Extension of the diffusion controlled electron transfer theory for intermittent fluorescence of quantum dots: inclusion of biexcitons and the difference of "on" and "off" time distributions.

The equations for the diffusion controlled electron transfer (DCET) theory of quantum dot blinking are extended to include biexcitons. In contrast to excitons, which undego resonant light to dark transitions, the biexcitons, having a much larger total energy, undergo a Fermi's Golden rule type transfer (many acceptance states). The latter immediately gives rise to an exponential tail for the light state, and it is explained why the dark state power law behavior is unaffected. Results are given for both continuous and pulsed excitation. The typical -3/2 power law for the light state at low light intensities, and for the dark state at all intensities, as well as dependence of the exponential tail on the square of the light intensity, and a decrease of the power in the power law for the light state from -3/2 to less negative values with increasing light intensity are all consistent with the theory. The desirability of measuring the dependence of the spectral diffusion coefficient on light intensity at room temperature as a test of several aspects of the theory is noted.

Bimolecular recombination reactions: K-adiabatic and K-active forms of RRKM theory, nonstatistical aspects, low-pressure rates, and time-dependent survival probabilities with application to ozone. 2.

We consider for bimolecular recombination reactions the K-adiabatic versus the K-active forms of RRKM theory, where K is the component of the total angular momentum along the axis of least moment of inertia of the recombination product. When that product is approximately a prolate symmetric top, with two moments of inertia of the product substantially larger than the third, K becomes a dynamically slowly varying quantity and the K-adiabatic form of RRKM theory is the appropriate version to use. Using classical trajectory results for the rate constant for ozone formation in the low-pressure region as an example, excellent agreement for the recombination rate constant k(rec) with the K-adiabatic RRKM theory is observed. Use of a two transition state (inner, outer TS) formalism also obviates any need for assessing recrossings in the exit channel. In contrast, the K-active form of RRKM theory for this system disagrees with the trajectory results by a factor of about 2.5. In this study we also consider the distribution of the (E, J) resolved time-dependent survival probabilities P(E, J, t) of the intermediate O3* formed from O + O2. It is calculated using classical trajectories. The initial conditions for classical trajectories were selected using action-angle variables and a total J representation for (E, J) resolved systems, as described in Part I.1 The difference between K-active and K-adiabatic treatments is reflected also in a difference of the K-active RRKM survival probability P(E, J, t) from its trajectory-based value and from its often non-single-exponential decay. It is shown analytically that krec (K-active) ≥ k(rec) (K-adiabatic), independent of the details of the TS (e.g., variational or fixed RRKM theory, 1-TS or 2-TS). Nonstatistical effects for O3* formation include a small initial recrossing of the transition state, a slow (several picoseconds) equipartitioning of energy among the two O-O bonds of the newly formed O3*, and a small nondissociation (a quasi-periodicity) of some trajectories originating in O3* (∼ 10%) and so, by microscopic reversibility, are not accessible from O + O2. An apparently new feature of the present results is the comparison of classical trajectories with K-adiabatic and K-active theories for rate constants of bimolecular recombinations. The quantum mechanical counterpart of classical K-adiabatic RRKM theory is also given, and its comparison with the experimental k(rec) for O3 is given elsewhere.

On the infrared fluorescence of monolayer 13CO:NaCl(100).

Computations are presented to describe and analyze the high levels of infrared laser induced vibrational excitation of a monolayer of absorbed (13)CO on a NaCl(100) surface. Extending the vibrational site-to-site surface hopping technique of Corcelli and Tully, kinetic Monte Carlo computations are used to incorporate single-quantum vibrational pooling and depooling of the (13)CO by phonon excitation to allow up to the n = 45 vibrational state under different lasing conditions. Previously unpredicted pooling peaks at n > 16 are calculated and, under the highest fluence conditions, pooling up to the n = 32 state is found in the calculation. These results lead to the prediction of a secondary local maximum in the dispersed fluorescence of monolayer CO:NaCl(100) under sufficiently high fluence excitation conditions. At times on the order of ms, we recover similar behavior for both high and low fluence results. The calculations confirm that, for situations where the Debye frequency limited n domain restriction approximately holds, the vibrational state population deviates from a Boltzmann population linearly in n, a result that we have derived earlier theoretically for a domain of n restricted to one-phonon transfers. This theoretically understood term, linear in n, dominates the Boltzmann term and is responsible for the inversion of the population of vibrational states, Pn.

Theory of vibrational equilibria and pooling at solid-diatom interfaces.

In the present paper we provide a statistical theory for the vibrational pooling and fluorescence time dependence observed in infrared laser excitation of CO on an NaCl surface. The pooling is seen in experiment and in computer simulations. In the theory, we assume a rapid equilibration of the quanta in the substrate and minimize the free energy subject to the constraint at any time t of a fixed number of vibrational quanta N(t). At low incident intensity, the distribution is limited to one-quantum exchanges with the solid and the Debye frequency of the solid plays a key role in limiting the range of this one-quantum domain. The resulting inverted vibrational equilibrium population depends only on fundamental parameters of the oscillator (ωe and ωeχe) and the surface (ωD and T). The relation to the Treanor gas phase treatment is discussed. Unlike the solid phase system, the gas phase system has no Debye-constraining maximum.

Semiclassical evaluation of kinetic isotope effects in 13-atomic system.

The semiclassical instanton approach discussed by Kryvohuz [J. Chem. Phys. 134, 114103 (2011)] is applied to calculate kinetic H/D isotope effect (KIE) of intramolecular hydrogen transfer in cis-1,3-pentadiene. All 33 vibrational degrees of freedom are treated quantum mechanically with semiclassical approximation. Nuclear quantum effects such as tunneling under the barrier and zero-point energy are automatically incorporated in the theory, and are shown to be responsible for the observed appreciable kinetic isotope effect in cis-1,3-pentadiene. Over the barrier passage is also automatically included. Numerical calculations are performed on an empirical valence bond potential energy surface and compared with the previous experimental and theoretical studies. An estimation of heavy-atom (12)C/(13)C KIE in the same system is also provided and the factors contributing to it are discussed.

Microscopic structure and dynamics of air/water interface by computer simulations--comparison with sum-frequency generation experiments.

The air/water interface was simulated and the mode amplitudes and their ratios of the effective nonlinear sum-frequency generation (SFG) susceptibilities (A(eff)'s) were calculated for the ssp, ppp, and sps polarization combinations and compared with experiments. By designating "surface-sensitive" free OH bonds on the water surface, many aspects of the SFG measurements were calculated and compared with those inferred from experiment. We calculate an average tilt angle close to the SFG observed value of 35, an average surface density of free OH bonds close to the experimental value of about 2.8 × 10(18) m(-2), computed ratios of A(eff)'s that are very similar to those from the SFG experiment, and their absolute values that are in reasonable agreement with experiment. A one-parameter model was used to calculate these properties. The method utilizes results available from independent IR and Raman experiments to obtain some of the needed quantities, rather than calculating them ab initio. The present results provide microscopic information on water structure useful to applications such as in our recent theory of on-water heterogeneous catalysis.

Isotopomer fractionation in the UV photolysis of N(2)O: 3. 3D Ab initio surfaces and anharmonic effects.

The wavelength-dependent isotopic fractionation of N(2)O is calculated, extending our previous work, Parts 1 and 2, in several aspects: (1) the fully three-dimensional ab initio electronic potential and transition dipole moment surfaces of S. Nanbu and M. S. Johnson (J. Chem. Phys. A 2004, 108, 8905) are used to calculate the absorption cross sections, instead of a 2D surface and (2) the vibrational frequencies and wave functions with anharmonicity correction are used for the ground electronic state. The results for the absorption spectrum and for the isotopic fractionation of the different isotopomers are discussed. One difference between experiments measuring the absorption coefficient (von Hessberg et al. Atmos. Chem. Phys. 2004, 4, 1237) and the others that measure instead the photodissociation is also discussed. Experiments on the quantum yield for wavelengths longer than 200 nm (>50 000 cm(-1)) would be helpful in treating the observed difference.

Coriolis coupling as a source of non-RRKM effects in triatomic near-symmetric top molecules: Diffusive intramolecular energy exchange between rotational and vibrational degrees of freedom.

A classical theory is proposed to describe the non-RRKM effects in activated asymmetric top triatomic molecules observed numerically in classical molecular dynamics simulations of ozone. The Coriolis coupling is shown to result in an effective diffusive energy exchange between the rotational and vibrational degrees of freedom. A stochastic differential equation is obtained for the K-component of the rotational angular momentum that governs the diffusion.

Coriolis coupling as a source of non-RRKM effects in ozone molecule: Lifetime statistics of vibrationally excited ozone molecules.

A theory that describes the non-RRKM (non-Rice-Ramsperger-Kassel-Marcus) effects in the lifetime statistics of activated ozone molecules is derived. The non-RRKM effects are shown to originate due to the diffusive energy exchange between vibrational and rotational degrees of freedom in ozone molecule. The lifetime statistics is found to be intramolecular diffusion controlled at long times. The theoretical results are in good agreement with the direct MD simulations of lifetime statistics.

Strange and unconventional isotope effects in ozone formation.

The puzzling mass-independent isotopic enrichment in ozone formation contrasts markedly with the more recently observed large unconventional mass-dependent ratios of the individual ozone formation rate constants in certain systems. An RRKM (Rice, Ramsperger, Kassel, Marcus)-based theory is used to treat both effects. Restrictions of symmetry on how energy is shared among the rotational/vibrational states of the ozone isotopomer, together with an analysis of the competition between the transition states of its two exit channels, permit the calculation of isotope effects consistent with a wide array of experimental results.

Dielectric dispersion interpretation of single enzyme dynamic disorder, spectral diffusion, and radiative fluorescence lifetime.

A formulation based on measurable dielectric dispersion of enzymes is developed to estimate fluctuations in electrostatic interaction energy on time scales as long as milliseconds to seconds at a local site in enzymes. Several single molecule experimental obsevations occur on this time scale, currently unreachable by real time computational trajectory simulations. We compare the experimental results on the autocorrelation function of the fluctuations of catalysis rate with the calculations using the dielectric dispersion formulation. We also discuss the autocorrelation functions of the fluorescence lifetime and of spectral diffusion. We use a previously derived relation between the observables and the electric field fluctuations and calculate the latter using dielectric dispersion data for the proteins and the Onsager regression hypothesis.

On collisional energy transfer in recombination and dissociation reactions: A Wiener-Hopf problem and the effect of a near elastic peak.

The effect of the large impact parameter near-elastic peak of collisional energy transfer for unimolecular dissociation/bimolecular recombination reactions is studied. To this end, the conventional single exponential model, a biexponential model that fits the literature classical trajectory data better, a model with a singularity at zero energy transfer, and the most realistic model, a model with a near-singularity, are fitted to the trajectory data in the literature. The typical effect of the energy transfer on the recombination rate constant is maximal at low pressures and this region is the one studied here. The distribution function for the limiting dissociation rate constant k(0) at low pressures is shown to obey a Wiener-Hopf integral equation and is solved analytically for the first two models and perturbatively for the other two. For the single exponential model, this method yields the trial solution of Troe. The results are applied to the dissociation of O(3) in the presence of argon, for which classical mechanical trajectory data are available. The k(0)'s for various models are calculated and compared, the value for the near-singularity model being about ten times larger than that for the first two models. This trend reflects the contribution to the cross section from collisions with larger impact parameter. In the present study of the near-singularity model, it is found that k(0) is not sensitive to reasonable values for the lower bound. Energy transfer values DeltaE's are also calculated and compared and can be similarly understood. However, unlike the k(0) values, they are sensitive to the lower bound, and so any comparison of a classical trajectory analysis for DeltaE's with the kinetic experimental data needs particular care.

Ketoconazole blocks adrenal steroidogenesis by inhibiting cytochrome P450-dependent enzymes.

Ketoconazole has recently been shown to interfere with steroidogenesis in patients and rat in vitro systems. In this study we attempted to elucidate the site of inhibition in the adrenal gland. Although ketoconazole impaired adrenocorticotropic hormone stimulated cyclic (c)AMP production, dibutyrl cAMP addition did not bypass the steroidogenic blockade indicating that the critical ketoconazole-inhibited step was distal to cAMP. Addition of radiolabeled substrates to isolated adrenal cells and analysis of products by high performance liquid chromatography demonstrated a ketoconazole block between deoxycorticosterone (DOC) and corticosterone. This 11-hydroxylase step is carried out by a P450-dependent mitochondrial enzyme. No restriction of progesterone or pregnenolone conversion to DOC was detected, steps carried out by non-P450-dependent microsomal enzymes. Inhibition of cholesterol conversion to pregnenolone by mitochondrial fractions indicated a second block at the side chain cleavage step, another mitochondrial P450-dependent enzyme. Adrenal malate dehydrogenase, a non-P450-dependent mitochondrial enzyme was not inhibited while renal 24-hydroxylase, a P450-dependent mitochondrial enzyme in another organ, was blocked by ketoconazole. We conclude that ketoconazole may be a general inhibitor of mitochondrial P450 enzymes. This finding suggests that patients receiving ketoconazole be monitored for side effects relevant to P450 enzyme inhibition. Further, we raise the possibility that this drug action may be beneficially exploited in situations where inhibition of steroidogenesis is a therapeutic goal.

H and other transfers in enzymes and in solution: theory and computations, a unified view. 2. Applications to experiment and computations.

Equations obtained in part I for the free-energy barrier to one-step enzymatic reactions between bound reactants are discussed. The rate is expressed in terms of lambdao (protein reorganization energy), DeltaG(o) (standard free energy of reaction of the H-transfer step), bond breaking/bond forming term, w (work terms), and H-transmission property. Two alternative approximations for the coupling of the bond breaking/bond forming and protein are distinguished experimentally in favorable cases by the DeltaG(o) where the maximum deuterium kinetic isotope effect occurs. Plots of log rate versus DeltaG(o) and properties such as DeltaS* and DeltaS(o) are discussed. The weak or zero T-dependence of the kinetic isotope effect for wild-type enzymes operating under physiological conditions is interpreted in terms of vanishing (or isotopically insensitive) w plus transfer from the lowest H-state. Static and dynamic protein flexibility is discussed. While the many correlations accessible for electron transfers are not available for H-transfers in enzymes, a combination of experiment, computation, and analytical approaches can assist in evaluating the utility of the present equations and in suggesting further experiments and computations. A protein reorganization energy lambdao is obtained in the literature from the extended valence bond formalism where diabatic electronic states are used. A method is suggested for extracting it when instead a bond distance difference coordinate is used. The results may provide a bridge between the two approaches.

Chain dynamics and power-law distance fluctuations of single-molecule systems.

Chain-dynamics-induced distance fluctuations between any two points in a finite chain with or without cross links are investigated. This model leads to three regimes of temporal behavior for distance autocorrelation: (i) initial flat time dependence, (ii) t(-alpha) power law, and (iii) long-time exponential decay. For an ideal Rouse chain with frequency-independent friction, alpha = 1/2. The span of the characteristic power-law behavior of a long chain could be reduced significantly with the presence of cross links.

Micelle-enhanced dissociation of a Ru cation /DNA complex.

Anionic surfactant monomers have a large catalytic effect on the dissociation rate constant of a Ru2(4+)-DNA complex, an effect further enhanced upon exceeding the critical micelle concentration. Electrostatic estimates are made of this effect, the effect of salt and temperature on the binding constant, and of the binding constant itself. The effects are compared with the experiment, and the calculated salt effect on the binding constant is compared with condensation theory. The results indicate that the catalytic effect is primarily nonelectrostatic (hydrophobic) in nature.

Bimolecular recombination reactions: low pressure rates in terms of time-dependent survival probabilities, total J phase space sampling of trajectories, and comparison with RRKM theory.

We consider the bimolecular formation and redissociation of complexes using classical trajectories and the survival probability distribution function P(E,J,t) of the intermediate complexes at time t as a function of the energy E and total angular momentum quantum number J. The P(E,J,t) and its deviation from single exponential behavior is a main focus of the present set of studies. Together with weak deactivating collisions, the P(E,J,t) and a cumulative reaction probability at the given E and J can also be used to obtain the recombination rate constant k at low pressures of third bodies. Both classical and quantum expressions are given for k in terms of P(E,J,t). The initial conditions for the classical trajectories are sampled for atom-diatom reactions for various (E,J)'s using action-angle variables. A canonical transformation to a total J representation reduces the sampling space by permitting analytic integration over several of the variables. A similar remark applies for the calculation of the density of states of the intermediate complex ρ and for the number of states N* of the transition state as a function of E and J. The present approach complements the usual approach based on the rate of the reverse reaction, unimolecular dissociation, and the equilibrium constant. It provides results not necessarily accessible from the unimolecular studies. The formalism is applied elsewhere to the study of nonstatistical aspects of the recombination and redissociation of the resulting ozone molecules and comparison with RRKM theory.