Towards an assessment of the accuracy of density functional theory for first principles simulations of water. II

A series of 20 ps ab initio molecular dynamics simulations of water at ambient density and temperatures ranging from 300 to 450 K are presented. Car-Parrinello (CP) and Born-Oppenheimer (BO) molecular dynamics techniques are compared for systems containing 54 and 64 water molecules. At 300 K, an excellent agreement is found between radial distribution functions (RDFs) obtained with BO and CP dynamics, provided an appropriately small value of the fictitious mass parameter is used in the CP simulation. However, we find that the diffusion coefficients computed from CP dynamics are approximately two times larger than those obtained with BO simulations for T>400 K, where statistically meaningful comparisons can be made. Overall, both BO and CP dynamics at 300 K yield overstructured RDFs and slow diffusion as compared to experiment. In order to understand these discrepancies, the effect of proton quantum motion is investigated with the use of empirical interaction potentials. We find that proton quantum effects may have a larger impact than previously thought on structure and diffusion of the liquid.     

Quantum sum formulae for the collision-induced spectroscopies: Molecular systems as H2-H2

Quantum expressions for the second moment of collision-induced spectra are developed in the low-density limit. Previous work by Moraldi is extended to account for the rotational structure of colliding linear molecules; isotropic interaction is assumed. Computations of the lowest three moments are presented for the case of infrared absorption and Raman scattering of molecular hydrogen pairs at temperatures from 77 to 300 K. The radial distribution functions of pairs, mean energy and angular momentum, which are required for that purpose, are obtained for the case of H₂ molecules interacting with H₂, and compared with their classical counterparts. The simple classical approximations with lowest-order Wigner-Kirkwood quantum corrections serve as an accurate representation of the quantum expressions at large separations and may be sufficient for massive systems at high temperatures.     

Correlations in liquid water for the TIP3P-Ewald, TIP4P-2005, TIP5P-Ewald, and SWM4-NDP models

Water is one of the simplest molecules in existence, but also one of the most important in biological and engineered systems. However, understanding the structure and dynamics of liquid water remains a major scientific challenge. Molecular dynamics simulations of liquid water were performed using the water models TIP3P-Ewald, TIP4P-2005, TIP5P-Ewald, and SWM4-NDP to calculate the radial distribution functions (RDFs), the relative angular distributions, and the excess enthalpies, entropies, and free energies. In addition, lower-order approximations to the entropy were considered, identifying the fourth-order approximation as an excellent estimate of the full entropy. The second-order and third-order approximations are ~20% larger and smaller than the true entropy, respectively. All four models perform very well in predicting the radial distribution functions, with the TIP5P-Ewald model providing the best match to the experimental data. The models also perform well in predicting the excess entropy, enthalpy, and free energy of liquid water. The TIP4P-2005 and SWM4-NDP models are more accurate than the TIP3P-Ewald and TIP5P-Ewald models in this respect. However, the relative angular distribution functions of the four water models reveal notable differences. The TIP5P-Ewald model demonstrates an increased preference for water molecules to act both as tetrahedral hydrogen bond donors and acceptors, whereas the SWM4-NDP model demonstrates an increased preference for water molecules to act as planar hydrogen bond acceptors. These differences are not uncovered by analysis of the RDFs or the commonly employed tetrahedral order parameter. However, they are expected to be very important when considering water molecules around solutes and are thus a key consideration in modelling solvent entropy.     

Structure of liquid chlorobenzene in the temperature range 293-363 K

The classical molecular dynamics method is used to simulate the structure of liquid chlorobenzene in the temperature range 293-363 K. Theradial angular distribution functions for the distances between the benzene molecular planes and the angle between them; the radial distribution functions for the distances between chlorine atoms; self-diffusion coefficients, local dipole moments, and permittivities are calculated. In the entire temperature range molecules are joined into agglomerates due to contacts between chlorine atoms (halogen aggregation) and to the specific interactions of benzene rings, which causes mainly parallel and perpendicular orientations of the rings in the first coordination sphere. The molecules in the agglomerates are mostly organized in the 1D motif: chains of chlorine atoms and stacks of benzene rings. With increasing temperature, the agglomerate structure is reorganized, with the most visible changes occurring in temperature ranges 293-298 K, 313-323 K, and 343-353 K.     

Ions in water: the microscopic structure of concentrated hydroxide solutions

Neutron-diffraction data on aqueous solutions of hydroxides, at solute concentrations ranging from 1 solute per 12 water molecules to 1 solute per 3 water molecules, are analyzed by means of a Monte Carlo simulation (empirical potential structure refinement), in order to determine the hydration shell of the OH- in the presence of the smaller alkali metal ions. It is demonstrated that the symmetry argument between H+ and OH- cannot be used, at least in the liquid phase at such high concentrations, for determining the hydroxide hydration shell. Water molecules in the hydration shell of K+ orient their dipole moment at about 45 degrees from the K+-water oxygen director, instead of radially as in the case of the Li+ and Na+ hydration shells. The K+-water oxygen radial distribution function shows a shallower first minimum compared to the other cation-water oxygen functions. The influence of the solutes on the water-water radial distribution functions is shown to have an effect on the water structure equivalent to an increase in the pressure of the water, depending on both ion concentration and ionic radius. The changes of the water structure in the presence of charged solutes and the differences among the hydration shells of the different cations are used to present a qualitative explanation of the observed cation mobility.     

Quantum effects in ice Ih

Quantum and classical simulations are carried out on ice Ih over a range of temperatures utilizing the TIP4P water model. The rigid-body centroid molecular dynamics method employed allows for the investigation of equilibrium and dynamical properties of the quantum system. The impact of quantization on the local structure, as measured by the radial and spatial distribution functions, as well as the energy is presented. The effects of quantization on the lattice vibrations, associated with the molecular translations and librations, are also reported. Comparison of quantum and classical simulation results indicates that shifts in the average potential energy are equivalent to rising the temperature about 80 K and are therefore non-negligible. The energy shifts due to quantization and the quantum mechanical uncertainties observed in ice are smaller than the values previously reported for liquid water. Additionally, we carry out a comparative study of melting in our classical and quantum simulations and show that there are significant differences between classical and quantum ice.     

A quantitative account of quantum effects in liquid water

We report converged quantum statistical mechanical simulations of liquid water with the Thole-type Model (version 2.1), Flexible, polarizable (TTM2.1-F) interaction potential for water. Simulations of total length of 600 ps with a 0.05 fs time step for a periodic unit cell of 256 molecules with up to 32 replicas per atom suggest that the quantum effects contribute 1.01+/-0.02 kcal/mol to the liquid enthalpy of formation at 298.15 K. They furthermore demonstrate for the first time a quantitative agreement with experiment for the heights and broadening of the intramolecular OH and HH peaks in the radial distribution functions.     

Structure and dynamics of methanol in water: a quantum mechanical charge field molecular dynamics study

An ab initio quantum mechanical charge field molecular dynamics simulation was carried out for one methanol molecule in water to analyze the structure and dynamics of hydrophobic and hydrophilic groups. It is found that water molecules around the methyl group form a cage-like structure whereas the hydroxyl group acts as both hydrogen bond donor and acceptor, thus forming several hydrogen bonds with water molecules. The dynamic analyses correlate well with the structural data, evaluated by means of radial distribution functions, angular distribution functions, and coordination number distributions. The overall ligand mean residence time, τ identifies the methanol molecule as structure maker. The relative dynamics data of hydrogen bonds between hydroxyl of methanol and water molecules prove the existence of both strong and weak hydrogen bonds. The results obtained from the simulation are in excellent agreement with the experimental results for dilute solution of CH(3)OH in water. The overall hydration shell of methanol consists in average of 18 water molecules out of which three are hydrogen bonded.     

A coupled density functional-molecular mechanics Monte Carlo simulation method: The water molecule in liquid water

A theoretical model to investigate chemical processes in solution is described. It is based on the use of a coupled density functional/molecular mechanics Hamiltonian. The most interesting feature of the method is that it allows a detailed study of the solute's electronic distribution and of its fluctuations. We present the results for isothermal-isobaric constant-NPT Monte Carlo simulation of a water molecule in liquid water. The quantum subsystem is described using a double-zeta quality basis set with polarization orbitals and nonlocal exchange-correlation corrections. The classical system is constituted by 128 classical TIP3P or Simple Point Charge (SPC) water molecules. The atom-atom radial distribution functions present a good agreement with the experimental curves. Differences with respect to the classical simulation are discussed. The instantaneous and the averaged polarization of the quantum molecule are also analyzed. © 1996 by John Wiley & Sons, Inc.     

The flexible, polarizable, thole-type interaction potential for water (TTM2-F) revisited

We present a revision of the flexible, polarizable, Thole-type interaction potential for water [J. Chem. Phys.2002, 116, 5115], which allows for condensed-phase simulations. The revised version (TTM2.1-F) of the potential correctly describes the individual water molecular dipole moment and alleviates problems arising at short intermolecular separations that can be sampled in the course of molecular dynamics and Monte Carlo simulations of condensed environments. Furthermore, its parallel implementation under periodic boundary conditions enables the efficient calculation of the macroscopic structural and thermodynamic properties of liquid water, as its performance scales superlinearly with up to a number of 64 processors for a simulation box of 512 molecules. We report the radial distribution functions, average energy, internal geometry, and dipole moment in the liquid as well as the density, dielectric constant, and self-diffusion coefficient at T = 300 K from (NVT) and (NPT) classical molecular dynamics simulations by using the revised version of the potential.     

Structural and dynamical properties of the Hg2+ aqua ion: a molecular dynamics study

Molecular dynamics simulations of the Hg2+ ion in aqueous solution have been carried out using an effective two-body potential derived from quantum mechanical calculations. A stable heptacoordinated structure of the Hg2+ first hydration shell has been observed and confirmed by extended X-ray absorption fine structure (EXAFS) experimental data. The structural properties of the Hg2+ hydration shells have been investigated using radial and angular distribution functions, while the dynamical behavior has been discussed in terms of reorientational correlation functions, mean residence times of water molecules in the first and second hydration shells, and self-diffusion coefficients. The effect of water-water interactions on the Hg2+ hydration properties has been evaluated using the SPC/E and TIP5P water models.     

Monte Carlo simulation of liquid hydroxylamine using ab initio intermolecular potential functions

A potential model for intermolecular interactions between hydroxylamine (NH₂OH) molecules based on ab initio quantum mechanical calculations is reviewed and critically assessed by analyzing results from a Monte Carlo simulation of liquid hydroxylamine. The liquid structure is studied in detail using radial, energy, and angular distribution functions, coordination numbers, and their distribution. Results indicate a large first solvation shell (5.3 Å), which contains 13 molecules, out of which only 4 are truly bonded by nonlinear, low-energy hydrogen bonds. These are of either the OH…O or the OH…N type, as NH…O and NH…N linear bonds are considerably suppressed, and no cyclic dimers are found. The dependence of the structural and physical properties on the simulation characteristics has also been investigated.     

液态水的分子动力学模拟

用分子动力学(MD)模拟方法在150~376K的温度范围内对液态水的微正则系统进行了研究。考察了液态水的结构及其性质。模拟采用了由从头算得出的柔性水-水相互作用势MCYL。对时间和空间的平均得出了液态中水分子几何构型及温度改变所引起的液态水结构变化。对径向分布函数gOH, gOO, gHH及配位数的分析表明, 在所考察的温度范围内, 每个水分子与相邻分子形成的氢键数为2~3, 水分子在参与的2个氢键中同时作为授受体。结合对振动谱的研究表明在低温时液态水形成的网络结构可能随温度的升高而形成小的簇结构。     

Structure and dynamics of Au+ ion in aqueous solution: ab initio QM/MM MD simulations

Structure and dynamics of hydrated Au(+) have been investigated by means of molecular dynamics simulations based on ab initio quantum mechanical molecular mechanical forces at Hartree-Fock level for the treatment of the first hydration shell. The outer region of the system was described using a newly constructed classical three-body corrected potential. The structure was evaluated in terms of radial and angular distribution functions and coordination number distributions. Water exchange processes between coordination shells and bulk indicate a very labile structure of the first hydration shell whose average coordination number of 4.7 is a mixture of 3-, 4-, 5-, 6-, and 7-coordinated species. Fast water exchange reactions between first and second hydration shell occur, and the second hydration shell is exceptionally large. Therefore, the mean residence time of water molecules in the first hydration shell (5.6 ps/7.5 ps for t*= 0.5 ps/2.0 ps) is shorter than that in the second shell (9.4 ps/21.2 ps for t*= 0.5 ps/2.0 ps), leading to a quite specific picture of a "structure-breaking" effect.     

Hydrated germanium (II): Irregular structural and dynamical properties revealed by a quantum mechanical charge field molecular dynamics study

Structural and dynamical properties of Ge (II) in aqueous solution have been investigated using the novel ab initio quantum mechanical charge field (QMCF) molecular dynamics (MD) formalism. The first and second hydration shells were treated by ab initio quantum mechanics at restricted Hartree–Fock (RHF) level using the cc‐pVDZ‐PP basis set for Ge (II) and Dunning double‐ζ plus polarization basis sets for O and H. Besides ligand exchange processes and mean ligand residence times to observe dynamics, tilt‐ and theta‐angle distributions along with an advanced structural parameter, namely radial and angular distribution functions (RAD) for different regions were also evaluated. The combined radial and angular distribution depicted through surface plot and contour map is presented to provide a detailed insight into the density distribution of water molecules around the Ge²⁺ ion. A strongly distorted hydration structure with two trigonal pyramidal substructures within the first hydration shell is observed, which demonstrates the lone‐pair influence and provides a new basis for the interpretation of the catalytic and pharmacological properties of germanium coordination compounds. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Semiempirical self-consistent polarization description of bulk water, the liquid-vapor interface, and cubic ice

We have applied an efficient electronic structure approach, the semiempirical self-consistent polarization neglect of diatomic differential overlap (SCP-NDDO) method, previously parametrized to reproduce properties of water clusters by Chang, Schenter, and Garrett [ J. Chem. Phys. 2008 , 128 , 164111 ] and now implemented in the CP2K package, to model ambient liquid water at 300 K (both the bulk and the liquid-vapor interface) and cubic ice at 15 and 250 K. The SCP-NDDO potential retains its transferability and good performance across the full range of conditions encountered in the clusters and the bulk phases of water. In particular, we obtain good results for the density, radial distribution functions, enthalpy of vaporization, self-diffusion coefficient, molecular dipole moment distribution, and hydrogen bond populations, in comparison to experimental measurements.     

Nuclear magnetic resonance chemical shifts and quadrupole couplings for different hydrogen-bonding cases occurring in liquid water: a computational study

Nuclear magnetic resonance (NMR) parameters are determined theoretically for the oxygen and hydrogen/deuterium nuclei of differently hydrogen-bonded water molecules in liquid water at 300 K. The parameters are the chemical shift, the shielding anisotropy, the asymmetry parameter of shielding, the nuclear quadrupole coupling constant, and the asymmetry parameter of the nuclear quadrupole coupling. We sample instantaneous configurations from a Car-Parrinello molecular dynamics simulation and feed nuclear coordinates into a quantum chemical program for the calculation of NMR parameters using density-functional theory with the three-parameter hybrid exchange-correlation (B3LYP) functional. In the subsequent analysis, molecules are divided into groups according to the number of hydrogen bonds they possess, and the full average NMR tensors are calculated separately for each group. The classification of the hydrogen-bonding cases is performed using a simple distance-based criterion. The analysis reveals in detail how the NMR tensors evolve as the environment changes gradually from gas to liquid upon increasing the number of hydrogen bonds to the molecule of interest. Liquid-state distributions of the instantaneous values of the NMR properties show a wide range of values for each hydrogen-bonding species with significant overlap between the different cases. Our study shows how local changes in the environment, along with classical thermal averaging, affect the NMR parameters in liquid water. For example, a broken or alternatively extra hydrogen bond induces major changes in the NMR tensors, and the effect is more pronounced for hydrogen or deuterium than for oxygen. The data sheds light on the usefulness of NMR experiments in investigating the local coordination of liquid water.