An approximate but fast method to impose flexible distance constraints in molecular dynamics simulations

A fast but approximative method to apply flexible constraints to bond lengths in molecular dynamics simulations is presented and the effects of the approximation are investigated. The method is not energy conserving, but coupling to a temperature bath results in stable simulations. The high frequencies from bond-length vibrations are successfully removed from the system while maintaining the flexibility of the bonds. As a test liquid neopentane is simulated at different pressures. Energetic and dynamic properties are not affected by the new flexible constraint simulation method.     

Free energy of liquid water from a computer simulation via cell theory

A method to calculate the free energy of water from computer simulation is presented. Based on cell theory, it approximates the potential energy surface sampled in the simulation by an anisotropic six-dimensional harmonic potential to model the three hindered translations and three hindered rotations of a single rigid water molecule. The potential is parametrized from the magnitude of the forces and torques measured in the simulation. The entropy of these six harmonic oscillators is calculated and summed with a conformational term to give the total entropy. Combining this with the simulation enthalpy yields the free energy. The six water models examined are TIP3P, SPC, TIP4P, SPC/E, TIP5P, and TIP4P-Ew. The results reproduce experiment well: free energies for all models are within 1.6 kJ mol(-1) and entropies are within 3.6 J K(-1) mol(-1). Approximately two-thirds of the entropy comes from translation, a third from rotation, and 5% from conformation. Vibrational frequencies match those in the experimental infrared spectrum and assist in their assignment. Intermolecular quantum effects are found to be small, with free energies for the classical oscillator lying 0.5-0.7 kJ mol(-1) higher than in the quantum case. Molecular displacements and vibrational and zero point energies are also calculated. Altogether, these results validate the harmonic oscillator as a quantitative model for the liquid state.     

Communication: Thermodynamics of water modeled using ab initio simulations

We regularize the potential distribution framework to calculate the excess free energy of liquid water simulated with the BLYP-D density functional. Assuming classical statistical mechanical simulations at 350 K model the liquid at 298 K, the calculated free energy is found in fair agreement with experiments, but the excess internal energy and hence also the excess entropy are not. The utility of thermodynamic characterization in understanding the role of high temperatures to mimic nuclear quantum effects and in evaluating ab initio simulations is noted.     

最小冰聚体结构单元模型及其对水性质影响的量化分析

水的一些奇特性质主要源于水分子之间存在的氢键, 但在分子尺度上的氢键结构和数据仍是目前研究和争论的焦点. 统计分析了目前文献中普遍采用的水分子和氢键结构数据, 并在此基础上应用AutoCAD图形软件模拟出(H2O)10结构的最小冰聚体结构单元(Minimum Ice Structural Unit, MISU)模型, 以及由MISU聚合而成的冰晶体三维模型. 根据MISU模型, 可以计算得到冰在0 ℃融化为水、水由0 ℃加热至100 ℃、水在100 ℃汽化为水蒸气的三相转化过程中分别需要吸收5.86, 4.40和24.94 kJ•mol－1的能量以断裂16.7%, 12.5%和70.8%的氢键. 如若不考虑氢键的影响, 那么计算得到水的融化热和汽化热分别为0.15和15.73 kJ•mol－1, 与VIA族氢化物H2S, H2Se, H2Te的融化热和汽化热基本呈线性关系. 另外, 由MISU模型计算得到冰在0 ℃融化为水时, 密度由923.17 kg•m－3增至999.89 kg•m－3, 亦与实际测量数据基本一致.     

Ejection of solvated ions from electrosprayed methanol/water nanodroplets studied by molecular dynamics simulations

The ejection of solvated small ions from nanometer-sized droplets plays a central role during electrospray ionization (ESI). Molecular dynamics (MD) simulations can provide insights into the nanodroplet behavior. Earlier MD studies have largely focused on aqueous systems, whereas most practical ESI applications involve the use of organic cosolvents. We conduct simulations on mixed water/methanol droplets that carry excess NH(4)(+) ions. Methanol is found to compromise the H-bonding network, resulting in greatly increased rates of ion ejection and solvent evaporation. Considerable differences in the water and methanol escape rates cause time-dependent changes in droplet composition. Segregation occurs at low methanol concentration, such that layered droplets with a methanol-enriched periphery are formed. This phenomenon will enhance the partitioning of analyte molecules, with possible implications for their ESI efficiencies. Solvated ions are ejected from the tip of surface protrusions. Solvent bridging prior to ion secession is more extensive for methanol/water droplets than for purely aqueous systems. The ejection of solvated NH(4)(+) is visualized as diffusion-mediated escape from a metastable basin. The process involves thermally activated crossing of a ~30 kJ mol(-1) free energy barrier, in close agreement with the predictions of the classical ion evaporation model.     

Multiple free energies from a single simulation: extending enveloping distribution sampling to nonoverlapping phase-space distributions

A recently proposed method to obtain free energy differences for multiple end states from a single simulation of a reference state which was called enveloping distribution sampling (EDS) [J. Chem. Phys. 126, 184110 (2007)] is expanded to situations where the end state configuration space densities do not show overlap. It uses a reference state Hamiltonian suggested by Han in 1992 [Phys. Lett. A 165, 28 (1992)] in a molecular dynamics implementation. The method allows us to calculate multiple free energy differences "on the fly" from a single molecular dynamics simulation. The influence of the parameters on the accuracy and precision of the obtained free energy differences is investigated. A connection is established between the presented method and the Bennett acceptance ratio method. The method is applied to four two-state test systems (dipole inversion, van der Waals perturbation, charge inversion, and water to methanol conversion) and two multiple-state test systems [dipole inversion with five charging states and five (dis-)appearing water molecules]. Accurate results could be obtained for all test applications if the parameters of the reference state Hamiltonian were optimized according to a given algorithm. The deviations from the exact result or from an independent calculation were at most 0.6 kJ/mol. An accurate estimation of the free energy difference is always possible, independent of how different the end states are. However, the convergence times of the free energy differences are longer in cases where the end state configuration space densities do not show overlap [charge inversion, water to methanol conversion, (dis-)appearing water molecules] than in cases where the configuration space densities do show some overlap [(multiple) dipole inversion and van der Waals perturbation].     

The inelastic hard dimer gas: a nonspherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution alpha<1, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting nonequilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalize to inelastic systems a recently method introduced [G. Ciccotti and G. Kalibaeva, J. Stat. Phys. 115, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres held together by rigid bonds. Each dimer consists of two hard disks of diameter d, whose centers are separated by a fixed distance a. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event-driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law t(-2), describing how the kinetic energy of an inelastic hard-sphere system with a constant coefficient of restitution decreases in time, holds even in the case of these nonspherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.     

Structure and dynamics of 1,2-dimethoxyethane and 1,2-dimethoxypropane in aqueous and non-aqueous solutions: a molecular dynamics study

Herein, we report a comparative modelling study of 1,2-dimethoxyethane (DME) and 1,2-dimethoxypropane (DMP) at 298 K and 318 K in the liquid state, water mixtures, and at infinite dilution condition in water, methanol, carbon tetrachloride, and n-heptane. Both DME and DMP are united-atom models compatible with GROMOS∕OPLS force fields. Calculated thermodynamic and structural properties of the pure DME and DMP liquids resulted in excellent agreement with the experimental data. In aqueous solutions, densities, diffusion coefficients, and concentration dependent conformers of DME, were in agreement with experimental data. The calculated free energy of solvation (ΔG(hyd)) at 298 K is equal to -22.1 ± 0.8 kJ mol(-1) in good agreement with the experimental value of 20.2 kJ mol(-1). In addition, the free energy of solvation of DME in non-aqueous solvents follows the trend methanol ≈ water < carbon tetrachloride < n-heptane, consistently with the dielectric constant of the solvents. On contrary, the presence of an extra methyl group on chiral carbon makes DMP less soluble than DME in water (ΔG(hyd) = -16.0 ± 1.1 kJ mol(-1)) but more soluble in non-polar solvents as n-heptane. Finally, for the DMP the chiral discrimination of the two enantiomers was calculated as solvation free energy difference of one DMP isomer in the solution of the other. The obtained value of ΔΔG(RS) = -3.7 ± 1.4 kJ mol(-1) indicates a net chiral discrimination of the two enantiomers.     

Comparison of rigid and flexible simple point charge water models at supercritical conditions

This study investigates the differences between the predictions of various properties of rigid and flexible simple point charge water models at supercritical conditions. Molecular dynamics simulations were conducted for supercritical water in a temperature range of 773–1073 K and densities in the range 115–659 kg/m³. We present thermodynamic data, pair correlation functions, self-diffusivity, power spectra, dielectric constants, and variaous measures of hydrogen bonding at different state conditions. The flexible water model performs better in predicting the pressures along the supercritical isotherms simulated. Agreement between experimental and calculated dielectric constants is superior for the flexible water model, particularly at high densities. The flexible model exhibits a greater degree of hydrogen bonding and more persistent hydrogen bonds than does the rigid model. The structural features of supercritical water at high densities are identical for the two water models. At low densities, however, the flexible potential exhibits pair correlation functions with enhanced peaks. Inclusion of flexibility in the potential model does not result in a significant shift in the position of the rotational/librational peak in the power spectrum. The self-diffusivities obtained from the simulations are within the accuracy of the experimental values for both the rigid and flexible models. On balance the inclusion of flexibility improves agreement with the properties of real supercritical water while incurring little or no additional computational burden. © 1996 by John Wiley & Sons, Inc.     

Effect of attractions on the structure of polymer solutions confined between surfaces: a density functional approach

A density functional theory is presented to study the effect of attractions on the structure of polymer solutions confined between surfaces. The polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres, both having Yukawa-type attractions and the mixture being confined between attractive Yukawa-type surfaces. The present theory treats the ideal gas free energy functional exactly and uses weighted density approximation for the hard chain and hard sphere contributions to the excess free energy functional. The attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions on the density profiles of the polymer and the solvent molecules are found to agree quite well with the Monte Carlo simulation results for varying densities, chain lengths, wall separations, and different sets of interaction potentials.     

Elastic Properties of Semi-Flexible Chains and Networks

Summary: Elastic properties of noncharged polymers of stiffness ranging from flexible to rigid chains are determined from Monte Carlo simulations. The discrete wormlike chain (WLC) model with self-interacting units is applied to chains of intermediate lengths. Elastic free energy and the force-extension profiles of chains of variable stiffness are computed in an isometric ensemble. Occurrence of a plateau on the force-extension curves at intermediate chain stiffness is noted. Qualitative differences are found between force profiles from simulations and from the standard (ideal) WLC model. The single-chain data on influence of bending stiffness were employed in the three-chain model of networks. Stress-strain relations for networks show a highly nonlinear behavior with the marked strain-stiffening effect.     

First principles and classical molecular dynamics simulations of solvated benzene

We have performed extensive ab initio and classical molecular dynamics (MD) simulations of benzene in water in order to examine the unique solvation structures that are formed. Qualitative differences between classical and ab initio MD simulations are found and the importance of various technical simulation parameters is examined. Our comparison indicates that nonpolarizable classical models are not capable of describing the solute-water interface correctly if local interactions become energetically comparable to water hydrogen bonds. In addition, a comparison is made between a rigid water model and fully flexible water within ab initio MD simulations which shows that both models agree qualitatively for this challenging system.     

Liquid structures of water, methanol, and hydrogen fluoride at ambient conditions from first principles molecular dynamics simulations with a dispersion corrected density functional

Using first principles molecular dynamics simulations in the isobaric-isothermal ensemble (T = 300 K, p = 1 atm) with the Becke-Lee-Yang-Parr exchange/correlation functional and a dispersion correction due to Grimme, the hydrogen bonding networks of pure liquid water, methanol, and hydrogen fluoride are probed. Although an accurate density is found for water with this level of electronic structure theory, the average liquid densities for both hydrogen fluoride and methanol are overpredicted by 50 and 25%, respectively. The radial distribution functions indicate somewhat overstructured liquid phases for all three compounds. The number of hydrogen bonds per molecule in water is about twice as high as for methanol and hydrogen fluoride, though the ratio of cohesive energy over number of hydrogen bonds is lower for water. An analysis of the hydrogen-bonded aggregates revealed the presence of mostly linear chains in both hydrogen fluoride and methanol, with a few stable rings and chains spanning the simulation box in the case of hydrogen fluoride. Only an extremely small fraction of smaller clusters was found for water, indicating that its hydrogen bond network is significantly more extensive. A special form of water with on average about two hydrogen bonds per molecule yields a hydrogen-bonding environment significantly different from the other two compounds.     

Thermodynamics of solutions of methanol and solvating components

A model is proposed to correlate the excess Gibbs free energies and excess enthalpies of binary solutions of methanol and a solvating component. Solution nonideality from ideal solutions is given by the sum of the chemical contribution term, which is due to self-association of methanol and solvation between methanol and a nonassociating component, and the physical contribution term with allowance for the NRTL equation. The model uses the following data for methanol: two enthalpies for formation of the hydrogen bonds for the dimer and all larger polymeric species, three equilibrium constants of stepwise association for the dimer, trimer and other polymeric species, and an equilibrium constant for cyclic species of more than tetramer. The association model further includes an additional solvation equilibrium to allow for the interaction between the terminal hydroxyl group of methanol polymeric species and a solvating component. The model is extended to predict vapor—liquid equilibria, liquid—liquid equilibria and excess enthalpies for ternary solutions containing methanol and two nonassociating components from only binary information. Calculated results are in good agreement with experimental data as shown by selected illustrative examples.     

Probing the configurational space of a metalloprotein core: an ab initio molecular dynamics study of Duo Ferro 1 binuclear Zn cofactor

We present three theoretical models of various degree of completeness to explore the chemical phase space available to the Glu4His2Zn2 cofactor found in the four-helix bundle of de novo designed metalloprotein Duo Ferro 1. We have found that the planewave DFT geometry optimization of 94-atom Model I, which contains both the protein scaffold constraints as well as the second shell hydrogen bonding network, reproduces the crystal structure bonding with remarkable accuracy (0.34 A). Surprisingly, the geometry optimization of 66-atom Model II (lacking the second shell hydrogen bonding) and 48-atom Model III (being also free of the protein scaffold constraints) still result in the fidelity with the crystallographic structure (RMSDs 0.29 and 0.34 A, respectively). To examine whether these structures are close to the global minimum as well as to investigate various conformational transitions to which the di-Zn cofactor may be susceptible to, we have carried out a 10 ps Car-Parrinello Molecular Dynamics (CPMD) simulation of Model III. We suggest that weak hydrogen bonds between imidazole hydrogens and carboxylate oxygens modulate the dynamical behavior of the system. One part of the molecule was found to be rigid due to the particular H(imidazole)-O(carboxylate) interaction restricting both the motion of the imidazole ring as well as the terminal carboxylate conformational mobility. The second half of the system was very flexible demonstrating a coupling of a transient formation of H(imidazole)-O(carboxylate) bonds with the spinning of the imidazole ring and syn-anti isomerization of the terminal carboxylate group. In addition, two low-energy snapshots from the 10 ps CPMD run were quenched, and their geometries were optimized, leading to two new isomers 48 kJ/mol lower in energy than the one associated with the crystal structure. We suggest that periodic quenching of the CPMD simulation snapshots of a minimalist model may be used as an efficient method to generate a large number of competitive local minima, which may be consequently pruned by imposing the protein scaffold constraints as well as further tuned by the second shell hydrogen bonding network.     

Constraint dynamics algorithm for simulation of semiflexible macromolecules

Semiflexible models are often used to study macromolecules containing stable structural elements. Based on rigid body dynamics, we developed a rigid fragment constraint dynamics algorithm for the simulation of semiflexible macromolecules. Stable structural elements are treated as rigid fragments. Rigid fragment constraints, defined as combinations of distance constraints and position constraints, are introduced to limit internal molecular motion to the required mode. The constraint forces are solved separately for each rigid fragment constraint and iteratively until all constraint conditions are satisfied within a given tolerance at each time step, as is done for the bond length constraint in the SHAKE algorithm. The orientation of a rigid fragment is represented by the quaternion parameters, and both translation and rotation are solved by the leap-frog formulation. We tested the algorithm with molecular dynamics simulations of a series of peptides and a small protein. The computation cost for the constraints is roughly proportional to the size of the molecule. In the microcanonical ensemble simulation of polyvalines, the total energy was conserved satisfactorily with time steps as large as 20 fs. A helix folding simulation of a synthetic peptide was carried out to show the efficiency of the algorithm in a conformational search. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1555–1566, 1998     

Treatment of dilute clusters of methanol and water by ab initio quantum mechanical calculations

Large molecular clusters can be considered as intermediate states between gas and condensed phases, and information about them can help us understand condensed phases. In this paper, ab initio quantum mechanical methods have been used to examine clusters formed of methanol and water molecules. The main goal was to obtain information about the intermolecular interactions and the structure of methanol/water clusters at the molecular level. The large clusters (CH(4)O...(H(2)O)(12) and H(2)O...(CH(4)O)(10)) containing one molecule of one component (methanol or water) and many (12, 10) molecules of the other component were considered. M?ller-Plesset perturbation theory (MP2) was used in the calculations. Several representative cluster geometries were optimized, and nearest-neighbor interaction energies were calculated for the geometries obtained in the first step. The results of the calculations were compared to the available experimental information regarding the liquid methanol/water mixtures and to the molecular dynamics and Monte Carlo simulations, and good agreement was found. For the CH(4)O...(H(2)O)(12) cluster, it was shown that the molecules of water can be subdivided into two classes: (i) H bonded to the central methanol molecule and (ii) not H bonded to the central methanol molecule. As expected, these two classes exhibited striking energy differences. Although they are located almost the same distance from the carbon atom of the central methanol molecule, they possess very different intermolecular interaction energies with the central molecule. The H bonding constitutes a dominant factor in the hydration of methanol in dilute aqueous solutions. For the H(2)O...(CH(4)O)(10) cluster, it was shown that the central molecule of water has almost three H bonds with the methanol molecules; this result differs from those in the literature that concluded that the average number of H bonds between a central water molecule and methanol molecules in dilute solutions of water in methanol is about two, with the water molecules being incorporated into the chains of methanol. In contrast, the present predictions revealed that the central water molecule is not incorporated into a chain of methanol molecules, but it can be the center of several (2-3) chains of methanol molecules. The molecules of methanol, which are not H bonded to the central water molecule, have characteristics similar to those of the methane molecules around a central water molecule in the H(2)O...(CH(4))(10) cluster. The ab initio quantum mechanical methods employed in this paper have provided detailed information about the H bonds in the clusters investigated. In particular, they provided full information about two types of H bonds between water and methanol molecules (in which the water or the methanol molecule is the proton donor), including information about their energies and lengths. The average numbers of the two types of H bonds in the CH(4)O...(H(2)O)(12) and H(2)O...(CH(4)O)(10) clusters have been calculated. Such information could hardly be obtained with the simulation methods.     

Oxidation of methanol by FeO2+ in water: DFT calculations in the gas phase and ab initio MD simulations in water solution

We investigate the mechanism of methanol oxidation to formaldehyde by ironoxido ([Fe(IV)O]2+), the alleged active intermediate in the Fenton reaction. The most likely reaction mechanisms are explored with density functional theory (DFT) calculations on microsolvated clusters in the gas phase and, for a selected set of mechanisms, with constrained Car-Parrinello molecular dynamics (CPMD) simulations in water solution. Helmholtz free energy differences are calculated using thermodynamic integration in a simulation box with 31 water molecules at 300 K. The mechanism of the reaction is investigated with an emphasis on whether FeO2+ attacks methanol at a C-H bond or at the O-H bond. We conclude that the most likely mechanism is attack by the oxido oxygen at the C-H bond ("direct CH mechanism"). We calculate an upper bound for the reaction Helmholtz free energy barrier in solution of 50 kJ/mol for the C-H hydrogen transfer, after which transfer of the O-H hydrogen proceeds spontaneously. An alternative mechanism, starting with coordination of methanol directly to Fe ("coordination OH mechanism"), cannot be ruled out, as it involves a reaction Helmholtz free energy barrier in solution of 44 +/- 10 kJ/mol. However, this coordination mechanism has the disadvantage of requiring a prior ligand substitution reaction, to replace a water ligand by methanol. Because of the strong acidity of [FeO(H2O)5]2+, we also investigate the effect of deprotonation of a first-shell water molecule. However, this is found to increase the barriers for all mechanisms.     

SHAKE,rattle, and roll: Efficient constraint algorithms for linked rigid bodies

We present an iterative constraint algorithm, QSHAKE, for use with semirigid molecules in molecular dynamics simulations. The algorithm is based on “SHAKE-ing” bond constraints between rigid bodies, whose equations of motion are solved in the quaternion framework. The algorithm is derived and its performance compared with SHAKE for liquid octane. QSHAKE is significantly more efficient whenever SHAKE requires triangles (or tetrahedra) of constraints to maintain molecular shape. Efficiencies are gained because QSHAKE reduces the number of holonomic constraints that must be solved iteratively and requires fewer iterations to obtain convergence. The gains in efficiency are most noticeable when a high degree of precision is imposed on the constraint criteria. QSHAKE is also stable at larger time steps than SHAKE, thus allowing for even more efficient exploration of phase space for semirigid molecules. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 102–111, 1998