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Collagen is a triple-helical protein unique to the extracellular matrix, conferring rigidity and stability to tissues such as bone and tendon. For the [(PPG) 10 ] 3 collagen-mimetic peptide at room temperature, our molecular dynamics simulations show that these properties result in a remarkably ordered first hydration layer of water molecules hydrogen bonded to the backbone carbonyl (bb-CO) oxygen atoms. This originates from the following observations. The radius of gyration attests that the PPG triplets are organized along a straight line, so that all triplets (excepting the ends) are equivalent. The solvent-accessible surface area (SASA) for the bb-CO oxygens shows a repetitive regularity for every triplet. This leads to water occupancy of the bb-CO sites following a similar regularity. In the crystal-phase X-ray data, as well as in our 100 K simulations, we observe a 0-2-1 water occupancy in the P-P-G triplet. Surprisingly, a similar (0-1.7-1) regularity is maintained in the liquid phase, in spite of the sub-nsec water exchange rates, because the bb-CO sites rarely remain vacant. The manifested ordered first-shell water molecules are expected to produce a cylindrical electrostatic potential around the peptide, to be investigated in future work. [ABSTRACT FROM AUTHOR]

Sometimes, all that remains from the history of a place is its name. Thus, toponyms may provide valuable information. Moving backward in time, we trace the ancient history of the Arab/Crusader village Bēt ˁAṭab in western Judea, with remains from Middle-Bronze II (MB II), Iron III and Hellenistic periods. In Roman times it was Eusebius' Ēnadab, 'Spring of ˁaṭab', identified near the spring of this name mentioned in the Survey of Western Palestine. While missing from Masoretic Biblical town lists, Tatami of the Septuagint derives by dropping the b- from reconstructed batˁaṭami, traced to Northwest Semitic languages exhibiting the ay>ā diphthong contraction. The MB II final -i is analysed as an enclitic -mi, found also in the Execration Text (ET) Shechem, and as enclitic -ma in personal names from Alalaḫ VII. The 'prince' of nearby ET 'Ashnah (=Beth Shemesh) had an identical name as later Niqmi-epuh, King of Yamḫad, suggesting settlers from Yamḫad/Alalaḫ during the early 2nd millennium bce. In Bronze Age Bēt-X toponyms X was a deity. Thus, batˁaṭami = 'place of the vulture-goddess shrine'. This, and additional evidence, suggest that Egyptian king Senwosret III could have set a shrine to goddess Nekhbet on Bēt ˁAṭab's summit during his Shechem campaign. [ABSTRACT FROM AUTHOR]

The sodium cation is ubiquitous in aqueous chemistry and biological systems. Yet, in spite of numerous studies, the (average) distance between the sodium cation and its water ligands, and the corresponding ionic radii, are still controversial. Recent experimental values in solution are notably smaller than those from previous X-ray studies and ab initio molecular dynamics. Here we adopt a "bottom-up" approach of obtaining these distances from quantum chemistry calculations [full MP2 with the 6-31++G(d,p) and cc-pVTZ basis-sets] of gas-phase Na + ( H 2 O) n clusters, as a function of the sodium coordination number (CN = 2–6). The bulk limit is obtained by the polarizable continuum model, which acts to increase the interatomic distances at small CN, but has a diminishing effect as the CN increases. This extends the CN dependence of the sodium-water distances from crystal structures (CN = 4–12) to lower CN values, revealing a switch between two power laws, having a small exponent at small CNs and a larger one at large CNs. We utilize Bader's theory of atoms in molecules to bisect the Na+–O distances into Na+ and water radii. Contrary to common wisdom, the water radius is not constant, decreasing even more than that of Na+ as the CN decreases. We also find that the electron density at the bond critical point increases exponentially as the sodium radius decreases. [ABSTRACT FROM AUTHOR]

Aqueous solutions are complex due to hydrogen bonding (HBing). While gas-phase clusters could provide clues on the solution behavior, most neutral clusters were studied at cryogenic temperatures. Recent results of Shimamori and Fujii provide the first IR spectrum of warm phenol-(H2O)2 clusters. To understand the temperature (T) effect, we have revisited the structure and spectroscopy of phenol- (H2O)2 at all T. While older quantum chemistry work concluded that the cyclic isomers are the most stable, the inclusion of dispersion interactions reveals that they are nearly isoenergetic with isomers forming π-HBs with the phenyl ring. Whereas the OH-stretch bands were previously assigned to purely local modes, we show that at low T they involve a concerted component. We have calculated the (static) anharmonic IR spectra for all low-lying isomers, showing that at the MP2 level, one can single out one isomer (udu) as accounting for the low-T spectrum to 3 cm-1 accuracy. Yet no isomer can explain the substantial blueshift of the phenyl-OH band at elevated temperatures. We describe the temperature effect using ab initio molecular dynamics with a density functional and basis-set (B3LYP-D3/aug-cc-pVTZ) that provide a realistic description of OH. . .O vs. OH. . . π HBing. From the dipole moment autocorrelation function, we obtain good description for both low- and high-T spectra. Trajectory visualization suggests that the ring structure remains mostly intact even at high T, with intermittent switching between OH. . .O and OH. . . π, HBing and lengthening of all 3 HBs. The phenyl-OH blueshift is thus attributed to strengthening of its OH bond. A model for three beads on a ring suggests that this shift is partly offset by the elimination of coupling to the other OH bonds in the ring, whereas for the two water molecules these two effects nearly cancel. [ABSTRACT FROM AUTHOR]

Proton transfer in macromolecular systems is a fascinating yet elusive process. In the last ten years, molecular simulations have shown to be a useful tool to unveil the atomistic mechanism. Notwithstanding, the large number of degrees of freedom involved make the accurate description of the process very hard even for the case of proton diffusion in bulk water. Here, multi-state empirical valence bond molecular dynamics simulations in conjunction with complex network analysis are applied to study proton transfer in liquid water. Making use of a transition network formalism, this approach takes into account the time evolution of several coordinates simultaneously. Our results provide evidence for a strong dependence of proton transfer on the length of the hydrogen bond solvating the Zundel complex, with proton transfer enhancement as shorter bonds are formed at the acceptor site. We identify six major states (nodes) on the network leading from the "special pair" to a more symmetric Zundel complex required for transferring the proton. Moreover, the second solvation shell specifically rearranges to promote the transfer, reiterating the idea that solvation beyond the first shell of the Zundel complex plays a crucial role in the process. [ABSTRACT FROM AUTHOR]

The kinetics of a diffusing particle near a reversible trap may be described by an extension of the Feynman-Kac equation to the case of reversible binding, which can occur within a finite reaction sphere. We obtain the Green's function solution for the Laplace transform of this equation when the particle is initially either bound or unbound. We study the solution in the time-domain by either inverting the Laplace transform numerically or propagating the partial differential equation in the time-domain. We show that integrals of this solution over the reaction sphere agree with previously obtained solutions. [ABSTRACT FROM AUTHOR]

We provide an analytic solution for diffusion-influenced geminate reaction with multiple (N) reversible binding sites (of which one may be irreversible). The solution obtained in the Laplace domain, for two different initial conditions, is valid for the case when the sites are overlapping spheres with no long-range interactions with the diffusing particle. The possibility to invert into the time domain is determined by a characteristic polynomial. When all its roots are distinct, it is possible to apply the Lagrange interpolation formula and obtain a partial-fraction expansion that can be termwise inverted. At long times the occupancy of all sites, and for all initial conditions, decays as t-3/2. The behavior at short times depends on the initial condition: when starting from contact, the binding probability rises as t1/2, but if the particle is initially bound to one of the sites, the occupancy of the others rises as t3/2. In between these two power laws we observe an intermediate-time kinetics consisting of N decaying exponentials. Those which are slower than a characteristic diffusion time are in the reaction-control regime and fit a discrete-state kinetic approximation with no adjustable parameters, whereas the faster kinetic steps are diffusion controlled. The model solved herein may depict a wide range of physical situations, from multisite proton transfer kinetics to hydrogen-bond dynamics of liquid water. [ABSTRACT FROM AUTHOR]

The (history independent) autocorrelation function for a hydrogen-bonded water molecule pair, calculated from classical molecular dynamics trajectories of liquid water, exhibits a t-3/2 asymptotic tail. Its whole time dependence agrees quantitatively with the solution for reversible diffusion-influenced geminate recombination derived by Agmon and Weiss [J. Chem. Phys. 91, 6937 (1989)]. Agreement with diffusion theory is independent of the precise definition of the bound state. Given the water self-diffusion constant, this theory enables us to determine the dissociation and bimolecular recombination rate parameters for a water dimer. (The theory is indispensable for obtaining the bimolecular rate coefficient.) Interestingly, the activation energies obtained from the temperature dependence of these rate coefficients are similar, rather than differing by the hydrogen-bond (HB) strength. This suggests that recombination requires displacing another water molecule, which meanwhile occupied the binding site. Because these activation energies are about twice the HB strength, cleavage of two HBs may be required to allow pair separation. The autocorrelation function without the HB angular restriction yields a recombination rate coefficient that is larger than that for rebinding to all four tetrahedral water sites (with angular restrictions), suggesting the additional participation of interstitial sites. Following dissociation, the probability of the pair to be unbound but within the reaction sphere rises more slowly than expected, possibly because binding to the interstitial sites delays pair separation. An extended diffusion model, which includes an additional binding site, can account for this behavior. [ABSTRACT FROM AUTHOR]

Bond-order analysis is introduced to facilitate the study of cooperative many-molecule effects on proton mobility in liquid water, as simulated using the multistate empirical valence-bond methodology. We calculate the temperature dependence for proton mobility and the total effective bond orders in the first two solvation shells surrounding the H5O2+ proton-transferring complex. We find that proton-hopping between adjacent water molecules proceeds via this intermediate, but couples to hydrogen-bond dynamics in larger water clusters than previously anticipated. A two-color classification of these hydrogen bonds leads to an extended mechanism for proton mobility.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Several recent theories of the kinetics of diffusion influenced excited-state association–dissociation reactions are tested against accurate Brownian dynamics simulation results for a wide range of parameters. The theories include the relaxation time approximation (RTA), multiparticle kernel decoupling approximations and the so-called kinetic theory. In the irreversible limit, none of these theories reduce to the Smoluchowski result. For the pseudo-first-order target problem, we show how the RTA can be modified so that the resulting formalism does reduce correctly in the irreversible limit. We call this the unified Smoluchowski approximation, because it unites modern theories of reversible reactions with Smoluchowski’s theory of irreversible reactions. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We discuss two fundamental reversible diffusion influenced reactions: (i) A+B⇋C and (ii) A+B⇋C+D. In the pseudo-unimolecular case, we prove that reaction (i) is a special case of (ii), which thus constitutes a unified reversible problem of multiparticle kinetics. For static A and C (the “target” limit), we suggest to treat this problem as follows. First we generalize the Smoluchowski theory to reaction (ii). In Laplace space, we combine this with a power-law theory, determining the combination coefficient so that the unified theory reduces correctly in all known limits. We also show how to rewrite it in the time domain, with the generalized Smoluchowski theory as the leading term. Comparison with Brownian simulations shows near perfect agreement for both versions of our theory under all conditions.© 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report a microscopic simulation for the reversible A+B⇌ C1D reaction in its pseudo-unimolecular limit. The simulations are used to assess the validity of various approximate theories for the time dependence of the approach to equilibrium, up to its long-time asymptotic behavior. To available theories we have added a new theory, the generalized multiparticle kernel 1 (GMPK1) theory. It is shown to be in very good agreement with our simulations than all other theories. The asymptotic behavior of both simulations and GMPK1 agrees with that derived by Gopich and Szabo [Chem. Phys. 284, 91 (2002)]. [ABSTRACT FROM AUTHOR]

We obtain exact analytic solution for the Green functions and survival probabilities of the reversible, geminate diffusion-influenced reaction A+B↔C+D in Laplace space, and in the time domain for various spatial dimensionalities. The asymptotic behavior (in one and three dimensions) goes as t[sub -½], like in the irreversible case, but approach to this limit may occur from either above or below. The implications of these results are demonstrated and discussed. [ABSTRACT FROM AUTHOR]

We report a first microscopic simulation for the diffusional kinetics of a reversible excited-state reaction, A+B+ ↔ AB, where A and AB have different lifetimes and the B-particles are in excess. When the excited species equilibrate fast compared with the excited-state lifetimes, one obtains the pre-equilibrium approximation. The full time-dependence in this case is approximated by a shifted infinite-lifetime expression, and this allows us to derive an analytic expression for the asymptotic exponent. Multiplying this exponential is a t[sup -3/2] term. When the excited-state decay of AB is fast, we obtain the quasistationary approximation. Quantitative comparison between various theories and simulation is presented. [ABSTRACT FROM AUTHOR]

We report three-dimensional simulations of the reversible reaction A+B↔C for a single static A molecule and a uniform initial concentration of noninteracting B-molecules. The results are compared with various analytic approximations for the time-dependence of the binding probability. They are in excellent agreement with a recent theory of Sung and Lee [J. Chem. Phys. 111, 796 (1999)] for all times and rate parameters. The second-order term in the long-time expansion of this theory is incorrect, yet it explains an apparent kinetic transition observed when the B-concentration increases. We also investigate the concentration profiles near the reversible trap. [ABSTRACT FROM AUTHOR]

Discusses the derivation of an analytic solution for the Green function and survival probability of excited-state reversible recombination reactions of noninteracting geminate particles in solution. Behavior of the three roots of the cubic polynomial; Types of complex plane maps identified on which transitions may occur.

A closed-form expression is obtained for the time evolution of the territory covered by N independently diffusing particles starting from the origin in one-dimension, with and without bias. For the latter case, the transcendental-approximation derived is essentially exact for any number of particles. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Many-body effects on reversible pseudo-unimolecular reactions are investigated using a combination of theory, simulation, and experiment. Theoretically, we rederive the superposition approximation starting from the fundamental N-particle equations. All the relations obtained are actually rigorous, except for a requirement that the concentration profile outside a vacant trap obeys a diffusion equation. Our derivation also yields a new numerical procedure for evaluating the superposition solution. Brownian dynamics simulations of one-dimensional competitive binding are presented over an unprecedented time regime. Comparison with the superposition approximation shows that this mean-field theory is exact at infinite dilution, but breaks down at high particle concentration. The main discrepancy is not at asymptotically long times as previously suspected, but rather at intermediate times, where a new power law-phase emerges. This is reflected in a maximum in the logarithmic derivative of the survival probability, which is more pronounced in our simulation as compared with the approximate theory. Finally, we show that the transient fluorescence data from an excited dye molecule which transfers a proton reversibly to water, develops a similar maximum in its logarithmic derivative at low pH values. [ABSTRACT FROM AUTHOR]

A Brownian dynamics algorithm is developed for simulating many-body effects in one dimensional competitive reversible binding of otherwise noninteracting particles. It allows time steps hundreds of times larger than in conventional lattice random walks and enables us to simulate systems which are sufficiently large to approach the thermodynamic limit. The asymptotic long-time behavior is compared with mean-field predictions. [ABSTRACT FROM AUTHOR]

Theory and practice of reaction dynamics on two-dimensional potential energy surfaces is investigated. Nonequilibrium multidimensional barrier crossing, occurring when the initial density is located near the ridgeline separating reactants and products, is treated by solving the time-dependent Smoluchowski equation as a function of diffusion anisotropy. For a locally separable potential, and slow relaxation in the perpendicular mode, the problem reduces to a one-dimensional Smoluchowski equation with a sink term. It may be further approximated as a first-order reaction with a time-dependent rate coefficient. These approximations are compared with exact two-dimensional propagations on a potential surface representing CO binding to α heme. The intermediate-time power-law decay of the survival probability is analyzed with the aid of the above approximations. The power also shows some kind of critical behavior near the isotropic diffusion limit, where these approximations are no longer valid. For fast relaxation, a nonmonotonic survival probability is observed. The long time decay of the survival probability is governed by the equilibrium rate coefficient. We calculate its anisotropy dependence and compare it with two asymptotic expansions for the lowest eigenvalue of the Smoluchowski operator-for the one-dimensional sink-Smoluchowski operator and the fully two-dimensional operator. The difference between the fast relaxation limit of these one- and two-dimensional equations may provide a quantitative explanation for previous problems in extrapolating to high temperatures using the Agmon–Hopfield model. The implications of these results to heme protein dynamics are discussed and new experiments are proposed. [ABSTRACT FROM AUTHOR]

A unified theory of reversible diffusion-influenced geminate and pseudo- first-order reactions is developed. Explicit results are presented for the time dependence of the fraction of molecules that are dissociated at time t for a variety of initial conditions. To introduce the basic ideas of our approach, an elementary and rather complete treatment of the irreversible reaction between a pair of interacting, spherically symmetric particles is presented. The focus is on deriving relations among survival probabilities and bimolecular time-dependent rate coefficients for the radiation and absorbing boundary conditions and the asymptotic behavior of these quantities. These relations are then generalized to reversible geminate reactions. For example, it is shown that the separation probability for an initially bound pair satisfies a simple convolution relation involving the survival probability of an irreversibly reacting geminate pair initially at contact. An analytic expression is obtained for this separation probability that is exact for free diffusion and is an accurate approximation for interacting particles. Finally, the Smoluchowski approach to irreversible pseudo-first-order reactions is extended to reversible reactions. The analysis is based on the generalization of the convolution relations that are rigorously valid for isolated pairs. [ABSTRACT FROM AUTHOR]

We consider a reversible dissociation–recombination reaction in solution which is described by a distribution of waiting times rather than a single dissociation rate constant. This is a non-Markovian generalization of the backreaction boundary condition. We formulate the new boundary condition in terms of the residence time in the bound state and illustrate the theory by assuming a stable-law density for the residence time. Explicit expressions are found for the Laplace transform of the survival probability in one and three dimensions, which can be inverted analytically for special values of the stable-law parameter α and numerically for other values of α. We derive the long-time behavior of the survival probability for arbitrary α, and note that the survival probability undergoes a first-order phase transition in one dimension, in which its asymptotic value changes abruptly at α=1/2. In three dimensions it undergoes a second-order phase transition at α=1, in which only the asymptotic slope of the survival probability changes discontinuously. [ABSTRACT FROM AUTHOR]

Properties of chemical reactions in systems undergoing diffusional motion depend on the ratio of chemical to diffusional rates. The present work deals with perturbation expansions in this quantity. For bounded diffusion, the Laplace transformed survival probability, mean lifetime, eigenvalues, and eigenfunctions are expanded in this ratio. The theory is developed mainly in the fast diffusion limit. In this limit, the survival probability for an initial equilibrium state is shown to be exponential up to linear order. For unbounded diffusion, expansions are derived for the steady-state concentration profile and rate coefficient. By inverting the series one obtains Padé-like approximations for rate coefficients with much improved convergence. Several examples are worked out in detail. These include the ‘‘radiation’’ boundary condition, barrierless isomerization, steady-state binding, and Förster quenching. [ABSTRACT FROM AUTHOR]

Our calculations of proton–anion distance distribution functions for HPTS dissociation recombination in the excited state are extended to the nanosecond time regime. When these functions are used for averaging the ground-state recombination probability, good agreement with experimental ground-state recombination yields is obtained. The relation with the theory of ‘‘delayed’’ geminate recombination is briefly discussed. [ABSTRACT FROM AUTHOR]

The diffusional and kinetic approaches are compared for geminate dissociation–recombination reactions. When steady-state rate coefficients to and from a distance defined as a ‘‘complex cage’’ are evaluated from the diffusion equation, one obtains encouraging agreement between the transient analytic solution of the rate equations and the exact numerical solution for diffusion with backreaction over a finite time regime. However, the rate equations cannot accurately describe the decay of the dissociating molecule for very long times, since as we prove below, the asymptotic decay according to the diffusional scheme is t-3/2, while for the rate equations it is exponential. New experiments, over an extended time regime confirm these conclusions. [ABSTRACT FROM AUTHOR]

The kinetics of reversible dissociation of a single ion pair inside a finite sphere is described by the transient solution of the Debye–Smoluchowski diffusion equation, with backreaction boundary conditions at contact, and a reflective boundary condition at the sphere’s radius. At long times the solution tends to an equilibrium state. A simple analytic expression for the equilibrium coefficient is derived. For an infinitely large sphere (‘‘infinite dilution’’) it reduces to an expression similar to that of Fuoss, while its dependence on the sphere’s radius is qualitatively similar to the concentration dependence of activity coefficients. [ABSTRACT FROM AUTHOR]

For the process of one-dimensional diffusion in a medium with random traps and homogeneous scavenging, we derive exact expressions for the ultimate trapping and scavenging probabilities and for the lifetimes associated with the two processes. This is done for free diffusion, where results agree with those previously found for discrete random walk, as well as for diffusion in a linear potential. The asymptotic expansions, for small and large ratio of trap concentration to scavenging rate, are given and compared numerically to the exact integrals. [ABSTRACT FROM AUTHOR]

Part II. Studies the effect of contact quenching by the geminate partner on the excited-state reversible geminate reaction. Background on the reversible geminate recombination reaction in the excited state; Approximate solutions.

Examines the electrostatic potential of a point charge within multilayered dielectric medium through Legendre expansion. Process of confirming computed and analytic solutions; Identification of electrostatic interactions within structures such as liposomes and multilamellar vesicles; Utilization of a reaction field of Brownian dynamics.

In addition to overall mean lifetimes, with which one is well acquainted in the theory of reactive diffusion processes, mean conditional lifetimes for absorption in a given sink also have physical significance. In the theory of geminate recombination of nonisolated pairs, when one imposes an additional outer absorbing sphere, the conditional lifetime for absorption in the inner sphere is the risetime for the recombination products. In the theory of geminate recombination in an homogeneous scavenger concentration, both overall and conditional lifetimes are physically significant. The first describes reactants’ decay, the second products’ formation. We derive, in the backward equation formalism, equations governing the initial variable dependence of these lifetimes. We give the explicit solution for geminate recombination of neutrals (free diffusion). Experimental measurements of recombination lifetimes would supply new data, independent of the yields typically measured in such experiments. [ABSTRACT FROM AUTHOR]

Relaxation time for diffusion between reflecting boundaries is defined and the theory for its evaluation using the backward-equation approach is presented. A few simple examples are given and comparison with other results in the literature is made. We expect that relaxation time for nonreactive processes might assume the role of mean first passage times in reactive processes. [ABSTRACT FROM AUTHOR]

Highlights • Unprecedented agreement of theoretical IR spectra for H+(H 2 O) 3 with experiment. • Complete assignment of the observed fundamental and combination bands. • Discovery of two "giant" Fermi resonances dominating these spectra. • Possible role for Fermi resonance in gating proton transport. Abstract The protonated water trimer is a prototype "proton wire" that can transport two protons nearly concertedly. This "proton transfer mode" (PTM) is an important contributor to the infrared spectrum of the isolated gas-phase cluster. We have simulated its infrared spectrum for both the hydrated and deuterated isotopologues, using vibrational 2nd order perturbation theory (VPT2) and ab initio molecular dynamics (AIMD) trajectories. VPT2 calculations explain quantitatively the experimental spectra at both high and low frequencies, provided that high-level quantum chemistry is utilized. In the D 2 -tagged hydrated cluster, the PTM undergoes giant Fermi resonances (FR's) with two combination bands. In the deuterated analogue, one observes a single FR of "normal" intensity, manifested as the doublet recently reported experimentally. We provide band assignment for both isotopologues, with and without the D 2 tag applied in experiment. We discuss possible manifestations of the giant resonance on proton transfer through water wires. [ABSTRACT FROM AUTHOR]

Ionic radii play a central role in all branches of chemistry, in geochemistry, solid-state physics and biophysics. While authoritative compilations of experimental radii are available, their theoretical basis is unclear and no quantitative derivation exists. Here we show how a quantitative calculation of ionic radii for cations with spherically symmetric charge distribution is obtained by charge-weighted averaging of outer and inner radii. The outer radius is the atomic (covalent) radius and the inner is that of the underlying closed-shell orbital. The first is available from recent experimental compilations, whereas the second is calculated from a "modified Slater theory", in which the screening (S) and effective principal quantum number (n*) were previously obtained by fitting experimental ionization energies in isoelectronic series. This reproduces the experimental Shannon-Prewitt "effective ionic radii" (for coordination number 6) with mean absolute deviation of 0.025 Å, approximately the accuracy of the experimental data itself. The remarkable agreement suggests that the calculation of other cationic attributes might be based on similar principles. [ABSTRACT FROM AUTHOR]

Gas-phase H9O4+ has been considered an archetypal Eigen cation, H3O+(H2O)3. Yet ab initio molecular dynamics (AIMD) suggested that its infrared spectrum is explained by a linear-chain Zundel isomer, alone or in a mixture with the Eigen cation. Recently, hole-burning experiments suggested a single isomer, with a second-order vibrational perturbation theory (VPT2) spectrum agreeing with the Eigen cation. To resolve this discrepancy, we have extended both calculations to more advanced DFT functionals, better basis sets, and dispersion correction. For Zundel-isomers, we find VPT2 anharmonic frequencies for four low-frequency modes involving the excess proton unreliable, including the 1750 cm-1 band that is pivotal for differentiating between Zundel and Eigen isomers. Because the analogous bands of the H5O2+ cation show little effect of anharmonicity, we utilize the harmonic frequencies for these modes. With this caveat, both AIMD and VPT2 agree on the spectrum as originating from a Zundel isomer. VPT2 also shows that both isomers have the same spectrum in the high frequency region, so that the hole burning experiments should be extended to lower frequencies. [ABSTRACT FROM AUTHOR]

Understanding the structure and dynamics of water's constituent ions, proton and hydroxide, has been a subject of numerous experimental and theoretical studies over the last century. Besides their obvious importance in acid-base chemistry, these ions play an important role in numerous applications ranging from enzyme catalysis to environmental chemistry. Despite a long history of research, many fundamental issues regarding their properties continue to be an active area of research. Here, we provide a review of the experimental and theoretical advances made in the last several decades in understanding the structure, dynamics, and transport of the proton and hydroxide ions in different aqueous environments, ranging from water clusters to the bulk liquid and its interfaces with hydrophobic surfaces. The propensity of these ions to accumulate at hydrophobic surfaces has been a subject of intense debate, and we highlight the open issues and challenges in this area. Biological applications reviewed include proton transport along the hydration layer of various membranes and through channel proteins, problems that are at the core of cellular bioenergetics. [ABSTRACT FROM AUTHOR]

The infrared (IR) spectrum of the ammoniated ammonium dimer is more complex than those of the larger protonated ammonia clusters due to close-lying fundamental and combination bands and possible Fermi resonances (FR). To date, the only theoretical analysis involved partial dimensionality quantum nuclear dynamic simulations, assuming a symmetric structure (D3d) with the proton midway between the two nitrogen atoms. Here we report an extensive study of the less symmetric (C3v) dimer, utilizing both second order vibrational perturbation theory (VPT2) and ab initio molecular dynamics (AIMD), from which we calculated the Fourier transform (FT) of the dipole-moment autocorrelation function (DACF). The resultant IR spectrum was assigned using FTed velocity autocorrelation functions (VACFs) of several interatomic distances and angles. At 50 K, we have been able to assign all 21 AIMD fundamentals, in reasonable agreement with MP2-based VPT2, about 30 AIMD combination bands, and a difference band. The combinations involve a wag or the NN stretch as one of the components, and appear to follow symmetry selection rules. On this basis, we suggest possible assignments of the experimental spectrum. The VACF-analysis revealed two possible FR bands, one of which is the strongest peak in the computed spectrum. Raising the temperature to 180 K eliminated the "proton transfer mode" (PTM) fundamental, and reduced the number of observed combination bands and FRs. With increasing temperature, fundamentals red-shift, and the doubly degenerate wags exhibit larger anharmonic splittings in their VACF bending spectra. We have repeated the analysis for the H3ND+NH3 isotopologue, finding that it has a simplified spectrum, with all the strong peaks being fundamentals. Experimental study of this isotopologue may thus provide a good starting point for disentangling the N2H7+ spectrum. [ABSTRACT FROM AUTHOR]

Protonatedwater clusters that are hydrogen-bonded to a neutralbenzene molecule are a reductionist model for protons at hydrophobicsurfaces, which are of fundamental importance in biological energytransduction processes. Of particular interest is the protonated waterdimer (“Zundel ion”) on benzene, whose gas-phase messengerIR spectrum has been previously interpreted in terms of an asymmetricbinding of the protonated water dimer to the benzene ring througha single water molecule. This “standing Eigen” isomerhas a hydronium core. We have found an alternative “crouchingZundel” isomer, which attaches to the benzene ring symmetricallyvia both of its water molecules. When Ar-tagged, it has an IR spectrumin much better agreement with experiment than the standing Eigen isomer,particularly at the lower frequencies. These conclusions are basedon static harmonic (and anharmonic) normal-mode analysis using densityfunctional theory with various (dispersion corrected) functionalsand particularly on dynamic anharmonic spectra obtained from the dipoleautocorrelation functions from classical ab initio molecular dynamicswith the BLYP, PBE, and B3LYP functionals. Possible implications toprotons on water/organic-phase interfaces are discussed. [ABSTRACT FROM AUTHOR]

Highlights: [•] Atomic radii can be calculated from ionization energies. [•] Slater theory without the Slater rules. [•] Effective single-electron atomic model. [ABSTRACT FROM AUTHOR]

In liquid water the transfer of an excess proton between two water molecules occurs through the Zundel cation, H2O···H+···OH2. The proton-transfer mode is the asymmetric stretch of the central O···H+···O moiety, but there is no consensus on its identification in the infrared spectra of acidic aqueous solutions. Also, in experiments with protonated gas-phase water clusters, its position shifts with cluster size, which makes its relationship with solution spectra unclear. Here we introduce a 'clusters-in-liquid' approach for calculating the infrared spectrum from any set of charges, even single protons. We apply this procedure to multistate empirical valence-bond trajectories of protonated liquid water and to ab initio molecular dynamics of the protonated water dimer and hexamer in the gas phase. The calculated proton-transfer mode is manifested in both systems as a peak near 1,740 cm?1, in quantitative agreement with a band of similar frequency in the experimental infrared spectrum of protonated water clusters. [ABSTRACT FROM AUTHOR]

The residence time of a single dye molecule diffusing within a laser spot is propotional to the total number of photons emitted by it. With this application in mind, we solve the spherically symmetric "residence time equation" (RTE) to obtain the solution for the Laplace transform of the mean residence time (MRT) within a d-dimensional ball, as a function of the initial location of the particle and the observation time. The solutions for initial conditions of potential experimental interest, starting in the center, on the surface or uniformly within the ball, are explicitly presented. Special cases for dimensions 1, 2, and 3 are obtained, which can be Laplace inverted analytically for d = I and 3. In addition, the analytic short- and long-time asymptotic behaviors of the MRT are derived and compared with the exact solutions for d = 1, 2, and 3. As a demonstration of the simplification afforded by the RTE, the Appendix obtains the residence time distribution by solving the Feynman-Kac equation, from which the MRT is obtained by differentiation. Single-molecule diffusion experiments could be devised to test the results for the MRT presented in this work. [ABSTRACT FROM AUTHOR]

Abstract: A model for a proton collecting apparatus on a protein surface includes a ring-shaped collecting domain on which reversible receptors are scattered. These transport a proton by surface diffusion, until it reaches a central orifice where it is absorbed. Mathematically, this scenario is represented approximately by two-dimensional diffusion on the ring, with steady-state rate coefficients for adsorption/desorption of protons from the bulk (which depend on the bulk diffusion coefficient), and a boundary condition mimicking an irreversible reaction on the orifice perimeter. The ensuing differential equation is of the modified Bessel type, and can therefore be solved analytically in terms of modified Bessel functions. The most general solution involves a reflecting boundary condition on the outer perimeter of the ring, and a radiation one on its inner perimeter. This solution admits numerous special cases, such as when the ring becomes infinite, the inner boundary absorbing, or some parameter small or large. These various limits are discussed, as well as possible implications to experiment. [Copyright &y& Elsevier]

We analyse the distributions of donor and acceptor HBs in liquid water and their relation to deviations from tetrahedral symmetry. Their joint, unconditional and conditional distributions are calculated at several temperatures from classical molecular dynamics trajectories for two water models. Surprisingly, the distribution of acceptor HBs terminating at the water lone-pairs is wider than the donor distribution emanating from its hydrogen atoms. This correlates with a higher probability of forming over-coordinated oxygen (OCO) atoms as compared with bifurcated hydrogen bonds (BHBs). Such bonds are possibly formed by HB exchange reactions competing with HB cleavage and formation. The latter obey the binomial distribution, whereas OCOs and BHBs deviate from it considerably. The conditional HB probabilities indicate that acceptor and donor HBs are correlated, so that forming a HB of one type increases the probability of the other, particularly for polarizable water. Conditional distributions exhibit a common intersection suggestive of two types of water structures: high coordination (tetrahedral) and low coordination (polygons). The temperature effect shows that the enthalpy required to cleave a HB in the AMOEBA polarizable model is 9.4 kJ mol-1, close to the experimental value of 10.5 kJ mol-1. As a result, the fraction of HBs decreases with T near room temperature with a slope closer to experiment than older simulations. [ABSTRACT FROM AUTHOR]

Abstract: By fitting time-resolved measurements to models of diffusion influenced reactions it is possible to determine only parameters with no spatial dependence. The original set of distance-dependent parameters is reduced to a set of distance-independent parameters, and only these can be determined by fitting the model to the data. The present work demonstrates this point for reversible geminate recombination in one and three dimensions, showing how the reduced set of parameters is found by utilizing dimensional analysis or known analytic solutions. It is applied to the kinetic detection of proton-wires in the green fluorescent protein. [Copyright &y& Elsevier]

An accurate semi-analytic solution for reversible diffusion-influenced kinetics is presented in the pseudo-unimolecular target limit. It is shown to exhibit excellent agreement with Brownian simulations of the A+B⇌C+D reaction. [Copyright &y& Elsevier]

Modern laser-chemistry techniques allow the preparation of initially correlated pairs as precursors to electron or atom exchange in solution. We obtain a rigorous analytic solution for the two coupled ‘backward’ diffusion equations describing the survival and reaction probabilities. Investigating its long-time asymptotic behavior reveals a transition from monotonic to non-monotonic approach to equilibrium, usually unexpected for elementary single-step reactions. We suggest the synthesis of ‘detachable bifunctional compounds’, that may undergo peculiar kinetics as described herein. [Copyright &y& Elsevier]

Examines the electronic determinants of photoacidity in cyanonaphthols. Semiempirical calculations for the ground and excited state of 2-naphthol and some of its cyano derivatives in the gas phase; Electronic charge distribution on the distal ring of the anion; Quinodal structure of the ring system of the anion in its ground state.

States that trehalose prevents sperm whale myoglobin collapse and preserves its internal mobility. Characterizations of inhomogeneous rebinding and protein collapse; Ways of protein relaxation in trehalose; Procedure for assessing the extent of inhomogeneity; Raman evidence for relaxation and dehydration; Explanation of the ability of trehalose to prevent protein collapse.

Emphasizes that from the correspondence between diffusion and electrostatics, the distribution of absorption points out on an arbitrary surface is the same as the normalized surface charge distribution induced on a grounded conducting surface by a fixed external point charge. Generalization of the Luty, McCammon and Zhou algorithm to nonspherical domains.

The article focuses on the diffusion of protons in membranes. It states that bacteriorhodopsin pumped protons in membranes and diffuse laterally around membrane surface about as fast as the water. It mentions that based on the study conducted by Peter Pohl and colleagues, ultraviolet irradiation produces protons, which travels across the membrane. It adds that ultra-fast diffusion and high isotope effect indicate proton migration along water-wire segments. Moreover, a one-dimensional diffusion equation was formulated which was designed to solve the problems associated to membrane and bulk.

Abstract: The residence time of a diffusing particle in a prescribed spatial region recently finds an increasing number of applications in physics and chemistry. A partial differential equation for the residence time moments is derived, as a generalization of the ordinary differential equation for the first passage time moments. When one seeks to calculate only the mean residence time and not its full distribution, this “residence time equation” constitutes a significant simplification over the conventional Feynman–Kac approach. We demonstrate this for a ball in d-dimensional space with an infinite observation time. The present approach may be useful also for other Brownian functionals. [ABSTRACT FROM AUTHOR]