Special Pair Research Articles

Ultrafast Symmetry-Breaking Charge Separation in a Perylene Bisimide Dimer Enabled by Vibronic Coupling and Breakdown of Adiabaticity.

Perylene bisimides (PBIs) have received great attention in their applicability to optoelectronics. Especially, symmetry-breaking charge separation (SB-CS) in PBIs has been investigated to mimic the efficient light capturing and charge generation in natural light-harvesting systems. However, unlike ultrafast CS dynamics in donor-acceptor heterojunction materials, ultrafast SB-CS in a stacked homodimer has still been challenging due to excimer formation in the absence of rigidifying surroundings such as a special pair in the natural systems. Herein, we present the detailed mechanism of ultrafast photoinduced SB-CS occurring in a 1,7-bis(N-pyrrolidinyl) PBI dimer within a cyclophane. Through narrow-band and broad-band transient absorption spectroscopy, we demonstrate that ultrafast SB-CS in the dimer is enabled by the combination of (1) vibrationally coherent charge-transfer resonance-enhanced excimer formation and (2) breakdown of adiabaticity (formation of SB-CS diabats) in the excimer state via structural and solvent fluctuation. Quantum chemical calculations also underpin that the participation of strong electron-donating substituents in overall vibrational modes plays a crucial role in triggering the ultrafast SB-CS. Therefore, our work provides an alternative route to facilitate ultrafast SB-CS in PBIs and thereby establishes a novel strategy for the design of optoelectronic materials.

Current state of the primary charge separation mechanism in photosystem I of cyanobacteria.

This review analyzes new data on the mechanism of ultrafast reactions of primary charge separation in photosystem I (PS I) of cyanobacteria obtained in the last decade by methods of femtosecond absorption spectroscopy. Cyanobacterial PS I from many species harbours 96 chlorophyll a (Chl a) molecules, including six specialized Chls denoted Chl1A/Chl1B (dimer P700, or PAPB), Chl2A/Chl2B, and Chl3A/Chl3B arranged in two branches, which participate in electron transfer reactions. The current data indicate that the primary charge separation occurs in a symmetric exciplex, where the special pair P700 is electronically coupled to the symmetrically located monomers Chl2A and Chl2B, which can be considered together as a symmetric exciplex Chl2APAPBChl2B with the mixed excited (Chl2APAPBChl2B)* and two charge-transfer states P700 +Chl2A - and P700 +Chl2B -. The redistribution of electrons between the branches in favor of the A-branch occurs after reduction of the Chl2A and Chl2B monomers. The formation of charge-transfer states and the symmetry breaking mechanisms were clarified by measuring the electrochromic Stark shift of β-carotene and the absorption dynamics of PS I complexes with the genetically altered Chl 2B or Chl 2A monomers. The review gives a brief description of the main methods for analyzing data obtained using femtosecond absorption spectroscopy. The energy levels of excited and charge-transfer intermediates arising in the cyanobacterial PS I are critically analyzed.

Rough Semiring-Valued Fuzzy Sets with Application

Many of the new fuzzy structures with complete MV-algebras as value sets, such as hesitant, intuitionistic, neutrosophic, or fuzzy soft sets, can be transformed into one type of fuzzy set with values in special complete algebras, called AMV-algebras. The category of complete AMV-algebras is isomorphic to the category of special pairs (R,R∗) of complete commutative semirings and the corresponding fuzzy sets are called (R,R∗)-fuzzy sets. We use this theory to define (R,R∗)-fuzzy relations, lower and upper approximations of (R,R∗)-fuzzy sets by (R,R∗)-relations, and rough (R,R∗)-fuzzy sets, and we show that these notions can be universally applied to any fuzzy type structure that is transformable to (R,R∗)-fuzzy sets. As an example, we also show how this general theory can be used to determine the upper and lower approximations of a color segment corresponding to a particular color.

Theoretical Model of the Far-Red-Light-Adapted Photosystem I Reaction Center of Cyanobacterium Acaryochloris marina Using Chlorophyll d and the Effect of Chlorophyll Exchange

A theoretical model of the far-red-light-adapted photosystem I (PSI) reaction center (RC) complex of a cyanobacterium, Acaryochloris marina (AmPSI), was constructed based on the exciton theory and the recently identified molecular structure of AmPSI by Hamaguchi et al. (Nat. Commun., 2021, 12, 2333). A. marina performs photosynthesis under the visible to far-red light (400-750 nm), which is absorbed by chlorophyll d (Chl-d). It is in contrast to the situation of all the other oxygenic photosynthetic processes of cyanobacteria and plants, which contains chlorophyll a (Chl-a) that absorbs only 400-700 nm visible light. AmPSI contains 70 Chl-d, 1 Chl-d', 2 pheophytin a (Pheo-a), and 12 carotenoids in the currently available structure. A special pair of Chl-d/Chl-d' acts as the electron donor (P740) and two Pheo-a act as the primary electron acceptor A0 as the counterparts of P700 and Chl-a, respectively, of Chl-a-type PSIs. The exciton Hamiltonian of AmPSI was constructed considering the excitonic coupling strength and site energy shift of individual pigments using the Poisson-TrESP (P-TrESP) and charge density coupling (CDC) methods. The model was constructed to fit the experimentally measured spectra of absorption and circular dichroism (CD) spectra during downhill/uphill excitation energy transfer processes. The constructed theoretical model of AmPSI was further compared with the Chl-a-type PSI of Thermosynechococcus elongatus (TePSI), which contains only Chl-a and Chl-a'. The functional properties of AmPSI and TePSI were further examined by the in silico exchange of Chl-d by Chl-a in the models.

Exact simulation of pigment-protein complexes unveils vibronic renormalization of electronic parameters in ultrafast spectroscopy

The primary steps of photosynthesis rely on the generation, transport, and trapping of excitons in pigment-protein complexes (PPCs). Generically, PPCs possess highly structured vibrational spectra, combining many discrete intra-pigment modes and a quasi-continuous of protein modes, with vibrational and electronic couplings of comparable strength. The intricacy of the resulting vibronic dynamics poses significant challenges in establishing a quantitative connection between spectroscopic data and underlying microscopic models. Here we show how to address this challenge using numerically exact simulation methods by considering two model systems, namely the water-soluble chlorophyll-binding protein of cauliflower and the special pair of bacterial reaction centers. We demonstrate that the inclusion of the full multi-mode vibronic dynamics in numerical calculations of linear spectra leads to systematic and quantitatively significant corrections to electronic parameter estimation. These multi-mode vibronic effects are shown to be relevant in the longstanding discussion regarding the origin of long-lived oscillations in multidimensional nonlinear spectra.

The terminal enzymes of (bacterio)chlorophyll biosynthesis.

(Bacterio)chlorophylls are modified tetrapyrroles that are used by phototrophic organisms to harvest solar energy, powering the metabolic processes that sustain most of the life on Earth. Biosynthesis of these pigments involves enzymatic modification of the side chains and oxidation state of a porphyrin precursor, modifications that differ by species and alter the absorption properties of the pigments. (Bacterio)chlorophylls are coordinated by proteins that form macromolecular assemblies to absorb light and transfer excitation energy to a special pair of redox-active (bacterio)chlorophyll molecules in the photosynthetic reaction centre. Assembly of these pigment–protein complexes is aided by an isoprenoid moiety esterified to the (bacterio)chlorin macrocycle, which anchors and stabilizes the pigments within their protein scaffolds. The reduction of the isoprenoid ‘tail’ and its addition to the macrocycle are the final stages in (bacterio)chlorophyll biosynthesis and are catalysed by two enzymes, geranylgeranyl reductase and (bacterio)chlorophyll synthase. These enzymes work in conjunction with photosynthetic complex assembly factors and the membrane biogenesis machinery to synchronize delivery of the pigments to the proteins that coordinate them. In this review, we summarize current understanding of the catalytic mechanism, substrate recognition and regulation of these crucial enzymes and their involvement in thylakoid biogenesis and photosystem repair in oxygenic phototrophs.

Special Fractional Curve Pairs with Fractional Calculus

In this study, the effect of fractional derivatives, whose application area is increasing day by day, on curve pairs is investigated. As it is known, there are not many studies on a geometric interpretation of fractional calculus. When examining the effect of fractional analysis on a curve, the Conformable fractional derivative that fits the algebraic structure of differential geometry derivative is used. This effect is examined with the help of examples consistent with the theory and visualized for different values of the Conformable fractional derivative. The difference of this study from others is the use of Conformable fractional derivatives and integrals in calculations. Fractional calculus has applications in many fields such as physics, engineering, mathematical biology, fluid mechanics,signal processing, etc. Fractional derivatives and integrals have become an extremely important and new mathematical method in solving various problems in many sciences.

Understanding Complex Electron Radiolysis in Saline Solution by Big Data Analysis.

In this article, we developed a new method to analyze the complex chemical reactions induced by electron beam radiolysis based on big data analysis. At first, we built an element transport network to show the chemical reactions. Furthermore, the linearity between the species was quantified by Pearson correlation coefficient analysis. Based on the analysis, the mechanism of the high linearity between the special species pairs was interpreted by the element transport roadmap and chemical equations. The time variation of the pH of the solution and bubble formation in the solution were analyzed by simulation and data analysis. The simulation indicates that O2 and H2 can easily oversaturate and form bubbles. Finally, the radiolysis of high-energy electrons in pure water was analyzed as a reference for the radiolysis of high-energy electrons in saline solution. This work provides a new method for investigating a high-energy electron radiolysis process and for simplifying a complex chemical reaction based on quantitative analysis of the species variation in the reaction.

Structural basis for the absence of low-energy chlorophylls in a photosystem I trimer from Gloeobacter violaceus.

Photosystem I (PSI) is a multi-subunit pigment-protein complex that functions in light-harvesting and photochemical charge-separation reactions, followed by reduction of NADP to NADPH required for CO2 fixation in photosynthetic organisms. PSI from different photosynthetic organisms has a variety of chlorophylls (Chls), some of which are at lower-energy levels than its reaction center P700, a special pair of Chls, and are called low-energy Chls. However, the sites of low-energy Chls are still under debate. Here, we solved a 2.04-Å resolution structure of a PSI trimer by cryo-electron microscopy from a primordial cyanobacterium Gloeobacter violaceus PCC 7421, which has no low-energy Chls. The structure shows the absence of some subunits commonly found in other cyanobacteria, confirming the primordial nature of this cyanobacterium. Comparison with the known structures of PSI from other cyanobacteria and eukaryotic organisms reveals that one dimeric and one trimeric Chls are lacking in the Gloeobacter PSI. The dimeric and trimeric Chls are named Low1 and Low2, respectively. Low2 is missing in some cyanobacterial and eukaryotic PSIs, whereas Low1 is absent only in Gloeobacter. These findings provide insights into not only the identity of low-energy Chls in PSI, but also the evolutionary changes of low-energy Chls in oxyphototrophs.

Symmetry-Breaking Charge Separation in Molecular Constructs for Efficient Light Energy Conversion

The generation of electron–hole radical pair at the active layer of organic photovoltaics through symmetry-breaking charge separation (SB-CS) has a crucial role in enhancing open-circuit voltage (Voc) and thereby increasing power conversion efficiency. Since the SB-CS materials achieve intramolecular charge separation with a negligible energetic driving force and decelerated charge recombination (CR) rate, SB-CS has been subjected to extensive experimental and theoretical studies. This Focus Review assesses the fundamentals of photosynthetic reaction centers, especially the “special pair”, and discusses how covalent control over the geometric arrangement, surrounding dielectric medium, and substitutions on multichromophoric perylenediimide architecture affects the energy landscape of SB-CS and CR. We systematically summarize the kinetically favored undesirable radiative and non-radiative deactivation channels of SB-CS and CR processes on diverse chromophoric arrangements. Here, we suggest new rational design principles to fine-tune the electron-transfer dynamics at the molecular level to improve the performance of light–energy conversion devices.

Photocatalytic CO2 reduction sensitized by a special-pair mimic porphyrin connected with a rhenium(i) tricarbonyl complex.

Zn porphyrins with an imidazolyl group at the meso position generate a highly stable porphyrin dimer by complementary coordination from the imidazolyl to the Zn ion in noncoordinating solvents such as chloroform, which mimics the natural special pair in photosynthesis. In this work, we have synthesized an imidazolyl-substituted Zn porphyrin connected with a Re 2,2-bipyridine tricarbonyl complex as a CO2 reduction catalyst via a p-phenylene linker, affording a homodimer with two Re complexes on both sides (ReDRe). The dimeric structure is easily dissociated into the corresponding monomers in coordinating solvents. Therefore, we prepared a mixture containing a heterodimer with the Re carbonyl complex on one side (ReD) by simple mixing with an imidazolyl Zn porphyrin and evaporating the solvent. Using the Grubbs catalyst, the subsequent olefin metathesis reaction of the mixture gave covalently linked porphyrin dimers through the allyloxy side chains, enabling the isolation of the stable hetero- (ReD′) and homo-dimers (ReD′Re) with gel permeation chromatography. The Zn porphyrin dimers have intense absorption bands in the visible light region and acted as good photosensitizers in photocatalytic CO2 reduction in a mixture of N,N-dimethylacetamide and triethanolamine (5 : 1 v/v) containing 1,3-dimethyl-2-phenyl-2,3-dihydro-1H-benzo[d]imidazole as the electron donor, giving CO with high selectivity and durability. Under irradiation with strong light intensity, the reaction rate in ReD′ exceeded that of the previous porphyrin Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> Re complex dyad, ZnP-phen=Re. For instance, after irradiation at 560 nm for 18 h, the turnover number (TONCO) of ReD′ reached 2800, whereas the TONCO of ZnP-phen=Re was 170. The high activity in the system using the porphyrin dimer originates from no accumulation of the one-electron reduced species of the porphyrin that inhibit light absorption due to the inner-filter effect.

Distance and Potential Dependence of Charge Transport Through the Reaction Center of Individual Photosynthetic Complexes

AbstractCharge separation and transport through the reaction center of photosystem I (PSI) is an essential part of the photosynthetic electron transport chain. A strategy is developed to immobilize and orient PSI complexes on gold electrodes allowing to probe the complex's electron acceptor side, the chlorophyll special pair P700. Electrochemical scanning tunneling microscopy (ECSTM) imaging and current–distance spectroscopy of single protein complex shows lateral size in agreement with its known dimensions, and a PSI apparent height that depends on the probe potential revealing a gating effect in protein conductance. In current–distance spectroscopy, it is observed that the distance‐decay constant of the current between PSI and the ECSTM probe depends on the sample and probe electrode potentials. The longest charge exchange distance (lowest distance‐decay constant β) is observed at sample potential 0 mV/SSC (SSC: reference electrode silver/silver chloride) and probe potential 400 mV/SSC. These potentials correspond to hole injection into an electronic state that is available in the absence of illumination. It is proposed that a pair of tryptophan residues located at the interface between P700 and the solution and known to support the hydrophobic recognition of the PSI redox partner plastocyanin, may have an additional role as hole exchange mediator in charge transport through PSI.

Macroscale superlubricity achieved via hydroxylated hexagonal boron nitride nanosheets with ionic liquid at steel/steel interface

Macroscale superlubricity is a prospective strategy in modern tribology to dramatically reduce friction and wear of mechanical equipment; however, it is mainly studied for point-to-surface contact or special friction pairs in experiments. In this study, a robust macroscale superlubricity for point-to-point contact on a steel interface was achieved for the first time by using hydroxylated modified boron nitride nanosheets with proton-type ionic liquids (ILs) as additives in ethylene glycol aqueous (EGaq). The detailed superlubricity process and mechanism were revealed by theoretical calculations and segmented experiments. The results indicate that hydration originating from hydrated ions can significantly reduce the shear stress of EGaq, which plays an essential role in achieving superlubricity. Moreover, the IL induces a tribochemical reaction to form a friction-protective film. Hydroxylated boron nitride nanosheets (HO-BNNs) function as a polishing and self-repairing agent to disperse the contact stress between friction pairs. Superlubricity involves the change in lubrication state from boundary lubrication to mixed lubrication. This finding can remarkably extend the application of superlubricity for point-to-point contact on steel surfaces for engineering applications.

On zero-sum subsequences of length [formula omitted] II

Let G be an additive finite abelian group of exponent exp⁡(G). For every positive integer k, let skexp⁡(G)(G) denote the smallest integer t such that every sequence over G of length t has a zero-sum subsequence of length kexp⁡(G). Let ηkexp⁡(G)(G) denote the smallest integer t such that every sequence over G of length t has a zero-sum subsequence of length between 1 and kexp⁡(G). It is conjectured by Gao et al. that skexp⁡(G)(G)=ηkexp⁡(G)(G)+kexp⁡(G)−1 for all pairs of (G,k). This conjecture is a common generalization of several previous conjectures and has been confirmed for some special pairs of (G,k). In this paper we shall prove this conjecture for more pairs of (G,k). We also study the inverse problem associated with skexp⁡(G)(G), i.e., we determine the structure of sequences S of length skexp⁡(G)(G)−1 that have no zero-sum subsequence of length kexp⁡(G).

Generalization of the Gross–Pitaevskii equation for multi-particle cases

A new method is proposed to obtain Gross–Pitaevskii equation by the chain of Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) quantum kinetic equations. In that sense, we investigate the dynamics of a quantum system including infinite number of identical particles which interact via a (special) pair potential on the form of Dirac delta-function.

Resolving the Structural Debate for the Hydrated Excess Proton in Water.

It has long been proposed that the hydrated excess proton in water (aka the solvated "hydronium" cation) likely has two limiting forms, that of the Eigen cation (H9O4+) and that of the Zundel cation (H5O2+). There has been debate over which of these two is the more dominant species and/or whether intermediate (or "distorted") structures between these two limits are the more realistic representation. Spectroscopy experiments have recently provided further results regarding the excess proton. These experiments show that the hydrated proton has an anisotropy reorientation time scale on the order of 1-2 ps. This time scale has been suggested to possibly contradict the picture of the more rapid "special pair dance" phenomenon for the hydrated excess proton, which is a signature of a distorted Eigen cation. The special pair dance was predicted from prior computational studies in which the hydrated central core hydronium structure continually switches (O-H···O)* special pair hydrogen-bond partners with the closest three water molecules, yielding on average a distorted Eigen cation with three equivalent and dynamically exchanging distortions. Through state-of-art simulations it is shown here that anisotropy reorientation time scales of the same magnitude are obtained that also include structural reorientations associated with the special pair dance, leading to a reinterpretation of the experimental results. These results and additional analyses point to a distorted and dynamic Eigen cation as the most prevalent hydrated proton species in aqueous acid solutions of dilute to moderate concentration, as opposed to a stabilized or a distorted (but not "dancing") Zundel cation.

Dynamics of diverse coherences in primary charge separation of bacterial reaction center at 77K revealed by wavelet analysis.

To uncover the mechanism behind the high photo-electronic conversion efficiency in natural photosynthetic complexes it is essential to trace the dynamics of electronic and vibrational quantum coherences. Here we apply wavelet analysis to two-dimensional electronic spectroscopy data for three purple bacterial reaction centers with mutations that produce drastically different rates of primary charge separation. From the frequency distribution and dynamic evolution features of the quantum beating, electronic coherence with a dephasing lifetime of ~50fs, vibronic coherence with a lifetime of ~150fs and vibrational/vibronic coherences with a lifetime of 450fs are distinguished. We find that they are responsible for, or couple to, different specific steps during the primary charge separation process, i.e., intradimer charge transfer inside the special bacteriochlorophyll pair followed by its relaxation and stabilization of the charge-transfer state. The results enlighten our understanding of how quantum coherences participate in, and contribute to, a biological electron transfer reaction.

Analytical expression for the angular correlation function of two Lyman- α photons in the photodissociation of hydrogen molecules

An analytical expression of the angular correlation function of a pair of Lyman-$\ensuremath{\alpha}$ photons in the photodissociation of a hydrogen molecule is derived theoretically in a manner based on both atomic and molecular physics and quantum optics. The angular correlation function turns out to be expressed in terms of cosine (sine) functions of four angular variables of detectors with five coefficients. The angular correlation function is expanded in terms of the spherical harmonics for investigating which terms are involved, and we discuss the reason why they are involved. Interesting features are revealed in the expansion. We then search for a special detector arrangement where the angular-dependent terms vanish in the angular correlation function expressed in terms of the spherical harmonics. It turns out that no such detector arrangement in fact exists, but there is a special pair of detector arrangements where the angular-dependent terms vanish in the summation of two values of the angular correlation function expressed in terms of the spherical harmonics. We refer to such a pair of detector arrangements as a magic pair.

Lift the mystery veil on chlorophyllases

Photosystem II (PSII) is a large membrane-protein complex that catalyzes the splitting of water into protons, electrons, and oxygen via harvesting light energy (Johnson, 2016). The reaction center of PSII, operating like an electron pump, is a special pair of chlorophyll a (Chl a), referred to as P680, bound to D1 and D2 subunits, each with its set of electron carriers. Upon absorption of light energy, P680 is excited and donates an electron to the neighboring pheophytin (Pheo), producing a pair of radicals (⋅P680+ and ⋅Pheo−), called charge separation.

Dimeric Corrole Analogs of Chlorophyll Special Pairs.

Chlorophyll special pairs in photosynthetic reaction centers function as both exciton acceptors and primary electron donors. Although the macrocyclic natural pigments contain Mg(II), the central metal in most synthetic analogs is Zn(II). Here we report that insertion of either Al(III) or Ga(III) into an imidazole-substituted corrole affords an exceptionally robust photoactive dimer. Notably, attractive electronic interactions between dimer subunits are relatively strong, as documented by signature changes in NMR and electronic absorption spectra, as well as by cyclic voltammetry, where two well-separated reversible redox couples were observed. EPR spectra of one-electron oxidized dimers closely mimic those of native special pairs, and strong through-space interactions between corrole subunits inferred from spectroscopic and electrochemical data are further supported by crystal structure analyses (3 Å interplanar distances, 5 Å lateral shifts, and 6 Å metal to metal distances).