Hamiltonian Reduction of Quantum Systems Controlled by Pulses

We explores Hamiltonian reduction in pulse-controlled finite-dimensional quantum systems with near-degenerate eigenstates. A quantum system with a non-degenerate ground state and several near-degenerate excited states is controlled by a short pulse, and the objective is to maximize the collective population on all excited states when we treat all of them as one level. Two cases of the systems are shown to be equivalent to effective two-level systems. When the pulse is weak, simple relations between the original systems and the reduced systems are obtained. When the pulse is strong, these relations are still available for pulseswith only one frequency under the first-order approximation.     

Photoinduced Electron and H-atom Transfer Reactions of Xanthone by Laser Flash Photolysis

The property of the lowest excited triplet states of xanthone in acetonitrile was investigated using time-resolved laser °ash photolysis at 355 nm. The transient absorption spectra and the quenching rate constants(kq) of the excited xanthone with several amines were determined. Good correlation between lgkq and the driving force of the reactions suggests the electron transfer mechanism, except aniline and 3-nitroaniline (3-NO2-A) which showed energy transfer mechanism. With the appearance of ketyl radical, hydrogen atom transfer also happened between xanthone and dimethyl-p-toluidine, 3,5,N,N-tetramethylaniline, N,N-dimethylaniline, and triethylamine. Therefore, both electron transfer and H-atom transfer occured in these systems. Great discrepancies of kq values were discovered in H-atom abstraction reactions for alcohols and phenols, which can be explained by di?erent abstraction mechanisms. The quenching rate constants between xanthone and alcohols correlate well with the ?-C?H bonding energy of alcohols.     

Electron injection into the surface states of ZrO2 nanoparticles from photoexcited quinizarin and its derivatives: effect of surface modification

The effect of surface modification on interfacial electron transfer (IET) dynamics into the surface states of ZrO(2) nanoparticles sensitized by quinizarin (Qz) and its derivatives has been carried out using time-resolved emission spectroscopy. The surface of ZrO(2) nanoparticles has been modified by sodium dodecyl benzyl sulfonate . We have observed that Qz's can form a strong charge-transfer (CT) complex with both unmodified and surface-modified (SM) ZrO(2) nanoparticles. We have confirmed electron injection into the surface states of ZrO(2) nanoparticles from the photoexcited Qz molecule in our earlier work (J. Phys. Chem. B 2004, 108, 4775; Langmuir 2004, 20, 7342). In the present investigation, we have observed electron injection from photoexcited Qz derivatives into the surface states of both unmodified and SM ZrO(2) nanoparticles and also detected CT emission. Monitoring CT emission, we have determined back electron transfer (BET) dynamics of the dye-nanoparticle systems. We have found that the BET rate for the QZs/ZrO(2) systems decreases as the relative driving force increases following Marcus inverted region kinetic behavior for an IET process. BET dynamics was found to be faster on SM ZrO(2) nanoparticles as compared to that of the unmodified (bare) one. Our time-resolved emission data indicates that upon surface modification the majority of the deeper trap states of ZrO(2) nanoparticles can be removed with the formation of some new shallower trap states in the band gap region.     

Enhanced intersystem crossing via a high energy charge transfer state in a perylenediimide-perylenemonoimide dyad

The electronic relaxation processes of a photoexcited linear perylenediimide-perylenemonoimide (PDI-PMI) acceptor-donor dyad were studied. PDI-PMI serves as a model compound for donor-acceptor systems in photovoltaic devices and has been designed to have a high-energy PDI (-*)-PMI (+*) charge transfer (CT) state. Our study focuses on the minimal Gibbs free energy (Delta G ET) required to achieve quantitative CT and on establishing the role of charge recombination to a triplet state. We used time-resolved photoluminescence and picosecond photoinduced absorption (PIA) to investigate excited singlet (S 1) and CT states and complemented these experiments with singlet oxygen ( (1)Delta g) luminescence and PIA measurements on longer timescales to study the population of triplet excited states (T 1). In an apolar solvent like cyclohexene (CHX), photoinduced electron transfer does not occur, but in more polar solvents such as toluene (TOL) and chlorobenzene (CB), photoexcitation is followed by a fast electron transfer, populating the PDI (-*)-PMI (+*) CT state. We extract rate constants for electron transfer (ET; S 1-->CT), back electron transfer (BET; S 1<--CT), and charge recombination (CR) to lower-energy states (CT-->S 0 and CT-->T 1). Temperature-dependent measurements yield the barriers for the transfer reactions. For ET and BET, these correspond to predictions from Marcus-Jortner theory and show that efficient, near quantitative electron transfer ( k ET/ k BET >or= 100) can be obtained when Delta G ET approximately -120 meV. With respect to triplet state formation, we find a relatively low triplet quantum yield (Phi T < 25%) in CHX but much higher values (Phi T = 30-98%) in TOL and CB. We identify the PDI (-*)-PMI (+*) state as a precursor to the T 1 state. Recombination to T 1, rather than to the ground-state S 0, is required to rationalize the experimental barrier for CR. Finally, we discuss the relevance of these results for electron donor-acceptor films in photovoltaic devices.     

Long-lived triplet charge-separated state in naphthalenediimide based donor–acceptor systems

1,4,5,8-Naphthalenediimides (NDIs) are widely used motifs to design multichromophoric architectures due to their ease of functionalisation, their high oxidative power and the stability of their radical anion. The NDI building block can be incorporated in supramolecular systems by either core or imide functionalization. We report on the charge-transfer dynamics of a series of electron donor–acceptor dyads consisting of a NDI chromophore with one or two donors linked at the axial, imide position. Photo-population of the core-centred π–π* state is followed by ultrafast electron transfer from the electron donor to the NDI. Due to a solvent dependent singlet–triplet equilibrium inherent to the NDI core, both singlet and triplet charge-separated states are populated. We demonstrate that long-lived charge separation in the triplet state can be achieved by controlling the mutual orientation of the donor–acceptor sub-units. By extending this study to a supramolecular NDI-based cage, we also show that the triplet charge-separation yield can be increased by tuning the environment.

Ultrafast electron transfer from singlet and triplet excited states in equilibrium results in the population of both singlet and triplet charge-separated states.     

Interplay between barrier width and height in electron tunneling: photoinduced electron transfer in porphyrin-based donor-bridge-acceptor systems

The rate of electron tunneling in molecular donor-bridge-acceptor (D-B-A) systems is determined both by the tunneling barrier width and height, that is, both by the distance between the donor and acceptor as well as by the energy gap between the donor and bridge moieties. These factors are therefore important to control when designing functional electron transfer systems, such as constructs for photovoltaics, artificial photosynthesis, and molecular scale electronics. In this paper we have investigated a set of D-B-A systems in which the distance and the energy difference between the donor and bridge states (DeltaEDB) are systematically varied. Zinc(II) and gold(III) porphyrins were chosen as electron donor and acceptor because of their suitable driving force for photoinduced electron transfer (-0.9 eV in butyronitrile) and well-characterized photophysics. We have previously shown, in accordance with the superexchange mechanism for electron transfer, that the electron transfer rate is proportional to the inverse of DeltaEDB in a series of zinc/gold porphyrin D-B-A systems with bridges of constant edge to edge distance (19.6 A) and varying DeltaEDB (3900-17 600 cm(-1)). Here, we use the same donor and acceptor but the bridge is shortened or extended giving a set of oligo-p-phenyleneethynylene bridges (OPE) with four different edge to edge distances ranging from 12.7 to 33.4 A. These two sets of D-B-A systems-ZnP-RB-AuP+ and ZnP-nB-AuP+-have one bridge in common, and hence, for the first time both the distance and DeltaEDB dependence of electron transfer can be studied simultaneously in a systematic way.     

Proton-coupled electron transfer versus hydrogen atom transfer: generation of charge-localized diabatic states

The distinction between proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms is important for the characterization of many chemical and biological processes. PCET and HAT mechanisms can be differentiated in terms of electronically nonadiabatic and adiabatic proton transfer, respectively. In this paper, quantitative diagnostics to evaluate the degree of electron-proton nonadiabaticity are presented. Moreover, the connection between the degree of electron-proton nonadiabaticity and the physical characteristics distinguishing PCET from HAT, namely, the extent of electronic charge redistribution, is clarified. In addition, a rigorous diabatization scheme for transforming the adiabatic electronic states into charge-localized diabatic states for PCET reactions is presented. These diabatic states are constructed to ensure that the first-order nonadiabatic couplings with respect to the one-dimensional transferring hydrogen coordinate vanish exactly. Application of these approaches to the phenoxyl-phenol and benzyl-toluene systems characterizes the former as PCET and the latter as HAT. The diabatic states generated for the phenoxyl-phenol system possess physically meaningful, localized electronic charge distributions that are relatively invariant along the hydrogen coordinate. These diabatic electronic states can be combined with the associated proton vibrational states to generate the reactant and product electron-proton vibronic states that form the basis of nonadiabatic PCET theories. Furthermore, these vibronic states and the corresponding vibronic couplings may be used to calculate rate constants and kinetic isotope effects of PCET reactions.     

The electronic structure of Mn in oxides, coordination complexes, and the oxygen-evolving complex of photosystem II studied by resonant inelastic X-ray scattering

Resonant inelastic X-ray scattering (RIXS) was used to collect Mn K pre-edge spectra and to study the electronic structure in oxides, molecular coordination complexes, as well as the S1 and S2 states of the oxygen-evolving complex (OEC) of photosystem II (PS II). The RIXS data yield two-dimensional plots that can be interpreted along the incident (absorption) energy or the energy transfer axis. The second energy dimension separates the pre-edge (predominantly 1s to 3d transitions) from the main K-edge, and a detailed analysis is thus possible. The 1s2p RIXS final-state electron configuration along the energy transfer axis is identical to conventional L-edge absorption spectroscopy, and the RIXS spectra are therefore sensitive to the Mn spin state. This new technique thus yields information on the electronic structure that is not accessible in conventional K-edge absorption spectroscopy. The line splittings can be understood within a ligand field multiplet model, i.e., (3d,3d) and (2p,3d) two-electron interactions are crucial to describe the spectral shapes in all systems. We propose to explain the shift of the K pre-edge absorption energy upon Mn oxidation in terms of the effective number of 3d electrons (fractional 3d orbital population). The spectral changes in the Mn 1s2p(3/2) RIXS spectra between the PS II S1 and S2 states are small compared to that of the oxides and two of the coordination complexes (Mn(III)(acac)3 and Mn(IV)(sal)2(bipy)). We conclude that the electron in the step from S1 to S2 is transferred from a strongly delocalized orbital.     

Photoinduced Electron‐Transfer Processes in Fullerene‐Based Donor–Acceptor Systems

Photoinduced electron‐transfer processes in fullerene‐based donor–acceptor dyads (D? B? A) in homogeneous and cluster systems are summarized. Stabilization of charge has been achieved through the use of fullerene substituted‐aniline/heteroaromatic dyads with tunable ionization potentials and also by using fullerene clusters. The rate constants for charge separation (k_CS) and charge recombination (k_CR) in fullerene substituted‐aniline/heteroaromatic dyads show that forward electron transfer falls in the normal region of the Marcus curve and the back electron transfer in the inverted region of the Marcus parabola. Clustering of fullerene‐based dyads assists in effective delocalization of the separated charge and thereby slows down the back electron transfer in these cases.     

Electronic coupling for charge transfer in donor-bridge-acceptor systems. Performance of the two-state FCD model

Electronic coupling is a key parameter that determines the rate of electron transfer reactions and electrical conductivity of molecular wires. To examine the performance of a two-state approach based on the orthogonal transformation of adiabatic states to diabatic states, we compare the effective donor-acceptor coupling V(DA) computed with three different approaches in model donor-bridge-acceptor (D-B-A) systems. It is found that V(DA) derived with the two-state method accounts properly for both the direct and superexchange interactions. The approach becomes, however, less accurate with the increasing energy difference of the donor and acceptor states. We suggest a simple diagnostic to identify the situation when the estimated coupling might be inaccurate and consider how to improve the performance of the two-state scheme in such a case.     

Bridge-dependent electron transfer in porphyrin-based donor-bridge-acceptor systems.

Photoinduced electron transfer in donor-bridge-acceptor systems with zinc porphyrin (or its pyridine complex) as the donor and gold(III) porphyrin as the acceptor has been studied. The porphyrin moieties were covalently linked with geometrically similar bridging chromophores which vary only in electronic structure. Three of the bridges are fully conjugated pi-systems and in a fourth, the conjugation is broken. For systems with this bridge, the quenching rate of the singlet excited state of the donor was independent of solvent and corresponded to the rate of singlet energy transfer expected for a F?rster mechanism. In contrast, systems with a pi-conjugated bridging chromophore show a solvent-dependent quenching rate that suggests electron transfer in the Marcus normal region. This is supported by picosecond transient absorption measurements, which showed formation of the zinc porphyrin radical cation only in systems with pi-conjugated bridging chromophores. On the basis of the Marcus and Rehm-Weller equations, an electronic coupling of 5-20 cm(-)(1) between the donor and acceptor is estimated for these systems. The largest coupling is found for the systems with the smallest energy gap between the donor and bridge singlet excited states. This is in good agreement with the coupling calculated with quantum mechanical methods, as is the prediction of an almost zero coupling in the systems with a nonconjugated bridging chromophore.     

Mono- and dinuclear ruthenium(II) and osmium(II) polypyridine complexes built around spiro-bridged bis(phenanthroline) ligands: synthesis, electrochemistry, and photophysics

Two new dyads have been synthesized in which terminal Ru(II) and Os(II) polypyridine complexes are separated by sterically constrained spiro bridges. The photophysical properties of the corresponding mononuclear complexes indicate the importance of the decay of the lowest-energy triplet states localized on the metallo fragments through the higher-energy metal-centered excited states. This effect is minimized at 77 K, where triplet lifetimes are relatively long, and for the Os(II)-based systems relative to their Ru(II)-based counterparts. Intramolecular triplet energy transfer takes place from the Ru(II)-based fragment to the appended Os(II)-based unit, the rate constant being dependent on the molecular structure and on temperature. In all cases, the experimental rate constant matches surprisingly well with the rate constant calculated for F?rster-type dipole-dipole energy transfer. As such, the disparate rates shown by the two compounds can be attributed to stereochemical factors. It is further concluded that the spiro bridging unit does not favor through-bond electron exchange interactions, a situation confirmed by cyclic voltammetry.     

A schematic model for energy and charge transfer in the chlorophyll complex

A theory for simultaneous charge and energy transfer in the carotenoid-chlorophyll-a complex is presented here and discussed. The observed charge transfer process in these chloroplast complexes is reasonably explained in terms of this theory. In addition, the process leads to a mechanism to drive an electron in a lower to a higher-energy state, thus providing a mechanism for the ejection of the electron to a nearby molecule (chlorophyll) or into the environment. The observed lifetimes of the electronically excited states are in accord/agreement with the investigations of Sundstr?m et al. and are in the range of pico-seconds and less. The change in electronic charge distribution in internuclear space as the system undergoes an electronic transition to a higher-energy state could, under appropriate physical conditions, lead to oscillating dipoles capable of transmitting energy from the carotenoid-chlorophylls chromophore to the reaction center by sending an electromagnetic wave (a photon) which provides a novel new mechanism for energy production. In the simplest version of the F?rster?CDexter theory, the excitation energy of a donor is transferred to an acceptor and then de-excited to the ground state by fluorescence with no electron being transferred. In the process proposed herein, charge and energy both are transferred from donor to acceptor which can further de-excite by fluorescence. The charge transfer time scale involving an actual transfer of electron is in the pico-second range.     

Near-IR excitation transfer and electron transfer in a BF2-chelated dipyrromethane-azadipyrromethane dyad and triad

A molecular dyad and triad, comprised of a known photosensitizer, BF(2)-chelated dipyrromethane (BDP), covalently linked to its structural analog and near-IR emitting sensitizer, BF(2)-chelated tetraarylazadipyrromethane (ADP), have been newly synthesized and the photoinduced energy and electron transfer were examined by femtosecond and nanosecond laser flash photolysis. The structural integrity of the newly synthesized compounds has been established by spectroscopic, electrochemical, and computational methods. The DFT calculations revealed a molecular-clip-type structure for the triad, in which the BDP and ADP entities are separated by about 14 ? with a dihedral angle between the fluorophores of around 70°. Differential pulse voltammetry studies have revealed the redox states, allowing estimation of the energies of the charge-separated states. Such calculations revealed a charge separation from the singlet excited BDP ((1)BDP*) to ADP (BDP(.+)-ADP(.-)) to be energetically favorable in nonpolar toluene and in polar benzonitrile. In addition, the excitation transfer from the singlet BDP to ADP is also envisioned due to good spectral overlap of the BDP emission and ADP absorption spectra. Femtosecond laser flash photolysis studies provided concrete evidence for the occurrence of energy transfer from (1)BDP* to ADP (in benzonitrile and toluene) and electron transfer from BDP to (1)ADP* (in benzonitrile, but not in toluene). The kinetic study of energy transfer was measured by monitoring the rise of the ADP emission and revealed fast energy transfer (ca. 10(11) s(-1)) in these molecular systems. The kinetics of electron transfer via (1)ADP*, measured by monitoring the decay of the singlet ADP at λ=820 nm, revealed a relatively fast charge-separation process from BDP to (1)ADP*. These findings suggest the potential of the examined ADP-BDP molecules to be efficient photosynthetic antenna and reaction center models.     

Rotational averaging and optimization of laser-induced population transfer in molecules

The dynamics of a molecule subject to a short laser pulse is investigated, with focus on the averaging over initial rotational states and on the optimization of laser parameters for the efficient population transfer between vibrational and electronic states. A relation is established between final-state populations obtained with a fixed orientation and those based on a full treatment of the rotational degrees of freedom. In the short-pulse approximation, rotational averaging amounts to integrating the fixed molecule results over all orientations. The theory is applied to a variety of model systems and verified with numerical calculations using Gaussian pulses. We calculate target state populations with three procedures, optimizing the laser pulse for a fixed orientation without orientational averaging, averaging without changing the laser parameters, and reoptimizing the parameters after averaging. The analysis of the two-level system provides a reference for the order of magnitude of the effects of averaging. The three-level system brings out the relevant role of the geometry of polarization vectors and transition dipoles. The multiphoton excitation of a Morse oscillator shows the importance of taking into account the dependence of resonance frequencies on the laser intensity. Within a proton transfer model we discuss the results obtained with and without chirping and we show that "optimizing after averaging" can be as effective as choosing a more refined pulse shape.     

Long-lived charge-transfer states in compact donor-acceptor dyads.

Photoinduced electron transfer is a widely applied method to convert photon energy into a useful (electro)chemical potential, both in nature and in artificial devices. There is a continuing effort to develop molecular systems in which the charge-transfer state, populated by photoinduced electron transfer, survives sufficiently long to tap the energy stored in it. In general this has been found to require the construction of rather complex molecular systems, but more recently a few approaches have been reported that allow the use of much more simple and relatively small electron donor-acceptor dyads for this purpose. The most successful examples of such systems seem to be those that apply "electron spin control" to slow down the spontaneous decay of the charge-transfer state, and these are reviewed in this minireview, with a discussion of the underlying principles and a critical evaluation of some of the claims made with regard to using a pronounced "inverted-region effect" as an alternative method to prolong the lifetime of charge-transfer states.     

An extended dead-end elimination algorithm to determine gap-free lists of low energy states

Proteins are flexible systems and commonly populate several functionally important states. To understand protein function, these states and their energies have to be identified. We introduce an algorithm that allows the determination of a gap-free list of the low energy states. This algorithm is based on the dead-end elimination (DEE) theorem and is termed X-DEE (extended DEE). X-DEE is applicable to discrete systems whose state energy can be formulated as pairwise interaction between sites and their intrinsic energies. In this article, the computational performance of X-DEE is analyzed and discussed. X-DEE is implemented to determine the lowest energy protonation states of proteins, a problem to which DEE has not been applied so far. We use X-DEE to calculate a list of low energy protonation states for two bacteriorhodopsin structures that represent the first proton transfer step of the bacteriorhodopsin photocycle.     

Electron and energy transfer modulation with photochromic switches

This tutorial review illustrates how work on the reversible interconversion between the colorless and colored forms of photochromic compounds can be exploited to modulate electron and energy transfer processes. Indeed, a photochrome can be designed to accept electrons or energy from a complementary donor in one of its two states only. Alternatively, the photoinduced transformations associated with a photochromic switch can be engineered to control the relative orientation and distance of donor-acceptor pairs. If either the donor or the acceptor is fluorescent, the photoregulated transfer of energy or electrons results in the modulation of the emission intensity. Thus, these fascinating molecular and supramolecular systems can advance the basic understanding of electron and energy transfer processes, while leading to viable operating principles to control light with light.     

Exact solution of a model of condensed-phase electron transfer with non-Condon effects

Non-Condon effects are important in the analysis of electron transfer in many systems coupled to a condensed-phase environment. We detail a novel condensed-phase electron transfer Hamiltonian that extends the spin-boson model to account for non-Condon effects. We show that the relevant reduced system density matrix dynamics can be calculated exactly for a particular class of bath Hamiltonians and system-bath couplings. An explicit formula for the long-time behavior of these systems is derived. We show that they exhibit non-Boltzmann long-time behavior that is independent of temperature, and depends on the system Hamiltonian and the initial system density matrix.     

Direct evidence of active-site reduction and photodriven catalysis in sensitized hydrogenase assemblies

We report photocatalytic H(2) production by hydrogenase (H(2)ase)-quantum dot (QD) hybrid assemblies. Quenching of the CdTe exciton emission was observed, consistent with electron transfer from the quantum dot to H(2)ase. GC analysis showed light-driven H(2) production in the presence of a sacrificial electron donor with an efficiency of 4%, which is likely a lower limit for these hybrid systems. FTIR spectroscopy was employed for direct observation of active-site reduction in unprecedented detail for photodriven H(2)ase catalysis with sensitivity toward both H(2)ase and the sacrificial electron donor. Photosensitization with Ru(bpy)(3)(2+) showed distinct FTIR photoreduction properties, generating all of the states along the steady-state catalytic cycle with minimal H(2) production, indicating slow, sequential one-electron reduction steps. Comparing the H(2)ase activity and FTIR results for the two systems showed that QDs bind more efficiently for electron transfer and that the final enzyme state is different for the two sensitizers. The possible origins of these differences and their implications for the enzymatic mechanism are discussed.