Using porphyrin–amino acid pairs to model the electrochemistry of heme proteins: experimental and theoretical investigations

Deconstructing the complex electrochemistry of heme proteins into simpler heme–amino acid interactions.

Effect of interionic interactions on the structure and dynamics of ionic solvation shells in aqueous electrolyte solutions

Molecular dynamics (MD) simulations to explore the structure and dynamics of the ionic solvation shell of alkali ions and halide ions in aqueous solution.

A molecular dynamics study and molecular level explanation of pressure dependence of ionic conductivity of potassium chloride in water

Experimental ionic conductivity of different alkali ions in water shows markedly different dependences on pressure. Existing theories such as that of Hubbard-Onsager are unable to explain these dependences on pressure of the ionic conductivity for all ions. We report molecular dynamics investigation of potassium chloride solution at low dilution in water at several pressures between 1 bar and 2 kbar. Two different potential models have been employed. One of the models successfully reproduces the experimentally observed trend in ionic conductivity of K(+) ions in water over the 0.001-2 kbar range. We also propose a theoretical explanation, albeit at a qualitative level, to account for the dependence of ionic conductivity on pressure in terms of the previously studied Levitation Effect. It also provides a microscopic picture in terms of the pore network in liquid water.

Ions in water: role of attractive interactions in size dependent diffusivity maximum

A molecular dynamics study of model ions in water is reported. The van der Waals diameter of both the cations and anions is varied. We have carried out two sets of simulations--with and without dispersion interaction--between the ion and water. Self-diffusivity of the ions exhibits an anomalous maximum as a function of the van der Waals diameter for both these sets. This existence of a maximum in self-diffusivity when there is no dispersion interaction between the ion and the water is attributed to the attractive term from electrostatic interactions. Detailed analysis of this effect shows that the solvent shell is more strongly defined in the presence of dispersion interactions. A smaller ion exhibits biexponential decay while a single exponential decay is seen for the ion with maximum diffusivity in the self-part of the intermediate scattering function. The solvent structure around the ion appears to determine much of the dynamics of the ion. Interesting trends are seen in the activation energies and these can be understood in terms of the levitation effect.

Breakdown of the Stokes−Einstein Relationship: Role of Interactions in the Size Dependence of Self-Diffusivity

Einstein and others derived the reciprocal dependence of the self-diffusivity D on the solute radius r(u) for large solutes based on kinetic theory. We examine here (a) the range of r(u) over which Stokes-Einstein (SE) dependence is valid and (b) the precise dependence for small solutes outside of the SE regime. We show through molecular dynamics simulations that there are two distinct regimes for smaller solutes: (i) the interaction or Levitation effect (LE) regime for solutes of intermediate size and (ii) the D proportional, variant 1/r(u)(2) for still smaller solutes. We show that as the solute-solvent size ratio decreases, the breakdown in the Stokes-Einstein relationship leading to the LE regime has its origin in dispersion interaction between the solute and the solvent. These results explain reports of enhanced solute diffusion in solvents existing in the literature seen for small solutes for which no explanation exists.

Existence of a size-dependent diffusivity maximum for uncharged solutes in water and its implications

Recent studies suggest that there exists a size-dependent diffusivity maximum in binary mixtures interacting via Lennard-Jones potential when the size of one of the two components is varied (Ghorai, P. K.; Yashonath, S. J. Phys. Chem., 2005, 109, 5824). We discuss in the present paper the importance of the existence of a size-dependent maximum for an uncharged solute in liquid or amorphous solid water and its relation to the ionic conductivity maximum in water. We report molecular dynamics investigations into the size dependence of the self-diffusivity, D, of the uncharged solutes in water at low temperatures (30 K) with immobile as well as mobile water. We find that a maximum in self-diffusivity exists as a function of the size of solute diffusing within water at low temperatures but not at high temperatures. This is due to the relatively weak interactions between the solute and the water compared to the kinetic energy at room temperature. Previously, we have shown that a similar maximum exists for guests sorbed in zeolites and is known as the levitation effect (LE). Thus, it appears that the existence of a size-dependent maximum is universal and extends from zeolites to simple liquids to solvents of polyatomic species. We examine the implications of this for the size-dependent maximum in ionic conductivity in polar solvents known for over a hundred years. These results support the view that the size-dependent maximum seen for ions in water has its origin in the LE (see Ghorai, P. Kr.; Yashonath, S.; Lynden-Bell, R. M. J. Phys. Chem. 2005, 109, 8120).

Evidence in Support of Levitation Effect as the Reason for Size Dependence of Ionic Conductivity in Water: A Molecular Dynamics Simulation

We report extensive molecular dynamics simulations of (i) model ions in water at high concentrations as a function of the size and charge of the ion as well as (ii) realistic simulation of Cl- and Br- ions at low concentrations in water at room temperature. We also analyze existing experimental data in light of the results obtained here. The halide ion simulations have been carried out using the interaction potentials of Koneshan et al. (J. Phys. Chem. B 1998, 102, 4193). We compute structural and dynamical properties of ions in water and explore their variation with size and charge of the ion. We find that ions of certain intermediate sizes exhibit a maximum in self-diffusivity in agreement with previous experimental measurements and computer simulations. We analyze molecular dynamics trajectories in light of the previous understanding of the levitation effect (LE) and the recent suggestion that ionic conductivity has its origin in LE (J. Phys. Chem. B 2005, 109, 8120). We report the distribution of void and neck radii that exist amidst water. Our analysis suggests that the ion with maximum self-diffusivity is characterized by a lower activation energy and a single-exponential decay of F(s)(k,t). The behavior of these and other related quantities of the ion with maximum self-diffusivity are characteristic of the anomalous regime of the LE. The simulation results of Br- and Cl- ions in water also yield results in agreement with the predictions of LE. A plot of experimental conductivity data in the literature for alkali ions in water by Kay and Evans (J. Phys. Chem. 1966, 70, 2325) also yields a lower activation energy for the ion with maximum conductivity in excellent agreement with the LE. To the best of our knowledge, none of the existing theories predict a lower activation energy for the ion with maximum conductivity.

Separation of Mixtures at Nano Length Scales: Blow Torch and Levitation Effect

A new conceptual basis for the separation of multicomponent molecular mixtures is proposed. A separation method where different components of the mixtures are driven in opposite directions is realized by a judicious combination of two effects, viz., levitation and blow torch effects. Monte Carlo simulations of two Lennard-Jones binary mixtures with different-sized components are shown to be separated well if at least one of the components lies in the anomalous regime and the others lie in the linear regime. A separation factor of 10(8) is obtained on nano length scales as compared to 10(3), obtainable through conventional methods of separation on macrolength scales.

Large Distinct Diffusivity in Binary Mixtures Confined to Zeolite NaY

Mutual diffusion coefficients have been computed from molecular dynamics simulation of two different binary mixtures confined to zeolite NaY. In one of these mixtures, where one component is from the linear regime and the other from the anomalous regime of the levitation effect [S. Yashonath, P. Santikary, J. Phys. Chem., 1994, 98, 6368], the magnitude of distinct diffusivity, Dd, is unusually large and comparable to the mixture self-diffusivity Ds. Distinct van Hove correlations suggest that the large Dd seems to arise from the presence of distinct physisorption sites for the two components. The contribution from Dd might be important for achieving good separation of mixtures, for which zeolites are used extensively.

High-pressure study of adamantane: variable shape simulations up to 26 GPa

We report simulations of adamantane by carefully combining ab initio and empirical approaches to enable simulations with internal degrees of freedom on crystalline adamantane up to a pressure of 26 GPa. Two sets of simulations, assuming the adamantane molecule as a rigid (RB) and flexible body (FB), have been carried out as a function of pressure up to 26 GPa to understand changes in the crystal structure as well as molecular structure. The flexible body simulations have been performed by including 6 lowest frequency internal modes (obtained from DFT calculations performed with Gaussian98) out of the total of 72. The calculated variation in c/a and V/V(0) from the RB and FB calculations as a function of pressure have been compared with the experimental curve. Other relevant thermodynamic and structural properties reported are the radial distribution functions, deviation in the position of a given type of atom with respect to its position at standard pressure, delta(s), cell parameters, volume, and energy. With an increase in pressure, three additional peaks are seen to develop gradually at three different pressures in the center of mass (com)-com radial distribution function (rdf). We attribute these changes to structural transformations (probably second-order phase transitions) which is consistent with the three phase transitions reported by Vijayakumar et al. for adamantane in the pressure range of 1 atm-15 GPa. Our simulations also show that these additional peaks in the rdf's are associated with the differences between opposite and parallel spin neighbors of Greig and Pawley as well as the crystallographic directional dependence of intermolecular distances in the first three shells of the neighbors. Also, the structural quantities from the RB calculation show considerable deviation from the FB calculation for pressures greater than 5 GPa, which suggests that the rigid body assumption for molecules may not be valid above this pressure.

Diffusion maximum as a function of size in dense liquids

We study the diffusion of small guest particles of different sizes in a host fluid at liquid densities using molecular dynamics simulations. We observe an enhancement of the diffusivity of guest particles for a size related to the structure of the void space of the host fluid, analogous to the "levitation effect" observed for guest diffusion in porous solids. Friction and activation energy are found to be minimum for the guest size with maximum self-diffusivity. Wavelength dependent self-diffusivity indicates a monotonic and oscillatory dependence on wave number k for anomalous and linear regimes, respectively. These are associated with single and bi-exponential decay of the incoherent intermediate scattering function.

Effect of Pressure on Pedal Motion in Stilbene Molecular Crystals and Its Dependence on the Crystallographic Site

We report computer simulation of a stilbene molecular crystal as a function of pressure up to 4 GPa. Molecular structure and the crystal structure of stilbene have been characterized by calculating the radial distribution function and dihedral angle distribution, features associated with pedal motion and cell parameters. Results suggest that the population of minor conformer at site 2 disappears altogether above 1.25 GPa. In contrast, the population of minor conformer at site 1 remains at around 12%. Pedal motion is not observed beyond a pressure of 0.8 and 1.4 GPa at site 1 and site 2, respectively. Specific heat and compressibility exhibit an anomaly around 1.25 GPa. The anomaly seems to be associated with the disappearance of pedal motion at site 2. Initially, increase in pressure leads to an increase in the magnitude of lattice energy, but beyond 0.5 GPa it decreases.

Size-Dependent Maximum in Ion Conductivity: The Levitation Effect Provides an Alternative Explanation

We propose an alternative explanation of the size-dependent maximum in ion mobility in water in terms of the levitation effect, which accounts for the observed size-dependent maximum in the mobility of guest diffusion in porous media. In this explanation, the size at which the maximum occurs is related to the structure of the void space of the water; at the mobility maximum, the diffusant passes smoothly through necks connecting voids, and its potential energy shows minimum fluctuations. Molecular dynamics simulations of charged spheres of varying sizes are used to support this hypothesis. As in the levitation effect, the friction coefficient, the potential energy fluctuations, and the activation energy are found to be minima for particles with maximum self diffusivities similar to the guest diffusion in zeolites. Wavelength-dependent self diffusivities indicate a monotonic and oscillatory dependence, respectively, on wavenumber k for anomalous (AR) and linear regimes (LR). These are associated with single and biexponential decay of the incoherent intermediate scattering function.

Levitation effect: Size-dependent maximum in rotational diffusion in confined systems

Molecular dynamics of a model guest tetrahedral molecule AX(4) with differing bond lengths l(AX) for A-X bonds have been carried out in a sphere with different surface roughness. The rotational-diffusion coefficient D(R) shows a maximum for a particular value of l(AX). We show that this corresponds to the distance at which the interaction of the guest with the atoms of the host is most favorable. Although, the intensity of the maximum decreases with increase in the roughness of the confining surface, it is seen that the maximum exists even for a reasonably high degree of roughness. The observed maximum arises from the minimum in the torque on the tetrahedral molecule from its interaction with the confining medium due to mutual cancellation of forces. Activation energy for rotation is seen to be also a minimum for the bond length for which D(R) is a maximum. These results suggest that there is a maximum in the rotational-diffusion coefficient when the rotating molecule is confined to a sphere of comparable size similar to the maximum in translational diffusion coefficient seen in porous solids (the levitation effect) [Yashonath and Santikary J. Phys. Chem. 98, 6368 (1994)]. On increase in the roughness of the sphere surface, the value of l(AX) at which the maximum in D(R) is seen decreases.

The Stokes−Einstein Relationship and the Levitation Effect: Size-Dependent Diffusion Maximum in Dense Fluids and Close-Packed Disordered Solids

We report a molecular dynamics study of a binary mixture consisting of a large (host) particle and a smaller (guest) particle whose radius is varied over a range. These simulations investigate the possible existence of a diffusion anomaly or levitation effect in dense fluids, previously seen for guest molecules diffusing within porous solids. The voids in the larger component have been characterized in terms of void and neck distributions by means of Voronoi polyhedral analysis. Four different mixtures with differing ratios of guest to host diffusivities (D) have been studied. The results suggest that the diffusion anomaly is seen in both close-packed solids with disorder and dense fluids. In the latter, the void network is constantly and dynamically changing and possesses a considerable degree of disorder. The two regimes, viz., the linear regime (LR) and the anomalous regime (AR), found for porous solids are shown to exist for a dense medium as well. The linear regime is characterized by D(g) proportional to 1/sigma(gg)(2), where sigma(gg) is the diameter of the guest. The anomalous regime exhibits a maximum in D up to rather high temperatures (T = 1.663), even though in porous solids the maximum disappears at higher temperatures. In agreement with previous studies on porous solids, a particle in the AR is associated with lower activation energy, lower friction, and less backscattering in the velocity autocorrelation function when compared to a particle in the LR. Wavevector dependent self-diffusivity, Delta, and decay of the intermediate scattering function, F(s)(k, t), exhibit contrasting behaviors for the LR and AR. For LR, Delta exhibits a minimum at values of k at which there are spatial correlations in S(k) while a smooth decrease with k is seen for AR. For LR, F(s)(k, t) shows a biexponential decay corresponding to two different time scales of motion. Probably, the fast decay is associated with motion within the first shell of solvent neighbors and the slow decay with motion past these shells. For AR, a single-exponential decay is seen. The results indicate a breakdown of the Stokes-Einstein (SE) relationship. The relevant quantity that determines the validity of the SE relationship is the levitation parameter which is indirectly related to the solute/solvent radius ratio and not either the size of the solute or the solvent alone.

Levitation Effect: Distinguishing Anomalous from Linear Regime of Guests Sorbed in Zeolites through the Decay of Intermediate Scattering Function and Wavevector Dependence of Self-Diffusivity

Previous work investigating the dependence of self-diffusivity, D, on the size of the guest diffusing within the porous solid such as zeolite has reported the existence of an anomalous maximum in the diffusion coefficient (J. Phys. Chem. 1994, 98, 6368). Two distinct regimes of dependence of D on sigma(gg), diameter of the guest were reported. D proportional to 1/sigma(gg)2, often referred to as linear regime (LR), is found when sigma(gg) is smaller than sigma(v), the diameter of the void. A maximum in D has been observed when sigma(gg) is comparable to sigma(v) and this regime is referred to as anomalous regime (AR). Here we report the intermediate scattering function for a particle from LR and AR in zeolite faujasite. A particle from LR exhibits a biexponential decay while a particle from AR exhibits a single-exponential decay at small k. Variation with k of the full width at half-maximum of the self-part of the dynamic structure factor is nonmonotonic for a particle in the linear regime. In contrast, this variation is monotonic for a particle in the anomalous regime. These results can be understood in terms of the existence of energetic barrier at the bottleneck, the 12-ring window, in the path of diffusion. They provide additional signatures for the linear regime and anomalous regimes and therefore for levitation effect (LE).

Pressure-Induced Ordering in Adamantane: A Monte Carlo Simulation Study

Isothermal-isobaric ensemble Monte Carlo simulation of adamantane has been carried out with a variable shape simulation cell. The low-temperature crystalline phase and the room-temperature plastic crystalline phases have been studied employing the modified Williams potential. We show that at room temperature, the plastic crystalline phase transforms to the crystalline phase on increase in pressure. Further, we show that this is the same phase as the low-temperature ordered tetragonal phase of adamantane. The high-pressure ordered phase appears to be characterized by a slightly larger shift of the first peak toward a lower value of r in C-C, C-H, and H-H radial distribution functions as compared to the low-temperature tetragonal phase. The coexistence curve between the crystalline and plastic crystalline phase has been obtained approximately up to a pressure of 4 GPa.

Pressure Induced Orientational Ordering in p-Terphenyl

Three different interaction potentials existing in the literature along with a model proposed here have been used to model p-terphenyl under standard conditions. Of these, the model that predicts the room-temperature crystal structure well has been used to understand the behavior of p-terphenyl under pressure. Lattice parameters show good agreement with the X-ray diffraction values reported by Puschnig et al. (Puschnig, P.; Heimel, G.; Weinmeier, K.; Resel, R.; Ambrosch-Draxl, C. High Pressure Res. 2002, 22, 105). The nonplanar structure of p-terphenyl transforms to a planar structure with gradual disappearance of disorder associated with ring flipping. We show that the transformation is accompanied by a change in the potential energy profile from W-shaped to a U-shaped form, which is associated with complete planarization between 1.0 and 1.5 GPa. Our results reported here are in excellent agreement with X-ray diffraction results which also suggest the existence of a similar transition as a function of pressure in polyphenyls such as biphenyl and p-hexaphenyl. Interestingly, the amplitude of the torsional motion is largest at an intermediate pressure of 1.0 GPa. This is attributed to the rather flat potential energy landscape which occurs during the transition from W- to U-shaped potential.

Translational and rotational diffusion of SF6 in zeolite NaY

Temperature dependence of equilibrium as well as dynamical properties of SF(6) in zeolite NaY have been investigated by molecular dynamics simulation. By about 200 K, SF(6) begins to have increased mobility. Strong orientational preference is exhibited by SF(6) during its passage through the 12-ring window, the bottleneck for diffusion. The preference is for orientation with C(3) followed by C(2) and then C(4) molecular symmetry axis perpendicular to the window plane. Translational motion is diffusive with an activation energy of 5.5 kJ/mol. Rotational-diffusion coefficient has an activation energy of 2.83 kJ/mol. Rotational motion is facile within the alpha-cage. Translational motion is hindered during passage through the 12-ring window when C(4) is perpendicular to the window plane. Orientational correlation functions P(1) and P(2) around C(2), C(3) and C(4) are reported. Only the long time decay of C(4) shows oscillations. This is attributed to the hindered rotation during intercage migration while passing through the 12-ring window.

n-Pentane and isopentane in one-dimensional channels

Molecular dynamics studies of n-pentane and isopentane in one-dimensional channels of AlPO(4)-5 and a carbon nanotube are reported. Variation of the structure and energetics in AlPO(4)-5 along the channel axis of isopentane is similar to what has been found for other rigid molecular systems. In n-pentane, these properties exhibit more frequent undulations along the channel due to flexibility. The end-to-end distance of n-pentane is a function of its position along the channel in AlPO(4)-5, suggesting that n-pentane has to alternately stretch in the narrow part and destretch or coil in the broader part of the channel. n-Pentane lies flat instead of upright on the inner surface of the carbon nanotube. Both of the species exhibit diffusive motion in AlPO(4)-5, and the self-diffusivity is higher than that in bulk. Isopentane has a higher diffusivity than does n-pentane. This is attributed to the higher cross section of isopentane, which is closer to the void cross section. Further, the coupling of the translational motion with the slower dihedral angle reorientation in the case of n-pentane decreases its mobility. Superdiffusive motion is seen for both species in the carbon nanotube. These results can be understood in terms of the levitation effect.

Rotational dynamics of propane in Na-Y zeolite: a molecular dynamics and quasielastic neutron-scattering study

We report results from molecular dynamics (MD) simulations and quasielastic neutron-scattering (QENS) measurements on the rotational dynamics of propane in Na-Y zeolite at room temperature with a loading of four molecules per alpha cage. Rotational part of the intermediate scattering function F(Q,t) obtained from the MD simulation suggests that rotational motion is faster relative to the translational motion. Various rotational models fitted to the MD data suggest that rotation is isotropic. It is found that the hydrogen atoms lie, on the average, on a sphere of radius 1.88+/-0.05 A, which is also the average distance of the hydrogen atoms from the center of mass of the propane molecule. Results from QENS measurements are in excellent agreement with those obtained from MD, suggesting that the intermolecular potential employed in the MD simulation provides a realistic description of propane motion within faujasite. The rotational diffusion constant D(R) is 1.05+/-0.09 x 10(12) sec(-1) from the QENS data, which may be compared with that obtained from the MD data (0.82+/-0.05 x 10(12) sec(-1)).

Mutual diffusion in a binary Ar-Kr mixture confined within zeolite NaY

Molecular dynamics investigations of the mutual diffusion coefficients in an Ar-Kr mixture confined in the zeolite NaY are reported. Velocity auto- and cross correlations were computed at two different temperatures (200 and 600 K). The importance of the appropriate choice of reference frame while evaluating the time correlation functions is illustrated for argon in the zeolite NaY. Mutual diffusivities in the mixture were obtained in the barycentric reference frame. Recently, Zhou and Miller showed that the distinct diffusivity D(d) is zero for the Ar-Kr mixture in bulk. On confinement, it is seen that at 200 K the ratio R=D(11)/D(s)=0.77, where D11 is the mutual diffusivity and D(s) is the mixture self-diffusivity. However, at 600 K, R=0.97, implying that the contribution from distinct diffusion is only slightly negative. The large negative D(d) at 200 K could be attributed to strong localization of Ar and Kr in the physisorption sites within the zeolite cages. Analysis of error bars and an efficient computational algorithm for evaluation of the velocity cross correlation function are also presented. The results have implications in biology, chemistry, and other situations where transport of confined mixtures is encountered.

Source of reaction-diffusion coupling in confined systems due to temperature inhomogeneities

Diffusion is often accompanied by a reaction or sorption which can induce temperature inhomogeneities. Monte Carlo simulations of Lennard-Jones atoms in zeolite NaCaA are reported with a hot zone presumed to be created by a reaction. Our simulations show that localized hot regions can alter both the kinetic and transport properties. Further, enhancement of the diffusion constant is greater for larger barrier height, a surprising result of considerable significance to many chemical and biological processes. We find an unanticipated coupling between reaction and diffusion due to the presence of hot zone in addition to that which normally exists via concentration.