理解随机过程分子动力学中的真实/虚拟动力学

Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed for the Langevin equation[J. Chem. Phys. 147, 184104 (2017)] in principle exists in other types of stochastic thermostats as well. The recommended "middle" scheme[J. Chem. Phys. 147, 034109 (2017)] of the Andersen thermostat is investigated as an example. As shown by both analytic and numerical results, while the real and virtual dynamics cases approach the same plateau of the characteristic correlation time in the high collision frequency limit, the accuracy and efficiency of sampling are relatively insensitive to the value of the collision frequency in a broad range. After we compare the behaviors of the Andersen thermostat to those of Langevin dynamics, a heuristic schematic representation is proposed for understanding efficient stochastic thermostatting processes with molecular dynamics.     

Phase Space Optimization of Quantum Representations: Non-Cartesian Coordinate Spaces

In an earlier article [Found. Phys. 30, 1191 (2000)], a quasiclassical phase space approximation for quantum projection operators was presented, whose accuracy increases in the limit of large basis size (projection subspace dimensionality). In a second paper [J. Chem. Phys. 111, 4869 (1999)], this approximation was used to generate a nearly optimal direct-product basis for representing an arbitrary (Cartesian) quantum Hamiltonian, within a given energy range of interest. From a few reduced-dimensional integrals, the method determines the optimal 1D marginal Hamiltonians, whose eigenstates comprise the direct-product basis. In the present paper, this phase space optimized direct-product basis method is generalized to incorporate non-Cartesian coordinate spaces, composed of radii and angles, that arise in molecular applications. Analytical results are presented for certain standard systems, including rigid rotors, and three-body vibrators.     

Augmented Langevin approach to fluctuations in nonlinear irreversible processes

A Fokker-Planck equation derived from statistical mechanics by M. S. Green [J. Chem. Phys. 20:1281 (1952)] has been used by Grabertet al. [Phys. Rev. A 21:2136 (1980)] to study fluctuations in nonlinear irreversible processes. These authors remarked that a phenomenological Langevin approach would not have given the correct reversible part of the Fokker-Planck drift flux, from which they concluded that the Langevin approach is untrustworthy for systems with partly reversible fluxes. Here it is shown that a simple modification of the Langevin approach leads to precisely the same covariant Fokker-Planck equation as that of Grabertet al., including the reversible drift terms. The modification consists of augmenting the usual nonlinear Langevin equation by adding to the deterministic flow a correction term which vanishes in the limit of zero fluctuations, and which is self-consistently determined from the assumed form of the equilibrium distribution by imposing the usual potential conditions. This development provides a simple phenomenological route to the Fokker-Planck equation of Green, which has previously appeared to require a more microscopic treatment. It also extends the applicability of the Langevin approach to fluctuations in a wider class of nonlinear systems.     

A quasi-classical trajectory study of the Cl + H<Subscript>2</Subscript> (D<Subscript>2</Subscript>) reaction on a new BW3 potential energy surface

Molecular reaction dynamics of Cl + H₂ (D₂) has been studied on the latest analytical potential energy surface called BW3 using the Monte Carlo quasi-classical trajectory method. Excitation functions, differential cross sections and angular distributions of HCl and DCl products have been calculated. The excitation functions of the Cl (²P_3/2) + n-H₂ and Cl(²P_3/2) + n-D₂ reactions are also studied. The results are compared with those of quasi-classical trajectory [M. Alagia et al.: Phys. Chem. Chem. Phys. 2 (2000); F. J. Aoiz et al.: J. Phys. Chem. 100 (1996)], quantum mechanical (QM) calculations [F. J. Aoiz et al.:J. Chem. Phys. 115 (2001)] and experimental data [S. H. Lee et al.: J. Chem. Phys. 110 (1999); F. Dong et al.: J. Chem. Phys. 115 (2001)]. Discussions are given to some new results.     

Stochastic analysis of symmetry-breaking bifurcations: Master equation approach

The multivariate master equation for a general reaction-diffusion system is solved perturbatively, in the vicinity of a bifurcation point leading to symmetry-breaking transitions. The possibility to express the result through a Brazovskii type of potential is examined, and a comparison with the Langevin analysis of Walgraefet al. [Adv. Chem. Phys. 49:311 (1982)] is performed.     

Numerical integration of projective Hamiltonian dynamics

Projective Hamiltonian dynamics [S. Melchionna, J. Chem. Phys. 121, 4534 (2004)] is an approach to reduce mode spreading in complex systems, thus improving the performances of Molecular Dynamics simulations. A numerical integration of the dynamics requires proper treatment of the non-separable form of the Hamiltonian. Due to its symplectic nature, the generalized leapfrog scheme is shown to provide robust and reliable numerical trajectories even in the case of stiff projective forces.     

Numerical entropy and phason elastic constants of plane random tilings with any 2D-fold symmetry

We perform Transition matrix Monte Carlo simulations to evaluate the entropy of rhombus tilings with fixed polygonal boundaries and 2D-fold rotational symmetry. We estimate the large-size limit of this entropy for D=4 to 10. We confirm analytic predictions of [N. Destainville et al., J. Stat. Phys. 120, 799 (2005) and M. Widom et al., J. Stat. Phys. 120, 837 (2005)], in particular that the large size and large D limits commute, and that entropy becomes insensible to size, phason strain and boundary conditions at large D. We are able to infer finite D and finite size scalings of entropy. We also show that phason elastic constants can be estimated for any D by measuring the relevant perpendicular space fluctuations.     

Shrinking stacking fault through glide of the Shockley partial dislocation in hard-sphere crystal under gravity

Disappearance of a stacking fault in the hard-sphere crystal under gravity, such as reported by Zhuet al. [Nature 387, 883 (1997)], has successfully been demonstrated by Monte Carlo simulations. We previously found that a less ordered (or defective) crystal formed above a bottom ordered crystal under stepwise controlled gravity [Moriet al. J. Chem. Phys. 124, 174507 (2006)]. A defect in the upper defective region has been identified with a stacking fault for the (001) growth. We have looked at the shrinking of a stacking fault mediated by the motion of the Shockley partial dislocation; the Shockley partial dislocation terminating the lower end of the stacking fault glides. In addition, the presence of crystal strain, which cooperates with gravity to reduce stacking faults, has been observed.     

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.     

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

Yukawa potentials may be long-ranged when the Debye screening length is large. In computer simulations, such long-ranged potentials have to be taken into account with convenient algorithms to avoid systematic bias in the sampling of the phase space. Recently, we provided Ewald sums for quasi-two-dimensional systems with Yukawa interaction potentials [J. Chem. Phys. 126, 056101 (2007); Molec. Phys. paper I of this series]. Sometimes, Lekner sums are used as an alternative to Ewald sums for Coulomb systems. In the present work, we derive the Lekner sums for quasi-two-dimensional systems with Yukawa interaction potentials and we give numerical tests for practical implementations. The main result of this paper is to emphasize that Lekner sums cannot be considered as an alternative to Ewald sums for Yukawa potentials. As a conclusion to this work: Lekner sums should not be used for quasi-two-dimensional systems with Yukawa interaction potentials.     

New massively parallel linear-response coupled-cluster module in ACES III: application to static polarisabilities of closed-shell molecules and oligomers and of open-shell radicals

ABSTRACT

Stemming from our implementation of parallel coupled-cluster (CC) capabilities for electron spin resonance properties [J. Chem. Phys. 139, 174103 (2013)], we present a new massively parallel linear response CC module within ACES III. Unlike alternative parallel CC modules, this general purpose module evaluates any type of first- and second-order CC properties of both closed- and open-shell molecules employing restricted, unrestricted and restricted-open-shell Hartree–Fock (HF) references. We demonstrate the accuracy and usefulness of this module through the calculation of static polarisabilities of large molecules. Closed-shell calculations are performed at the following levels: second-order many-body perturbation theory [MBPT(2)], CC with single- and double-excitations (CCSD), coupled-perturbed HF and density functional theory (DFT), and open-shell calculations at the unrestricted CCSD (UCSSD) one. Applications involve eight closed-shell organic-chemistry molecules (Set I), the first four members of the closed-shell thiophene oligomer series (Set II), and five open-shell radicals (Set III). In Set I, all calculated average polarisabilities agree reasonably well with experimental data. In Set II, all calculated average polarisabilities vs. the number of monomers show comparable values and saturation patterns and demonstrate that experimental polarisabilities may be inaccurate. In Set III, UCCSD perpendicular polarisabilities show a reasonable agreement with previous UCCSD(T) and restricted-open-shell-MBPT(2) values.     

Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution

Using a Maximum Entropy Production Principle (MEPP), we derive a new type of relaxation equations for two-dimensional turbulent flows in the case where a prior vorticity distribution is prescribed instead of the Casimir constraints [R. Ellis, K. Haven, B. Turkington, Nonlinearity 15, 239 (2002)]. The particular case of a Gaussian prior is specifically treated in connection to minimum enstrophy states and Fofonoff flows. These relaxation equations are compared with other relaxation equations proposed by Robert and Sommeria [Phys. Rev. Lett. 69, 2776 (1992)] and Chavanis [Physica D 237, 1998 (2008)]. They can serve as numerical algorithms to compute maximum entropy states and minimum enstrophy states with appropriate constraints. We perform numerical simulations of these relaxation equations in order to illustrate geometry induced phase transitions in geophysical flows.     

Stochastic analysis of a Hopf bifurcation: Master equation approach

The effect of inhomogeneous fluctuations in a reaction-diffusion system exhibiting a Hopf bifurcation is analyzed using the master equation approach. A Taylor expansion of the logarithm of the stationary probability, known as the stochastic potential, is calculated. This procedure displays marked analogies with the theory of normal forms. The critical potential, reduced to its local expansion around an arbitrary point of the limit cycle, brings out the essential role played by the phase of the oscillating variables. A comparison with the Langevin analysis of Walgraefet al. [J. Chem. Phys. 78(6):3043 (1983)] is performed.     

An Elementary Proof of Lyapunov Exponent Pairing for Hard-Sphere Systems at Constant Kinetic Energy

The conjugate pairing of Lyapunov exponents for a field-driven system with smooth inter-particle interaction at constant total kinetic energy was first proved by Dettmann and Morriss [Phys. Rev. E 53:R5545 (1996)] using simple methods of geometry. Their proof was extended to systems interacting via hard-core inter-particle potentials by Wojtkowski and Liverani [Comm. Math. Phys. 194:47 (1998)], using more sophisticated methods. Another, and somewhat more direct version of the proof for hard-sphere systems has been provided by Ruelle [J. Stat. Phys. 95:393 (1999)]. However, these approaches for hard-sphere systems are somewhat difficult to follow. In this paper, a proof of the pairing of Lyapunov exponents for hard-sphere systems at constant kinetic energy is presented, based on a very simple explicit geometric construction, similar to that of Ruelle. Generalizations of this construction to higher dimensions and arbitrary shapes of scatterers or particles are trivial. This construction also works for hard-sphere systems in an external field with a Nosé–Hoover thermostat. However, there are situations of physical interest, where these proofs of conjugate pairing rule for systems interacting via hard-core inter-particle potentials break down.     

On the Zero Mass Limit of Tagged Particle Diffusion in the 1-d Rayleigh-Gas

We consider the M→0 limit for tagged particle diffusion in a 1-dimensional Rayleigh-gas, studied originaly by Sinai and Soloveichik [Ya. G. Sinai, M. R. Soloveichik, Commun. Math. Phys. 104:423–443 (1986)], and by Szász and Tóth [D. Szász, B. Tóth, Commun. Math. Phys. 104:445–457 (1986)], respectively. In this limit we derive a new type of model for tagged particle diffusion, for which the two central particles, in addition to elastic collisions with the rest of the gas, interact with Calogero-Moser-Sutherland (i.e. inverse quadratic) potential. Computer simulations on this new model reproduce exactly the numerical value of the limiting variance obtained by Boldrighini, Frigio and Tognetti in [C. Boldrighini, S. Frigio, D. Tognetti, J. Stat. Phys. 108:703–712 (2002)]. Dedicated to Domokos Szász on his 65th birthday.     

On the Relation Between Projections of the Reweighted Path Ensemble

We derive several distribution functions for the recently introduced reweighted path ensemble [Rogal et al. in J. Chem. Phys. 133:174109, 2010]: the configurational and path densities, the reactive current, and the generalized committors for the different path types. We relate these distributions to the free energy and to the expressions for the rate constant in the transition state theory, the reactive flux method, the transition path (interface) sampling framework, and the Bayesian path statistics. In addition, we compute the transmission coefficient (distribution) from the reweighted path ensemble. Finally, we derive the path sampling shooting point distributions. For a simple two dimensional Langevin model we illustrate how these novel distributions can be used as analysis tools in rare event simulations.     

Symplectic integration approach for metastable systems

Nonadiabatic behavior of metastable systems modeled by anharmonic Hamiltonians is reproduced by the Fokker-Planck and imaginary time Schr?dinger equation scheme with subsequent symplectic integration. Example solutions capture ergodicity breaking, reassure the H-theorem of global stability [M. Shiino, Phys. Rev. A 36, 2393 (1987)], and reproduce spatially extended response under alternate source fields.     

Theoretical reason for the lack of influence of 1H–14N cross-relaxation on the water proton T 1 NMRD profile in slow tumbling proteins

For immobilized protein the water proton T ₁-NMRD profile displays three enhanced relaxation peaks (QP). For slow tumbling proteins these relaxation peaks are not experimentally observed. However, the theoretically determined QP effect on the amide proton T ₁-NMRD profile displays a distorted Lorentzian dispersion profile. The question arises as to whether there is also a distortion of the water-proton T ₁-NMRD profile due to QP. The model of Sunde and Halle [J. Magn. Reson. 203, 257 (2010)] predicts a decreasing QP relaxation contribution and, with the aid of a model for tumbling proteins [P.-O. Westlund, Phys. Chem. Chem. Phys, 12, 3136 (2010)], it is shown that the QP effect is absent in water-proton T ₁-NMRD profiles for slow tumbling proteins with τ_R?I.     

On the limitation of the van der Waals-Platteeuw-based thermodynamic models for hydrates with multiple occupancy of cavities

Thermodynamic models based on the van der Waals–Platteeuw statistical theory (Adv. Chem. Phys. 2, 1 (1959)) can be very accurate in describing hydrate equilibrium conditions, even for some occasions when multiple cavity occupancy occurs. These are cases outside the range of assumptions used for the development of the original statistical theory. However, during multiple cavity occupancy such models can perform poorly when calculating the cavity occupancies. This paper reports novel Grand Canonical Monte Carlo molecular simulations for the case of pure structure II N₂ hydrate and compares the calculated cavity occupancies with experimental data and observe reasonable agreement. Also examined are the van der Waals–Platteeuw-based modifications that retained the single-occupancy assumption of the original theory and how they perform when predicting cavity occupancies and hydrate equilibrium pressures.     

Vibrationally resolved K-shell photoionization cross sections of methane

We use an extension of the static-exchange density functional theory (DFT) method, previously reported in [E. Plésiat et al., Phys. Rev. A 2, 023409 (2012), E. Plésiat, P. Decleva, F. Martín, Phys. Chem. Chem. Phys. 31, 10853 (2012)], to evaluate vibrationally resolved (total and angular) K-shell photoelectron cross sections of methane. The calculated cross sections are in very good agreement with the existing experimental measurements at low photoelectron energies. We show that, in contrast with the rich interference patterns previously observed in molecular frame C(1s) photoelectron angular distributions of methane at both low and high photoelectron energy, no interference effects are observed in the calculated β parameters, even at high photon energies.