On-the-fly reconstruction of free-energy profiles using logarithmic mean-force dynamics.

Mean-force dynamics (MFD), which is a fictitious dynamics for a set of collective variables on a potential of mean-force, is a powerful algorithm to efficiently explore free-energy landscapes. Recently, we have introduced logarithmic MFD (LogMFD) (Morishita et al., Phys. Rev. E 2012, 85, 066702) which overcomes difficulties encounterd in free-energy calculations using standard approaches such as thermodynamic integration. Here, we present a guide to implementing LogMFD calculations paying attention to the practical issues in choosing the parameters in LogMFD. A primary focus is given to the effect of the parameters on the accuracy of the reconstructed free-energy profiles. A recipe for reducing the errors due to energy dissipation is presented. We also demonstrate that multidimensional free-energy landscapes can be reconstructed on-the-fly using LogMFD, which cannot be accomplished using any other free-energy calculation techniques.

Effects of conformational flexibility of alkyl chains of cations on diffusion of ions in ionic liquids.

Molecular dynamics simulations of ionic liquids [1-alkyl-3-methylimidazolium (alkyl = ethyl, butyl and hexyl), N-butylpyridinium, N-butyl-N,N,N-trimethylammonium and N-butyl-N-methylpyrrolidinium cations combined with the (CF(3)SO(2))(2)N(-) (TFSA) anion] show that the conformational flexibility of the alkyl chains in the cations is one of the important factors determining the diffusion of ions. Artificial constraint imposed on the internal rotation of alkyl chains significantly decreases the self-diffusion coefficients of cations and anions. The internal rotation of the C-N bond connecting the alkyl chain and the aromatic ring has large effects on the diffusion of ions in imidazolium and pyridinium based ionic liquids. The calculated self-diffusion coefficients of cations and anions decrease 20-40% by imposing the torsional constraint of the C-N bond. On the other hand the torsional constraint of the C-N bond does not largely change the diffusion of ions in the quaternary alkyl ammonium based ionic liquids. The conformational flexibility of the terminal C-C-C-C bond of the alkyl chains has large effects on the diffusion of ions in the quaternary alkyl ammonium based ionic liquids. The influence of the electrostatic interactions and the high density of ionic liquids on the diffusion of ions were studied. The electrostatic interactions have the paramount importance on the slow diffusion of ions in ionic liquids, while the high density of ionic liquids is also responsible for the slow diffusion. The electrostatic interactions and the high density of ionic liquids enhance the effects of the torsional constraint on the diffusion of ions, which suggests that the charge-ordering structure and small free volume originated in the strong electrostatic interactions are the causes of the significant effects of the conformational flexibility on the diffusion of ions in ionic liquids.

The electronic and structural properties of novel organomodified Si nanosheets.

We show that the properties of a new class of functional materials, silicon nanosheets modified with phenyl groups and H atoms, are highly promising for applications such as electronic devices. This novel material retains the sp(3) structure after functionalisation, resulting in a wide (direct) band gap of 1.92 eV.

Magnitude and nature of carbohydrate-aromatic interactions in fucose-phenol and fucose-indole complexes: CCSD(T) level interaction energy calculations.

The CH/π contact structures of the fucose-phenol and fucose-indole complexes and the stabilization energies by formation of the complexes (E(form)) were studied by ab initio molecular orbital calculations. The three types of interactions (CH/π and OH/π interactions and OH/O hydrogen bonds) were compared and evaluated in a single molecular system and at the same level of theory. The E(form) calculated for the most stable CH/π contact structure of the fucose-phenol complex at the CCSD(T) level (-4.9 kcal/mol) is close to that for the most stable CH/π contact structure of the fucose-benzene complex (-4.5 kcal/mol). On the other hand the most stable CH/π contact structure of the fucose-indole complex has substantially larger E(form) (-6.5 kcal/mol). The dispersion interaction is the major source of the attraction in the CH/π contact structures of the fucose-phenol and fucose-indole complexes as in the case of the fucose-benzene complex. The electrostatic interactions in the CH/π contact structures are small (less than 1.5 kcal/mol). The nature of the interactions between the nonpolar surface of the carbohydrate and aromatic rings is completely different from that of the conventional hydrogen bonds where the electrostatic interaction is the major source of the attraction. The distributed multipole analysis and DFT-SATP analysis show that the dispersion interactions in the CH/π contact structure of fucose-indole complex are substantially larger than those in the CH/π contact structures of fucose-benzene and fucose-phenol complexes. The large dispersion interactions are responsible for the large E(form) for the fucose-indole complex.

Magnitude and nature of carbohydrate-aromatic interactions: ab initio calculations of fucose-benzene complex.

The stable geometries of fucose-benzene complex and the stabilization energies by formation of the complex (E(form)) were studied by ab initio molecular orbital calculations. The benzene ring has close contact with an O-H or C-H bond of fucose in the optimized geometries (OH/pi hydrogen-bonded structures and CH/pi contact structures). The E(form) calculated for the most stable OH/pi hydrogen-bonded structure was -5.1 kcal/mol. The E(form) calculated for the most stable CH/pi contact structure was -4.5 kcal/mol, which shows that significant attraction exists between the nonpolar surface of fucose and a benzene. The E(form) is close to the interaction energies in typical hydrogen-bonded complexes. A few nearly isoenergetic CH/pi contact structures were found by the calculations, which suggests that the directionality of the carbohydrate-aromatic interaction is weak. The dispersion interaction is the major source of the attraction in the complex. The electrostatic contributions to the attraction are relatively small. Although the size of the interaction energy is not largely different from that of typical hydrogen bonds, the nature of the carbohydrate-aromatic interaction, which is sometimes denoted as a CH/pi hydrogen bond, is completely different from that of typical hydrogen bonds, which have strong directionality due to the strong electrostatic interactions.

Molecular dynamics simulations of ionic liquids: cation and anion dependence of self-diffusion coefficients of ions.

Molecular dynamics simulations of a series of ionic liquids [1-alkyl-3-methylimidazolium (alkyl = methyl, ethyl, butyl, hexyl, and octyl), 1-butylpyridinium, N-butyl-N,N,N-trimethylammonium and N-butyl-N-methylpyrrolidinium cations combined with a (CF(3)SO(2))(2)N(-) anion ([mmim][TFSA], [emim][TFSA], [bmim][TFSA], [C(6)mim][TFSA], [C(8)mim][TFSA], [bpy][TFSA], [(n-C(4)H(9))(CH(3))(3)N][TFSA], and [bmpro][TFSA]) and a 1-butyl-3-methylimidazolium combined with BF(4)(-), PF(6)(-), CF(3)CO(2)(-), CF(3)SO(3)(-), and (C(2)F(5)SO(2))(2)N(-) anions ([bmim][BF(4)], [bmim][PF(6)], [bmim][CF(3)CO(2)], [bmim][CF(3)SO(3)], and [bmim][BETA])] were carried out using the OPLS force field for ionic liquids. The force field was refined on the basis of ab initio molecular orbital calculations of isolated ions and experimental densities for four ionic liquids. The densities calculated for the 13 ionic liquids agreed with the experimental values within a 2% error. The self-diffusion coefficients calculated for the ions in the 13 ionic liquids were compared with the experimental values obtained by the NMR measurements. Although the calculated self-diffusion coefficients were about 1 order smaller than the experimental ones, the cation and anion dependence (the effects of alkyl chain length in imidazolium, cation structures, and anion species) of the experimental self-diffusion coefficients was reproduced by the simulations quite well in most cases. The translational motion of the terminal carbon atoms in the alkyl chains of the imidazolium cations on the time scale of a few nanoseconds is significantly faster than that of the atoms in the imidazolium rings and anions, which suggests that the dynamics of atoms in the polar domains of the ionic liquids is significantly different from that in the nonpolar domains. The factors determining the self-diffusion coefficients of the ions are also discussed.

Reversible structure transformation in ice nanocluster.

Water freezes to ice by cooling. Once ice is formed, the phase does not change unless heated over the melting point. This is a familiar phenomenon observed in our everyday life. Here, we demonstrate non-bulk-like behavior of nanosized ice by molecular-dynamics simulation using the TIP4P potential. Our 100 micros simulations reveal that the structure of the (H(2)O)(20) nanocluster reversibly changes and a variety of solidlike phases, such as bilayer structures composed of three pentagonal prisms, square and pentagonal ice nanotubes, and stuffed-fullerenelike (H(2)O)@(H(2)O)(19) structures, dynamically coexists even at 52% of the bulk melting point.

Efficient free energy calculation of water across lipid membranes.

An efficient free energy (FE) calculation of a water molecule to go across lipid membranes is presented. Both overlapping distribution and cavity insertion Widom methods are complementarily used. The former is useful for a dense region where water molecules are found, i.e., from the interfacial to bulk water region, while the latter works well in the low density region, i.e., the hydrocarbon region. Since both methods evaluate the excess chemical potential of water, the obtained FE profile is free from the fitting problem usually arisen when a FE difference method is used. A diphytanyl phosphatidylcholine bilayer is used for our test calculations. An excellent and fast convergence of the chemical potential is obtained when each method is applied for the appropriate region. The estimated FE barrier using the Ewald method for the electrostatic interaction is approximately 7.2 kcal/mol, which is higher than that using the interaction cutoff of 20 A by about 0.9 kcal/mol.

Enhanced hydrophobicity of fluorinated lipid bilayer: a molecular dynamics study.

A molecular dynamics simulation of a partially fluorinated phospholipid bilayer has been carried out to understand the effects of fluorination of the hydrophobic chains on the structure and water permeability across the membrane. Fluorocarbon chains typically have an all-trans conformation, showing a highly ordered structure in the membrane core compared to ordinary hydrocarbon chains. The free energy profiles of water across the bilayers were successfully estimated by a revised cavity insertion Widom method. The fluorinated bilayer showed a higher free energy barrier than an ordinary nonfluorinated lipid bilayer by about 1.2 kcal/mol, suggesting a lower water permeability of the fluorinated bilayer membrane. A cavity distribution analysis elucidated the reduced free volume in the fluorinated membrane due to the neatly packed chains, which should account for the higher free energy barrier.

Molecular dynamics study of crystallization of polymer systems confined in small nanodomains.

We study the ordering dynamics of polymer crystallization using molecular dynamics simulations, in which the polymers are confined to small nanodomains surrounded by a noncrystalline medium. Although the adsorption process and surface diffusion of polymer chains play a major role in the case of the crystalline interface, the domain interface which consists of noncrystalline medium does not have such a crystal substrate to induce the growth of a crystal layer, which may lead to different ordering dynamics. We found that existence of a noncrystalline domain interface has two opposite effects. In the case of semiflexible polymer systems, the domain interface accelerates crystallization in the initial period, whereas it suppresses crystallization in the intermediate or late period. When the rigidity of polymer chains increases, the acceleration effect of the initial crystallization induced by the domain interface is sometimes hidden by spontaneous homogeneous nucleation. These ordering behaviors can be explained by the restriction on the local chain direction near the domain surface in the crystal nucleation stage and the restriction of large orientation relaxation and coalescence in the crystal growth stage. Simulation results reveal that the confinement by the noncrystalline medium does not have a simple effect on the polymer crystallization dynamics, but has various conflicting effects combined with the time stage, the rigidity of polymer chains, and the strength of the surrounding domain interface.

Molecular dynamics simulation of swollen membrane of perfluorinated ionomer.

Molecular dynamics simulations of the swollen membrane of perfluorinated ionomer, which is composed of poly(tetrafluoroethylene) backbones and perfluosulfonic pendant side chains, have been undertaken to analyze the static and dynamic properties of the water and the side chain in the membrane. The calculations were carried out for four different water contents, 5, 10, 20 and 40 wt %, at 358.15 K and 0.1 MPa. The results are summarized as follows: (1) The sulfonic acid is the unique site to which water molecules can bind, and the other sites in the pendant side chain have no bound water even at high water concentration. (2) Sulfonic acids aggregate in the short range within 4.6-7.7 A despite the electrostatic repulsion between them. In such aggregates, a water molecule bridges two sulfonic acids. (3) Pendant side chains prefer to orient perpendicular to the hydrophilic/hydrophobic interface, and long-range correlation of side chain orientations is observed at 20 and 40 wt % water uptake membranes. (4) In a low water uptake membrane, the dynamics of water is substantially restricted due to strong attractive interactions with acidic sites. In contrast, at high water content, even the water locating near the sulfonic acid is relatively mobile. The short residence time of the bound water reveals that such water can frequently exchange position with relatively free water, which locates in the center of water cluster, in highly swollen membranes.

Molecular dynamics study of the methanol effect on the membrane morphology of perfluorosulfonic ionomers.

The membranes of a perfluorosulfonic acid polymer swollen in 10-80 wt % methanol solution were investigated to elucidate the methanol effect on their morphologies, such as size of the solvent cluster, solvent location, and polymer structure, by using isothermal-isobaric molecular dynamics simulations. In higher methanol concentrations, we found less-spherical solvent aggregation and a more spread polymer structure because of the ampholytic nature of methanol. The partial radial distribution functions between solvent oxygen and fluorocarbons, which are composed of the main chain, clearly show that methanol is located closer to the polymer matrix than water. On the other hand, water is preferentially located in the vicinity of an acidic headgroup, SO(3)(-), compared with methanol, although both have similar attractive interaction energies to the acidic group. Furthermore, we discussed solvent dynamics and hydrogen bonding between sulfonic oxygen and solvent O-H groups.

Free-energy calculation via mean-force dynamics using a logarithmic energy landscape.

A method for free-energy calculation based on mean-force dynamics (fictitious dynamics on a potential of mean force) is presented. The method utilizes a logarithmic form of free energy to enhance crossing barriers on a free-energy landscape, which results in efficient sampling of "rare" events. Invoking a conserved quantity in mean-force dynamics, free energy can be estimated on-the-fly without postprocessing. This means that an estimate of the free-energy profile can be locally made in contrast to the other methods based on mean-force dynamics such as metadynamics. The method is benchmarked against conventional methods and its high efficiency is demonstrated in the free-energy calculation for a glycine dipeptide molecule.

Molecular dynamics study of the effects of chain properties on the order formation dynamics of self-assembled monolayers of long-chain molecules.

The order formation dynamics of self-assembled monolayers (SAM) of long-chain molecules were studied using coarse-grained molecular dynamics simulations. The primary kinetic processes of surface order formation from solution are adsorption to the surface and surface diffusion. For long-chain molecules, the degrees of freedom of the chain structure and motion add various complexities to the order formation dynamics. Specifically, the strength of the chain interaction, the chain flexibility and the chain length play a significant role, and this work focused on the effects of these chain properties on the order formation dynamics. The adsorption dynamics of SAM molecules can be explained by the same theoretical framework as the polymer brush. On the other hand, the evolution of highly ordered structure is specific to SAM systems. Simulation results revealed that the development of oriented domains can be grouped into three types, isolated island growth, packing growth, and growth suppression, which depend on temperature and chain flexibility. In packing growth, oriented domains are formed gradually due to the decrease in free volume as the surface density becomes high, while the tilt of the adsorbed chain molecules does not become upright gradually as a whole. Rather, inside the oriented domains, the adsorbed chains adopt "standing" states with tilt angles almost equal to the final values, which contributes to the gradual increase in the total tilt order. The effect of chain length was also studied. In the case of semirigid chain molecules, longer-chain systems showed slightly slower growth in adsorption but faster growth in oriented domains. These simulation results reveal how chain properties influence the dynamics of oriented structure formation on surfaces.

First-principles lattice energy calculation of urea and hexamine crystals by a combination of periodic DFT and MP2 two-body interaction energy calculations.

This article proposes a new method for the accurate evaluation of the lattice energies (stabilization energies associated with the formation of crystals from isolated molecules) of molecular crystals by a combination of DFT and MP2 calculations. The interactions of well-separated molecules were evaluated by periodic DFT calculations. The interactions with neighboring molecules were evaluated by MP2-level two-body interaction energy calculations with the neighboring molecules. The sublimation energies calculated for crystals of urea and hexamine using the proposed method (21.2 and 20.0 kcal/mol, respectively) were close to the experimental values (20.9-23.6 and 17.7-18.8 kcal/mol, respectively). The lattice energies calculated for the two crystals by the proposed method are significantly different from those obtained by DFT calculations, suggesting that the dispersion contribution to the lattice energy is significant even in the crystal, where molecules are bound by hydrogen bonds. Lattice energies calculated by changing the range of the neighboring molecules show that the nearest-neighboring molecules are mainly responsible for the dispersion interactions in the crystals.

Interactions of perfluoroalkyltrifluoroborate anions with li ion and imidazolium cation: effects of perfluoroalkyl chain on motion of ions in ionic liquids.

The stabilization energies (E(form)) for the formation of the perfluoroalkyltrifluoroborate complexes with Li(+) and 1-ethyl-3-methylimidazolium cation (emim(+)) were calculated at the MP2/6-311G** level. The E(form) values calculated for the Li[BF(4)], Li[BF(3)CF(3)], Li[BF(3)C(2)F(5)], Li[BF(3)C(3)F(7)], and Li[BF(3)C(4)F(9)] complexes were -144.1, -139.3, -137.4, -136.3, and -135.4 kcal/mol, respectively. The E(form) values calculated for the [emim][BF(4)], [emim][BF(3)CF(3)], [emim][BF(3)C(2)F(5)], [emim][BF(3)C(3)F(7)], and [emim][BF(3)C(4)F(9)] complexes were -85.2, -81.2, -79.7, -79.7, and -79.2 kcal/mol, respectively. The electrostatic interactions are the major source of the attraction in the complexes, whereas the contribution of the induction interactions to the attraction is not negligible. The interactions of the perfluoroalkyltrifluoroborate anions with Li(+) and emim(+) are substantially weaker than those of the BF(4)(-) because of the weaker electrostatic interactions. The analysis of the interactions suggests that the weaker interactions between the BF(3)CF(3)(-) and emim(+) compared with those between the BF(4)(-) and emim(+) are the cause of the lower viscosity of the [emim][BF(3)CF(3)] ionic liquid compared with the [emim][BF(4)] ionic liquid. The order of experimental self-diffusion coefficients of the cations and anions in the ionic liquids is BF(4)(-) < BF(3)CF(3)(-) approximately BF(3)C(2)F(5)(-) > BF(3)C(3)F(7)(-) > BF(3)C(4)F(9)(-), which is well reproduced by the molecular dynamic simulations. The analysis of the rotational relaxation of emim(+) suggests that the translational diffusion of cations and anions is associated with the rotational diffusion of emim(+).

Mechanism of orientational isomerism of unsymmetrical guests in a heterodimeric capsule: analysis by ab initio molecular orbital calculations.

The geometries and interaction energies of the heterodimeric capsule [tetrakis(4-hydroxyhphenyl)-cavitand 1 and tetra(4-pyridyl)-cavitand 2] complexes with methyl p-acetoxybenzoate 3, methyl p-ethoxybenzeoate 4, and p-ethoxyiodobenzene 5 were studied by ab initio molecular orbital calculations. The optimized structures and charge distributions of the complexes suggest that the electrostatic interactions of oxygen atoms in the guest molecules with the hydrogen atoms of aromatic rings and methylene-bridge rim in the heterodimeric capsule stabilize the complexes. The calculated relative energies of the two orientational isomers of the complexes well reproduce the experimentally observed orientational selectivity of the guest molecules. The calculated stabilization energies for the major orientational isomers of the heterodimeric capsule (1.2) complexes with guest molecules (3, 4, and 5) are -21.6, -19.6, and -19.4 kcal/mol, respectively. Those for the minor orientational isomers are 1.5, 3.5, and 3.7 kcal/mol smaller (less negative), respectively. The magnitude of the calculated energy differences agrees well with the order of the experimental population of the major orientational isomer (3 < 4 approximately 5). The large electron correlation contributions to the attraction (-27.0 to -31.8 kcal/mol) show that the dispersion interactions are the major source of the attraction in the complexes, while the electrostatic interactions (-4.9 to -12.5 kcal/mol) are also an important source of the attraction. Although the electrostatic interactions are weaker than the dispersion interactions, the highly orientation dependent electrostatic interactions mainly determine the orientation of the unsymmetrical guest molecules in the complexes. The electrostatic interactions in the major orientational isomer are 2.6-3.9 kcal/mol larger (more negative) than those in the minor orientational isomer, while the differences of other energy terms are small (less than 1.1 kcal/mol). The interaction energies calculated for model complexes show that the CH/pi interactions are not playing important roles in controlling the orientation of the guest molecules in the complexes.

CH/pi interactions in methane clusters with polycyclic aromatic hydrocarbons.

Geometries and interaction energies for methane clusters with naphthalene and pyrene were studied. Estimated CCSD(T) interaction energies for the clusters at the basis set limit were -1.92 and -2.50 kcal mol(-1), respectively. Dispersion is mainly responsible for the attraction. Electrostatic interaction is very small. Although the benzene-methane cluster prefers a monodentate structure, in which a C-H bond of the methane points toward the benzene, the methane clusters with the polycyclic aromatic hydrocarbons do not prefer monodentate structures. In the benzene-methane cluster, the weak electrostatic interaction stabilizes the monodentate structure. On the other hand the dispersion interaction controls the orientation of methane in the naphthalene and pyrene clusters. The dispersion interactions in these clusters are significantly larger than those in the benzene-methane cluster. The methane prefers the orientation which is suitable for stabilization by dispersion. Hydrogen atoms of the methane locate above the centers of hexagonal rings of the polycyclic aromatic hydrocarbons in the stable structures. The structures have a small steric repulsion and this positions them only a short distance from the aromatic plane. The large dispersion contribution to the attraction shows that interactions between carbon atoms are mainly responsible for the attraction, and that hydrogen atoms are not important for the attraction. This shows that the interactions between the methane and polycyclic aromatic hydrocarbons are not pi-hydrogen bonds.

Enhanced sampling via strong coupling to a heat bath: relationship between Tsallis and multicanonical algorithms.

We show that Tsallis and multicanonical statistical mechanics are equivalent under specific conditions and that they describe a system strongly coupled to a heat bath. The concept of the strong coupling to a heat bath, in which energy fluctuation is larger than that in the canonical ensemble [J. Chem. Phys. 119, 7075 (2003)], plays a key role in relating Tsallis formalism to multicanonical formalism. The equivalence between these formalisms allows us to obtain an appropriate q parameter in the Tsallis algorithm to enhance the sampling in the phase space in a manner similar to the multicanonical algorithm. An enhanced sampling in the configurational space by use of the strong coupling formalism is demonstrated in a Lennard-Jones fluid.

Origin of attraction, magnitude, and directionality of interactions in benzene complexes with pyridinium cations.

Geometries and interaction energies of benzene complexes with pyridine, pyridinium, N-methylpyridinium were studied by ab initio molecular orbital calculations. Estimated CCSD(T) interaction energies of the complexes at the basis set limit were -3.04, -14.77, and -9.36 kcal/mol, respectively. The interactions in the pyridinium and N-methylpyridinium complexes should be categorized into a cation/pi interaction, because the electrostatic and induction interactions greatly contribute to the attraction. On the other hand, the interaction in the pyridine complex is a pi/pi interaction. The dispersion interaction is mainly responsible for the attraction in the benzene-pyridine complex. Short-range interactions including charge-transfer interactions are not important for the attraction in the three complexes. The most stable pyridinium complex has a T-shaped structure, in which the N-H bond points toward the benzene, while the N-methylpyridinium complex prefers a slipped-parallel structure. The benzene-pyridine complex has two nearly isoenergetic (Slipped-parallel and T-shaped) structures.