Proton momentum distribution in water: an open path integral molecular dynamics study

Recent neutron Compton scattering experiments have detected the proton momentum distribution in water. The theoretical calculation of this property can be carried out via "open" path integral expressions. In this work, present an extension of the staging path integral molecular dynamics method, which is then employed to calculate the proton momentum distributions of water in the solid, liquid, and supercritical phases. We utilize a flexible, single point charge empirical force field to model the system's interactions. The calculated momentum distributions depict both agreement and discrepancies with experiment. The differences may be explained by the deviation of the force field from the true interactions. These distributions provide an abundance of information about the environment and interactions surrounding the proton.     

Efficient stochastic thermostatting of path integral molecular dynamics

The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.     

Atomic and molecular quantum mechanics by the path integral molecular dynamics method

The quantum path integral molecular dynamics method was applied to studies of excess electron localization by a Na⁺ ion and by a NaCl molecule. Spatial and energetic characterization of the ground state of the excess electron compare favorably with results of model potential calculations for Na and with SCF Cl calculations for NaCl⁻.     

Accelerating the convergence of path integral dynamics with a generalized Langevin equation

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.     

Proton transport in triflic acid pentahydrate studied via ab initio path integral molecular dynamics

Trifluoromethanesulfonic acid hydrates provide a well-defined system to study proton dissociation and transport in perfluorosulfonic acid membranes, typically used as the electrolyte in hydrogen fuel cells, in the limit of minimal water. The triflic acid pentahydrate crystal (CF(3)SO(3)H·5H(2)O) is sufficiently aqueous that it contains an extended three-dimensional water network. Despite it being extended, however, long-range proton transport along the network is structurally unfavorable and would require considerable rearrangement. Nevertheless, the triflic acid pentahydrate crystal system can provide a clear picture of the preferred locations of local protonic defects in the water network, which provides insights about related structures in the disordered, low-hydration environment of perfluorosulfonic acid membranes. Ab initio molecular dynamics simulations reveal that the proton defect is most likely to transfer to the closest water that has the expected presolvation and only contains water in its first solvation shell. Unlike the tetrahydrate of triflic acid (CF(3)SO(3)H·4H(2)O), there is no evidence of the proton preferentially transferring to a water molecule bridging two of the sulfonate groups. However, this could be an artifact of the crystal structure since the only such water molecule is separated from the proton by long O-O distances. Hydrogen bonding criteria, using the two-dimensional potential of mean force, are extracted. Radial distribution functions, free energy profiles, radii of gyration, and the root-mean-square displacement computed from ab initio path integral molecular dynamics simulations reveal that quantum effects do significantly extend the size of the protonic defect and increase the frequency of proton transfer events by nearly 15%. The calculated IR spectra confirm that the dominant protonic defect mostly exists as an Eigen cation but contains some Zundel ion characteristics. Chain lengths and ring sizes determined from the hydrogen bond network, counted using graph theory techniques, are only moderately sensitive to quantum effects. Deliberately introducing a structural defect into the native crystal yields a protonic defect with one hydrogen bond to a sulfonate group that was found to be metastable for at least 10 ps.     

Ab initio centroid path integral molecular dynamics: application to vibrational dynamics of diatomic molecular systems

An ab initio centroid molecular dynamics (CMD) method is developed by combining the CMD method with the ab initio molecular orbital method. The ab initio CMD method is applied to vibrational dynamics of diatomic molecules, H2 and HF. For the H2 molecule, the temperature dependence of the peak frequency of the vibrational spectral density is investigated. The results are compared with those obtained by the ab initio classical molecular dynamics method and exact quantum mechanical treatment. It is shown that the vibrational frequency obtained from the ab initio CMD approaches the exact first excitation frequency as the temperature lowers. For the HF molecule, the position autocorrelation function is also analyzed in detail. The present CMD method is shown to well reproduce the exact quantum result for the information on the vibrational properties of the system.     

Car-Parrinello and path integral molecular dynamics study of the hydrogen bond in the chloroacetic acid dimer system

We have studied the double proton transfer (DPT) reaction in the cyclic dimer of chloroacetic acid using both classical and path integral Car-Parrinello molecular dynamics. We also attempt to quantify the errors in the potential energy surface that arise from the use of a pure density functional. In the classical dynamics a clear reaction mechanism can be identified, where asynchronized DPT arises due to coupling between the O-H stretching oscillator and several low energy intermolecular vibrational modes. This mechanism is considerably altered when quantum tunneling is permitted in the simulation. The introduction of path integrals leads to considerable changes in the thermally averaged molecular geometry, leading to shorter and more centered hydrogen bond linkages.     

Accuracy and convergence of higher order distorted wave perturbation theory

A distorted wave perturbation theory which allows for a different distortion potential for each channel is investigated. The method is closely related to a perturbative solution of close coupled equations. Improvement in first order is found. However, higher order terms are not significantly improved over other computationally more convenient approaches. For purposes of comparison, numerical results are given for the oscillator atom collinear collision. The convergence of series solutions is studied as a function of scattering parameters. The accuracy of several approximation schemes is also investigated.     

Isotope effect of proton and deuteron adsorption site on zeolite-templated carbon using path integral molecular dynamics

To analyze the proton/deuteron (H/D) isotope effect on the stable adsorption sites on zeolite-templated carbon (ZTC), we have performed path integral molecular dynamics simulations including thermal and nuclear quantum effects with the semi-empirical PM3 potential at 300?K. Here, for the adsorption sites of additional proton (H*) and deuteron (D*), we chose different five carbon atoms labeled as ??-, ??₁-, ??₂-, ??-, and ??-carbons from edge to bottom for inside of buckybowl (C₃₆H₁₂ and C₃₆D₁₂). The stable adsorption sites of D* are observed on all carbon atoms, while those of H* are not observed on ??-carbon atom, but only on ??-, ??₁-, ??₂-, and ??-carbon atoms. This result is explained by the fact that H* can easily go over the barrier height for hydrogen transferring from ??- to ??₂-carbons at 300?K, since the zero-point energy of H* is greater than that of D*.     

Effects of higher order Jahn-Teller coupling on the nuclear dynamics

In this paper effects of higher order Jahn-Teller coupling terms on the nonadiabatic dynamics are studied. Of particular interest is the case when the potential energy surfaces of the degenerate state show pronounced anharmonicity. In order to demonstrate the effects a two-dimensional E multiply sign in circle e Jahn-Teller model system is treated which is based on the e(') stretching vibration of the photoactive (2)E(') state of NO(3) as a realistic example. The sixth order E multiply sign in circle e Jahn-Teller Hamiltonian is derived in the diabatic representation which is valid for any system with a C(3) rotation axis. This diabatization scheme is compared to lower-order Jahn-Teller Hamiltonians and to symmetry adapted as well as ad hoc approximations. Lower-order potentials result in pronounced quantitative and qualitative differences in the dynamics, including differences in the evolution of mean values, the autocorrelation functions (and thus the corresponding spectra), and the electronic population evolution. In the particular example treated, the results of fourth and fifth order potentials are very similar to the sixth order reference system. In contrast, the approximate sixth order Hamiltonians, though the corresponding adiabatic surfaces seem to be nearly identical, results in pronounced differences. The possible consequences for the dynamics of realistic systems with higher dimensionality are briefly discussed.     

Direct assessment of quantum nuclear effects on hydrogen bond strength by constrained-centroid ab initio path integral molecular dynamics

The impact of quantum nuclear effects on hydrogen (H-) bond strength has been inferred in earlier work from bond lengths obtained from path integral molecular dynamics (PIMD) simulations. To obtain a direct quantitative assessment of such effects, we use constrained-centroid PIMD simulations to calculate the free energy changes upon breaking the H-bonds in dimers of HF and water. Comparing ab initio simulations performed using PIMD and classical nucleus molecular dynamics (MD), we find smaller dissociation free energies with the PIMD method. Specifically, at 50 K, the H-bond in (HF)(2) is about 30% weaker when quantum nuclear effects are included, while that in (H(2)O)(2) is about 15% weaker. In a complementary set of simulations, we compare unconstrained PIMD and classical nucleus MD simulations to assess the influence of quantum nuclei on the structures of these systems. We find increased heavy atom distances, indicating weakening of the H-bond consistent with that observed by direct calculation of the free energies of dissociation.     

Application of accelerated molecular dynamics schemes to the production of amorphous silicon

The evolving nature of a Stillinger-Weber modeled silicon glass is studied using two accelerated molecular dynamics scheme, specifically, hyperdynamics and self-guided algorithms due to Voter and due to Wu and Wang, respectively. We obtain an acceleration of the dynamics, a "boost," on the order of 20 without incurring any significant computational overhead. The validity of the results using accelerated methods is provided by comparison to a conventional molecular dynamics (MD) algorithm simulated under constant temperature conditions for more than 100 ns. We found that performing a sensitivity analysis of the effect of the parameters lambda and t1 before applying the self-guided MD scheme was important. Values of lambda greater than 0.1 and t1 equal to 1 ps were found to give improved structural evolution as compared to a conventional MD scheme. The hyperdynamics approximation scheme was found to be effective in obtaining boosts in the range of 4-12 for a small system without changing the dynamics of the evolution. However, for a large system size such an approach introduces significant perturbations to the pertinent equations of motion.     

HD isotope effect on the dihydrogen bond of NH+4...BeH2 by ab initio path integral molecular dynamics simulation

In order to investigate the HD isotope effect on a dihydrogen bonded cation system, we have studied NH+4...BeH2 and its isotopomers by ab initio path integral molecular dynamics. It is found that the dihydrogen bond can be exchanged by NH+(4) rotation. The deuterated isotopomer (ND+(4)...BeD(2); DD) can exchange the dihydrogen bond more easily than other isotopomers such as (NH+4...BeH2; HH). This unusual isotope effect is ascribed to the "quantum localization" which occurs when the effective energy barrier for the rotational mode becomes higher by the zero point energy of other modes. We also found that the binding energy of dihydrogen bonds for DD species is the smallest among the isotopomers.     

Improving the performance of molecular dynamics simulations on parallel clusters

In this article a procedure is derived to obtain a performance gain for molecular dynamics (MD) simulations on existing parallel clusters. Parallel clusters use a wide array of interconnection technologies to connect multiple processors together, often at different speeds, such as multiple processor computers and networking. It is demonstrated how to configure existing programs for MD simulations to efficiently handle collective communication on parallel clusters with processor interconnections of different speeds.     

Characterization of the solvation dynamics of an ionic liquid via molecular dynamics simulation

The solvation dynamics of ionic liquids have been the subject of intense experimental study but remain poorly understood. We present the results of molecular dynamics simulations of the solvation dynamics of the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate in response to photoexcitation of the fluorescent dye coumarin-153. We reproduce the time-resolved fluorescence Stokes shift using linear response theory, then use novel statistical techniques to analyze cation and anion contributions to the signal. We find that the solvation dynamics are dominated by collective ionic motion and characterize the time scale for various features of the collective response. Further, we use the Steele analysis [Mol. Phys. 61, 1031 (1987)] to characterize the contributions to the observed Stokes shift made by translational and rovibrational degrees of freedom. Our results indicate that in contrast to molecular liquids, the rovibrational response is trivial and the observed fluorescence response arises almost entirely from ionic translation. Our results resolve previously open questions in the literature about the nature of the rapid dynamics in room-temperature ionic liquids and offer insight into the physical principles governing ionic liquid behavior on longer time scales.     

Ab initio molecular dynamics studies of tetrasulfur. Dynamics coupling the C2v open and D2h closed forms of S4

Ab initio molecular dynamics (AIMD) simulations were performed on the closed D(2h) and open C(2v) isomers of tetrasulfur. After a careful calibration of the electronic structure method, the calculations were done using the BPW91/aug-cc-pVTZ method. This combination of method/basis set adequately reproduces the relative benchmark CCSD(T) energy difference [Matus, M.; Dixon, D.; Peterson, K. A.; Harkless, J. A. W.; Francisco, J. S. J. Chem. Phys. 2007, 127, 174305] between these two isomers and, crucially, the fact that the D(2h) structure is a transition state linking two equivalent (mirror images) C(2v) isomers. The trajectories show that the symmetric open C(2v) isomers interconvert when passing through the D(2h) closed transition state structure and that, unlike tetraoxygen, no three-dimensional structures arise. The dynamic vibrational analysis yields peaks in good agreement with the static CCSD(T) harmonic frequencies and explains higher peaks as overtones, thus showing that unlike previous AIMD DFT-based approaches, carefully calibrated exchange-correlation functionals can produce reliable molecular dynamics results for complex PESs as the one corresponding to the lowest singlet of S(4).