Path Integral Centroid Molecular Dynamics Research Articles

Two liquid states of distinguishable helium-4: The existence of another non-superfluid frozen by heating.

We show that two liquid states can exist in distinguishable helium-4 (4He) obeying Boltzmann statistics by path integral centroid molecular dynamics (CMD) simulations. This is an indication of quantum liquid polyamorphism induced by the nuclear quantum effect. For 0.08-3.3K and 1-500bar, we extensively conducted the isothermal-isobaric CMD simulations to explore not only possible states and state diagram but also the state characteristics. The distinguishable 4He below 25bar does not freeze down to 0.1K even though it includes no Bosonic exchange effect and, therefore, no Bose condensation. One liquid state, low quantum-dispersion liquid (LQDL), is nearly identical to normal liquid He-I of real 4He. The other is high quantum-dispersion liquid (HQDL) consisting of atoms with longer quantum wavelength. This is another non-superfluid existing below 0.5K or the temperatures of LQDL. The HQDL is also a low-entropy and fragile liquid to exhibit, unlike conventional liquids, rather gas-like relaxation of velocity autocorrelation function, while there the atoms diffuse without noticeable contribution from quantum tunneling. The LQDL-HQDL transition is not a thermodynamic phase transition but a continuous crossover accompanied by the change in the expansion factor of quantum wavelength. Freezing of HQDL into the low quantum-dispersion amorphous solid occurs by heating from 0.2 to 0.3K at 40-50bar, while this P-T condition coincides with the Kim-Chan normal-supersolid phase boundary of real 4He. The obtained state diagram was compared to that of the confined subnano-scale 4He systems, where Bosonic correlation is considerably suppressed.

Quantum polyamorphism in compressed distinguishable helium-4.

We demonstrate that two amorphous solid states can exist in 4He consisting of distinguishable Boltzmann atoms under compressed conditions. The isothermal compression of normal or supercritical fluid 4He was conducted at 3-25K using the isobaric-isothermal path integral centroid molecular dynamics simulation. The compression of fluid first produced the low-dispersion amorphous (LDA) state possessing modest extension of atomic necklaces. Further isothermal compression up to the order of 10 kbar to 1 Mbar or an isobaric cooling of LDA induced the transition to the high-dispersion amorphous (HDA) state. The HDA was characterized by long quantum wavelengths of atoms extended over several Angstroms and the promotion of atomic residual diffusion. They were related to the quantum tunneling of atoms bestriding the potential saddle points in this glass. The change in pressure or temperature induced the LDA-HDA transition reversibly with hysteresis, while it resembled the coil-globule transition of classical polymers. The HDA had lower kinetic and higher Gibbs free energies than the LDA at close temperature. The HDA was absent at T ≥ 13 K, while the LDA-HDA transition pressure significantly decreased with lowering temperature. The LDA and HDA correspond to the trapped and tunneling regimes proposed by Markland et al. [J. Chem. Phys. 136, 074511 (2012)], respectively. The same reentrant behavior as they found was observed for the expansion factor of the quantum wavelength as well as for atomic diffusivity.

Classical and path-integral molecular-dynamics study on liquid water and ice melting using non-empirical TTM2.1-F model

The TTMF2.1-F model is a non-empirical intermolecular water potential parametrised from ab-initio calculations of the water dimer with a complete basis set limit including dispersion correction from second-order Moller-Plesset perturbation theory. In this work, using two-phase ice-water NVT molecular-dynamics (MD) simulations, we found the ice melting temperature using the TTM2.1-F potential is close to 273 K when the nuclear quantum effects (NQEs) were included using path-integral centroid MD. Detailed analysis of the radial distribution functions, angle distribution functions, and associated joint probability for both liquid water and the two-phase cases showed that the melting-point-temperature drop when using path-integral simulation is due to the weakening of hydrogen bonds vis-à-vis classically-propagated MD.

Quantumness and state boundaries hidden in supercritical helium-4: A path integral centroid molecular dynamics study.

Isothermal-isobaric path integral centroid molecular dynamics simulations were conducted for fluid 4He at more than 600 state points in the proximity of the critical point to reveal the detailed states and relevant quantumness underlying the supercritical state. Through intensive analyses of the thermodynamic, dynamic, and quantum properties, we revealed the hidden state boundaries that separate the liquid-like and gas-like states in the supercritical region of this fluid. The Widom line, defined as the locus of the maxima of isobaric heat capacity C P , is also the quantum boundary at which there are changes in the isobaric temperature-dependence of the quantum wavelength, λ quantum, i.e., maximum amplitude of the Feynman imaginary-time paths (necklaces) of individual atoms. The Frenkel line, the famous dynamic state boundary, was observed to start from nearly the same point, 0.73-0.76 T c, on the P-T plane as observed for classical fluids. Several state boundaries based on the new criteria were found to emanate from the critical point or its vicinity on the P-T plane and are discussed in comparison with these boundaries. The quantumness of this fluid was expressed as (a) non-classical significant depression of C P observed in the liquid-like state; (b) the depression of the slopes dP/dT of the Widom line and the liquid-gas coexistence line near the critical point; and (c) the depression of the heat of pseudo-boiling across the Widom line. This is explained in terms of the decreasing kinetic energy with temperature observed in the liquid-like state below the Widom temperature T Widom, or alternatively in terms of the lattice model heat capacity, including the λ quantum.

Transport coefficients of normal liquid helium-4 calculated by path integral centroid molecular dynamics simulation

Thermal conductivity, shear viscosity, and bulk viscosity of normal liquid 4He at 1.7–4.0K are calculated using path integral centroid molecular dynamics (CMD) simulations. The calculated thermal conductivity and shear viscosity above lambda transition temperature are on the same order of magnitude as experimental values, while the agreement of shear viscosity is better. Above 2.3K the CMD well reproduces the temperature dependences of isochoric shear viscosity and of the time integral of the energy current and off-diagonal stress tensor correlation functions. The calculated bulk viscosity, not known in experiments, is several times larger than shear viscosity.

Path integral centroid molecular dynamics simulation of para-hydrogen sandwiched by graphene sheets

The carbon-hydrogen composite systems of para-hydrogen (p-H2) sandwiched by a couple of graphene sheets have been investigated by means of path integral centroid molecular dynamics simulations at 17K. It has been shown that sandwiched hydrogen is liquid-like but p-H2 molecules are preferably adsorbed onto the graphene sheets because of attractive graphene-hydrogen interaction. The diffusion coefficient of p-H2 molecules in the direction parallel to the graphene sheets is comparable to that in pure liquid p-H2. There exists a characteristic mode of 140cm−1 of the p-H2 molecules, attributed to adsorption-binding motion perpendicular to the graphene sheets.

Expansion in Lorentzian functions of spectra of quantum autocorrelations

We show that in a quantum mechanical many-body system of Boltzmann particles having space inversion symmetry the spectrum of the autocorrelation function of a local observable can always be given, similarly to the classical case [Phys. Rev. E 85, 022102 (2012)], in terms of a series of Lorentzian functions multiplied by the proper quantum detailed balance factor. This is done by transforming the continued fraction representation, which is derived via recurrent relations and without the use of the generalized Langevin equation hierarchy, into a series expansion. In this way characteristic frequencies can be defined, also in quantum mechanics, which refer to the particular autocorrelation. These are the frequencies of the eigenmodes of the relaxation function connected to the observable. We also show that in practical cases of interest in experimental spectroscopy, and particularly in inelastic neutron and x-ray scattering, the use of a finite number of Lorentzian shapes for an approximate description of the data is related to a reduction of the number of the relevant dynamical variables taken into account, equivalent to the lowering of the dimensionality of the orthogonalized space onto which the dynamic of the system is projected. Examples of application are given for the spectrum of the velocity autocorrelation function of liquid parahydrogen, calculated with a quantum simulation algorithm (path-integral centroid molecular dynamics), and for the molecular center-of mass dynamic structure factor in liquid carbon dioxide as computed by means of classical molecular dynamics simulation.

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In this study, we conducted analysis of quantum effect of the hydrogen molecules on the p-V-T relation of cryogenic hydrogen using classical Molecular Dynamics (MD) and path integral Centroid MD (CMD) method. We performed MD simulation across a wide temperature region in the constant density and compared the pressure formulations of each method. In addition, we calculated the diffusion coefficient using Green-Kubo method. As a result, it was confirmed that classical MD cannot reproduce the experimental data in the low temperature region and underestimates the virial pressure compared to the CMD. Moreover, it was clarified that taking the quantum effect into account produces broader repulsive region and shallower the potential well. Because of this mechanism, the intermolecular interaction of hydrogen diminishes and the virial pressure increases. In addition, it was confirmed that the diffusivity increase compared with classical representation.

経路積分セントロイド分子動力学法による BCC 金属中の水素拡散性とその温度依存性の評価

We have analyzed the diffusion behavior of interstitial hydrogen in bcc iron and niobium using path-integral centroid molecular dynamics (CMD) method, which can describe the real-time evolution of particles based on quantum statistical mechanics. In this study, the embedded-atom-method (EAM) potential model for the iron-hydrogen interaction is developed to reproduce the ab initio minimum energy path of hydrogen migration based on the density functional theory (DFT) data in the literature, while the description of niobium-hydrogen interaction is based on an empirical potential model. Time evolutions of mean-square displacements of hydrogen atoms in the two bulk metals are calculated at various temperatures, and then diffusion coefficients and activation energies of hydrogen migration are evaluated. Especially in the case of iron, the results are in good agreement with experimental measurements over a wide temperature range. In order to characterize the quantum effects on the hydrogen diffusion process, the CMD results are compared with those obtained from classical molecular dynamics method. The obtained results indicate that the quantum effects can play a significant role in hydrogen diffusivity over a wide temperature range in these bcc metals.

Ab initio path integral ring polymer molecular dynamics: Vibrational spectra of molecules

The path integral ring polymer molecular dynamics method is combined with ‘on-the-fly’ ab initio electronic structure calculations and applied to vibrational spectra of small molecules, LiH and H 2O, at the room temperature. The results are compared with those of the numerically exact solution and ab initio path integral centroid molecular dynamics calculation. The peak positions in the calculated spectra are found to be reasonable, showing the red-shift due to potential anharmonicity. This unification enables the investigation of real-time quantum dynamics of chemically complex molecular systems on the ab initio Born-Oppenheimer potential energy surface.

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.

An accurate and simple quantum model for liquid water

The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.

Centroid molecular dynamics approach to the transport properties of liquid para-hydrogen over the wide temperature range.

Fundamental transport properties of liquid para-hydrogen (p-H(2)), i.e., diffusion coefficients, thermal conductivity, shear viscosity, and bulk viscosity, have been evaluated by means of the path integral centroid molecular dynamics (CMD) calculations. These transport properties have been obtained over the wide temperature range, 14-32 K. Calculated values of the diffusion coefficients and the shear viscosity are in good agreement with the experimental values at all the investigated temperatures. Although a relatively large deviation is found for the thermal conductivity, the calculated values are less than three times the amount of the experimental values at any temperature. On the other hand, the classical molecular dynamics has led all the transport properties to much larger deviation. For the bulk viscosity of liquid p-H(2), which was never known from experiments, the present CMD has given a clear temperature dependence. In addition, from the comparison based on the principle of corresponding states, it has been shown that the marked deviation of the transport properties of liquid p-H(2) from the feature which is expected from the molecular parameters is due to the quantum effect.

Connection between the observable and centroid structural properties of a quantum fluid: application to liquid para-hydrogen.

It is shown that the discrepancy between path integral Monte Carlo [M. Zoppi et al., Phys. Rev. B 65, 092204 (2002)] and path integral centroid molecular dynamics [F. J. Bermejo et al., Phys. Rev. Lett. 84, 5359 (2000)] calculations of the static structure factor of liquid para-hydrogen can be explained based on a deconvolution equation connecting centroid and physical radial distribution functions. An explicit expression for the kernel of the deconvolution equation has been obtained using functional derivative techniques. In the superposition approximation, this kernel is given by the functional derivative of the effective potential with respect to the pairwise classical potential. Results of path integral Monte Carlo calculations for the radial distribution function and the static structure factor of liquid para-hydrogen are presented.

Theoretical study on photoexcitation dynamics of the K atom attached to helium clusters and the solvation structures of K*Hen exciplexes

The dynamics of the K atom attached to the 300-atom helium cluster upon photoexcitation has been studied theoretically based on the quantum molecular dynamics method. With the use of a hybrid method between time-dependent quantum dynamics and semiclassical path integral centroid molecular dynamics, the calculation includes the electronic state mixing for the K(2P) states as well as the quantum motions of helium atoms. It was found from the calculated trajectories that the K atom mostly desorbs by itself from the surface of the helium cluster without depending on the types of initial electronic excited states. It was also found that the K*He exciplex can be formed only as a minor product, following the initial excitation to the Π-type electronic state alone. Helium solvation structures of the K*Hen exciplexes were also investigated by path integral molecular dynamics simulations. The result implies that stable exciplexes can be formed up to n = 6 on the lowest excited state until the first solvation shell around the 4p orbital of K* is completed. Meanwhile, it was found that only two helium atoms can be bound to the K(2P) atom on the second lowest excited state.

Transport properties of liquid para-hydrogen: The path integral centroid molecular dynamics approach

Several fundamental transport properties of a quantum liquid para-hydrogen (p-H2) at 17 K have been numerically evaluated by means of the quantum dynamics simulation called the path integral centroid molecular dynamics (CMD). For comparison, classical molecular dynamics (MD) simulations have also been performed under the same condition. In accordance with the previous path integral simulations, the calculated static properties of the liquid agree well with the experimental results. For the diffusion coefficient, thermal conductivity, and shear viscosity, the CMD predicts the values closer to the experimental ones though the classical MD results are far from the reality. The agreement of the CMD result with the experimental one is especially good for the shear viscosity with the difference less than 5%. The calculated diffusion coefficient and the thermal conductivity agree with the experimental values at least in the same order. We predict that the ratio of bulk viscosity to shear viscosity for liquid p-H2 is much larger than classical van der Waals simple liquids such as rare gas liquids.

Theoretical simulations on photoexcitation dynamics of the silver atom embedded in helium clusters

Quantum molecular dynamics simulations have been performed to study the photoexcitation Ag(5p 2PJ)←Ag(5s 2S1/2) in size-selected helium clusters considering electronically nonadiabatic transitions. We employed the hybrid method in which the electronic degree of freedom of Ag(2P) was treated quantum mechanically while the motions of helium atoms were described by the semiclassical path integral centroid molecular dynamics method in order to take the quantum fluctuation effect into account. It has been found that the dynamics after photoexcitation is dominantly nonadiabatic in all cluster sizes studied, and that nonadiabatic transitions are enhanced by quantum fluctuation of helium motions. Most of the photoexcited AgHen clusters decompose into an isolated Ag atom and free helium atoms within several picoseconds. However, Ag*Hen (n=1–5) exciplex formation was also found to occur for all helium cluster sizes studied, although this process is found to be minor.

Molecular collective dynamics in solid para-hydrogen and ortho-deuterium: The Parrinello–Rahman-type path integral centroid molecular dynamics approach

The single-particle and collective dynamics of hydrogen/deuterium molecules in solid hcp para-hydrogen (p-H2) and ortho-deuterium (o-D2) has been investigated by using the path integral centroid molecular dynamics (CMD) simulations at zero-pressure and 5.4 and 5.0 K, respectively. For this purpose, we have newly unified the standard CMD method with the Parrinello–Rahman–Nosé–Hoover-chain-type isothermal–isobaric technique. The phonon density of states have been obtained and the dynamic structure factors have been calculated to observe the phonon dispersion relations of both crystals. For solid p-H2, the high energy edge of the phonon energies of solid p-H2 is >13 meV, and the calculated phonon energies are significantly higher than those observed in Nielsen’s previous neutron scattering experiments in the energy region >9 meV. The relationship between the present results and the data reported so far is discussed to resolve the outstanding controversy regarding the phonon energies in solid p-H2. On the other hand, the excitation energies for solid o-D2 are in fairly good agreement with those of the neutron experiments. The calculated isothermal compressibility of solid p-H2 is found to be very close to the experimental result.

Photodissociation of Cl 2 in helium clusters: an application of hybrid method of quantum wavepacket dynamics and path integral centroid molecular dynamics

The photodissociation dynamics of Cl 2 embedded in helium clusters is studied by numerical simulation with an emphasis on the effect of quantum character of helium motions. The simulation is based on the hybrid model in which Cl–Cl internuclear dynamics is treated in a wavepacket technique, while the helium motions are described by a path integral centroid molecular dynamics approach. It is found that the cage effect largely decreases when the helium motion is treated quantum mechanically. The mechanism is affected not only by the zero-point vibration in the helium solvation structure, but also by the quantum dynamics of helium.

Microscopic structure factor of liquid para-hydrogen

We have calculated, by means of path integral Monte Carlo (PIMC) simulations, the microscopic structure factor of liquid para-hydrogen at $T=15.7 \mathrm{K}.$ The present simulation results are compared with a recent experimental determination of the structure factor at a similar thermodynamic state, as well as with a previous path integral centroid molecular dynamics (PICMD) simulation. The comparison is less than satisfactory. While the PICMD results are not consistent with the PIMC data, also the experimental results do not quantitatively agree with the present simulations and are not of the accuracy level attainable for other simple liquids.