Non-Born-Oppenheimer molecular dynamics of Na...FH photodissociation

The accuracy of non-Born-Oppenheimer (electronically nonadiabatic) semiclassical trajectory methods for simulations of "deep quantum" systems is reevaluated in light of recent quantum mechanical calculations of the photodissociation of the Na...FH van der Waals complex. In contrast to the conclusion arrived at in an earlier study, semiclassical trajectory methods are shown to be qualitatively accurate for this system, thus further validating their use for systems with large electronic energy gaps. Product branching in semiclassical surface hopping and decay-of-mixing calculations is affected by a region of coupling where the excited state is energetically forbidden. Frustrated hops in this region may be attributed to a failure of the treatment of decoherence, and a stochastic model for decoherence is introduced into the surface hopping method and is shown to improve the agreement with the quantum mechanical results. A modification of the decay-of-mixing method resulting in faster decoherence in this region is shown to give similarly improved results.     

Influence of environment induced correlated fluctuations in electronic coupling on coherent excitation energy transfer dynamics in model photosynthetic systems

Two-dimensional photon-echo experiments indicate that excitation energy transfer between chromophores near the reaction center of the photosynthetic purple bacterium Rhodobacter sphaeroides occurs coherently with decoherence times of hundreds of femtoseconds, comparable to the energy transfer time scale in these systems. The original explanation of this observation suggested that correlated fluctuations in chromophore excitation energies, driven by large scale protein motions could result in long lived coherent energy transfer dynamics. However, no significant site energy correlation has been found in recent molecular dynamics simulations of several model light harvesting systems. Instead, there is evidence of correlated fluctuations in site energy-electronic coupling and electronic coupling-electronic coupling. The roles of these different types of correlations in excitation energy transfer dynamics are not yet thoroughly understood, though the effects of site energy correlations have been well studied. In this paper, we introduce several general models that can realistically describe the effects of various types of correlated fluctuations in chromophore properties and systematically study the behavior of these models using general methods for treating dissipative quantum dynamics in complex multi-chromophore systems. The effects of correlation between site energy and inter-site electronic couplings are explored in a two state model of excitation energy transfer between the accessory bacteriochlorophyll and bacteriopheophytin in a reaction center system and we find that these types of correlated fluctuations can enhance or suppress coherence and transfer rate simultaneously. In contrast, models for correlated fluctuations in chromophore excitation energies show enhanced coherent dynamics but necessarily show decrease in excitation energy transfer rate accompanying such coherence enhancement. Finally, for a three state model of the Fenna-Matthews-Olsen light harvesting complex, we explore the influence of including correlations in inter-chromophore couplings between different chromophore dimers that share a common chromophore. We find that the relative sign of the different correlations can have profound influence on decoherence time and energy transfer rate and can provide sensitive control of relaxation in these complex quantum dynamical open systems.     

Three-dimensionally arranged windmill and grid porphyrin arrays by AgI-promoted meso-meso block oligomerization

The syntheses of soluble windmill and grid porphyrin arrays through the AgI-promoted coupling reaction of 1,4-phenylene-bridged linear porphyrin arrays, which are comprised of a central ZnII beta-free porphyrin and flanking peripheral NiII beta-octaalkylporphyrins, are described. The coupling reaction is advantageous in light of its high regioselectivity occurring only at the meso-position of the ZnII beta-free porphyrin as well as its easy extension to large porphyrin arrays. The windmill porphyrin arrays in turn serve as an effective substrate for further coupling reactions, to give three-dimensionally arranged grid porphyrin arrays. Further the grid porphyrin 12-mer (a tetramer of the linear porphyrin trimer) was also coupled to afford grid porphyrins (24-mer, 36-mer, and 48-mer). These porphyrin arrays were isolated in a discrete form by repetitive GPC/HPLC (GPC= gel-permiation chromatography). Competitive experiments with three linear porphyrin trimers bearing different peripheral metalloporphyrins (ZnII, NiII, and Cull), and the trapping experiment of the radical cation at the peripheral porphyrin with AgNO2, suggested that an initial one-electron oxidation of the easily oxidizable peripheral ZnII beta-octaalkylporphyrin with an AgI ion and a subsequent endothermic hole transfer assist the generation of the radical cation at the central ZnII beta-free porphyrin. In all ZnII-metallated windmill porphyrin arrays, the energy level of the S1 state of the meso-meso-linked diporphyrin core is lower than that of the peripheral porphyrins, thereby allowing an energy flow from the peripheral porphyrins to the central diporphyrin core; this has been confirmed by measurements of fluorescence lifetimes and picosecond time-resolved fluorescence spectra. The excitation energy transfer in the arrays encourages their potential use as an light-harvesting antenna.     

Decoherence in an anharmonic oscillator coupled to a thermal environment: a semiclassical forward-backward approach

The decoherence of an anharmonic oscillator in a thermal harmonic bath is examined via a semiclassical approach. A computational strategy is presented and exploited to calculate the time dependence of the purity and the decay of individual matrix elements in the energy representation for a variety of initial states. The time dependence of the decoherence is found to depend on the temperature of the bath, the coupling strength, the initial state of the oscillator, and the choice of quantity measuring the decoherence. Recurrences in the purity and in the off-diagonal matrix elements are observed, as well as the collapse of these matrix elements to the diagonal, providing evidence for the retention of quantum coherence for time scales longer than that indicated by the purity. The results are used to analyze the utility of the Caldeira-Leggett and Redfield models of decoherence and to assess the dependence of dephasing rates on the degree of structure in phase space. In several cases we find that the dephasing dynamics can be described as an initial Zeno-effect regime, followed by a Caldeira-Leggett region, followed by recurrences.     

Site-directed electronic tunneling in a dissipative molecular environment

The ability to control electronic tunneling in complex molecular networks of multiple donor/acceptor sites is studied theoretically. Our past analysis, demonstrating the phenomenon of site-directed transport, was limited to the coherent tunneling regime. In this work we consider electronic coupling to a dissipative molecular environment including the effect of decoherence. The nuclear modes are classified into two categories. The first kind corresponds to the internal molecular modes, which are coupled to the electronic propagation along the molecular bridges. The second kind corresponds to the external solvent modes, which are coupled to the electronic transport between different segments of the molecular network. The electronic dynamics is simulated within the effective single electron picture in the framework of the tight binding approximation. The nuclear degrees of freedom are represented as harmonic modes and the electronic-nuclear coupling is treated within the time-dependent Redfield approximation. Our results demonstrate that site-directed tunneling prevails in the presence of dissipation, provided that the decoherence time is longer than the time period for tunneling oscillations (e.g., at low temperatures). Moreover, it is demonstrated that the strength of electronic coupling to the external nuclear modes (the solvent reorganization energy) controls the coherent intramolecular tunneling dynamics at short times and may be utilized for the experimental control of site-directed tunneling in a complex network.     

Single-molecule spectroscopic investigation of energy migration processes in cyclic porphyrin arrays

Covalently linked cyclic porphyrin arrays have been synthesized to mimic natural light-harvesting apparatuses and to investigate the highly efficient energy migration processes occurring in these systems for future applications in molecular photonics. To avoid an ensemble-averaged picture, we performed a single-molecule spectroscopic study on the energy migration processes of cyclic porphyrin arrays and a linear model compound embedded in a rigid polymer matrix by recording fluorescence intensity trajectories, by performing coincidence measurements, and by doing wide-field defocused imaging. Our study demonstrates efficient energy migration within the cyclic porphyrin arrays at the single-molecule level. By comparison with the data of the linear model compound, we could pinpoint the role of the dipole-dipole coupling between diporphyrin subunits and the rigidity of the cyclic structures on the energy transfer processes.     

Correlated intermolecular coupling fluctuations in photosynthetic complexes

The functioning and efficiency of natural photosynthetic complexes is strongly influenced by their embedding in a noisy protein environment, which can even serve to enhance the transport efficiency. Interactions with the environment induce fluctuations of the transition energies and couplings between the chlorophyll molecules, and due to the fact that different fluctuations will partially be caused by the same environmental factors, correlations between the various fluctuations will occur. We argue that fluctuations of the couplings should, in general, not be neglected, as these have a considerable impact on population transfer rates, decoherence rates, and the efficiency of photosynthetic complexes. Furthermore, while correlations between transition energy fluctuations have been studied, we provide the first quantitative study of the effect of correlations between coupling fluctuations and transition energy fluctuations, and of correlations between the various coupling fluctuations. It is shown that these additional correlations typically lead to changes in interchromophore transfer rates and population oscillations and can lead to a limited enhancement of the light harvesting efficiency.     

Dissipative geometric phase and decoherence in parity-violating chiral molecules

Within a generalized Langevin framework for open quantum systems, the cyclic evolution of a two-level system is analyzed in terms of the geometric phase extended to dissipative systems for Ohmic friction. This proposal is applied to the dynamics of chiral molecules where the tunneling and parity violating effects are competing. The effect of different system-bath coupling functions in the dissipated energy is shown to be crucial to understand the behavior of the geometric phase as well as the decoherence displayed by the corresponding interference patterns.     

Nebulisation on a disposable array structured with phononic lattices

We demonstrate the use of a phononic crystal to enable the nebulisation of liquid droplets from low-cost disposable arrays, using surface acoustic waves (SAW). The SAWs were generated using interdigitated transducers (IDT) on a piezoelectric surface (LiNbO(3)) and the acoustic waves were coupled into a disposable phononic crystal structure, referred to as a superstrate. Using its excellent reflecting properties, the phononic structures confined the acoustic field within the superstrate, resulting in the concentration of the acoustic energy, in a manner controllable by the excitation frequency. We show that this capability mitigates against coupling losses incurred by the use of a disposable superstrate, greatly reducing the time needed to nebulise a drop of water with respect to an unstructured superstrate for a given power. We also demonstrate that by changing the excitation frequency, it is possible to change the spatial position at which the acoustic energy is concentrated, providing a means to specifically nebulise drops across an array. These results open up a promising future for the use of phonofluidics in high-throughput sample handling applications, such as drug delivery or the "soft" transfer of samples to a mass spectrometer in the field of proteomics.     

Stochastic quantum molecular dynamics for finite and extended systems

We present a detailed account of the technical aspects of stochastic quantum molecular dynamics, an approach introduced recently by the authors [H. Appel, M. Di Ventra, Phys. Rev. B 80 (2009) 212303] to describe coupled electron-ion dynamics in open quantum systems. As example applications of the method we consider both finite systems with and without ionic motion, as well as describe its applicability to extended systems in the limit of classical ions. The latter formulation allows the study of important phenomena such as decoherence and energy relaxation in bulk systems and surfaces in the presence of time-dependent fields.     

Excitation of local magnetic moments by tunneling electrons

The advent of milli-kelvin scanning tunneling microscopes (STM) with inbuilt magnetic fields has opened access to the study of magnetic phenomena with atomic resolution at surfaces. In the case of single atoms adsorbed on a surface, the existence of different magnetic energy levels localized on the adsorbate is due to the breaking of the rotational invariance of the adsorbate spin by the interaction with its environment, leading to energy terms in the meV range. These structures were revealed by STM experiments in IBM Almaden in the early 2000s for atomic adsorbates on CuN surfaces. The experiments consisted in the study of the changes in conductance caused by inelastic tunneling of electrons (IETS, inelastic electron tunneling spectroscopy). Manganese and Iron adatoms were shown to have different magnetic anisotropies induced by the substrate. More experiments by other groups followed up, showing that magnetic excitations could be detected in a variety of systems: e.g. complex organic molecules showed that their magnetic anisotropy was dependent on the molecular environment, piles of magnetic molecules showed that they interact via intermolecular exchange interaction, spin waves were excited on ferromagnetic surfaces and in Mn chains, and magnetic impurities have been analyzed on semiconductors. These experiments brought up some intriguing questions: the efficiency of magnetic excitations was very high, the excitations could or could not involve spin flip of the exciting electron and singular-like behavior was sometimes found at the excitation thresholds. These facts called for extended theoretical analysis; perturbation theories, sudden-approximation approaches and a strong coupling scheme successfully explained most of the magnetic inelastic processes. In addition, many-body approaches were also used to decipher the interplay between inelastic processes and the Kondo effect. Spin torque transfer has been shown to be effective in changing spin orientations of an adsorbate in theoretical works, and soon after it was shown experimentally. More recently, the previously mentioned strong coupling approach was extended to treat the excitation of spin waves in atomic chains and the ubiquitous role of electron–hole pair creation in de-exciting spins on surfaces has been analyzed. This review article expounds these works, presenting the theoretical approach by the authors while trying to thoroughly review parallel theoretical and experimental works.     

Excitation energy transport processes of porphyrin monomer,dimer, cyclic trimer,and hexamer probed by ultrafast fluorescence anisotropy decay

Femtosecond fluorescence anisotropy measurements for a variety of cyclic porphyrin arrays such as Zn(II)porphyrin m-trimer and hexamer are reported along with o-dimer and monomer as reference molecules. In the porphyrin arrays, a pair of porphyrin moieties are joined together via triphenyl linkage to ensure cyclic and rigid structures. Anisotropy decay times of the porphyrin arrays can be well described by the F?rster incoherent excitation hopping process between the porphyrin units. Exciton coupling strengths of 74 and 264 cm(-1) for the m-trimer and hexamer estimated from the observed excitation energy hopping rates are close to those of B800 and B850, respectively, in the LH2 bacterial light-harvesting antenna. Thus, these cyclic porphyrin array systems have proven to be useful in understanding energy migration processes in a relatively weak interaction regime in light of the similarity in overall structures and constituent chromophores to natural light-harvesting arrays.     

Synthesis of thiol-derivatized porphyrin dimers and trimers for studies of architectural effects on multibit information storage

We present the rational design and synthesis of multiporphyrin arrays containing thiol-derivatized linkers for the purpose of multibit molecular information storage. Porphyrin dimers and trimers were synthesized by the Pd-mediated coupling of iodo-substituted and ethynyl-substituted porphyrin building blocks in 5-51% yields. Each porphyrin dimer bears one S-acetylthio group. The architecture of the trimers incorporates a trans-substituted porphyrin (central) bearing two S-acetylthio groups and two diphenylethyne-linked porphyrins (wings) in a trans geometry. The central porphyrin and the wing porphyrins bear distinct substituents and central metals, thereby affording different oxidation potentials. The S-acetylthio groups provide a means for attachment of the arrays to an electroactive surface. The dimers are designed for vertical orientation on an electroactive surface while the trimers are designed for horizontal orientation of the central porphyrin. Altogether seven different arrays were synthesized. Each array forms a self-assembled monolayer (SAM) on gold via in situ cleavage of the S-acetyl protecting group. The SAM of each array is electrochemically robust and exhibits multiple, reversible oxidation waves. In general, however, the trimeric arrays appear to form more highly ordered monolayers that exhibit sharper, better-defined redox features.     

Communication: Standard surface hopping predicts incorrect scaling for Marcus' golden-rule rate: the decoherence problem cannot be ignored

We evaluate the accuracy of Tully's surface hopping algorithm for the spin-boson model for the case of a small diabatic coupling parameter (V). We calculate the transition rates between diabatic surfaces, and we compare our results to the expected Marcus rates. We show that standard surface hopping yields an incorrect scaling with diabatic coupling (linear in V), which we demonstrate is due to an incorrect treatment of decoherence. By modifying standard surface hopping to include decoherence events, we recover the correct scaling (~V(2)).     

Adiabatic states derived from a spin-coupled diabatic transformation: semiclassical trajectory study of photodissociation of HBr and the construction of potential curves for LiBr+

The development of spin-coupled diabatic representations for theoretical semiclassical treatments of photodissociation dynamics is an important practical goal, and some of the assumptions required to carry this out may be validated by applications to simple systems. With this objective, we report here a study of the photodissociation dynamics of the prototypical HBr system using semiclassical trajectory methods. The valence (spin-free) potential energy curves and the permanent and transition dipole moments were computed using high-level ab initio methods and were transformed to a spin-coupled diabatic representation. The spin-orbit coupling used in the transformation was taken as that of atomic bromine at all internuclear distances. Adiabatic potential energy curves, nonadiabatic couplings and transition dipole moments were then obtained from the diabatic ones and were used in all the dynamics calculations. Nonadiabatic photodissociation probabilities were computed using three semiclassical trajectory methods, namely, coherent switching with decay of mixing (CSDM), fewest switches with time uncertainty (FSTU), and its recently developed variant with stochastic decoherence (FTSU/SD), each combined with semiclassical sampling of the initial vibrational state. The calculated branching fraction to the higher fine-structure level of the bromine atom is in good agreement with experiment and with more complete theoretical treatments. The present study, by comparing our new calculations to wave packet calculations with distance-dependent ab initio spin-orbit coupling, validates the semiclassical trajectory methods, the semiclassical initial state sample scheme, and the use of a distance-independent spin-orbit coupling for future applications to polyatomic photodissociation. Finally, using LiBr(+) as a model system, it is shown that accurate spin-coupled potential curves can also be constructed for odd-electron systems using the same strategy as for HBr.     

Cover Picture

The cover picture shows a schematic representation of a supramolecular rod composed of meso-meso-coupled porphyrins. The Ag(I)-promoted meso-meso coupling of Zn(II) 5,15-diarylporphyrins enabled regularly arranged arrays with 2-128 porphyrins to be assembled. An examination of the absorption spectra of these rods show that they all exhibit split Soret bands as a result of exciton coupling. As the number of porphyrins increases the low-energy Soret band is shifted to longer wavelength while the high-energy Soret band stays at nearly the same wavelength, which results in a progressive increase in the splitting energy. A study of the fluorescence spectra of the arrays shows the S(1) states are delocalized over 6-8 porphyrin units. The 128mer at 0.1-μm long is the longest monodisperse, rodlike molecule so far known, and should, together with the smaller arrays, have the potential for application as light-harvesting wires. Further details are reported by A. Osuka et al. on p. 1458 ff.[ Magnified Cover Picture ]