Sum rule comparison of narrowband and broadband sum frequency generation spectra and comparison with theory.

Earlier sum frequency generation (SFG) experiments involve one infrared and one visible laser, and a measurement of the intensity of the response, yielding data on the surface sensitive properties of the sample. Recently, both the real and imaginary components of the susceptibility were measured in two different sets of experiments. In one set, a broadband infrared laser was used, permitting observations at very short times, while in another set the infrared laser was narrowband, permitting higher spectral resolution. The differences in the spectrum obtained by the two will be most evident in studying narrow absorption bands, e.g., the band due to dangling OH bonds at a water interface. The direct comparisons in the integrated amplitude (sum rule) of the imaginary part of the dangling OH bond region differ by a factor of 3. Due to variations in experimental setup and data processing, corrections were made for the quartz reference, Fresnel factors, and the incident visible laser wavelength. After the corrections, the agreement differs now by the factors of 1.1 within broadband and narrowband groups and the two groups now differ by a factor of 1.5. The 1.5 factor may arise from the extra heating of the more powerful broadband laser system on the water surface. The convolution from the narrowband SFG spectrum to the broadband SFG spectrum is also investigated and it does not affect the sum rule. Theory and narrowband experiments are compared using the sum rule and agree to a factor of 1.3 with no adjustable parameters.

F1-ATPase Rotary Mechanism: Interpreting Results of Diverse Experimental Modes With an Elastic Coupling Theory.

In this chapter, we review single-molecule observations of rotary motors, focusing on the general theme that their mechanical motion proceeds in substeps with each substep described by an angle-dependent rate constant. In the molecular machine F1-ATPase, the stepping rotation is described for individual steps by forward and back reaction rate constants, some of which depend strongly on the rotation angle. The rotation of a central shaft is typically monitored by an optical probe. We review our recent work on the theory for the angle-dependent rate constants built to treat a variety of single-molecule and ensemble experiments on the F1-ATPase, and relating the free energy of activation of a step to the standard free energy of reaction for that step. This theory, an elastic molecular transfer theory, provides a framework for a multistate model and includes the probe used in single-molecule imaging and magnetic manipulation experiments. Several examples of its application are the following: (a) treatment of the angle-dependent rate constants in stalling experiments, (b) use of the model to enhance the time resolution of the single-molecule imaging apparatus and to detect short-lived states with a microsecond lifetime, states hidden by the fluctuations of the imaging probe, (c) treatment of out-of-equilibrium "controlled rotation" experiments, (d) use of the model to predict, without adjustable parameters, the angle-dependent rate constants of nucleotide binding and release, using data from other experiments, and (e) insights obtained from correlation of kinetic and cryo-EM structural data. It is also noted that in the case where the release of ADP would be a bottleneck process, the binding of ATP to another site acts to accelerate the release by 5-6 orders of magnitude. The relation of the present set of studies to previous and current theoretical work in the field is described. An overall goal is to gain mechanistic insight into the biological function in relation to structure.

The Drude-Smith Equation and Related Equations for the Frequency-Dependent Electrical Conductivity of Materials: Insight from a Memory Function Formalism.

The front cover artwork is provided by Wei-Chen Chen and Rudolph A. Marcus. The image shows an electron undergoing backscattering in a disordered solid, a phenomenon commonly described using the Drude-Smith equation represented by the damping curve. Read the full text of the Article at 10.1002/cphc.202100299.

The Drude-Smith Equation and Related Equations for the Frequency-Dependent Electrical Conductivity of Materials: Insight from a Memory Function Formalism.

The Drude-Smith equation is widely used for treating the frequency-dependent electrical conductivity of materials in the terahertz region. An attractive feature is its sparsity of adjustable parameters. A significant improvement over Drude theory for these materials, the theory includes backscattering of the charge carriers. It has nevertheless been criticized, including by Smith himself, because of the arbitrariness of a step in the derivation. We recall a somewhat similar behavior of back scattering in fluids observed in molecular dynamics computations and discussed in terms of memory functions. We show how theories such as Drude-Smith and Cocker et al. are examples of a broader class of theories by showing how they also arise as particular cases of a memory function formalism that divides the interactions into short and long range.

On the theory of charge transport and entropic effects in solvated molecular junctions.

Experimental studies on single-molecule junctions are typically in need of a simple theoretical approach that can reproduce or be fitted to experimentally measured transport data. In this context, the single-level variant of the Landauer approach is most commonly used, but methods based on Marcus theory are also gaining popularity. Recently, a generalized theory unifying these two approaches has also been developed. In the present work, we extend this theory so that it includes entropic effects (which can be important when polar solvents are involved but are likely minor for solid-state systems). We investigate the temperature-dependence of the electric current and compare it to the behavior predicted by the Landauer and the conventional Marcus theory. We argue that this generalized theory provides a simple yet effective framework for understanding charge transport through molecular junctions. Furthermore, we explore the role of the entropic effects in different transport regimes and suggest experimental criteria for detecting them in solvated molecular junctions. Finally, in order to account for nuclear tunneling effects, we also demonstrate how lifetime broadening can be introduced into the Marcus-Levich-Dogonadze-Jortner-type description of electron transport.

Sum frequency generation, calculation of absolute intensities, comparison with experiments, and two-field relaxation-based derivation.

The experimental sum frequency generation (SFG) spectrum is the response to an infrared pulse and a visible pulse and is a highly surface-sensitive technique. We treat the surface dangling OH bonds at the air/water interface and focus on the absolute SFG intensities for the resonant terms, a focus that permits insight into the consequences of some approximations. For the polarization combinations, the calculated linewidths for the water interface dangling OH SFG band at 3,700 [Formula: see text] are, as usual, too large, because of the customary neglect of motional narrowing. The integrated spectrum is used to circumvent this problem and justified here using a Kubo-like formalism and theoretical integrated band intensities rather than peak intensities. Only relative SFG intensities are usually reported. The absolute integrated SFG intensities for three polarization combinations for sum frequency, visible, and infrared beams are computed. We use molecular dynamics and the dipole and the polarizability matrix elements obtained from infrared and Raman studies of [Formula: see text]O vapor. The theoretical expressions for two of the absolute susceptibilities contain only a single term and agree with experiment to about a factor of 1.3, with no adjustable parameters. The Fresnel factors are included in that comparison. One of the susceptibilities contains instead four positive and negative terms and agrees less well. The expression for the SFG correlation function is normally derived from a statistical mechanical formulation using a time-evolving density matrix. We show how a derivation based on a two-field relaxation leads to the same final result.

Method to extract multiple states in F1-ATPase rotation experiments from jump distributions.

A method is proposed for analyzing fast (10 µs) single-molecule rotation trajectories in F1 adenosinetriphosphatase ([Formula: see text]-ATPase). This method is based on the distribution of jumps in the rotation angle that occur in the transitions during the steps between subsequent catalytic dwells. The method is complementary to the "stalling" technique devised by H. Noji et al. [Biophys. Rev. 9, 103-118, 2017], and can reveal multiple states not directly detectable as steps. A bimodal distribution of jumps is observed at certain angles, due to the system being in either of 2 states at the same rotation angle. In this method, a multistate theory is used that takes into account a viscoelastic fluctuation of the imaging probe. Using an established sequence of 3 specific states, a theoretical profile of angular jumps is predicted, without adjustable parameters, that agrees with experiment for most of the angular range. Agreement can be achieved at all angles by assuming a fourth state with an ∼10 µs lifetime and a dwell angle about 40° after the adenosine 5'-triphosphate (ATP) binding dwell. The latter result suggests that the ATP binding in one ß subunit and the adenosine 5'-diphosphate (ADP) release from another ß subunit occur via a transient whose lifetime is ∼10 µs and is about 6 orders of magnitude smaller than the lifetime for ADP release from a singly occupied [Formula: see text]-ATPase. An internal consistency test is given by comparing 2 independent ways of obtaining the relaxation time of the probe. They agree and are ∼15 µs.

Monitoring Electron-Phonon Interactions in Lead Halide Perovskites Using Time-Resolved THz Spectroscopy.

Lead halide perovskite semiconductors have low-frequency phonon modes within the lead halide sublattice and thus are considered to be soft. The soft lattice is considered to be important in defining their interesting optoelectronic properties. Electron-phonon coupling governs hot-carrier relaxation, carrier mobilities, carrier lifetimes, among other important electronic characteristics. Directly observing the interplay between free charge carriers and phonons can provide details on how phonons impact these properties (e.g., exciton populations and other collective modes). Here, we observe a delicate interplay among carriers, phonons, and excitons in mixed-cation and mixed-halide perovskite films by simultaneously resolving the contribution of charge carriers and phonons in time-resolved terahertz photoconductivity spectra. We are able to observe directly the increase in phonon population during carrier cooling and discuss how thermal equilibrium populations of carriers and phonons modulate the carrier transport properties, as well as reduce the population of carriers within band tails. We are also able to observe directly the formation of free charge carriers when excitons interact with phonons and dissociate and to describe how free carriers and exciton populations exchange through phonon interactions. Finally, we also time-resolve how the carriers are screened via the Coulomb interaction at low and room temperatures. Our studies shed light on how charge carriers interact with the low-energy phonons and discuss implications.

What can be learned about the enzyme ATPase from single-molecule studies of its subunit F1?

We summarize the different types of single molecule experiments on the F1 component of FOF1-ATP Synthase and what has been learned from them. We also describe results from our recent studies on interpreting the experiments using a chemical-mechanical theory for these biological motors.

Theory of long binding events in single-molecule-controlled rotation experiments on F1-ATPase.

The theory of elastic group transfer for the binding and release rate constants for nucleotides in F1-ATPase as a function of the rotor angle is further extended in several respects. (i) A method is described for predicting the experimentally observed lifetime distribution of long binding events in the controlled rotation experiments by taking into account the hydrolysis and synthesis reactions occurring during these events. (ii) A method is also given for treating the long binding events in the experiments and obtaining the rate constants for the hydrolysis and synthesis reactions occurring during these events. (iii) The theory in the previous paper is given in a symmetric form, an extension that simplifies the application of the theory to experiments. It also includes a theory-based correction of the reported "on" and "off" rates by calculating the missed events. A near symmetry of the data about the angle of -40° and a "turnover" in the binding rate data vs. rotor angle for angles greater than [Formula: see text]40° is also discussed.

Theory of single-molecule controlled rotation experiments, predictions, tests, and comparison with stalling experiments in F1-ATPase.

A recently proposed chemomechanical group transfer theory of rotary biomolecular motors is applied to treat single-molecule controlled rotation experiments. In these experiments, single-molecule fluorescence is used to measure the binding and release rate constants of nucleotides by monitoring the occupancy of binding sites. It is shown how missed events of nucleotide binding and release in these experiments can be corrected using theory, with F1-ATP synthase as an example. The missed events are significant when the reverse rate is very fast. Using the theory the actual rate constants in the controlled rotation experiments and the corrections are predicted from independent data, including other single-molecule rotation and ensemble biochemical experiments. The effective torsional elastic constant is found to depend on the binding/releasing nucleotide, and it is smaller for ADP than for ATP. There is a good agreement, with no adjustable parameters, between the theoretical and experimental results of controlled rotation experiments and stalling experiments, for the range of angles where the data overlap. This agreement is perhaps all the more surprising because it occurs even though the binding and release of fluorescent nucleotides is monitored at single-site occupancy concentrations, whereas the stalling and free rotation experiments have multiple-site occupancy.

Phonon Mode Transformation Across the Orthohombic-Tetragonal Phase Transition in a Lead Iodide Perovskite CH3NH3PbI3: A Terahertz Time-Domain Spectroscopy Approach.

We study the temperature-dependent phonon modes of the organometallic lead iodide perovskite CH3NH3PbI3 thin film across the terahertz (0.5-3 THz) and temperature (20-300 K) ranges. These modes are related to the vibration of the Pb-I bonds. We found that two phonon modes in the tetragonal phase at room temperature split into four modes in the low-temperature orthorhombic phase. By use of the Lorentz model fitting, we analyze the critical behavior of this phase transition. The carrier mobility values calculated from the low-temperature phonon mode frequencies, via two theoretical approaches, are found to agree reasonably with the experimental value (∼2000 cm(2) V(-1) s(-1)) from a previous time-resolved THz spectroscopy work. Thus, we have established a possible link between terahertz phonon modes and the transport properties of perovskite-based solar cells.

Theory for rates, equilibrium constants, and Brønsted slopes in F1-ATPase single molecule imaging experiments.

A theoretical model of elastically coupled reactions is proposed for single molecule imaging and rotor manipulation experiments on F1-ATPase. Stalling experiments are considered in which rates of individual ligand binding, ligand release, and chemical reaction steps have an exponential dependence on rotor angle. These data are treated in terms of the effect of thermodynamic driving forces on reaction rates, and lead to equations relating rate constants and free energies to the stalling angle. These relations, in turn, are modeled using a formalism originally developed to treat electron and other transfer reactions. During stalling the free energy profile of the enzymatic steps is altered by a work term due to elastic structural twisting. Using biochemical and single molecule data, the dependence of the rate constant and equilibrium constant on the stall angle, as well as the Børnsted slope are predicted and compared with experiment. Reasonable agreement is found with stalling experiments for ATP and GTP binding. The model can be applied to other torque-generating steps of reversible ligand binding, such as ADP and Pi release, when sufficient data become available.

Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films.

Apart from broadband absorption of solar radiation, the performance of photovoltaic devices is governed by the density and mobility of photogenerated charge carriers. The latter parameters indicate how many free carriers move away from their origin, and how fast, before loss mechanisms such as carrier recombination occur. However, only lower bounds of these parameters are usually obtained. Here we independently determine both density and mobility of charge carriers in a perovskite film by the use of time-resolved terahertz spectroscopy. Our data reveal the modification of the free carrier response by strong backscattering expected from these heavily disordered perovskite films. The results for different phases and different temperatures show a change of kinetics from two-body recombination at room temperature to three-body recombination at low temperatures. Our results suggest that perovskite-based solar cells can perform well even at low temperatures as long as the three-body recombination has not become predominant.

On the mechanism of photoinduced dimer dissociation in the plant UVR8 photoreceptor.

UV-B absorption by the photoreceptor UV resistance locus 8 (UVR8) consisting of two identical protein units triggers a signal chain used by plants in connection with protection and repair of UV-B induced damage. X-ray structural analysis of the purified protein [Christie JM, et al. (2012) Science 335(6075):1492-1496] [Wu D, et al. (2012) Nature 484(7393): 214-220] has revealed that the dimer is held together by arginine-aspartate salt bridges. In this paper we address the initial processes in the signal chain. On the basis of high-level quantum-chemical calculations, we propose a mechanism for the photodissociation of UVR8 that consists of three steps: (i) In each monomer, multiple tryptophans form an extended light-harvesting system in which the La excited state of Trp233 experiences strong electrostatic stabilization by the protein environment. The strong stabilization singles out this tryptophan to be an efficient exciton acceptor that accumulates the excitation energy from the entire protein subunit. (ii) A fast decay of the locally excited state by charge separation generates the radical ion pair Trp285(+)-Trp233(-) with a dipole moment of ∼18 D. (iii) Key to the proposed mechanism is that this large dipole moment drives the breaking of the salt bridges between the two monomer subunits. The suggested mechanism for the UV-B-driven dissociation of the dimer that rests on the prominent players Trp233 and Trp285 explains the experimental results obtained from mutagenesis of UVR8.

Computed and Experimental Absorption Spectra of the Perovskite CH3NH3PbI3.

Electronic structure and light absorption properties of the perovskite CH3NH3PbI3 are investigated by relativistic density functional theory with quasiparticle GW corrections and many-body interactions. The nature of the Wannier exciton is studied by solving the Bethe-Salpeter equation augmented with the analysis of a conceptual hydrogen-like model. The computed absorption spectrum unravels a remarkable absorption "gap" between the first two absorption peaks. This discontinuity is maintained in the calculated tetragonal structure that, however, is not stable at low temperature. Most importantly, the discontinuity is also observed in the experimental absorption spectrum of the orthorhombic single crystal at low temperature (4 K). However, in contrast to the single crystal, in a polycrystalline perovskite film at 5 K the "gap" is filled by a monotonously increasing absorption throughout the visible range. This feature of thin films points to the potential significance of defect absorption for the excellent light harvesting properties of perovskite-based solar cells.

Device modeling of dye-sensitized solar cells.

We review the concepts and methods of modeling of the dye-sensitized solar cell, starting from fundamental electron transfer theory, and using phenomenological transport-conservation equations. The models revised here are aimed at describing the components of the current-voltage curve of the solar cell, based on small perturbation experimental methods, and to such an end, a range of phenomena occurring in the nanoparticulate electron transport materials, and at interfaces, are covered. Disorder plays a major role in the definition of kinetic parameters, and we introduce single particle as well as collective function definitions of diffusion coefficient and electron lifetime. Based on these fundamental considerations, applied tools of analysis of impedance spectroscopy are described, and we outline in detail the theory of recombination via surface states that is successful to describe the measured recombination resistance and lifetime.

Theory of mass-independent fractionation of isotopes, phase space accessibility, and a role of isotopic symmetry.

Key experimental and theoretical features of mass-independent fractionation (MIF) of isotopes, also known as the η-effect, are summarized, including its difference from the exit channel zero-point energy difference effect. The latter exactly cancels in the MIF. One key experimental result is that the MIF for O3 formation is a low-pressure phenomenon and, moreover, that it decreases with increasing pressure of third bodies at pressures far below the "Lindemann fall-off" pressures for three-body recombination of O and O2. A possible origin of the MIF is discussed in terms of a role for isotopologue symmetry in intramolecular energy sharing. An explanation is suggested for the large difference in the fall-off pressure for recombination and the pressure for a large decrease in MIF, in terms of a difference between deactivating collisions and what we term here "symmetry-changing collisions". It is noted that the theory of the MIF involves four recombination rate constants and an equilibrium constant, for each trace isotope, seven rate constants in all and two equilibrium constants. A conceptual shortcut is noted. Experimental and computational information that may provide added insight into the MIF mechanism and tests is described.