Molecular dynamics simulations of liquid water using various long-range electrostatics techniques

Water is one of the most extensively studied molecules, owing to its crucial role in biological processes. The water molecule is both highly polar and highly polarizable. Properties of water computed from molecular simulations are therefore critically dependent on both the intermolecular potential and the method for computing long-range electrostatic corrections. In this paper, the effects of the potential and the long-range electrostatic corrections are quantified for liquid water from 260 to 400?K. Simulations were carried out for a system of 256 molecules in the NVT ensemble. Thermodynamic, structural, dynamical, hydrogen bonding and dielectric properties have been computed for the flexible SPC and rigid SPC, SPC/E, TIP4P, TIP4P-Ew and TIP4P-FQ potentials, using the Lekner, Ewald and reaction field techniques to handle long-range electrostatics. The Lekner method gave the best overall agreement with experimental data, while the reaction field approach produced poorer results. Some measurable differences were found between the Lekner and Ewald techniques. For dielectric properties, the performance of the TIP4P-FQ model was superior relative to other potentials. For 256 molecules, the computational speeds of the Ewald and reaction field methods were found to be 2.5 to 3 times and 3.5 to 5 times faster than the Lekner technique, respectively.     

Convergence properties of the cluster expansion for equal- time Green functions in scalar theories

We investigate the convergence properties of the cluster expansion of equal-time Green functions in scalar theories with quartic self-coupling in (0 + 1), (1 + 1), and (2 + 1) space-time dimensions. The computations are carried out within the equal-time correlation dynamics approach, which consists in a closed set of coupled equations of motion for connected Green functions as obtained by a truncation of the BBGKY hierarchy. We find that the cluster expansion shows good convergence as long as the system is in a localized state (single phase configuration) and that it breaks down in a non-localized state (two phase configuration), as one would naively expect. Furthermore, in the case of dynamical calculations with a time dependent Hamiltonian for the evaluation of the effective potential we find two timescales determining the adiabaticity of the propagation; these are the time required for adiabaticity in the single phase region and the time required for tunneling into the non-localized lowest energy state in the two phase region. Our calculations show a good convergence for the effective potentials in (1 + 1) and (2+1) space-time dimensions since tunneling is suppressed in higher space-time dimensions.     

Spectral accuracy in fast Ewald-based methods for particle simulations

A spectrally accurate fast method for electrostatic calculations under periodic boundary conditions is presented. We follow the established framework of FFT-based Ewald summation, but obtain a method with an important decoupling of errors: it is shown, for the proposed method, that the error due to frequency domain truncation can be separated from the approximation error added by the fast method. This has the significance that the truncation of the underlying Ewald sum prescribes the size of the grid used in the FFT-based fast method, which clearly is the minimal grid. Both errors are of exponential-squared order, and the latter can be controlled independently of the grid size. We compare numerically to the established SPME method by Essmann et al. and see that the memory required can be reduced by orders of magnitude. We also benchmark efficiency (i.e. error as a function of computing time) against the SPME method, which indicates that our method is competitive. Analytical error estimates are proven and used to select parameters with a great degree of reliability and ease.     

Direct experimental method for the determination of x-ray reflection phases

A direct experimental method is described for the phase determination of x-ray reflections from single crystals. This method utilizes the coherent dynamical interaction of diffracted x-ray beams in a 3-beam multiple Bragg reflection to reveal the signs,S _P, of triplet-phase products. This dynamical effect and the relative rotation of the crystal lattice with respect to the Ewald sphere are considered. The phase dependence of the reflected intensity profile is observed and is in agreement with the theory. It is found thatS _P=S _L ·S _R,S _L being the sign defined from the multiple diffraction line profile.S _R is determined by the rotation of the crystal lattice relative to the Ewald sphere. The new method can be applied to a direct experimental determination of phases without carrying out the complicated dynamical calculations.On leave from Instituto de Fisica, Universidade Estadual de Campinas, Campinas, S.P. 13100, Brazil     

A new global potential energy surface of the ground state of SiH2+ (X2A1) system and dynamics calculations of the Si+ + H2 (v0 = 2, j0 = 0) → SiH+ + H reaction

A global potential energy surface (PES) of the ground state of SiH$_{2}^{+}$ system is built by using neural network method based on 18223 ab initio points. The topographic properties of PES are presented and compared with previous theoretical and experimental studies. The results indicate that the spectroscopic parameters obtained from the new PES are in good agreement with the experimental data. In order to further verify the validity of the new PES, a test dynamics calculation of the Si$^{+} +$ H$_{2}$ ($v_0 = 2, j_{0} = 0$) $\to $ H $+$ SiH$^{+}$ reaction has been carried out by using the time-dependent wave packet method. The integral cross sections and rate constants are computed for the title reaction. The reasonable dynamical behavior indicates that the newly constructed PES is suitable for relevant dynamics investigations.     

Calculation of Vacuum Wavefunction and Mass .Gap from Improved (2+l)-Dimensional SU(2) Lattice Gauge Field Hamiltonian

The truncated eigenvalue equation of SU(N) lattice gauge theory is studied by using improved lattice gauge Hamiltonian with a proper truncation scheme that preserves the continuum limit. The calculations of vacuum state wavefunction and glueball mass of (2+1)-dimensional SU(2) theory up to third order are carried out, the results show the improvement of scaling behavior in deep weak coupling region.     

A comparative study of the dynamic critical behavior of the four-state Potts like models

We investigate the short-time critical dynamics of the Baxter-Wu (BW) and n=3 Turban (3TU) models to estimate their global persistence exponent θ_g. We conclude that this new dynamical exponent can be useful in detecting differences between the critical behavior of these models which are very difficult to obtain in usual simulations. In addition, we estimate again the dynamical exponents of the four-state Potts (FSP) model in order to compare them with results previously obtained for the BW and 3TU models and to decide between two sets of estimates presented in the current literature. We also revisit the short-time dynamics of the 3TU model in order to check if, as already found for the FSP model, the anomalous dimension of the initial magnetization x₀ could be equal to zero.     

Evaluation of the electrostatic potential at the surface of an ionic solid

A method to evaluate the electrostatic potential at and near the surface of a semi-infinite ionic solid is presented. It utilizes the Ewald equation for an infinite crystal and Parry's extension of the Ewald equation for an infinite slab. The method was applied to calculate the potentials at the (100), (110), (021̄), and the (111) surfaces of NaCl. Results for the nonpolar (100) and (110) surfaces agree with results by other methods. Results for the polar (111) surface differ from results of slab calculations. The difference is thought to be due to the presence of a second surface in the slab calculations. Its application to a relaxed surface is also demonstrated.     

Two-δ- Function Generalized Plasma Pole Model for First Principle Calculations of Quasiparticle Energies in Many-Electron Systems

To evaluate the dynamical effects of the screened interaction in the calculations of quasiparticle energies in many-electron systems a two-δ-function generalized plasma pole model (GPP) is introduced to simulate the dynamical dielectric function. The usual single δ-function GPP model has the drawback of over simplifications and for the crystals without.the center of symmetry is inappropriate to describe the finite frequency behavior for dielectric function matrices. The discrete frequency summation method requires too much computation to achieve converged results since ab initio calculations of dielectric function matrices are to be carried out for many different frequencies. The two-δ GPP model is an op timization of the two approaches. We analyze the two-δ GPP model and propose a method to determine from the first principle calculations the amplitudes and effective frequencies of these δ functions. Analytical solutions are found for the second order equations for the parameter matrices entering the model. This enables realistic applications of the method to the first principle quasiparticle calculations and makes the calculations truly adjustable parameter free.     

Yukawa potentials in systems with partial periodic boundary conditions. I. Ewald sums for quasi-two-dimensional systems

Yukawa potentials are often used as effective potentials for systems such as colloids, plasmas, etc. When the Debye screening length is large, the Yukawa potential tends to the non-screened Coulomb potential; in this small screening limit, or Coulomb limit, the potential is long-ranged. As is well known in computer simulation, a simple truncation of the long-ranged potential and the minimum image convention are insufficient to obtain accurate numerical data on systems. The Ewald method for bulk systems, i.e. with periodic boundary conditions in all three directions of space, has already been derived for the Yukawa potential [Molec. Phys. 88, 1357 (1996); J. Chem. Phys. 113, 10459 (2000)], but for systems with partial periodic boundary conditions, the Ewald sums have only recently been obtained [J. Chem. Phys. 126, 056101 (2007)]. In this paper, we provide a closed derivation of the Ewald sums for Yukawa potentials in systems with periodic boundary conditions in only two directions and for any value of the Debye length. Special attention is paid to the Coulomb limit and its relation to the electroneutrality of systems.     

硝酸钾电解质溶液水化结构的分子动力学模拟

应用分子动力学方法对硝酸钾溶液中离子团簇的结构和离子的水化性质进行模拟研究．水分子采用简单点电荷模型，钾离子被看作带电硬球，硝酸根离子采用刚性四节点模型，同时考虑了节点间的库仑长程作用和L-J相互作用，库仑长程作用采用EWALD求和方法处理，得到了溶液中各种离子对的微观构型和径向分布函数，考察了溶液浓度对离子水化性质的影响．研究表明, 在KNO3溶液中存在一定程度的离子缔合，在高离子浓度情形，可以观察到二聚体、三聚体、溶剂分离阴阳离子对以及其它更复杂的离子团簇构型；离子水化数随离子浓度的升高而降低，对不同浓度的溶液得到的K+的水化数为5?7，NO3-的水化数为3.5?4.7，与蒙特卡罗模拟结果和飞行时间中子衍射实验的测量结果一致．     

Recent studies in heavy ion induced fission reactions

Nuclear fission process involves large scale shape changes of the nucleus, while it evolves from a nearly spherical configuration to two separated fission fragments. The dynamics of these shape changes in the nuclear many body system is governed by a strong interplay of the collective and single particle degrees of freedom. With the availability of heavy ion accelerators, there has been an impetus to study the nuclear dynamics through the investigations of nucleus-nucleus collisions involving fusion and fission process. From the various investigations carried out in the past years, it is now well recognized that there is large scale damping of collective modes in heavy ion induced fission reactions, which in other words implies that nuclear motion is highly viscous. In recent years, there have been many experimental observations in heavy ion induced fission reactions at medium bombarding energies, which suggest possible occurrence of various non-equilibrium modes of fission such as quasi-fission, fast fission and pre-equilibrium fission, where some of the internal degrees of freedom of the nucleus is not fully equilibrated. We have carried out extensive investigations on the fission fragment angular distributions at near barrier bombarding energies using heavy fissile targets. The measured fragment anisotropies when compared with the standard saddle point model (SSPM) calculations show that for projectile-target systems having zero or low ground state spins, the angular anisotropy exhibits a peak-like behaviour at the sub barrier energies, which cannot be explained by the SSPM calculations. For projectiles or targets with large ground state spins, the anomalous peaking gets washed out due to smearing of the K-distribution by the intrinsic entrance channel spins. Recently studies have been carried out on the spin distributions of fission fragments through the gamma ray multiplicity measurements. The fission fragments acquire spin mainly from two sources: (i) due to rigid rotation of the nascent fragments at scission and (ii) due to statistical excitation of the spin bearing collective modes in the fissioning nucleus. One of the collective modes — the tilting mode depends on the K quantum number and is responsible for the emission angle dependence of fragment spin. In our studies, we have shown conclusively that the collective statistical spin modes get strongly suppressed for high K values corresponding to large rotational frequencies along the fission axis. These results bring out the importance of the dynamical effects in the heavy ion induced fusion-fission reactions. The present article will review the work carried out on the above aspects in heavy ion fission reactions as well as on the fission time scales, and some of the recent studies on the mass-energy correlations of fission fragments at near-barrier bombarding energies.     

NEUTRON SCATTERING AND LATTICE DYNAMICAL STUDIES OF THE HIGH-PRESSURE PHASE ICE (II)

Lattice dynamical calculations have been carried out for ice II based on the force field constructed for ice Ih. In order to fully understand ice II inelastic neutron scattering spectra, the decomposed phonon density of states was shown mode by mode. Calculated results have shown that the hydrogen bond force constant between the six-molecule rings is significantly weaker, 75eV/nm², compared with the force constant, 220eV/nm², within the rings. Inelastic neutron scattering spectra of clathrate hydrate H₂O+He are almost the same as ice II. This means that the absorption of He atoms cannot affect the bond strengths of the ice II host lattice. Based on the force field model for ice II, the van der Waals interactions between water molecules and helium atoms are considered. The results obtained are consistent with experimental data. Lattice dynamical calculations have been carried out for ice II using seven rigid pairwise potentials. It was found that MCY makes the stretching and bending interactions in ice II too weak and makes the O-O bond length too long (～5%), thus its lattice densities are obviously lower than other potential lattices or experimental values.     

Inelastic neutron scattering and lattice dynamics of GaPO<Subscript>4</Subscript>

We report here measurements of phonon spectrum and lattice dynamical calculations for GaPO₄. The measurements in low-cristobalite phase of GaPO₄ are carried out using high-resolution medium-energy chopper spectrometer at ANL, USA in the energy transfer range 0–160 meV. Semiempirical interatomic potential in GaPO₄, previously determined using ab-initio calculations have been widely used in studying the phase transitions among various polymorphs. The calculated phonon spectrum using the available potential show fair agreement with the experimental data. However, the agreement between the two is improved by including the polarisability of the oxygen atoms in the framework of the shell model. The lattice dynamical models are also exploited for calculations of various thermodynamic properties of GaPO₄.     

Numerical calculations of potential distribution in non-ideal quadrupole trap and simulations of anharmonic oscillations

A quadrupole ion trap consisting of electrode structures symmetric about z-axis is an important tool for conducting several precision experiments. In practice the field inside the trap does not remain purely quadrupolar, and can be calculated using numerical methods. We have used boundary element method to calculate the potential inside the truncated as well as symmetrically misaligned quadrupolar ion trap. The calculated potential values are fitted to multipole expansion and the weights of multipole moments have been evaluated by minimizing the least square deviation. The higher-order multipole contribution in the fabricated hyperbolic electrodes due to truncation and machining imperfections is discussed. Non-linear effects arising due to the superposition of octupole moment manifest as anharmonic oscillations of trapped ions in the non-ideal Paul trap. Theoretical simulations of non-linear effects have been carried out.      

Thermodynamic and transport properties of simple fluids using lattice sums: bulk phases and liquid-vapour interface

Molecular dynamics simulations in the canonical ensemble have been performed to obtain the thermodynamic and transport properties of the Lennard-Jones fluid. The dispersion interactions were calculated using lattice sums. This method makes it possible to simulate the full potential avoiding the inclusion of the long range corrections (LRC) during or at the end of simulations. In the calculation of dynamic properties in bulk phases and thermodynamic quantities of inhomogeneous systems where the interface is physically present, in general the LRC cannot easily be included. By using the lattice sums method, the results are independent of the truncation of the potential. In the liquid-vapour interface simulations it is not necessary to make any pre-judgments about the form of the LRC formula to calculate coexisting properties such as the surface tension. The lattice sums method has been applied to evaluate how well the full interaction can be calculated in the liquid phase and in the liquid-vapour interface. In the liquid phase the pressure, configurational energy, diffusion coefficient and shear viscosity were obtained. The results of the thermodynamic properties are compared with those obtained using the spherically truncated and shifted (STS) potential with the LRC added at the end of simulations, and excellent agreement is found. The transport properties are calculated on different system sizes for a state near the triple point. The diffusion coefficient using the lattice sums method increases with the number of molecules, and the results are higher than those of the STS model truncated at 2.5σ (STS2.5). The shear viscosity does not show any system size dependence for systems with more than 256 molecules, and the lattice sums results are essentially the same as those for the STS2.5. In the liquid-vapour equilibria the coexisting densities and vapour pressures for the full potential agree well with those obtained using the Gibbs ensemble and the NPT + test particle methods. The surface tension using lattice sums and truncation of forces at 2.5σ agrees well with STS results using large system sizes and cutoff distances.     

An alternative construction of the Ewald sum

Periodicity is a popular way to handle boundaries in atomistic simulations in the bulk. However, slowly decaying Coulomb interactions lead to ill-defined energies and forces. The Ewald sum is a common way of giving meaning to these terms, but its derivation, based on Fourier series, is not transparent. Described in this article is a derivation based on the limiting behaviour as the cutoff goes to infinity of a truncated and shifted Coulomb potential. This observation strengthens the case for the use of the original Ewald sum. And such a construction may offer advantages for computation and/or modelling.     

使用基于MAPPING哈密顿的对称准经典动力学方法和基于ML-MCTDH的量子动力学方法研究超快电子转移

Symmetrical quasi-classical (SQC) method based on mapping Hamiltonian is an efficient approach that is potentially useful to treat the nonadiabatic dynamics of very large systems. We try to evaluate the performance of this method in the ultrafast electron transfer processes involving a few of electronic states and a large number of vibrational modes. The multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) method was used to get the accurate dynamical results for benchmark. Although the population dynamics in the longtime limit show differences in the ML-MCTDH and SQC calculations, the SQC method gives acceptable results.