Proton transport through water-filled carbon nanotubes

Biasing the center of charge in molecular dynamics simulations with empirical valence bond models: free energetics of an excess proton in a water droplet

Multistate empirical valence bond (EVB) models provide an accurate description of the energetics of proton transfer and solvation in complex molecular systems and can be efficiently used in molecular dynamics computer simulations. Within such models, the location of the moving protonic charge can be specified by the so-called center of charge, defined as a weighted average over the diabatic states of the EVB model. In this paper, we use first-order perturbation theory to calculate the molecular forces that arise if a bias potential is applied to the center of charge. Such bias potentials are often necessary when molecular dynamics simulations are used to determine free energies related to proton transfer and not all relevant proton positions are sampled with sufficient frequency during the available computing time. The force expressions we derive are easy to evaluate and do not create any significant computational cost compared with unbiased EVB simulations. As an illustration of the method, we study proton transfer in a small liquid water droplet consisting of 128 water molecules plus an excess proton. Contrary to predictions of continuum electrostatics, but in agreement with previous computer simulations of similar systems, we observe that the excess proton is predominantly located at the surface of the droplet. Using the formalism developed in this paper, we calculate the reversible work required to carry the protonic charge from the droplet surface to its core, finding a value of roughly 4 k(B)T.

Gadonanotubes as ultrasensitive pH-smart probes for magnetic resonance imaging

With their nanoscalar, superparamagnetic Gd(3+)-ion clusters (1 x 5 nm) confined within ultrashort (20-80 nm) single-walled carbon nanotube capsules, gadonanotubes are high-performance T1-weighted contrast agents for magnetic resonance imaging (MRI). At 1.5 T, 37 degrees C, and pH 6.5, the r1 relaxivity (ca. 180 mM(-1) s(-1) per Gd(3+) ion) of gadonanotubes is 40 times greater than any current Gd(3+) ion-based clinical agent. Herein, we report that gadonanotubes are also ultrasensitive pH-smart probes with their r1/pH response from pH 7.0-7.4 being an order of magnitude greater than for any other MR contrast agent. This result suggests that gadonanotubes might be excellent candidates for the development of clinical agents for the early detection of cancer where the extracellular pH of tumors can drop to pH=7 or below. In the present study, gadonanotubes have also been shown to maintain their integrity when challenged ex vivo by phosphate-buffered saline solution, serum, heat, and pH cycling.

Computer modeling in biotechnology: a partner in development

Computational modeling can be a useful partner in biotechnology, in particular, in nanodevice engineering. Such modeling guides development through nanoscale views of biomolecules and devices not available through experimental imaging methods. We illustrate the role of computational modeling, mainly of molecular dynamics, through four case studies: development of silicon bionanodevices for single molecule electrical recording, development of carbon nano-tube-biomolecular systems as in vivo sensors, development of lipoprotein nanodiscs for assays of single membrane proteins, and engineering of oxygen tolerance into the enzyme hydrogenase for photosynthetic hydrogen gas production. The four case studies show how molecular dynamics approaches were adapted to the specific technical uses through (i) multi-scale extensions, (ii) fast quantum chemical force field evaluation, (iii) coarse graining, and (iv) novel sampling methods. The adapted molecular dynamics simulations provided key information on device behavior and revealed development opportunities, arguing that the "computational microscope" is an indispensable nanoengineering tool.

An improved multistate empirical valence bond model for aqueous proton solvation and transport

A new multistate empirical valence bond model (MS-EVB3) is developed for proton solvation and transport in aqueous solutions. The new model and its quantum version (qMS-EVB3) are based on the MS-EVB2 model [Day et al., J. Chem. Phys. 2002, 117, 5839] and recently developed flexible water models-the SPC/Fw model [Wu et al. J. Chem. Phys. 2006, 124, 24503] and the qSPC/Fw model [Paesani et al. J. Chem. Phys. 2006, 125, 184507]-for classical and quantum simulations, respectively. Using ab initio data as benchmarks, the binding energies and optimized geometries calculated with the new model for protonated water clusters, as well as the potential energy surface for proton shuttling between water molecules in a cluster environment, are improved in comparison to the MS-EVB2 model. For aqueous solutions, classical and quantum molecular dynamics simulations with the MS-EVB3 model yield a more accurate description of the solvation structure and diffusive dynamics of the excess proton. New insight is also provided into the proton solvation and hopping dynamics in water, as well as the "amphiphilic" nature of the hydrated proton that has been predicted to give rise to its enhanced concentration at aqueous interfaces and an effectively lower pH of the air-water interface [Petersen et al. J. Phys. Chem. B 2004, 108, 14804].

Generalized gradient-augmented harmonic Fourier beads method with multiple atomic and/or center-of-mass positional restraints

We describe a generalization of the gradient-augmented harmonic Fourier beads method for finding minimum free-energy transition path ensembles and similarly minimum potential energy paths to allow positional restraints on the centers of mass of selected atoms. The generalized gradient-augmented harmonic Fourier beads (ggaHFB) method further extends the scope of the HFB methodology to studying molecule transport across various mobile phases such as lipid membranes. Furthermore, the new implementation improves the applicability of the HFB method to studies of ligand binding, protein folding, and enzyme catalysis as well as modeling equilibrium pulling experiments. Like its predecessor, the ggaHFB method provides accurate energy profiles along the specified paths and in certain simple cases avoids the need for path optimization. The utility of the ggaHFB method is demonstrated with an application to the water permeation through a single-wall (5,5) carbon nanotube with a diameter of 6.78 A and length of 16.0 A. We provide a simple rationale as to why water enters the hydrophobic nanotube and why it does so in pulses and in wire assembly.

Effects of Confinement on Small Water Clusters Structure and Proton Transport

Analyses of the structure of two to four water molecule clusters confined between two benzene and between two naphthalene molecules have been performed using ab initio methods. The water clusters tend to maximize the number of hydrogen bonds via formation of a cyclic network. The oxygen atoms locate approximately in the middle of the confined geometry, and the dipole vectors arrange either parallel or pointing to the surfaces. Energy barriers for proton transfer calculated for H3O+-(H2O) complexes in the same confined geometries suggest that there is a specific range of confinement that helps to lower the energy barriers of the proton transfer. When the walls are too close to each other, at a separation of 4 A, the energy barriers are extremely high. Confinement does not lower the barrier energies of proton transfer when the H3O+-(H2O) complexes are located further from each of the surfaces by more than approximately 8 A.

Molecular dynamics simulation of a pressure-driven liquid transport process in a cylindrical nanopore using two self-adjusting plates

Fluid transport through a nanopore in a membrane was investigated by using a novel molecular dynamics approach proposed in this study. The advantages of this method, relative to dual-control-volume grand-canonical molecular dynamics method, are that it eliminates disruptions to the system dynamics that are normally created by inserting or deleting particles from control volumes, and that it functions well for dense systems due to the number of particles being fixed in the system. Using the proposed method, we examined liquid argon transport through a nanopore by performing nonequilibrium molecular dynamics (NEMD) simulations under different back pressures. Validation of the code was performed by comparing simulation results to published experimental data obtained under equilibrium conditions. NEMD results show that constant pressure difference across the membrane was readily achieved.

Molecular modeling of the short-side-chain perfluorosulfonic acid membrane

Presented here is a first principles based molecular modeling investigation of the possible role of the side chain in effecting proton transfer in the short-side-chain perfluorosulfonic acid fuel cell membrane under minimal hydration conditions. Extensive searches for the global minimum energy structures of fragments of the polymer having two pendant side chains of distinct separation (with chemical formula: CF(3)CF(O(CF(2))(2)SO(3)H)(CF(2))(n)CF(O(CF(2))(2)SO(3)H)CF(3), where n = 5, 7, and 9) with and without explicit water molecules have shown that the side chain separation influences both the extent and nature of the hydrogen bonding between the terminal sulfonic acid groups and the number of water molecules required to transfer the proton to the water molecules of the first hydration shell. Specifically, we have found that fully optimized structures at the B3LYP/6-311G** level revealed that the number of water molecules needed to connect the sulfonic acid groups scaled as a function of the number of fluoromethylene groups in the backbone, with one, two, and three water molecules required to connect the sulfonic acid groups in fragments with n = 5, 7, and 9, respectively. With the addition of explicit water molecules to each of the polymeric fragments, we found that the minimum number of water molecules required to effect proton transfer also increases as the number of separating tetrafluoroethylene units in the backbone is increased. Furthermore, calculation of water binding energies on CP-corrected potential energy surfaces showed that the water molecules bound more strongly after proton dissociation had occurred from the terminal sulfonic acid groups independent of the degree of separation of the side chains. Our calculations provide a baseline for molecular results that can be used to assess the impact of changes of polymer chemistry on proton conduction, including the side chain length and acidic functional group.

Dynamics of water confined in single- and double-wall carbon nanotubes

Using high-resolution quasielastic neutron scattering, we investigated the temperature dependence of single-particle dynamics of water confined in single- and double-wall carbon nanotubes with the inner diameters of 14+/-1 and 16+/-3 A, respectively. The temperature dependence of the alpha relaxation time for water in the 14 A nanotubes measured on cooling down from 260 to 190 K exhibits a crossover at 218 K from a Vogel-Fulcher-Tammann law behavior to an Arrhenius law behavior, indicating a fragile-to-strong dynamic transition in the confined water. This transition may be associated with a structural transition from a high-temperature, low-density (<1.02 gcm(3)) liquid to a low-temperature, high-density (>1.14 gcm(3)) liquid found in molecular dynamics simulation at about 200 K. However, no such dynamic transition in the investigated temperature range of 240-195 K was detected for water in the 16 A nanotubes. In the latter case, the dynamics of water simply follows a Vogel-Fulcher-Tammann law. This suggests that the fragile-to-strong crossover for water in the 16 A nanotubes may be shifted to a lower temperature.

Proton solvation and transport in aqueous and biomolecular systems: insights from computer simulations

The excess proton in aqueous media plays a pivotal role in many fundamental chemical (e.g., acid-base chemistry) and biological (e.g., bioenergetics and enzyme catalysis) processes. Understanding the hydrated proton is, therefore, crucial for chemistry, biology, and materials sciences. Although well studied for over 200 years, excess proton solvation and transport remains to this day mysterious, surprising, and perhaps even misunderstood. In this feature article, various efforts to address this problem through computer modeling and simulation will be described. Applications of computer simulations to a number of important and interesting systems will be presented, highlighting the roles of charge delocalization and Grotthuss shuttling, a phenomenon unique in many ways to the excess proton in water.

Modelling of morphology and proton transport in PFSA membranes

Computational modelling studies of the structure of perfluorosulfonic acid (PFSA) ionomer membranes consistently exhibit a nanoscopic phase-separated morphology in which the ionic side chains and aqueous counterions segregate from the fluorocarbon backbone to form clusters or channels. Although these investigations do not unambiguously predict the size or shape of the clusters, and whether or not the channels percolate the matrix or if the connections between them are more transient, the sequence of co-monomers along the main chain appears strongly to influence the domain size of the ionic regions, with more blocky sequences giving rise to larger domain sizes. The fundamental insight that substantial rearrangement of the sulfonic acid terminated side chains and fluorocarbon backbone takes place during swelling or shrinkage is borne out by both molecular and mesoscale simulations of model PFSA polymers, along with ab initio electronic structure calculations of minimally hydrated oligomeric fragments. Molecular-level modelling of proton transport in PFSA membranes attests to the complexity of the underlying mechanisms and the need to examine the chemical and physical processes at several distinct time and length scales. These investigations have revealed that the conformation of the fluorocarbon backbone, flexibility of the sidechains, and degree of aggregation and association of the sulfonic acid groups under minimally hydrated conditions collectively control the dissociation of the protons and the formation of Zundel and Eigen cations. The former appear to be the dominant charge carriers when the limiting water content allows only for the formation of a contact ion pair with the tethered sulfonate anion. As the water content increases, solvent-separated Eigen ions begin to appear, indicating that the dominant mechanism for diffusion of protons occurs over a region approximately 4 A away from the sulfonate groups. Finally, both the vehicular and Grotthuss shuttling mechanisms contribute to the mobility of the protons but, surprisingly, they are not always correlated, resulting in a lower overall diffusion coefficient. In summary, as the preceding observations indicate, the state of computational modelling of PFSA membranes has progressed sufficiently over the last decade to enable its use as a powerful predictive tool with which to guide the process of designing novel membrane materials for fuel cell applications.

Modeling the selective partitioning of cations into negatively charged nanopores in water

Partitioning and transport of water and small solutes into and through nanopores are important to a variety of chemical and biological processes and applications. Here we study water structure in negatively charged model cylindrical [carbon nanotube (CNT)-like] nanopores, as well as the partitioning of positive ions of increasing size (Na+, K+, and Cs+) into the pore interior using extensive molecular dynamics simulations. Despite the simplicity of the simulation system-containing a short CNT-like nanopore in water carrying a uniformly distributed charge of qpore=-ne surrounded by n (=0,...,8) cations, making the overall system charge neutral-the results provide new and useful insights on both the pore hydration and ion partitioning. For n=0, that is, for a neutral nanopore, water molecules partition into the pore and form single-file hydrogen-bonded wire spanning the pore length. With increasing n, water molecules enter the pore from both ends with preferred orientations, resulting in a mutual repulsion between oriented water molecules at the pore center and creating a cavity-like low density region at the center. For low negative charge densities on the pore, the driving force for partitioning of positive ions into the pore is weak, and no partitioning is observed. Increasing the pore charge gradually leads to partitioning of positive ions into the pore. Interestingly, over a range of intermediate negative charge densities, nanopores display both thermodynamic as well as kinetic selectivity toward partitioning of the larger K+ and Cs+ ions into their interior over the smaller Na+ ions. Specifically, the driving force is in the order K+>Cs+>Na+, and K+ and Cs+ ions enter the pore much more rapidly than Na+ ions. At higher charge densities, the driving force for partitioning increases for all cations-it is highest for K+ ions-and becomes similar for Na+ and Cs+ ions. The variation of thermodynamic driving force and the average partitioning time with the pore charge density together suggest the presence of free energy barriers in the partitioning process. We discuss the role of ion hydration in the bulk and in the pore interior as well as of the pore hydration in determining the barrier heights for ion partitioning and the observed thermodynamic and kinetic selectivities.

Kinetic models of redox-coupled proton pumping

Cytochrome c oxidase, the terminal enzyme of the respiratory chain, pumps protons across the inner mitochondrial membrane against an opposing electrochemical gradient by reducing oxygen to water. To explore the fundamental mechanisms of such redox-coupled proton pumps, we develop kinetic models at the single-molecule level consistent with basic physical principles. We demonstrate that pumping against potentials >150 mV can be achieved purely through electrostatic couplings, given an asymmetric arrangement of charge centers; however, nonlinear gates are essential for highly efficient real enzymes. The fundamental requirements for proton pumping identified here highlight a possible evolutionary origin of cytochrome c oxidase pumping. The general design principles are relevant also for other molecular machines and suggest future applications in biology-inspired fuel cells.

Energy transduction: proton transfer through the respiratory complexes

A series of metalloprotein complexes embedded in a mitochondrial or bacterial membrane utilize electron transfer reactions to pump protons across the membrane and create an electrochemical potential (DeltamuH+). Current understanding of the principles of electron-driven proton transfer is discussed, mainly with respect to the wealth of knowledge available from studies of cytochrome c oxidase. Structural, experimental, and theoretical evidence supports the model of long-distance proton transfer via hydrogen-bonded water chains in proteins as well as the basic concept that proton uptake and release in a redox-driven pump are driven by charge changes at the membrane-embedded centers. Key elements in the pumping mechanism may include bound water, carboxylates, and the heme propionates, arginines, and associated water above the hemes. There is evidence for an important role of subunit III and proton backflow, but the number and nature of gating mechanisms remain elusive, as does the mechanism of physiological control of efficiency.

Kinetics and mechanism of proton transport across membrane nanopores

We use computer simulations to study the kinetics and mechanism of proton passage through a narrow-pore carbon-nanotube membrane separating reservoirs of liquid water. Free energy and rate constant calculations show that protons move across the membrane diffusively along single-file chains of hydrogen-bonded water molecules. Proton passage through the membrane is opposed by a high barrier in the effective potential, reflecting the large electrostatic penalty for desolvation and reminiscent of charge exclusion in biological water channels. At neutral pH, we estimate a translocation rate of about 1 proton per hour and tube.

Mechanism of Ion Permeation in a Model Channel: Free Energy Surface and Dynamics of K+Ion Transport in an Anion-Doped Carbon Nanotube

The mechanism of the ion permeation is investigated for an anion-doped carbon nanotube, as a model of the K+ channel, by analyzing the free energy surface and the dynamics of the ion permeation through the model channel. It is found that the main rate-determining step is how an ion enters the channel. The entrance of the ion is mostly blocked by a water molecule located at this entrance. Only about 10% of K+ ions which reach the mouth of the channel can really enter the channel. The rejection rate sensitively depends on the location of this water molecule, which is easily controlled by the charge of the carbon nanotube; for example, the maximum permeation is obtained when the anion charge is at a certain value, -5.4e in the present model. At this charge, the facile translocation of the ion inside the channel is also induced due to the number of fluctuations of the ions inside the channel. Therefore, the so-called "Newton's balls", a toy model, combined with a simple ion diffusion model for explaining the fast ion permeation should be modified. The present analysis thus suggests that there exists an optimum combination of the length and the charge of the carbon nanotube for the most efficient ion permeation.

Effect of quantum partial charges on the structure and dynamics of water in single-walled carbon nanotubes

In this work, using quantum partial charges, computed from 6-31G(**)B3LYP density functional theory, in molecular dynamics simulations, we found that water inside (6,6) and (10,0) single-walled carbon nanotubes with similar diameters but with different chiralities has remarkably different structural and dynamical properties. Density functional calculations indicate that tubes with different chiralities have significantly different partial charges at the ends of tubes. The partial charges at the ends of a (10,0) tube are around 4.5 times higher than those of a (6,6) tube. Molecular dynamics simulations with the partial charges show different water dipole orientations. In the (10,0) tube, dipole vectors of water molecules at the end of the tube point towards the water reservoir resulting in the formation of an L defect in the center region. This is not observed in the (6,6) tube where dipole vectors of all the water molecules inside the tube point towards either the top or the bottom water reservoir. The water diffusion coefficient is found to increase in the presence of the partial charges. Water in the partially charged (10,0) tube has a lower diffusion coefficient compared to that of in the partially charged (6,6) tube.

Unusual Hydrogen Bonding in Water-Filled Carbon Nanotubes

We present the first experimental vibrational spectroscopy study providing direct evidence of a water phase inside single-walled carbon nanotubes that exhibits an unusual form of hydrogen-bonding due to confinement. Water adopts a stacked-ring structure inside nanotubes, forming intra- and inter-ring hydrogen bonds. The intra-ring hydrogen bonds are bulk-like while the inter-ring hydrogen bonds are relatively weak, having a distorted geometry that gives rise to a distinct OH stretching mode. The experimentally observed infrared mode at 3507 cm(-1) is assigned to vibrations of the inter-ring OH-groups based on detailed atomic-level modeling. The direct observation of unusual hydrogen bonding in nanotubes has potential implications for water in other highly confined systems, such as biological channels and nanoporous media.

Ion permeation dynamics in carbon nanotubes

Molecular dynamics simulations are carried out to investigate the permeation of ions and water in a membrane consisting of single wall carbon nanotubes possessing no surface charges connecting two reservoirs. Our simulations reveal that there are changes in the first hydration shell of the ions upon confinement in tubes of 0.82 or 0.90 nm effective internal diameter. Although the first minimum in the g(r) is barely changed in the nanotube compared to in the bulk solution, the hydration number of Na(+) ion is reduced by 1.0 (from 4.5 in bulk to 3.5 in the 0.90 nm tube) and the hydration number is reduced further in the 0.82 nm tube. The changes in the hydration shell of Cl(-) ion are negligible, within statistical errors. The water molecules of the first hydration shell of both ions exchange less frequently inside the tube than in the bulk solution. We compare ion trajectories for ions in the same tube under identical reservoir conditions but with different numbers of ions in the tubes. This permits investigation of changes in structure and dynamics which arise from multiple ion occupancy in a carbon nanotube possessing no surface charges. We also investigated the effects of tube flexibility. Ions enter the tubes so as to form a train of ion pairs. We find that the radial distribution profiles of Na(+) ions broaden significantly systematically with increasing number of ion pairs in the tube. The radial distribution profiles of Cl(-) ions change only slightly with increasing number of ions in the tube. Trajectories reveal that Na(+) ions do not pass each other in 0.90 nm tubes, while Cl(-) ions pass each other, as do ions of opposite charge. An ion entering the tube causes the like-charged ions preceding it in the tube to be displaced along the tube axis and positive or negative ions will exit the tube only when one or two other ions of the same charge are present in the tube. Thus, the permeation mechanism involves multiple ions and Coulomb repulsion among the ions plays an essential role.

Proton transfers in the bacteriorhodopsin photocycle

The steps in the mechanism of proton transport in bacteriorhodopsin include examples for most kinds of proton transfer reactions that might occur in a transmembrane pump: proton transfer via a bridging water molecule, coupled protonation/deprotonation of two buried groups separated by a considerable distance, long-range proton migration over a hydrogen-bonded aqueous chain, and capture as well as release of protons at the membrane-water interface. The conceptual and technical advantages of this system have allowed close examination of many of these model reactions, some at an atomic level.

Chance and design—Proton transfer in water, channels and bioenergetic proteins

Proton transfer and transport in water, gramicidin and some selected channels and bioenergetic proteins are reviewed. An attempt is made to draw some conclusions about how Nature designs long distance, proton transport functionality. The prevalence of water rather than amino acid hydrogen bonded chains is noted, and the possible benefits of waters as the major component are discussed qualitatively.

Conformational transformations induced by the charge-curvature interaction: Mean-field approach

A simple phenomenological model for describing the conformational dynamics of biological macromolecules via the nonlinearity-induced instabilities is proposed. It is shown that the interaction between charges and bending degrees of freedom of closed molecular aggregates may act as drivers giving impetus to conformational dynamics of biopolymers. It is demonstrated that initially circular aggregates may undergo transformation to polygonal shapes and possible application to aggregates of bacteriochlorophyl a molecules is considered.

Effects of electric fields on proton transport through water chains

Molecular dynamics simulations on quantum energy surfaces are carried out to study the effects of perturbing electric fields on proton transport (PT) in protonated water chains. As an idealized model of a hydrophobic cavity in the interior of a protein the water molecules are confined into a carbon nanotube (CNT). The water chain connects a hydrated hydronium ion (H3O+) at one end of the CNT and an imidazole molecule at the other end. Without perturbing electric fields PT from the hydronium proton donor to the imidazole acceptor occurs on a picosecond time scale. External perturbations to PT are created by electric fields of varying intensities, normal to the CNT axis, generated by a neutral pair of charges on the nanotube wall. For fields above approximately 0.5 VA, the hydronium ion is effectively trapped at the CNT center, and PT blocked. Fields of comparable strength are generated inside proteins by nearby polar/charged amino acids. At lower fields the system displays a rich dynamic behavior, where the excess charge shuttles back and forth along the water chain before reaching the acceptor group on the picosecond time scale. The effects of the perturbing field on the proton movement are analyzed in terms of structural and dynamic properties of the water chain. The implications of these observations on PT in biomolecular systems and its control by external perturbing fields are discussed.

Proton transfer in imidazole-based molecular crystals

Heterocycles' aggregates show rather good proton conductivity. In particular, condensed structures formed by imidazole rings that are held together by polymeric chains have attracted some interest as possible candidate materials for fuel cell membranes. However, the details of the proton diffusion process could not be resolved by means of experimental measurements because of the fast rearrangement of the structure after each proton exchange. In this work, we report in detail the results of ab initio molecular dynamics calculations, which were briefly presented in a previous Letter [M. Iannuzzi and M. Parrinello, Phys. Rev. Lett. 93, 025901 (2004)]. The conformational changes associated with the diffusion of protons in model crystalline structures containing chains of imidazole rings are described in the framework of an atomistic approach. In particular, the bonding pattern characterizing the structure of imidazole-2-ethylene-oxide doped by an excess proton is also studied through the calculation of the 1H NMR chemical shifts. The unresolved resonances appearing in the experimental spectra could be associated with specific structural features, in connection with the fluctuating hydrogen bonding. The analysis of the distortions that induce or are induced by the mobility of the protons offers some new hints for the engineering of new proton conducting materials.

Proton conduction along a chain of water molecules. Development of a linear model and quantum dynamical investigations using the multiconfiguration time-dependent Hartree method

Proton transfer along a chain of water molecules is discussed. A linear model for such a chain is developed and its parameters are determined by comparison to quantum chemistry calculations. Fully quantum mechanical dynamical simulations on the translocation process are performed for different chain lengths, with up to five water molecules. We found that tunneling is important for the proton-transfer process. Furthermore, translocation is accomplished through a strongly correlated motion involving both hydrogen and oxygen atoms. An approximate treatment, which limits or even neglects this correlation, may lead to severely incorrect results.

Salt permeation and exclusion in hydroxylated and functionalized silica pores

We use combined ab initio molecular dynamics (AIMD), grand canonical Monte Carlo, and molecular dynamics techniques to study the effect of pore surface chemistry and confinement on the permeation of salt into silica nanopore arrays filled with water. AIMD shows that 11.6 A diameter hydroxylated silica pores are relatively stable in water, whereas amine groups on functionalized pore surfaces abstract silanol protons, turning into NH3+. Free energy calculations using an ab initio parametrized force field show that the hydroxylated pores strongly attract Na+ and repel Cl- ions. Pores lined with NH3+ have the reverse surface charge polarity. Finally, studies of ions in carbon nanotubes suggest that hydration of Cl- is more strongly frustrated by pure confinement effects than Na+.

Adsorption and diffusion of carbon dioxide and nitrogen through single-walled carbon nanotube membranes

We have used atomically detailed simulations to examine the adsorption and transport diffusion of CO2 and N2 in single-walled carbon nanotubes at room temperature as a function of nanotube diameter. Linear and spherical models for CO2 are compared, showing that representing this species as spherical has only a slight impact in the computed diffusion coefficients. Our results support previous predictions that transport diffusivities of molecules inside carbon nanotubes are extremely rapid when compared with other porous materials. By examining carbon nanotubes as large as the (40,40) nanotube, we are able to compare the transport rates predicted by our calculations with recent experimental measurements. The predicted transport rates are in reasonable agreement with experimental observations.

Visible-Light-Induced Water-Splitting in Channels of Carbon Nanotubes

The visible-light-induced split of water confined in channels of single-walled carbon nanotubes (SWNTs) was experimentally studied. Arc-discharging synthesized SWNTs were used to adsorb water vapor and then were irradiated in a vacuum by using light from a camera flash. It was found that a great amount of hydrogen-rich gases could be repeatedly produced under several rapid flashes of light, occasionally accompanying evident charge emission phenomena. A quantitative method was developed to estimate the relative amount of gas components on the basis of the data acquired with an ion gauge and a quadrupole mass spectrometer. The results indicated that hydrogen occupied about 80 mol % of the photogenerated gases, with other components such as carbon oxides, helium, methane and trace of ethane, and the total gas yield in one flash (0.1-0.2 J/cm2, 8 ms) reached 400-900 ppm of the mass of the SWNTs. Such a yield could be repeatedly obtained in serial flashings until the adsorbed water was depleted, and then, by sufficiently adsorbing water vapor again, the same phenomena could be reproduced.

On the consequences of side chain flexibility and backbone conformation on hydration and proton dissociation in perfluorosulfonic acid membranes

The flexibility of the side chain and effects of conformational changes in the backbone on hydration and proton transfer in the short-side-chain (SSC) perfluorosulfonic acid fuel cell membrane have been investigated through first principles based molecular modelling studies. Potential energy profiles determined at the B3LYP/6-31G(d,p) level in the two pendant side chain fragments: CF(3)CF(-O(CF(2))(2)SO(3)H)-(CF(2))(7)-CF(-O(CF(2))(2)SO(3)H)CF(3) indicate that the largest CF(2)-CF(2) rotational barrier along the backbone is nearly 28.9 kJ mol(-1) higher than the minimum energy staggered trans conformation. Furthermore, the calculations reveal that the stiffest portion of the side chain is near to its attachment site on the backbone, with CF-O and O-CF(2) barriers of 38.1 and 28.0 kJ mol(-1), respectively. The most flexible portion of the side chain is the carbon-sulfur bond, with a barrier of only 8.8 kJ mol(-1). Extensive searches for minimum energy structures (at the B3LYP/6-311G(d,p) level) of the same polymeric fragment with 4-7 explicit water molecules reveal that the perfluorocarbon backbone may adopt either an elongated geometry, with all carbons in a trans configuration, or a folded conformation as a result of the hydrogen bonding of the terminal sulfonic acids with the water. These electronic structure calculations show that the fragments displaying the latter 'kinked' backbone possessed stronger binding of the water to the sulfonic acid groups, and also undergo proton dissociation with fewer water molecules. The calculations point to the importance of the flexibility in both the backbone and side chains of PFSA membranes to effectively transport protons under low humidity conditions.

Ion-nanotube terahertz oscillator

We report the intriguing dynamics of a potassium ion interacting with a 16 A carbon nanotube. The ion induces a strong dielectric response in the nanotube wall that can be described through a self-consistent tight-binding method. The polarization of the nanotube was found to play a critical role in the ion-nanotube interaction, which exhibits a low access barrier of only 1.05 kcal/mol and a deep, attractive well with a depth of about 30 kcal/mol. An ion bound in the nanotube is predicted to oscillate at a frequency of about 0.4 terahertz, dragging the electrons of the nanotube along. Besides its appealing nature in low-dimensional physics, such a nano-oscillator may serve as a room temperature terahertz wave detector.

Effect of flexibility on hydrophobic behavior of nanotube water channels

Carbon nanotubes can serve as simple nonpolar water channels. Here we report computer simulations exploring the relationship between the mechanical properties of such channels and their interaction with water. We show that on one hand, increasing the flexibility of the carbon nanotubes increases their apparent hydrophobic character, while on the other hand the presence of water inside the channel makes them more resistant to radial collapse. We quantify the effect of increasing flexibility on the hydrophobicity of the nanotube water channel. We also show that flexibility impedes water transport across the nanotube channel by increasing the free-energy barriers to such motion. Conversely, the presence of water inside the nanotube is shown to affect the energetics of radial collapse in a water nanotube, an ostensibly mechanical property. We quantify the magnitude of the effect and show that it arises from the formation of energetically favorable low-dimensional water structures inside the nanotube such as one-dimensional wires and two-dimensional sheets.

Observation of the dynamical change in a water monolayer adsorbed on a ZnO surface

A combined scanning tunneling microscopy and density-functional theory (DFT) study shows a rich structure of water monolayers adsorbed on ZnO(1010) at room temperature. Most of the water is in a lowest-energy configuration where every second molecule is dissociated. It coexists with an energetically almost degenerate configuration consisting of a fully molecular water monolayer. Parts of the layer continuously switch back and forth between these two states. DFT calculations reveal that water molecules repeatedly associate and dissociate in this sustained dynamical process.

Hydroxide and proton migration in aquaporins

Hypothetical hydroxide and proton migration along the linear water chain in Aquaporin GlpF from Escherichia coli are studied by ab initio Car-Parrinello molecular dynamics simulations. It is found that the protein stabilizes a bipolar single file of water. The single file features a contiguous set of water-water hydrogen bonds in which polarization of the water molecules vary with position along the channel axis. Deprotonation of the water chain promotes the reorientation of water molecules while the hydroxide ion rapidly migrates by sequentially accepting protons from the neighboring water molecules. The hydroxide ion is not attracted by a conserved, channel-lining arginine residue, but is immobilized at two centrally located, conserved Asparagine-Proline-Alanine motifs where fourfold coordination stabilizes the ion. Hydroxide transition from the channel vestibules into the channel lumen is strongly influenced by electrostatic coupling to two conserved oppositely aligned macrodipoles. This suggests that the macrodipole's negative poles play a role in preventing hydroxide ions from entering into the channel's inner vestibules. Water protonation within the lumen facilitates water reorientation and subsequent proton expelling occurs. In the periplasmic half-channel, expelling occurs via the Grotthuss mechanism. Protonation within the cytoplasmic half-channel implies wire-breakage at the Asn-Pro-Ala motifs. The proton is here diffusively rejected as (H(5)O(2))(+).

Empirical nanotube model for biological applications

An empirical model is developed to capture the electrostatics of finite-length single-walled armchair carbon nanotubes for biological applications. Atomic partial charges are determined to match the electrostatic potential field computed at the B3LYP/6-31G* level of density functional theory, and a tight-binding Hamiltonian is selected which permits one to reproduce the dielectric properties in good agreement with density functional theory results. The new description is applied to study movement of a water molecule through a finite-length nanotube channel in order to demonstrate the method's feasibility. We find that atomic partial charges on the tube edges dominate the interaction between the nanotube and the entering water molecule, while the polarization of the nanotube lowers the electrostatic energy of the water molecule inside the tube.

Curvature induced L-defects in water conduction in carbon nanotubes

We conduct molecular dynamics simulations to study the effect of the curvature induced static dipole moment of small open-ended single-walled carbon nanotubes (CNTs) immersed in water. This dipole moment generates a nonuniform electric field, changing the energy landscape in the CNT and altering the water conduction process. The CNT remains practically filled with water at all times, whereas intermittent filling is observed when the dipole term is not included. In addition, the dipole moment induces a preferential orientation of the water molecules near the end regions of the nanotube, which in turn causes a reorientation of the water chain in the middle of the nanotube. The most prominent feature of this reorientation is an L-defect in the chain of water molecules inside the CNT. The analysis of the water energetics and structural characteristics inside and in the vicinity of the CNT helps to identify the role of the dipole moment and to suggest possible mechanisms for controlled water and proton transport at the nanoscale.

Reaction coordinates and rates from transition paths

The molecular mechanism of a reaction in solution is reflected in its transition-state ensemble and transition paths. We use a Bayesian formula relating the equilibrium and transition-path ensembles to identify transition states, rank reaction coordinates, and estimate rate coefficients. We also introduce a variational procedure to optimize reaction coordinates. The theory is illustrated with applications to protein folding and the dipole reorientation of an ordered water chain inside a carbon nanotube. To describe the folding of a simple model of a three-helix bundle protein, we variationally optimize the weights of a projection onto the matrix of native and nonnative amino acid contacts. The resulting one-dimensional reaction coordinate captures the folding transition state, with formation and packing of helix 2 and 3 constituting the bottleneck for folding.

Distribution patterns and controllable transport of water inside and outside charged single-walled carbon nanotubes

The density distribution patterns of water inside and outside neutral and charged single-walled carbon nanotubes (SWNTs) soaked in water have been studied using molecular dynamics simulations based on TIP3P potential and Lennard-Jones parameters of CHARMM force field, in conjunction with ab initio calculations to provide the electron density distributions of the systems. Water molecules show different electropism near positively and negatively charged SWNTs. Different density distribution patterns of water, depending on the diameter and chirality of the SWNTs, are observed inside and outside the tube wall. These special distribution patterns formed can be explained in terms of the van der Waals and electrostatic interactions between the water molecules and the carbon atoms on the hexagonal network of carbon nanotubes. The electric field produced by the highly charged SWNTs leads to high filling speed of water molecules, while it prevents them from flowing out of the nanotube. Water molecules enter the neutral SWNTs slowly and can flow out of the nanotube in a fluctuating manner. It indicates that by adjusting the electric charge on the SWNTs, one can control the adsorption and transport behavior of polar molecules in SWNTs to be used as stable storage medium with template effect or transport channels. The transport rate can be tailored by changing the charge on the SWNTs.

Collective Solvent Coordinates for the Infrared Spectrum of HOD in D2O Based on an ab Initio Electrostatic Map

An ab initio MP2 vibrational Hamiltonian of HOD in an external electrostatic potential parametrized by the electric field and its gradient-tensor is constructed. By combining it with the fluctuating electric field induced by the D(2)O solvent obtained from molecular dynamics simulations, we calculate the infrared absorption of the O-H stretch. The resulting solvent shift and infrared line shape for three force fields (TIP4P, SPC/E, and SW) are in good agreement with the experiment. A collective coordinate response for the solvent effect is constructed by identifying the main electrostatic field and gradient components contributing to the line shape. This allows a realistic stochastic Liouville equation simulation of the line shapes which is not restricted to Gaussian frequency fluctuations.

Water alignment, dipolar interactions, and multiple proton occupancy during water-wire proton transport

A discrete multistate kinetic model for water-wire proton transport is constructed and analyzed using Monte Carlo simulations. In the model, each water molecule can be in one of three states: oxygen lone-pairs pointing leftward, pointing rightward, or protonated (H(3)O(+)). Specific rules for transitions among these states are defined as protons hop across successive water oxygens. Our model also includes water-channel interactions that preferentially align the water dipoles, nearest-neighbor dipolar coupling interactions, and Coulombic repulsion. Extensive Monte Carlo simulations were performed and the observed qualitative physical behaviors discussed. We find the parameters that allow the model to exhibit superlinear and sublinear current-voltage relationships, and show why alignment fields, whether generated by interactions with the pore interior or by membrane potentials, always decrease the proton current. The simulations also reveal a "lubrication" mechanism that suppresses water dipole interactions when the channel is multiply occupied by protons. This effect can account for an observed sublinear-to-superlinear transition in the current-voltage relationship.

Discrete kink dynamics in hydrogen-bonded chains: the two-component model

We study discrete topological solitary waves (kinks and antikinks) in two nonlinear diatomic chain models that describe the collective dynamics of proton transfers in one-dimensional hydrogen-bonded networks. The essential ingredients of the models are (i) a realistic (anharmonic) ion-proton interaction in the hydrogen bond, (ii) a harmonic coupling between the protons in adjacent hydrogen bonds, and (iii) a harmonic coupling between the nearest-neighbor heavy ions (an isolated diatomic chain with the lowest acoustic band) or instead a harmonic on-site potential for the heavy ions (a diatomic chain subject to a substrate with two optical bands), both providing a bistability of the hydrogen-bonded proton. Exact two-component (kink and antikink) discrete solutions for these models are found numerically. We compare the soliton solutions and their properties in both the one- (when the heavy ions are fixed) and two-component models. The effect of stability switchings, discovered previously for a class of one-component kink-bearing models, is shown to exist in these two-component models as well. However, the presence of the second component, i.e., the softness of the heavy-ion sublattice, brings principal differences, like a significant difference in the stability switchings behavior for the kinks and the antikinks. Water-filled carbon nanotubes are briefly discussed as possible realistic systems, where topological discrete (anti)kink states might exist.