.1 kcal mol(-1) for alpha- and beta-pinenes, respectively. Cleavage of primary ozonides yields carbonyl oxides with the barrier height of 12.2-17.5 kcal mol(-1). For the prompt reactions of carbonyl oxides from alpha- and beta-pinene ozonolysis, H migration to hydroperoxides represents the dominant pathway over ring closure to dioxiranes. The kinetic calculations indicate a significant portion of stabilization for alpha- and beta-carbonyl oxides. The yields of stabilized carbonyl oxides are estimated to be 0.34 for alpha-pinene and 0.22 for beta-pinene. The applicability of theoretical methods for investigation of oxidation reactions of large hydrocarbon molecules is demonstrated.

Bicyclic Monoterpenes↗
PubMed2005

Stochastic fluctuations in gene expression far from equilibrium: Omega expansion and linear noise approximation.

The Omega expansion of the master equation is used to investigate the intrinsic noise in an autoregulatory gene expression system. This Omega expansion provides a mesoscale description of the system and is used to analyze the effect of feedback regulation on intrinsic noise when the system state is far from equilibrium. Using the linear noise approximation, analytic results are obtained for a single gene system with linear feedback that is far from equilibrium. Additionally, analytic expressions are obtained for nonlinear systems near equilibrium. Simulations of such autoregulatory reaction schemes with nonlinear feedback show that during the approach to equilibrium the noise is not always reduced by the strength of the feedback. This is contrary to results seen in the equilibrium limit which show decreased noise with feedback strength. These results demonstrate that the behavior of linearized systems near equilibrium cannot be readily applied to systems far from equilibrium and highlight the need to explore nonequilibrium domains in mesoscopic systems.

Feedback, Physiological↗
PubMed2005

Spatiotemporal patterns driven by autocatalytic internal reaction noise.

The influence that intrinsic local-density fluctuations can have on solutions of mean-field reaction-diffusion models is investigated numerically by means of the spatial patterns arising from two species that react and diffuse in the presence of strong internal reaction noise. The dynamics of the Gray-Scott (GS) model [P. Gray and S. K. Scott, Chem. Eng. Sci. 38, 29 (1983); and ibid.39, 1087 (1984); and J. Phys. Chem. 89, 22 (1985)] with a constant external source is first cast in terms of a continuum field theory representing the corresponding master equation. We then derive a Langevin description of the field theory and use these stochastic differential equations in our simulations. The nature of the multiplicative noise is specified exactly without recourse to assumptions and turns out to be of the same order as the reaction itself, and thus cannot be treated as a small perturbation. Many of the complex patterns obtained in the absence of noise for the GS model are completely obliterated by these strong internal fluctuations, but we find novel spatial patterns induced by this reaction noise in the regions of parameter space that otherwise correspond to homogeneous solutions when fluctuations are not included.

Journal Article↗
PubMed2005

Cyclization of Rouse chains at long- and short-time scales.

We have investigated cyclization of a Rouse chain at long and short times by a Langevin dynamics simulation method. We measure St, the fraction of nonreacted chains, for polymerizations ranging from Z=5 to Z=800 and capture distances ranging from a=0.1b to a=8b where b is the bond length. Comparison is made with two theoretical approaches. The first is a decoupling approximation used by Wilemski and Fixman to close the relevant master equation [J. Chem. Phys. 58, 4009 (1973); 60, 866 (1974)]. The second approach is the renormalization group arguments of Friedman and O'Shaughnessy [Phys. Rev. Lett 60, 64 (1988); J. Phys. II 1, 471 (1991)]. We find that at long times St decays as a single exponential with rate k(infinity). The scaled decay rate K=k(infinity)tauR appears to approach a constant value independent of the capture distance for very large chains consistent with the predictions of both the renormalization group (RG) and Wilemski-Fixman closure approximation. We extract K*, the long chain limit of K, from the fixed point a=a* where K is independent of Z. K* is larger than both the RG and closure predictions but much closer to the RG result. More convincing evidence for the RG analysis is obtained by comparing the short-time decay of St to long-time results. The RG analysis predicts that dSdt should decay as a power law at early times and that the exponent in the power law is related to K by a simple expression with no free parameters. Our simulations find remarkable agreement with this parameter-free prediction even for relatively short chains. We discuss possible experimental consequences of our result.

Journal Article↗
PubMed2005

Microcanonical unimolecular rate theory at surfaces. III. Thermal dissociative chemisorption of methane on Pt(111) and detailed balance.

A local hot spot model of gas-surface reactivity is used to investigate the state-resolved dynamics of methane dissociative chemisorption on Pt(111) under thermal equilibrium conditions. Three Pt surface oscillators, and the molecular vibrations, rotations, and the translational energy directed along the surface normal are treated as active degrees of freedom in the 16-dimensional microcanonical kinetics. Several energy transfer models for coupling a local hot spot to the surrounding substrate are developed and evaluated within the context of a master equation kinetics approach. Bounds on the thermal dissociative sticking coefficient based on limiting energy transfer models are derived. The three-parameter physisorbed complex microcanonical unimolecular rate theory (PC-MURT) is shown to closely approximate the thermal sticking under any realistic energy transfer model. Assuming an apparent threshold energy for CH(4) dissociative chemisorption of E(0)=0.61 eV on clean Pt(111), the PC-MURT is used to predict angle-resolved yield, translational, vibrational, and rotational distributions for the reactive methane flux at thermal equilibrium at 500 K. By detailed balance, these same distributions should be observed for the methane product from methyl radical hydrogenation at 500 K in the zero coverage limit if the methyl radicals are not subject to side reactions. Given that methyl radical hydrogenation can only be experimentally observed when the CH(3) radicals are kinetically stabilized against decomposition by coadsorbed H, the PC-MURT was used to evaluate E(0) in the high coverage limit. A high coverage value of E(0)=2.3 eV adequately reproduced the experimentally observed methane angular and translational energy distributions from thermal hydrogenation of methyl radicals. Although rigorous application of detailed balance arguments to this reactive system cannot be made because thermal decomposition of the methyl radicals competes with hydrogenation, approximate applicability of detailed balance would argue for a strong coverage dependence of E(0) with H coverage--a dependence not seen for methyl radical hydrogenation on Ru(0001), but not yet experimentally explored on Pt(111).

Journal Article↗
PubMed2005

Influence of vibrational energy flow on isomerization of flexible molecules: incorporating non-Rice-Ramsperger-Kassel-Marcus kinetics in the simulation of dipeptide isomerization.

The conformational isomerization of a dipeptide, N-acetyl-tryptophan methyl amide (NATMA), is studied computationally by including important dynamical corrections to Rice-Ramsperger-Kassel-Marcus (RRKM) theory for the transition rate between pairs of isomers. The dynamical corrections arise from incomplete or sluggish vibrational energy flow in the dipeptide, a property suggested by the mode-selective chemistry that has been observed by Dian et al. [J. Chem. Phys. 120, 133 (2004)]. We compute the extent and rate of vibrational energy flow in NATMA quantum mechanically using local random matrix theory, which we then use to correct the RRKM theory rates. The latter rates are then introduced into a master equation to study the population dynamics of the dipeptide. Incomplete or slow vibrational energy flow is found to enhance the conformational selectivity of NATMA over RRKM estimates.

Chemistry, Physical↗
PubMed2005

End-evaporation dynamics revisited.

We present analytical results on the so-called end-evaporation kinetics in equilibrium polymeric systems following a temperature jump (T jump). A T jump prepares the system with a nonequilibrium length distribution, after which it relaxes back to its equilibrium state. Starting from a master equation, we develop a mean-field analytical theory based on a generating function approach, which allows explicit approximate expressions for the monomer and dimer concentrations to be derived in a discrete setting; the concentrations of the other chains as well as the average chain length were shown to be entirely expressible in terms of the monomer and dimer concentrations. We find that the calculated monomer and dimer concentrations as well as the average chain length are in good agreement with numerical simulation results and do not suffer from some of the defects of earlier continuum theories. Furthermore, the relaxation was shown to take place in three different stages. The first stage comprises the very fast relaxation of the monomers to almost their equilibrium concentration; the other polymer chains have hardly relaxed. During the second stage, which is highly nonlinear, a redistribution of material at practically constant monomer density takes place. Only in the final stage of the relaxation process the chain concentrations approach their true equilibrium values. In this stage there are only very small shifts in the concentrations of chains, which are governed by extremely slow "indirect" monomer-mediated processes.

Journal Article↗