Comparison of approximate quantum simulation methods applied to normal liquid helium at 4 K

The Feynman-Kleinert linearized path integral molecular dynamics (FK-LPI), ring polymer molecular dynamics (RPMD), and centroid molecular dynamics (CMD) methods are applied to the simulation of normal liquid helium. Comparisons of the simulation results at the T = 4 K and rho = 0.01873 A-3 state point are presented. The calculated quantum correlation functions for the three methods show significant differences, both in the short time and in the intermediate regions of the spectrum. Our simulation results are also compared to the recent results of other approximate quantum simulation methods. We find that FK-LPI qualitatively agrees with other approximate quantum simulation results while CMD and RPMD predict a qualitatively different impulsive rebound in the velocity autocorrelation function. Frequency space analysis reveals that RPMD exhibits a broad high-frequency tail similar to that from quantum mode coupling theory and numerical analytic continuation approaches, while FK-LPI provides a somewhat more rapid decay at high frequency than any of these three methods. CMD manifests a high-frequency component that is greatly reduced compared with the other methods.     

Complex-time velocity autocorrelation functions for Lennard-Jones fluids with quantum pair-product propagators

We use the pair-product approximation to the complex-time quantum mechanical propagator to obtain accurate quantum mechanical results for the symmetrized velocity autocorrelation function of a Lennard-Jones fluid at two points on the thermodynamic phase diagram. A variety of tests are performed to determine the accuracy of the method and understand its breakdown at longer times. We report quantitative results for the initial 0.3 ps of the dynamics, a time at which the correlation function has decayed to approximately one fifth of its initial value.     

液态水热容的量子校正

在不同温度下对液态水进行分子动力学模拟，研究各温度下液态水中各个原子的速度自相关函数密度谱，以考察液态水热容的量子校正随温度的变化规律．研究结果表明，水分子的三个内部振动模式对热容的量子校正不随温度变化，而转动和分子距平衡位置的摆动运动模式的量子校正随温度升高而逐步减小．对于分子动力学模拟结果经温度涨落计算所得的热容进行了量子校正，校正结果与实验值能符合．     

On the short-time limit of ring polymer molecular dynamics

We examine the short-time accuracy of a class of approximate quantum dynamical techniques that includes the centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) methods. Both of these methods are based on the path integral molecular dynamics (PIMD) technique for calculating the exact static equilibrium properties of quantum mechanical systems. For Kubo-transformed real-time correlation functions involving operators that are linear functions of positions or momenta, the RPMD and (adiabatic) CMD approximations differ only in the choice of the artificial mass matrix of the system of ring polymer beads that is employed in PIMD. The obvious ansatz for a general method of this type is therefore to regard the elements of the PIMD (or Parrinello-Rahman) mass matrix as an adjustable set of parameters that can be chosen to improve the accuracy of the resulting approximation. We show here that this ansatz leads uniquely to the RPMD approximation when the criterion that is used to select the mass matrix is the short-time accuracy of the Kubo-transformed correlation function. In particular, we show that the leading error in the RPMD position autocorrelation function is O(t(8)) and the error in the velocity autocorrelation function is O(t(6)), for a general anharmonic potential. The corresponding errors in the CMD approximation are O(t(6)) and O(t(4)), respectively.     

nMoldyn: a program package for a neutron scattering oriented analysis of molecular dynamics simulations

We present a new implementation of the program nMoldyn, which has been developed for the computation and decomposition of neutron scattering intensities from Molecular Dynamics trajectories (Comp. Phys. Commun 1995, 91, 191-214). The new implementation extends the functionality of the original version, provides a much more convenient user interface (both graphical/interactive and batch), and can be used as a tool set for implementing new analysis modules. This was made possible by the use of a high-level language, Python, and of modern object-oriented programming techniques. The quantities that can be calculated by nMoldyn are the mean-square displacement, the velocity autocorrelation function as well as its Fourier transform (the density of states) and its memory function, the angular velocity autocorrelation function and its Fourier transform, the reorientational correlation function, and several functions specific to neutron scattering: the coherent and incoherent intermediate scattering functions with their Fourier transforms, the memory function of the coherent scattering function, and the elastic incoherent structure factor. The possibility to compute memory function is a new and powerful feature that allows to relate simulation results to theoretical studies.     

Symmetrized correlation function for liquid para-hydrogen using complex-time pair-product propagators

We present a simple and efficient method for calculating symmetrized time correlation functions of neat quantum fluids. Using the pair-product approximation to each complex-time quantum mechanical propagator, symmetrized correlation functions are written in terms of a double integral for each degree of freedom with a purely positive integrand. At moderate temperatures and densities, where the pair-product approximation to the Boltzmann operator is sufficiently accurate, the method leads to quantitative results for the early time part of the correlation function. The method is tested extensively on liquid para-hydrogen at 25 K and used to obtain accurate quantum mechanical results for the initial 0.2 ps segment of the symmetrized velocity autocorrelation function of this system, as well as the incoherent dynamic structure factor at certain momentum transfer values.     

Complex autocorrelation function and energy spectrum by classical trajectory calculations

A quasiclassical method which enables evaluation of complex autocorrelation function from classical trajectory calculations is proposed. The method is applied for two highly excited nonlinearly coupled harmonic oscillators in regimes prevailed either by regular or chaotic classical motions. A good agreement of classical and quantum autocorrelation functions is found within short (Ehrnfest) time limit. Fourier transforms of the autocorrelation functions provide moderate resolved energy spectra, where classical and quantum results nearly coincide. The actual energy levels are obtained from approximate short-time autocorrelation functions with the help of filter diagonalization. This study is a follow up to our previous work [P. Zdanska and N. Moiseyev, J. Chem. Phys. 115, 10608 (2001)], where the complex autocorrelation has been obtained up to overall phase factors of recurrences.     

Estimating the viscoelastic moduli of complex fluids from observation of Brownian motion of a particle confined to a harmonic trap

A procedure is proposed to estimate the viscoelastic properties of a complex fluid from the behavior of the velocity autocorrelation function of a suspended Brownian particle, trapped in a harmonic potential. The procedure is tested for a model complex fluid with a given frequency-dependent shear viscosity. The analysis shows that the procedure can provide a rather accurate prediction of the viscoelastic properties of the fluid on the basis of experimental data on the velocity autocorrelation function of the trapped Brownian particle in a limited range of time.     

Diffusion and viscosity of liquid tin: Green-Kubo relationship-based calculations from molecular dynamics simulations

Molecular dynamics (MD) simulations of liquid tin between its melting point and 1600 °C have been performed in order to interpret and discuss the ionic structure. The interactions between ions are described by a new accurate pair potential built within the pseudopotential formalism and the linear response theory. The calculated structure factor that reflects the main information on the local atomic order in liquids is compared to diffraction measurements. Having some confidence in the ability of this pair potential to give a good representation of the atomic structure, we then focused our attention on the investigation of the atomic transport properties through the MD computations of the velocity autocorrelation function and stress autocorrelation function. Using the Green-Kubo formula (for the first time to our knowledge for liquid tin) we determine the macroscopic transport properties from the corresponding microscopic time autocorrelation functions. The selfdiffusion coefficient and the shear viscosity as functions of temperature are found to be in good agreement with the experimental data.     

Diffusion Spectrum of Polymer Melt Measured by Varying Magnetic Field Gradient Pulse Width in PGSE NMR

The translational motion of polymers is a complex process and has a big impact on polymer structure and chemical reactivity. The process can be described by the segment velocity autocorrelation function or its diffusion spectrum, which exhibit several characteristic features depending on the observational time scale—from the Brownian delta function on a large time scale, to complex details in a very short range. Several stepwise, more-complex models of translational dynamics thus exist—from the Rouse regime over reptation motion to a combination of reptation and tube-Rouse motion. Accordingly, different methods of measurement are applicable, from neutron scattering for very short times to optical methods for very long times. In the intermediate regime, nuclear magnetic resonance (NMR) is applicable—for microseconds, relaxometry, and for milliseconds, diffusometry. We used a variation of the established diffusometric method of pulsed gradient spin-echo NMR to measure the diffusion spectrum of a linear polyethylene melt by varying the gradient pulse width. We were able to determine the characteristic relaxation time of the first mode of the tube-Rouse motion. This result is a deviation from a Rouse model of polymer chain displacement at the crossover from a square-root to linear time dependence, indicating a new long-term diffusion regime in which the dynamics of the tube are also described by the Rouse model.     

Derivation of quantum langevin equation from an explicit molecule-medium treatment in interaction picture

A quantum mechanical form of the Langevin equation is derived from an explicit consideration of the molecule-medium interaction, as advocated by Simons in 1978, and by using two identities in the interaction picture. This can be easily reduced to the classical regime, and further simplified to the macroscopic Langevin equation by considering the stochastic Langevin force autocorrelation function. One of the so-called Einstein relations appears as a byproduct. By following the methodology proposed by Simons, an exact expression for the momentum autocorrelation function is obtained. The latter can be used to calculate the zero-frequency macroscopic diffusion coefficient that is observed to satisfy the second Einstein relation. The formalism described above gives rise to the possibility of explicitly computing the transport characteristics such as friction constant and diffusion coefficient from the corresponding quantum statistical mechanical expressions. A discussion on the Langevin equation becomes complete only when the corresponding Fokker-Planck equation is obtained. Therefore, the probability of the evolution of states with a particular absolute magnitude of linear momentum from those of another momentum eigenvalue is quantum mechanically defined. This probability appears as a special average value of a projection operator and as a special projection operator correlation function. A classical identity is introduced that is shown to be valid also for the quantum mechanically defined probability function. By using this identity, the so-called Fokker-Planck equation for the evolution probability is easily established.     

The flux-flux correlation function for anharmonic barriers

The flux-flux correlation function formalism is a standard and widely used approach for the computation of reaction rates. In this paper we introduce a method to compute the classical and quantum flux-flux correlation functions for anharmonic barriers essentially analytically through the use of the classical and quantum normal forms. In the quantum case we show that for a general f degree-of-freedom system having an index one saddle the quantum normal form reduces the computation of the flux-flux correlation function to that of an effective one-dimensional anharmonic barrier. The example of the computation of the quantum flux-flux correlation function for a fourth order anharmonic barrier is worked out in detail, and we present an analytical expression for the quantum mechanical microcanonical flux-flux correlation function. We then give a discussion of the short-time and harmonic limits.     

Scaling of the memory function and Brownian motion

It has been recently shown that the velocity autocorrelation function of a tracer particle immersed in a simple liquid scales approximately with the inverse of its mass. With increasing mass the amplitude is systematically reduced and the velocity autocorrelation function tends to a slowly decaying exponential, which is characteristic for Brownian motion. We give here an analytical proof for this behavior and comment on the usual explanation for Brownian dynamics which is based on the assumption that the memory function is proportional to a Dirac distribution. We also derive conditions for Brownian dynamics of a tracer particle which are entirely based on properties of its memory function.     

Dynamics of individual rotational states in an electrostatic guide for neutral molecules

The guiding properties of individual rotational states of deuterated ammonia inside an electrostatic hexapole guide are presented. The guide is combined with resonance enhanced multiphoton ionization detection to assess the guiding probabilities and velocity distributions as a function of the rotational quantum numbers J and K. Due to the differences in the effective dipole moment these states are prepared at significantly different translational temperatures. A model is presented that describes the velocity-distribution for individual M-sublevels, and this model is also used to determine a rotational-state dependent translational temperature. Furthermore, the hexapole field has been replaced by a dipole field in order to obtain a band-pass velocity filter. However, the resulting change in the final velocity distribution is similar to that obtained from a hexapole guide but with increased backing pressure, leading to collisional acceleration of the slow molecules.     

An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions

We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.     

Friction and diffusion of a Brownian particle in a mesoscopic solvent

The friction and diffusion coefficients of a massive Brownian particle in a mesoscopic solvent are computed from the force and the velocity autocorrelation functions. The mesoscopic solvent is described in terms of free streaming of the solvent molecules, interrupted at discrete time intervals by multiparticle collisions that conserve mass, momentum, and energy. The Brownian particle interacts with the solvent molecules through repulsive Lennard-Jones forces. The decays of the force and velocity autocorrelation functions are analyzed in the microcanonical ensemble as a function of the number N of solvent molecules and Brownian particle mass and diameter. The simulations are carried out for large system sizes and long times to assess the N dependence of the friction coefficient. The decay rates of these correlations are confirmed to vary as N(-1) in accord with earlier predictions. Hydrodynamic effects on the velocity autocorrelation function and diffusion coefficient are studied as a function of Brownian particle mass and diameter.     

Investigation of benzene-hexafluorobenzene dynamics in liquid binary mixtures

The structure and microscopic dynamics of liquid mixtures of benzene and hexafluorobenzene at room temperature and several compositions have been studied by molecular-dynamics simulations. In this implementation we have rescaled the intermolecular H-F cross potential parameters obtained from the Lorentz-Berthelot combining rules, in order to avoid the substantial overestimation of the energy of mixing predicted by the model when the usual rules are employed. We found that a reduction in the strength of cross H-F interactions by 50% relative to the geometric mean is required in order to get a good agreement with experiments. Radial-angular pair-correlation functions between like and unlike species have been computed and analyzed, by comparing them with the correlations in the corresponding neat liquids. We have also studied the microscopic intermolecular momentum transfer, by computing the time correlation function between the initial velocity of a central molecule and later velocities of neighboring molecules. Structural and dynamical information extracted from the mentioned functions seem to be consistent with the picture of relatively long-lived benzene-hexafluorobenzene (Bz-Hf) complexes present in the mixtures, which would be responsible for the considerable perturbation of the structure in the first shell of like species, and would be moving within the liquid in a parallel face-to-face configuration. Using the tools developed originally to estimate hydrogen-bond lifetimes in liquids, we have computed the lifetimes of the Bz-Hf complexes as a function of the mixture composition, by two different methods: the direct time-averaging scheme and from the autocorrelation function of bond occupation numbers. The obtained lifetimes are strongly dependent on the scheme chosen to compute the characteristic times. We have obtained for the Bz-Hf dimer in solution, at room temperature, lifetimes in the range of 30-40 ps from averaging schemes and around 60-120 ps from autocorrelation function methods. In the latter case, the longest times correspond to the equimolar mixture.