Effects of Ultrafast Solvation on the Rate of Adiabatic Outer-Sphere Electron Transfer Reactions

Recent studies have demonstrated that solvation dynamics in many common dipolar liquids contain an initial, ultrafast Gaussian component which may contribute even more than 60% to the total solvation energy. It is also known that adiabatic electron transfer reactions often probe the high-frequency components of the relevant solvent friction (Hynes, J. T. J. Phys. Chem. 1986, 90, 3701). In this paper, we present a theoretical study of the effects of the ultrafast solvent polar modes on the adiabatic electron transfer reactions by using the formalism of Hynes. Calculations have been carried out for a model system and also for water and acetonitrile. It is found that, in general, the ultrafast modes can greatly enhance the rate of electron transfer, even by more than an order of magnitude, over the rate obtained by using only the slow overdamped modes usually considered. For water, this acceleration of the rate can be attributed to the high-frequency intermolecular vibrational and librational modes. For a weakly adiabatic reaction, the rate is virtually indistinguishable from the rate predicted by the Marcus transition state theory. Another important result is that even in this case of ultrafast underdamped solvation, energy diffusion appears to be efficient so that electron transfer reaction in water is controlled essentially by the barrier crossing dynamics. This is because the reactant well frequency is-directly proportional to the rate of the initial Gaussian decay of the solvation time correlation function. As a result, the value of the friction at the reactant well frequency rarely falls below the value required for the Kramers turnover except when the polarizability of the water molecules may be neglected. On the other hand, in acetonitrile, the rate of electron transfer reaction is found to be controlled by the energy diffusion dynamics, although a significant contribution to the rate comes also from the barrier crossing rate. Therefore, the present study calls for a need to understand the relaxation of the high-frequency modes in dipolar liquids.

Highly selective sulfur transfer reaction in the solid state

Benzyltriethylammonium tetrathiomolybdate 1 reacts readily with benzyl halides, alkyl iodides and acyl halides in the solid state to give the corresponding disulfides in good yields and with remarkable selectivity.

Photoinduced electron transfer in zinc porphyrin-crown ether supramolecule with Eu3+ electron acceptor in crown void

Photoinduced electron transfer (ET) reactions in the zinc porphyrin-crown ether (ZnPCE) supramolecule, in which one crown ether moiety containing Eu3+ as electron acceptor is covalently linked to zinc porphyrin (ZnP), were studied by flash photolysis. In methanol solutions, highly efficient charge separation occurs via intramolecular ET from (ZnP)-Zn-3 to Eu3+ encapsulated in the crown ether void (k(1) = (3 +/- 1) X 10(3) s(-1)) and intramolecular ET from 3ZnP to uncomplexed Eu2+ (k(2) = (2.5 +/- 0.5) X 10(3) s(-1)). Intermolecular ET from Eu2+ escaped from the crown ether void to ZnP.+ (k(tau) = (4.3 +/- 0.7) X 10(8) M(-1) s(-1)) seems to be the main pathway of charge recombination.

Ricin-membrane interaction: membrane penetration depth by fluorescence quenching and resonance energy transfer

The entry of the plant toxin ricin and its A- and B-subunits in model membranes in the presence as well as absence of monosialoganglioside (GM(1)) has been studied. Dioleoylphosphatidylcholine and 5-, 10-, and 12-doxyl- or 9,10-dibromophosphatidylcholines serve as quenchers of intrinsic tryptophan fluorescence of the proteins. The parallax method of Chattopadhyay and London [(1987) Biochemistry 26, 39-45] has been employed to measure the average membrane penetration depth of tryptophans of ricin and its B-chain and the actual depth of the sole Trp 211 in the A-chain. The results indicate that both of the chains as well as intact ricin penetrate the membrane deeply and the C-terminal end of the A-chain is well inside the bilayer, especially at pH 4.5. An extrinsic probe N-(iodoacetyl)-N'-(5-sulfo-1-naphthyl) ethylenediamine (I-AEDANS) has been attached to Cys 259 of the A-chain, and the kinetics of penetration has been followed by monitoring the increase in AEDANS fluorescence at 480 nm. The insertion follows first-order kinetics, and the rate constant is higher at a lower pH. The energy transfer distance analysis between Trp 211 and AEDANS points out that the conformation of the A-chain changes as it inserts into the membrane. CD studies indicate that the helicity of the proteins increases after penetration, which implies that some of the unordered structure in the native protein is converted to the ordered form during this process. Hydrophobic forces seem to be responsible for stabilizing a particular protein conformation inside the membrane.

Time-resolved fluorescence studies on covalently linked porphyrin�nitroarene complexes. Conformational control of photoinduced electron transfer reactions

Time-resolved fluorescence studies were carried out on a series of free-base and zinc(II) derivatives of meso-tetraphenylporphyrins covalently linked to either 1,3-dinitrobenzene (DNB) or 1,3,5-trinitrobenzene (TNB) acceptor units. These acceptor units were linked at different sites (at the ortho, meta or para positions of one of the phenyl groups of meso-tetraphenylporphyrin) to the donor porphyrins such that the resulting isomeric intramolecular donor-acceptor complexes exhibit different centre-to-centre (ctc) distances and relative orientations. Biexponential fluorescence decay profiles observed for several of these covalently linked complexes were rationalized in terms of the presence of ''closed'' and ''extended'' conformers. Detailed analyses of the fluorescence decay data have provided a comprehensive understanding of the photoinduced electron transfer (PET) reactions occurring in systems containing zinc(II) porphyrin donors. It is observed that although DNB-linked zinc(II) complexes follow the trends predicted for the efficiency of PET with respect to donor-acceptor distance, the TNB-linked zinc(II) porphyrins exhibit a behaviour which is dictated by steric effects. Similarly, although the thermodynamic criteria predict a greater efficiency of charge separation in TNB-linked complexes compared with DNB-linked complexes, the reverse trend observed has been attributed to orientational effects. In the complexes containing free-base porphyrin donors, PET is expected to be less efficient from a thermodynamic viewpoint. In a few of these cases, fluorescence quenching seems to occur by parallel mechanisms other than PET.

A model for heat transfer in a honey bee swarm

A swarm is a temporary structure formed when several thousand honey bees leave their hive and settle on some object such as the branch of a tree. They remain in this position until a suitable site for a new home is located by the scout bees. A continuum model based on heat conduction and heat generation is used to predict temperature profiles in swarms. Since internal convection is neglected, the model is applicable only at low values of the ambient temperature T-a. Guided by the experimental observations of Heinrich (1981a-c, J. Exp. Biol. 91, 25-55; Science 212, 565-566; Sci. Am. 244, 147-160), the analysis is carried out mainly for non-spherical swarms. The effective thermal conductivity is estimated using the data of Heinrich (1981a, J. Exp. Biol. 91, 25-55) for dead bees. For T-a = 5 and 9 degrees C, results based on a modified version of the heat generation function due to Southwick (1991, The Behaviour and Physiology of Bees, PP 28-47. C.A.B. International, London) are in reasonable agreement with measurements. Results obtained with the heat generation function of Myerscough (1993, J. Theor. Biol. 162, 381-393) are qualitatively similar to those obtained with Southwick's function, but the error is more in the former case. The results suggest that the bees near the periphery generate more heat than those near the core, in accord with the conjecture of Heinrich (1981c, Sci. Am. 244, 147-160). On the other hand, for T-a = 5 degrees C, the heat generation function of Omholt and Lonvik (1986, J. Theor. Biol. 120, 447-456) leads to a trivial steady state where the entire swarm is at the ambient temperature. Therefore an acceptable heat generation function must result in a steady state which is both non-trivial and stable with respect to small perturbations. Omholt and Lonvik's function satisfies the first requirement, but not the second. For T-a = 15 degrees C, there is a considerable difference between predicted and measured values, probably due to the neglect of internal convection in the model.

Electron transfer reaction in the marcus inverted region: role of high frequency vibrational modes

A theoretical study of the dynamics of photo-electron transfer reactions in the Marcus inverted regime is presented. This study is motivated partly by the recent proposal of Barbara et al. (J. Phys. Chem. 96, 3728, 1991) that a minimal model of an electron transfer reaction should consist of a polar solvent mode (X), a low frequency vibrational mode (Q) and one high frequency mode (q). Interplay between these modes may be responsible for the crossover observed in the dynamics from a solvent controlled to a vibrational controlled electron transfer. The following results have been obtained. (i) In the case of slowly relaxing solvents, the proximity of the point of excitation to an effective sink on the excited surface is critical in determining the decay of the reactant population. This is because the Franck-Condon overlap between the reactant ground and the product excited states decreases rapidly with increase in the quantum number of the product vibrational state. (ii) Non-exponential solvation dynamics has an important effect in determining the rates of electron transfer. Especially, a biphasic solvation and a large coupling between the reactant and the product states both may be needed to explain the experimental results. ©1996 American Institute of Physics

Lectin binding to complex carbohydrate at the interface: a study by resonance energy transfer

The binding affinity of the oligosaccharide moiety of a neutral glycosphingolipid, asialoGM1, towards Ricinus communis agglutinin (RCAI) was determined for the first time by fluorescence resonance energy transfer (RET). The asialoGM1 was incorporated into a phospholipid (DMPC) vesicle doped with dansylated DPPE and then titrated with an increasing amount of the galactose specific RCAI. The efficiency of RET was determined by a saturable increase in the quenching of 'donor' fluorescence, i.e. the 'trp' residue of RCAI, due to the energy transfer from the 'acceptor' dansyl group on the surface of the vesicle. The apparent binding constant was found to be in the range of 10(5)-10(6) M-1 at 27 degrees C.

A transfer matrix approach for evaluation of the response of a multi-layer infinite plate to a two-dimensional pressure excitation

A 6 X 6 transfer matrix is presented to evaluate the response of a multi-layer infinite plate to a given two-dimensional pressure excitation on one of its faces or, alternatively, to evaluate the acoustic pressure distribution excited by the normal velocity components of the radiating surfaces. It is shown that the present transfer matrix is a general case embodying the transfer matrices of normal excitation and one-dimensional pressure excitation due to an oblique incident wave. It is also shown that the present transfer matrix obeys the necessary checks to categorize the physically symmetric multi-layer plate as dynamically symmetric. Expressions are derived to obtain the wave propagation parameters, such as the transmission, absorption and reflection coefficients, in terms of the elements of the transfer matrix presented. Numerical results for transmission loss and reflection coefficients of a two-layer configuration are presented to illustrate the effect of angles of incidence, layer characteristics and ambient media.

Mixed convection heat transfer from the bottom tip of a cylinder spinning about a vertical axis in a saturated porous medium

The present work is a numerical study of heat transfer characteristics from the bottom tip of a cylinder spinning about a vertical axis in an infinitely saturated porous medium. The problem is axisymmetric. The non-dimensionalized governing equations are solved using the SIMPLER algorithm on a staggered grid. The influence of rotational Reynolds numbers and Darcy numbers on the heat transfer for a Grashof number of 104 and Prandtl number of 7.0 is studied. It is found that for very high Darcy numbers, over a wide range of rotational Reynolds numbers, the heat transfer takes place mainly due to conduction. The convective heat transfer takes place for lower Darcy numbers and for higher rotational Reynolds numbers. Moreover, there is a rapid increase in the overall Nusselt number below a certain Darcy number with increase in the rotational Reynolds numbers. The effect of the Darcy number and the rotational Reynolds number on the heat transfer and fluid flow in the porous medium is depicted in the form of streamline and isotherm plots. The variation of the overall Nusselt number with respect to the Darcy number for various rotational Reynolds numbers is plotted. The variation of the local Nusselt number with respect to the radial coordinate at the heated tip of the vertical cylinder is plotted for various Darcy and rotational Reynolds numbers.

Molecular interpretation of the linear relationship between the entropy and the enthalpy of activation of charge transfer reactions in polar liquids

The well-known linear relationship (T?S# =??H# +?, where 1 >? > 0,? > 0) between the entropy (?S#) and the enthalpy (?H#) of activation for reactions in polar liquids is investigated by using a molecular theory. An explicit derivation of this linear relation from first principles is presented for an outersphere charge transfer reaction. The derivation offers microscopic interpretation for the quantities? and?. It has also been possible to make connection with and justify the arguments of Bell put forward many years ago.

Natural Convection Heat Transfer From an Isothermal Vertical Surface to a Stable Thermally Stratified Fluid

Natural convection from an isothermal vertical surface to a thermally stratified fluid is studied numerically. A wide range of stratification levels is considered. It is shown that at high levels of ambient thermal stratification, a portion at the top of the plate absorbs heat, while a horizontal plume forms around a location where the plate temperature equals the ambient temperature. The plume is shown to be inherently unsteady, and its transient nature is investigated in detail. The effect of the temperature defect in striating the plume is discussed. Average Nusselt number data are presented for Pr = 6.0 and 0.7.