Rate Of Electronic Energy Transfer Research Articles

Electron excitation and energy transfer rates for H2O in the upper atmosphere

Recent measurements of the cross sections for electronic state excitations in H2O have made it possible to calculate rates applicable to these excitation processes. We thus present here calculations of electron energy transfer rates for electronic and vibrational state excitations in H2O, as well as rates for excitation of some of these states by atmospheric thermal and auroral secondary electrons. The calculation of these latter rates is an important first step towards our aim of including water into a statistical equilibrium model of the atmosphere under auroral conditions.PACS Codes: 34.50.Gb 34.50.Ez

Energy Flow in a Purpose‐Built Cascade Molecule Bearing Three Distinct Chromophores Attached to the Terminal Acceptor

A multicomponent cluster has been synthesised in which four disparate chromophores have been covalently linked through a logical arrangement that favours efficient photon collection and migration to a terminal emitter. The primary energy acceptor is a boron dipyrromethene (Bodipy) dye and different polycyclic aryl hydrocarbons have been substituted in place of the regular fluorine atoms attached to the boron centre. The first such unit is perylene, linked to boron through a 1,4-diethynylphenyl unit, which collects photons in the 320-490 nm region. The other photon collector is pyrene, also connected to the boron centre by a 1,4-diethynylphenyl spacer and absorbing strongly in the 280-420 nm region, which itself is equipped with an ethynylfluorene residue that absorbs in the UV region. Illumination into any of the polycyclic aryl hydrocarbons results in emission from the Bodipy unit. The rates of intramolecular electronic energy transfer have been determined from time-correlated, single-photon counting studies and compared with the rates for Coulombic interactions computed from the Förster expression. It has been necessary to allow for i) a more complex screening potential, ii) multipole-multipole coupling, iii) an extended transition dipole moment vector and iv) bridge-mediated energy transfer. The bridge-mediated energy transfer includes both modulation of the donor transition dipole vector by bridge states and Dexter-type electron exchange. The latter is a consequence of the excellent electronic coupling properties of the 1,4-diethynylphenyl spacer unit. The net result is a large antenna effect that localises the photon density at the primary acceptor without detracting from its highly favourable photophysical properties.

Carbon dioxide electron cooling rates in the atmospheres of Mars and Venus

The cooling of electrons in collisions with carbon dioxide in the atmospheres of Venus and Mars is investigated. Calculations are performed with both previously accepted electron energy transfer rates and with new ones determined using more recent theoretical and experimental cross sections for electron impact on CO2. Emulation of a previous model for Venus confirms the validity of the current model and shows that use of the updated cross sections leads to cooling rates that are lower by one third. Application of the same model to the atmosphere of Mars gives more than double the previous cooling rates at altitudes where the electron temperature is very low.

Integral cross sections for electron impact excitation of the 1Σ+u and 1Πu electronic states in CO2

We apply the method of Kim (2007 J. Chem. Phys. 126 064305) in order to derive integral cross sections for the 1Σ+u and 1Πu states of CO2, from our corresponding earlier differential cross section measurements (Green et al 2002 J. Phys. B: At. Mol. Opt. Phys. 35 567). The energy range of this work is 20–200 eV. In addition, the BEf-scaling approach is used to calculate integral cross sections for these same states, from their respective thresholds to 5000 eV. In general, good agreement is found between the experimental integral cross sections and those calculated within the BEf-scaling paradigm, over the entire common energy range. Finally, we employ our calculated integral cross sections to determine the electron energy transfer rates for these states, for a thermal electron energy distribution. Such transfer rates are in principle important for understanding the phenomena in atmospheres where CO2 is a dominant constituent, such as on Mars and Venus.

Does Förster Theory Predict the Rate of Electronic Energy Transfer for a Model Dyad at Low Temperature?

The use of the Förster model to predict the dynamics of resonant electronic energy transfer (RET) in a model donor-acceptor dyad (a terphenyl-bridged perylene diimide (PDI)-terrylene diimide (TDI) dyad molecule) embedded at low temperature in a PMMA matrix is tested against experiment. The relevant ingredients involved in the Förster rate for RET, namely electronic coupling, spectral overlap, and screening effects, are accounted for in a quantitative manner. Electronic couplings are obtained from time-dependent density functional theory calculations, and the effect of the PMMA environment is included both on the transition densities and on their interaction through the IEFPCM model. We find that the presence of the terphenyl bridge induces a slight delocalization of the PDI and TDI transition densities over the bridge originating in a 56% increase in the coupling and in the breakdown of the dipole-dipole approximation. The spectral overlap is determined on the basis of a detailed simulation of the homogeneously broadened donor emission and acceptor absorption line shapes determined by fitting the single molecule spectra measured at 1.2 K. The corresponding distribution of spectral overlap throughout the ensemble is then estimated by assuming an uncorrelated inhomogeneous line broadening for the donor and acceptor. Combining the calculated electronic couplings and spectral overlaps sampled from Monte Carlo realizations of the energetic disorder, we obtain a mean RET time (approximately 8 ps) and a distribution in reasonable agreement with experiment.

Theoretical investigation of electronic excitation energy transfer in bichromophoric assemblies

Electronic excitation energy transfer (EET) rates in rylene diimide dyads are calculated using second-order approximate coupled-cluster theory and time-dependent density functional theory. We investigate the dependence of the EET rates on the interchromophoric distance and the relative orientation and show that Forster theory works quantitatively only for donor-acceptor separations larger than roughly 5 nm. For smaller distances the EET rates are over- or underestimated by Forster theory depending on the respective orientation of the transition dipole moments of the chromophores. In addition to the direct transfer rates we consider bridge-mediated transfer originating from oligophenylene units placed between the chromophores. We find that the polarizability of the bridge significantly enhances the effective interaction. We compare our calculations to single molecule experiments on two types of dyads and find reasonable agreement between theory and experiment.

On the Mechanism of Intramolecular Sensitization of Photocleavage of the 2-(2-Nitrophenyl)propoxycarbonyl (NPPOC) Protecting Group

A spectroscopic study of a variety of covalently linked thioxanthone(TX)-linker-2-(2-nitrophenyl)propoxycarbonyl(NPPOC)-substrate conjugates is presented. Herein, the TX chromophore functions as an intramolecular sensitizer to the NPPOC moiety, a photolabile protecting group used in photolithographic DNA chip synthesis. The rate of electronic energy transfer between TX and NPPOC was quantified by means of stationary fluorescence as well as nanosecond and femtosecond time-resolved laser spectroscopy. A dual mechanism of triplet-triplet energy transfer has been observed comprising a slower mechanism involving the T1(pipi*) state of TX with linker-length-dependent time constants longer than 20 ns and a fast mechanism with linker-length-dependent time constants shorter than 3 ns. Evidence is provided that the latter mechanism is due to energy transfer from the T2(npi*) state which is in fast equilibrium with the fluorescent S1(pipi*) state. In the case of direct linkage between the aromatic rings of TX and NPPOC, the spectroscopic properties are indicative of one united chromophore which, however, still shows the typical NPPOC cleavage reaction triggered by intramolecular hydrogen atom transfer to the nitro group.

Resonance energy transfer from a fluorescent dye molecule to plasmon and electron-hole excitations of a metal nanoparticle

The authors study the distance dependence of the rate of electronic excitation energy transfer from a dye molecule to a metal nanoparticle. Using the spherical jellium model, they evaluate the rates corresponding to the excitation of l=1, 2, and 3 modes of the nanoparticle. The calculation takes into account both the electron-hole pair and the plasmon excitations of the nanoparticle. The rate follows conventional R(-6) dependence at large distances while small deviations from this behavior are observed at shorter distances. Within the framework of the jellium model, it is not possible to attribute the experimentally observed d(-4) dependence of the rate to energy transfer to plasmons or electron-hole pair excitations.

How Solvent Controls Electronic Energy Transfer and Light Harvesting

The way that solvent (or host medium) modifies the rate of electronic energy transfer (EET) has eluded researchers for decades. By applying quantum chemical methods that account for the way solvent (in general any host medium including liquid, solid, or protein, etc.) responds to the interaction between transition densities, we quantify the solvent screening. We find that it attains a striking exponential attenuation at separations less than about 20 A, thus interpolating between the limits of no apparent screening and a significant attenuation of the EET rate. That observation reveals a previously unidentified contribution to the distance dependence of the EET rate.

Intramolecular electronic energy transfer in rhodamine–azulene bichromophoric molecule

Electron transfer and electronic energy transfer (EET) processes are ways by which different molecules can interact, signalling their state, by EET from a donor (D) to an acceptor (A). This D–A transfer is often observed in an intermolecular process but it can also occur intramolecularly, that is between two bridged parts of a bichromophoric molecule. In this paper we present results pertaining to electronic energy transfer in a newly synthesized rhodamine–azulene (Rh–Az) a bichromophoric molecule, in which a full adder can be implemented. The intramolecular EET rate constant in the Rh–Az molecule was found to be 7.81 × 10 9 s −1.

The effects of energy-level resonance on collision-induced electronic energy transfer: CD (A 2Δ ↔ B 2Σ−) coupling

Pulsed, time- and wavelength-resolved laser-induced fluorescence spectroscopy has been used to measure rate constants for collision-induced electronic energy transfer (EET) between the A (2)Delta and B (2)Sigma(-) states of the CD radical. EET rate constants in the exothermic direction from B (2)Sigma(-), v = 0 to the unresolved A (2)Delta, v = 0 and 1 levels span the range 0.1-2.4 x 10(-11) cm(3) s(-1) at room temperature (ca. 295 K) for the partners He, Ar, N(2), CO and CO(2). H(2) was also investigated, but was unsuitable for further study because of its rapid isotope exchange with CD(X (2)Pi). As expected, only CO results in a significant rate of removal on any distinct, unobserved channel, presumed to be chemical reaction. The efficient A (2)Delta, v = 1 --> 0 vibrational relaxation by CO(2) observed previously for CH was not found for CD. Despite the significant differences in their detailed rovibronic level structures, the overall efficiency of EET in CD was found to be very similar to that for CH. The positive correlation in a Parmenter-Seaver plot appears to confirm a role for long-range attractive forces in the EET process. However, the detailed deviations from this overall trend found reproducibly for CD and CH suggests that partner-specific interactions are also important.

Rovibrational resonance effects in collision-induced electronic energy transfer: I2(E,v=–2)+CF4

Collisions of I2 in the E(0(g)+) electronic state with CF4 molecules induce electronic energy transfer to the nearby D, beta, and D' ion-pair states. Simulations of dispersed fluorescence spectra reveal collision-induced electronic energy transfer rate constants and final vibrational state distributions within each final electronic state. In comparison with earlier reports on I2(upsilon(E)=0-2) collisions with He or Ar atoms, we find markedly different dynamics when I2, excited to the same rovibronic states, collides with CF4. Final vibrational state distributions agree with the associated Franck-Condon factors with the initially prepared state to a greater degree than those found with He or Ar collision partners and suggest that internal degrees of freedom in the CF4 molecule represent a substantial means for accepting the accompanying loss of I2 vibronic energy. Comparison of the E-->D transfer of I2 excited to the J=23 and J=55 levels of the upsilon(E)=0 state reveals the onset of specific, nonstatistical dynamics as the available energy is increased above the threshold for excitation of the low frequency nu2 bending mode of CF4.

Energy and Charge Transfer Dynamics in Fully Decorated Benzyl Ether Dendrimers and Their Disubstituted Analogues

We examine the photophysics of a series of molecules consisting of a benzthiadiazole core surrounded by a network of benzyl ether arms terminated by aminopyrene chromophores, which function as both energy and electron donors. Three classes of molecules are studied: dendrimers whose peripheries are fully decorated with aminopyrene donors (F), disubstituted dendrimers whose peripheries contain only two donors (D), and linear analogues in which a pair of benzyl ether arms link two donors to the central core (L). The electronic energy transfer (EET) and charge transfer (CT) rates are determined by fluorescence lifetime measurements on the energy donors and electron acceptors, respectively. In all three types of molecules, the EET time scales as the square root of the generation number G, consistent with the flexible nature of the benzyl ether framework. Transient anisotropy measurements confirm that donor-donor energy hopping does not play a major role in determining the EET times. The CT dynamics occur on the nanosecond time scale and lead to stretched exponential decays, probably due to conformational disorder. Measurements at 100 degrees C confirm that conformational fluctuations play a role in the CT dynamics. The average CT time increases with G in the L and D molecules but decreases for the F dendrimers. This divergent behavior as G increases is attributed to the competing effects of larger donor-acceptor distances (which lengthen the CT time) versus a larger number of donors (which shorten the average CT time). This work illustrates two important points about light-harvesting and charge-separation dendrimers. First, the use of a flexible dendrimer framework can lead to a more favorable scaling of the EET time (and thus the light-harvesting efficiency) with dendrimer size, relative to what would be expected for a fully extended dendrimer. Second, fully decorated dendrimers can compensate for the distance-dependent slowdown in CT rate as G increases by providing additional pathways for the CT reaction to occur.

Electronic Energy-Transfer Rate Constants for Geometrical Isomers of a Bichromophoric Macrocyclic Complex

The rate of electronic energy transfer (EET) between a naphthalene donor and an anthracene acceptor in [ZnL(3)](ClO(4))(2) and [ZnL(4)](ClO(4))(2) was determined by time-resolved fluorescence measurements, where L(3) and L(4) are the geometrical isomers of 6-[(anthracen-9-ylmethyl)amino]-trans-6,13-dimethyl-1,4,8,11-tetraazacyclotetradecane-13-amine (L(2)), substituted with either a naphthalen-1-ylmethyl or naphthalen-2-ylmethyl donor, respectively. The energy-transfer rate constant, k(EET), was determined to be (0.92 +/- 0.02) x 10(9) s(-1) for the naphthalen-1-ylmethyl-substituted isomer, while that for the naphthalen-2-ylmethyl-substituted isomer is somewhat faster, with k(EET) = (1.31 +/- 0.01) x 10(9) s(-1). The solid-state structure of [ZnL(3)Cl]ClO(4) has been determined, and using molecular modeling calculations, the likely distributions of solution conformations in CH(3)CN have been evaluated for both complexes. The calculated conformational distributions in the common trans-III N-based isomeric form gave Förster EET rate constants that account for the differences observed and are in excellent agreement with the experimental values. It is shown that the full range of conformers must be considered to accurately reproduce the observed EET kinetics.

Polaron-exciton model of resonance energy transfer

It is shown that Förster's expression for the electronic energy transfer rate can be recast in a form predicted for exciton motion that interacts strongly with molecular vibrations. Using a simple model based on the Kennard-Stepanov theory, Förster's expression for the spectral overlap is shown to be of a thermally activated form, as obtained previously by multiphonon theory. In contrast, the high-frequency internal vibrations contribute a factor which results from tunneling through a potential barrier between potential curves in the configuration coordinate diagram. We thus show that resonance energy transfer is equivalent to phonon-assisted hopping of a trapped excitonic polaron.

How do small water clusters bind an excess electron?

The arrangement of water molecules around a hydrated electron has eluded explanation for more than 40 years. Here we report sharp vibrational bands for small gas-phase water cluster anions, (H2O)(4-6)- and (D2O)(4-6)-. Analysis of these bands reveals a detailed picture of the diffuse electron-binding site. The electron is closely associated with a single water molecule attached to the supporting network through a double H-bond acceptor motif. The local OH stretching bands of this molecule are dramatically distorted in the pentamer and smaller clusters because the excited vibrational levels are strongly coupled to the electron continuum. The vibration-to-electronic energy transfer rates, as revealed by line shape analysis, are mode-specific and remarkably fast, with the symmetric stretching mode surviving for less than 10 vibrational periods [50 fs in (H2O)4-].

Production of vibrationally excited N 2 by electron impact

Energy transfer from electrons to neutral gases and ions is one of the dominant electron cooling processes in the ionosphere, and the role of vibrationally excited N 2 in this is particularly significant. We report here the results from a new calculation of electron energy transfer rates ( Q) for vibrational excitation of N 2, as a function of the electron temperature T e. The present study was motivated by the development of a new cross-section compilation for vibrational excitation processes in N 2 which supercedes those used in the earlier calculations of the electron energy transfer rates. We show that the energy dependence and magnitude of these cross sections, particularly in the region of the well-known 2Π g resonance in N 2, significantly affect the calculated values of Q. A detailed comparison between the current and previous calculated electron energy transfer rates is made and coefficients are provided so that these rates for transitions from level 0 to levels 1–10 can be calculated for electron temperatures less than 6000 K .

Production of vibrationally excited N2 by electron impact

Energy transfer from electrons to neutral gases and ions is one of the dominant electron cooling processes in the ionosphere, and the role of vibrationally excited N2 in this is particularly significant. We report here the results from a new calculation of electron energy transfer rates (Q) for vibrational excitation of N2, as a function of the electron temperature Te. The present study was motivated by the development of a new cross-section compilation for vibrational excitation processes in N2 which supercedes those used in the earlier calculations of the electron energy transfer rates. We show that the energy dependence and magnitude of these cross sections, particularly in the region of the well-known 2Πg resonance in N2, significantly affect the calculated values of Q. A detailed comparison between the current and previous calculated electron energy transfer rates is made and coefficients are provided so that these rates for transitions from level 0 to levels 1–10 can be calculated for electron temperatures less than 6000K.

Rates of Electronic Energy Transfer in Conformationally Flexible Bichromophoric Macrocyclic Complexes: A Combined Experimental and Molecular Modeling Study

Electronic energy transfer (EET) rate constants between a naphthalene donor and anthracene acceptor in [ZnL4a](ClO4)(2) and [ZnL4b](ClO4)(2) were determined by time-resolved fluorescence where L-4a and L-4b are the trans and cis isomers of 6-((anthracen-9-yl-methyl)amino)-6,13-dimethyl-13-((naphthalen-1-yl-methyl)amino)-1,4,8,11-tetraazacyclotetradecane, respectively. These isomers differ in the relative disposition of the appended chromophores with respect to the macrocyclic plane. The trans isomer has an energy transfer rate constant (k(EET)) of 8.7 x 10(8) s(-1), whereas that of the cis isomer is significantly faster (2.3 x 10(9) s(-1)). Molecular modeling was used to determine the likely distribution of conformations in CH3CN solution for these complexes in an attempt to identify any distance or orientation dependency that may account for the differing rate constants observed. The calculated conformational distributions together with analysis by H-1 NMR for the [ZnL4a](2+) trans complex in the common trans-III N-based isomer gave a calculated Forster rate constant close to that observed experimentally. For the [ZnL4b](2+) cis complex, the experimentally determined rate constant may be attributed to a combination of trans-Ill and trans-I N-based isomeric forms of the complex in solution.

New electron-energy transfer rates for vibrational excitation of O2

We report on our computation of electron-energy transfer rates for vibrational excitation ofO2.This work was necessitated by inadequacies in the electron-impact cross section databasesemployed in previous studies and, in one case, an inaccurate approximate formulation tothe rate equation. Both these inadequacies led to incorrect energy transfer rates beingpublished in the literature. We also demonstrate the importance of using cross sections thatencompass an energy range that is extended enough to appropriately describe theenvironment under investigation.