‘‘Ab initio’’ liquid water

A review of computational methods in materials science: examples from shock-wave and polymer physics

This review discusses several computational methods used on different length and time scales for the simulation of material behavior. First, the importance of physical modeling and its relation to computer simulation on multiscales is discussed. Then, computational methods used on different scales are shortly reviewed, before we focus on the molecular dynamics (MD) method. Here we survey in a tutorial-like fashion some key issues including several MD optimization techniques. Thereafter, computational examples for the capabilities of numerical simulations in materials research are discussed. We focus on recent results of shock wave simulations of a solid which are based on two different modeling approaches and we discuss their respective assets and drawbacks with a view to their application on multiscales. Then, the prospects of computer simulations on the molecular length scale using coarse-grained MD methods are covered by means of examples pertaining to complex topological polymer structures including star-polymers, biomacromolecules such as polyelectrolytes and polymers with intrinsic stiffness. This review ends by highlighting new emerging interdisciplinary applications of computational methods in the field of medical engineering where the application of concepts of polymer physics and of shock waves to biological systems holds a lot of promise for improving medical applications such as extracorporeal shock wave lithotripsy or tumor treatment.

Are there immobilized water molecules around hydrophobic groups? Aqueous solvation of methanol from first principles

Structural, dynamical, bonding, and electronic properties of water molecules around a soluted methanol molecule are studied from first principles. The results are compatible with experiments and qualitatively support the conclusions of recent classical molecular dynamics simulations concerning the controversial issue on the presence of "immobilized" water molecules around hydrophobic groups: the hydrophobic solute slightly reduces the mobility of many surrounding water molecules rather than immobilizing just the few ones which are closest to the methyl group. By generating maximally localized Wannier functions, a detailed description of the polarization effects in both solute and solvent molecules is obtained, which better elucidates the solvation process.

On the phase diagram of water with density functional theory potentials: The melting temperature of ice I(h) with the Perdew-Burke-Ernzerhof and Becke-Lee-Yang-Parr functionals

The melting temperature (T(m)) of ice I(h) was determined from constant enthalpy and pressure (NPH) Born-Oppenheimer molecular dynamics simulations to be 417+/-3 K for the Perdew-Burke-Ernzerhof and 411+/-4 K for the Becke-Lee-Yang-Parr density functionals using a coexisting ice (I(h))-liquid phase at constant pressures of P=2500 and 10,000 bar and a density rho=1 g/cm(3), respectively. This suggests that ambient condition simulations at rho=1 g/cm(3) will rather describe a supercooled state that is overstructured when compared to liquid water.

Mechanism of base-promoted dehydrochlorination of pentachloroethane: concerted or stepwise?

This paper reports a first-principles molecular dynamics simulation study of the microscopic mechanism of the base-catalyzed dehydrochlorination of pentachloroethane. So far the nature of the mechanism of this reaction is not understood: the concerted and stepwise mechanisms are under debate. By combining ab initio molecular dynamics with the method of constraints, we determine the reaction mechanism and associated free energy profile. We find that the reaction barrier is in good agreement with experimental findings and reveal that the reaction proceeds via a concerted mechanism. Our simulations provide no evidence for the presence of carbanion intermediate indicative of the stepwise pathway. This microscopic understanding will provide new implications for understanding the reduction of polyhalogenated alkanes and rational design of effective materials to treat these contaminants.

A first principles investigation of water dipole moment in a defective continuous hydrogen bond network

First principles molecular dynamics simulations of an aqueous solution salt system at finite concentration containing both Na(+) and Cl(-) ions show that a change in the distribution of the molecular dipole moment of H(2)O monomers appears when ions are present in solution. Simulations suggest a lowering of the dipole moments of the water molecules in the solvation shells of Na(+) and Cl(-) as compared to the pure water case, while the dipoles of the rest of the molecules are hardly affected. However, finer analysis in terms of the Wannier centers distribution suggests a change in the electronic structure of the water molecules even in the bulk. Also a change of the H-bond network arrangement was found and correlation between dipole and MOH parameter evidences such subtle effects, suggesting a lowering of tetrahedral order in salty solutions. All these changes can be related to observable quantities such as the infrared spectra thus allowing for a rationalization of the experimental outcome on neutral aqueous solutions.

Excited state properties of liquid water

In this paper, we give an overview of the state of the art in calculations of the electronic band structure and absorption spectra of water. After an introduction to the main theoretical and computational schemes used, we present results for the electronic and optical excitations of water. We focus mainly on liquid water, but spectroscopic properties of ice and vapor phase are also described. The applicability and the accuracy of first-principles methods are discussed, and results are critically presented.

A first principles theoretical study of vibrational spectral diffusion and hydrogen bond dynamics in aqueous ionic solutions: D2O in hydration shells of Cl(-) ions

A theoretical study of vibrational spectral diffusion and hydrogen bond dynamics in aqueous ionic solutions is presented from first principles without employing any empirical potential models. The present calculations are based on ab initio molecular dynamics for trajectory generation and wavelet analysis of the simulated trajectories for time dependent frequency calculations. Results are obtained for two different deuterated aqueous solutions: the first one is a relatively dilute solution of a single Cl(-) ion and the second one is a concentrated solution of NaCl ( approximately 3M) dissolved in liquid D(2)O. It is found that the frequencies of OD bonds in the anion hydration shell, i.e., those which are hydrogen bonded to the chloride ion, have a higher stretch frequency than those in the bulk water. Also, on average, the frequencies of hydration shell OD modes are found to increase with increase in the anion-water hydrogen bond distance. On the dynamical side, when the vibrational spectral diffusion is calculated exclusively for the hydration shell water molecules in the first solution, the dynamics reveals three time scales: a short-time relaxation ( approximately 200 fs) corresponding to the dynamics of intact ion-water hydrogen bonds, a slower relaxation ( approximately 3 ps) corresponding to the lifetimes of chloride ion-water hydrogen bonds, and another longer-time constant ( approximately 20 ps) corresponding to the escape dynamics of water from the anion hydration shell. Existence of such three time scales for hydration shell water molecules was also reported earlier for water containing a single iodide ion using classical molecular dynamics [B. Nigro et al., J. Phys. Chem. A 110, 11237 (2006)]. Hence, the present study confirms the basic results of this earlier work using a different methodology. However, when the vibrational spectral diffusion is calculated over all the OD modes, only two time scales of approximately 150 fs and approximately 2.7 ps are found without the slowest component of approximately 20 ps. This is likely because of the very small weight that the hydration shell water molecules carry to the overall spectral diffusion in the solution containing a single ion. For the concentrated solution also, the slowest component of approximately 20 ps is not found in the spectral diffusion of all water molecules because a distinct separation between the hydration shell and bulk water in terms of their stretch frequencies does not hold at this high concentration regime. The present first principles results are compared with those of the available experiments and classical simulations.

Ground-state properties of crystalline ice from periodic hartree-fock calculations and a coupled-cluster-based many-body decomposition of the correlation energy

Ground state properties of crystalline ice Ih are investigated by combining periodic Hartree-Fock calculations with a many-body expansion for the electron correlation energy using second-order many-body perturbation theory and coupled-cluster techniques. Very good agreement with experimental data can already be achieved by considering two-body correlation contributions up to the third coordination shell in crystalline ice. This hints at the possibility to accurately simulate ab initio water by using periodic Hartree-Fock calculations together with a parametrized two-body correlation potential.

Vibrational spectral diffusion and hydrogen bond dynamics in heavy water from first principles

We present a first-principles theoretical study of vibrational spectral diffusion and hydrogen bond dynamics in heavy water without using any empirical model potentials. The calculations are based on ab initio molecular dynamics simulations for trajectory generation and a time series analysis using the wavelet method for frequency calculations. It is found that, in deuterated water, although a one-to-one relation does not exist between the instantaneous frequency of an OD bond and the distance of its associated hydrogen bond, such a relation does hold on average. The dynamics of spectral diffusion is investigated by means of frequency-time correlation and spectral hole dynamics calculations. Both of these functions are found to have a short-time decay with a time scale of approximately 100 fs corresponding to dynamics of intact hydrogen bonds and a slower long-time decay with a time constant of approximately 2 ps corresponding to lifetimes of hydrogen bonds. The connection of the slower time scale to the dynamics of local structural relaxation is also discussed. The dynamics of hydrogen bond making is shown to have a rather fast time scale of approximately 100 fs; hence, it can also contribute to the short-time dynamics of spectral diffusion. A damped oscillation is also found at around 150-200 fs, which is shown to have come from underdamped intermolecular vibrations of a hydrogen-bonded water pair. Such assignments are confirmed by independent calculations of power spectra of intermolecular motion and hydrogen bond kinetics using the population correlation function formalism. The details of the time constants of frequency correlations and spectral shifts are found to depend on the frequencies of chosen OD bonds and are analyzed in terms of the dynamics of hydrogen bonds of varying strengths and also of free non-hydrogen-bonded OD groups.

An interpretation of the enhancement of the water dipole moment due to the presence of other water molecules

The dipole moment of the gas phase water monomer is 1.85 D. When solvated in bulk water, the dipole moment of an individual water molecule is observed to be enhanced to the much larger value of 2.9 +/- 0.6 D. To understand the origin of this dipole moment enhancement, the effective fragment potential (EFP) method is used to solvate an ab initio water molecule to predict the dipole moments for various cluster sizes. The dipole moment as a function of cluster size, nH 2O, is investigated [for n = 6-20 (even n), 26, 32, 41, and 50]. Localized charge distributions are used in conjunction with localized molecular orbitals to interpret the dipole moment enhancement. These calculations suggest that the enhancement of the dipole moment originates from the decrease of the angle between the dipole vectors of the lone pairs on oxygen as the number of hydrogen bonds to that oxygen increases. Thus, the decreased angle, and the consequent increase in water dipole moment, is most likely to occur in environments with a larger number of hydrogen bonds, such as the center of a cluster of water molecules.

Accelerating QM/MM free energy calculations: representing the surroundings by an updated mean charge distribution

Reliable studies of enzymatic reactions by combined quantum mechanical/molecular mechanics (QM(ai)/MM) approaches with an ab initio description of the quantum region presents a major challenge to computational chemists. The main problem is the need for very large computer time to evaluate the QM energy, which in turn makes it extremely challenging to perform proper configurational sampling. One of the most obvious options for accelerating QM/MM simulations is the use of an average solvent potential. In fact, the idea of using an average solvent potential is rather obvious and has implicitly been used in Langevin dipole/QM calculations. However, in the case of explicit solvent models the practical implementations are more challenging, and the accuracy of the averaging approach has not been validated. The present study introduces the average effect of the fluctuating solvent charges by using equivalent charge distributions, which are updated every m steps. Several models are evaluated in terms of the resulting accuracy and efficiency. The most effective model divides the system into an inner region with N explicit solvent atoms and an external region with two effective charges. Different models are considered in terms of the division of the solvent system and the update frequency. Another key element of our approach is the use of the free energy perturbation (FEP) and/or linear response approximation treatments that guarantees the evaluation of the rigorous solvation free energy. Special attention is paid to the convergence of the calculated solvation free energies and the corresponding solute polarization. The performance of the method is examined by evaluating the solvation of a water molecule and a formate ion in water and also the dipole moment of water in water solution. Remarkably, it is found that different averaging procedures eventually converge to the same value but some protocols provide optimal ways of obtaining the final QM(ai)/MM converged results. The current method can provide computational time saving of 1000 for properly converging simulations relative to calculations that evaluate the QM(ai)/MM energy every time step. A specialized version of our approach that starts with a classical FEP charging and then evaluates the free energy of moving from the classical potential to the QM/MM potential appears to be particularly effective. This approach should provide a very powerful tool for QM(ai)/MM evaluation of solvation free energies in aqueous solutions and proteins.

Polarizable interaction potential for water from coupled cluster calculations. II. Applications to dimer spectra, virial coefficients, and simulations of liquid water

The six-dimensional CC-pol interaction potential for the water dimer was used to predict properties of the dimer and of liquid water, in the latter case after being supplemented by a nonadditive potential. All the results were obtained purely from first principles, i.e., without any fitting to experimental data. Calculations of the vibration-rotation-tunneling levels of (H(2)O)(2) and (D(2)O)(2), a very sensitive test of the potential surface, gave results in good agreement with experimental high-resolution spectra. Also the virial coefficients and properties of liquid water agree well with measured values. The present model performs better than published force fields for water in a simultaneous reproduction of experimental data for dimer spectra, virials, and properties of the liquid.

The hydration of glucose: the local configurations in sugar-water hydrogen bonds

The hydration of a simple sugar is an essential model for understanding interactions between hydrophilic groups and interfacial water molecules. Here I perform first-principles molecular dynamics simulations on a glucose-water system and investigate how individual hydroxyl groups are locally hydrated. I demonstrate that the hydroxyl groups are less hydrated and more incompatible with a locally tetrahedral network of hydrogen bonds than previously thought. The results suggest that the hydroxyl groups form roughly two hydrogen bonds. Further, I find that the local hydration of the hydroxyl groups is sensitively affected by seemingly small variations in the local electronic structure and bond polarity of the groups. My findings offer insight into an atomic-level understanding of sugar-water interactions.

Quantum effects in liquid water from an ab initio-based polarizable force field

The importance of quantum effects as well as the accuracy of the ab initio-based polarizable TTM2.1-F force field in describing liquid water are quantitatively assessed by a detailed analysis of the temperature dependence of several thermodynamic and dynamical properties computed using the path-integral molecular dynamics and centroid molecular dynamics methods. The results show that quantum effects are not negligible even at relatively high temperatures, and their inclusion in simulations with the TTM2.1-F water model is necessary to achieve a more accurate description of the liquid properties. Comparison with the results reported in the literature for empirical, nonpolarizable force fields demonstrates that the effects of the nuclear quantization on the dielectric constant are dependent in part on how the electronic polarization is described in the underlying water model, while comparison with other ab initio-based force fields shows that the TTM2.1-F model provides an overall accurate description of liquid water. Analysis of the isotope effect on the dynamical properties does not display significant temperature dependence. This suggests that the contribution of quantum tunneling, which has been proposed as a possible cause for the different orientational dynamics observed for the HDO:H(2)O and HDO:D(2)O systems, appears to be small.

Quantum Wavepacket Ab Initio Molecular Dynamics: An Approach for Computing Dynamically Averaged Vibrational Spectra Including Critical Nuclear Quantum Effects

We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.

Assessment of the pairwise additive approximation and evaluation of many-body terms for water clusters

We have tested the ability of four commonly used density functionals (three of which are semilocal and one of which is nonlocal) to outperform accurate pairwise additive approximations in the prediction of binding energies for a series of water clusters ranging in size from dimer to pentamer. Comparison to results obtained with the Weizmann-1 (W1) level of wave function theory shows that while all density functionals are capable of outperforming the accurate pairwise data, the choice of basis set used is crucial to the performance of the method, and if a poor choice of basis set is made the errors obtained with density functional theory (DFT) can be larger than those obtained with the simple pairwise approximation. We have also compared the binding energies and many-body terms determined with DFT to those obtained with W1, and have found that all semilocal functionals have significant errors in the many-body components of the full interactions energy. Despite this limitation, however, we have found that, of the four functionals tested, PBE1W/MG3S is the most accurate for predicting the binding energies of the clusters.

Proton transfer 200 years after von Grotthuss: insights from ab initio simulations

In the last decade, ab initio simulations and especially Car-Parrinello molecular dynamics have significantly contributed to the improvement of our understanding of both the physical and chemical properties of water, ice, and hydrogen-bonded systems in general. At the heart of this family of in silico techniques lies the crucial idea of computing the many-body interactions by solving the electronic structure problem "on the fly" as the simulation proceeds, which circumvents the need for pre-parameterized potential models. In particular, the field of proton transfer in hydrogen-bonded networks greatly benefits from these technical advances. Here, several systems of seemingly quite different nature and of increasing complexity, such as Grotthuss diffusion in water, excited-state proton-transfer in solution, phase transitions in ice, and protonated water networks in the membrane protein bacteriorhodopsin, are discussed in the realms of a unifying viewpoint.

Simulating fluid-phase equilibria of water from first principles

Efficient Monte Carlo algorithms and a mixed-basis set electronic structure program were used to compute from first principles the vapor-liquid coexistence curve of water. A water representation based on the Becke-Lee-Yang-Parr exchange and correlation functionals yields a saturated liquid density of 900 kg/m3 at 323 K and normal boiling and critical temperatures of 350 and 550 K, respectively. An analysis of the structural and electronic properties of the saturated liquid phase shows an increase of the asymmetry of the local hydrogen-bonded structure despite the persistence of a 4-fold coordination and decreases of the molecular dipole moment and of the spread of the lowest unoccupied molecular orbital with increasing temperature.

Effective force field for liquid hydrogen fluoride from ab initio molecular dynamics simulation using the force-matching method

A recently developed force-matching method for obtaining effective force fields for condensed matter systems from ab initio molecular dynamics (MD) simulations has been applied to fit a simple nonpolarizable two-site pairwise force field for liquid hydrogen fluoride. The ab initio MD in this case was a Car-Parrinello (CP) MD simulation of 64 HF molecules at nearly ambient conditions within the Becke-Lee-Yang-Parr approximation to the electronic density functional theory. The force-matching procedure included a fit of short-ranged nonbonded forces, bonded forces, and atomic partial charges. The performance of the force-match potential was examined for the gas-phase dimer and for the liquid phase at various temperatures. The model was able to reproduce correctly the bent structure and energetics of the gas-phase dimer, while the results for the structural properties, self-diffusion, vibrational spectra, density, and thermodynamic properties of liquid HF were compared to both experiment and the CP MD simulation. The force-matching model performs well in reproducing nearly all of the liquid properties as well as the aggregation behavior at different temperatures. The model is computationally cheap and compares favorably to many more computationally expensive potential energy functions for liquid HF.

Dipolar correlations and the dielectric permittivity of water

The static dielectric properties of liquid and solid water are investigated within linear response theory in the context of ab initio molecular dynamics. Using maximally localized Wannier functions to treat the macroscopic polarization we formulate a first-principles, parameter-free, generalization of Kirkwood's phenomenological theory. Our calculated static permittivity is in good agreement with experiment. Two effects of the hydrogen bonds, i.e., a significant increase of the average local moment and a local alignment of the molecular dipoles, contribute in almost equal measure to the unusually large dielectric constant of water.

Dynamical properties of the soft sticky dipole-quadrupole-octupole water model: a molecular dynamics study

The dynamical properties of the soft sticky dipole-quadrupole-octupole (SSDQO) water model using SPC/E moments are calculated utilizing molecular dynamics simulations. This new potential for liquid water describes the water-water interactions by a Lennard-Jones term and a sticky potential, which is an approximate moment expansion with point dipole, quadrupole, and octupole moments, and reproduces radial distribution functions of pure liquid water using the moments of SPC/E [Ichiye and Tan, J. Chem. Phys. 124, 134504 (2006)]. The forces and torques of SSDQO water for the dipole-quadrupole, quadrupole-quadrupole, and dipole-octupole interactions are derived here. The simulations are carried out at 298 K in the microcanonical ensemble employing the Ewald method for the long-range dipole-dipole interactions. Here, various dynamical properties associated with translational and rotational motions of SSDQO water using the moments of SPC/E (SSDQO:SPC/E) water are compared with the results from SPC/E and also experiment. The self-diffusion coefficient of SSDQO:SPC/E water is found to be in excellent agreement with both SPC/E and experiment whereas the single particle orientational relaxation time for dipole vector is better than SPC/E water but it is somewhat smaller than experiment. The dielectric constant of SSDQO:SPC/E is essentially identical to SPC/E, and both are slightly lower than experiment. Also, molecular dynamics simulations of the SSDQO water model are found to be about twice as fast as three-site models such as SPC/E.

The Kohn-Sham density of states and band gap of water: from small clusters to liquid water

Electronic properties of water clusters (H2O)(n), with n=2, 4, 8, 10, 15, 20, and 30 molecules were investigated by sequential Monte Carlo/density-functional theory (DFT) calculations. DFT calculations were carried out over uncorrelated configurations generated by Monte Carlo simulations of liquid water with a reparametrized exchange-correlation functional that reproduces the experimental information on the electronic properties (first ionization energy and highest occupied molecular orbital-lowest unoccupied molecular orbital gap) of the water dimer. The dependence of electronic properties on the cluster size (n) shows that the density of states (DOS) of small water clusters (n>10) exhibits the same basic features that are typical of larger aggregates, such as the mixing of the 3a1 and 1b1 valence bands. When long-ranged polarization effects are taken into account by the introduction of embedding charges, the DOS associated with 3a1 orbitals is significantly enhanced. In agreement with valence-band photoelectron spectra of liquid water, the 1b1, 3a1, and 1b2 electron binding energies in water aggregates are redshifted by approximately 1 eV relative to the isolated molecule. By extrapolating the results for larger clusters the threshold energy for photoelectron emission is 9.6+/-0.15 eV (free clusters) and 10.58+/-0.10 eV (embedded clusters). Our results for the electron affinity (V0=-0.17+/-0.05 eV) and adiabatic band gap (E(G,Ad)=6.83+/-0.05 eV) of liquid water are in excellent agreement with recent information from theoretical and experimental works.

Theoretical calculations: Can Gibbs free energy for intermolecular complexes be predicted efficiently and accurately?

The theoretical study has been performed to refine the procedure for calculations of Gibbs free energy with a relative accuracy of less than 1 kcal/mol. Three benchmark intermolecular complexes are examined via several quantum-chemical methods, including the second-order Moller-Plesset perturbation (MP2), coupled cluster (CCSD(T)), and density functional (BLYP, B3LYP) theories augmented by Dunnings correlation-consistent basis sets. The effects of electron correlation, basis set size, and anharmonicity are systematically analyzed, and the results are compared with available experimental data. The results of the calculations suggest that experimental accuracy can be reached only by extrapolation of MP2 and CCSD(T) total energies to the complete basis set. The contribution of anharmonicity to the zero point energy and TDeltaSint values is fairly small. The new, economic way to reach chemical accuracy in the calculations of the thermodynamic parameters of intermolecular interactions is proposed. In addition, interaction energy (De) and free energy change (DeltaA) for considered species have been evaluated by Carr-Parrinello molecular dynamics (CPMD) simulations and static BLYP-plane wave calculations. The free energy change along the reaction paths were determined by the thermodynamic integration/"Blue Moon Ensemble" technique. Comparison between obtained values, and available experimental and conventional ab initio results has been made. We found that the accuracy of CPMD simulations is affected by several factors, including statistical uncertainty and convergence of constrained forces (TD integration), and the nature of DFT (density functional theory) functional. The results show that CPMD technique is capable of reproducing interaction and free energy with an accuracy of 1 kcal/mol and 2-3 kcal/mol respectively.