Comparison of modern Langevin integrators for simulations of coarse-grained polymer melts

For a wide range of phenomena, current computational ability does not always allow for atomistic simulations of high-dimensional molecular systems to reach time scales of interest. Coarse-graining (CG) is an established approach to alleviate the impact of computational limits while retaining the same algorithms used in atomistic simulations. It is important to understand how algorithms such as Langevin integrators perform on non-trivial CG molecular systems, and in particular how large of an integration time step can be used without introducing unacceptable amounts of error into averaged quantities of interest. To investigate this, we examined three different Langevin integrators on a CG polymer melt: the recently developed BAOAB method by Leimkuhler and Matthews [J. Chem. Phys. 138 (17), 05B601_1 (2013)], the Grønbech-Jensen and Farago method [Mol. Phys. 111 (8), 983-991 (2013)], or G-JF, and the frequently used Brünger–Brooks–Karplus integrator [Chem. Phys. Lett. 105 (5), 495-500 (1984)], known as BBK. We compute and analyse key statistical properties for each. Our results indicate that the integrators perform similarly for a small friction parameter; however outside this regime, the use of large integration steps produces significant deviations from the predicted diffusivity and steady-state distributions for all methods examined with the exception of G-JF.     

Is it possible to infer the equation of state of a mixture of hard discs from that of the one-component system?

Based on exact asymptotic properties of the composition-independent virial coefficients of a binary mixture of hard discs in the limits α = σ₂/σ₁ → 0, α → 1 and α → ∞, R. J. Wheatley (1998, Molec. Phys., 93, 965) has recently proposed an approximate interpolation equation for these coefficients. In this note, the equation of state equivalent to this interpolation is obtained, expressing the compressibility factor of the mixture in terms of that of the pure system. An extension to an arbitrary number of components is also given. The equation of state derived here is compared with another one recently proposed by following a different route (Santos, A., Yuste, S. B., and López de Haro, M., 1999, Molec. Phys., 96, 1) and with Monte Carlo simulation results. It is shown that the latter equation is more accurate than the former one, at least for not too disparate mixtures (0.7 < α < 1).     

On some empirical expressions of the contact values of the pair distribution functions and fluid-fluid phase separation in hard sphere mixtures

(Molec. Phys., 2001, 99, 2055–2060)     

Is it possible to infer the equation of state of a mixture of hard discs from that of the one-component system?

(Molec. Phys., 1999, 96, 1185–1188)     

Theoretical study of the Renner-Teller A 2A1 − X 2B1 system of NH2

(Molec. Phys., 1994, 81, 1445–1461)     

Relativistic corrections for the vibration-rotation levels of the ground electronic state of the hydrogen molecular cation H+ 2

Previous work [Moss, R. E., and Valenzano, L., 2002, Molec. Phys., 100, 649 and 1527] on the non-adiabatic properties of the vibration-rotation levels of the ground electronic state of the hydrogen molecular cation is extended to the calculation of relativistic corrections. Unlike the earlier calculations, in which all matrix elements were evaluated analytically, numerical methods are needed for some of the integrals.     

Equation of state for systems of soft diatomic molecules

A new potential that is a modification of the BBL (Bratko, D.,Blum, L., and Luzar, A.,1985, J. chem. Phys., 83, 6367; Blum, L., Vericat, F., and Bratko, D., 1995, J. chem. Phys., 102, 1461) potential and of the one recently solved analytically by Blum and Vericat (BV) (1995, Molec. Phys., 86, 809; 1996, J. phys. Chem., 100, 1197) is studied by Monte Carlo simulation. The main feature of this potential is that it can be solved using only a small number of parameters (3 in the case treated by BV), and therefore produces a substantial simplification of earlier work. The new potential has an orientational octupole–octupole interaction term which is found necessary to reproduce the broad peak of the oxygen–oxygen structure function due to the tetrahedral position of the second nearest neighbour water molecule. This important feature was absent in the original BBL potential. This model agrees also with the experimental pair correlation functions for oxygen–hydrogen and hydrogen–hydrogen, and yields 42·6 kJ mol^-1 for the internal energy of water, also in agreement with experiment. The hard core central repulsion causes the sharpness of the first peaks in all three correlation functions. This is not necessary but convenient for an analytical solution.     

Effect of short- and long-range forces on the properties of fluids. III. Dipolar and quadrupolar fluids

Using realistic pair potential models for acetone and carbon dioxide, both the spatial and orientational structure of these two typical multipolar (i.e. dipolar and quadrupolar, respectively) fluids is investigated in detail by computing the complete set of the site-site correlation functions, multipole-multipole correlation functions, and selected 2D correlation functions. The effect of the range of interactions on both the structural and thermodynamic properties of these fluids is studied by decomposing the potential into short- and long-range parts in the same manner as for water [Kolafa, J. and Nezbeda, I., 2000, Molec. Phys., 98, 1505; Nezbeda, I. and Lísal, M., 2001, Molec. Phys., 99, 291]. It is found that the spatial arrangement of the molecules is only marginally affected by the long-range forces. The effect of the electrostatic interactions is significant at short separations and cannot be neglected but nevertheless the overall structure of the short-range and full systems is similar as well as their dielectric constants. These findings are also reflected in the dependence of the thermodynamic properties on the potential range with the short-range models providing a very good approximation to those of the full system.     

Rotational viscosity of uniaxial molecules

Non-equilibrium molecular dynamics (NEMD) are used to calculate the vortex or rotational viscosity of fluids composed of uniaxial molecules. It is shown that the NEMD homogeneous spin flow algorithm proposed by Edberg, R., Evans, D. J., and Moriss, G. P., 1987, Molec. Phys., 62, 1357 considerably underestimates the vortex viscosity. A modified version of this algorithm is proposed and applied to liquid chlorine and nitrogen. The results are in good agreement with previous work using equilibrium or other NEMD methods, and also show that at high spin rates the vortex viscosity decreases with increase in magnitude of the external torque used to drive the spin flow.     

Buoyancy corrections for the potential of an impurity in a 4He nanodroplet

This paper presents correction terms for the effective potential for the translation and rotation of an impurity atom or molecule solvated in a helium nanodroplet that were previously published (Lehmann, K. K., 1999, Molec. Phys., 97, 645). The correction arises from changes in the total He-He potential energy of the displaced liquid as a function of the solute position within the droplet. For the alkali atoms, this buoyancy type correction removes the large barrier to ejection of the atom from the droplets, which is predicted if this term is neglected.     

Study on the analytical solution of the MSA for a one-component two-Yukawa potential in bovine serum albumin—NaC1 aqueous solution

Using the mean spherical approximation (MSA), an explicit analytical equation of state (EOS) with non-dimensional variables for one-component two-Yukawa fluid is established based on the work of Blum, L., and Ubriaco, M., 2000, Molec. Phys., 98, 829. A simple and directly iterative method is found for obtaining an acceptable solution. The strict two-Yukawa EOS is used to correlate the experimental osmotic pressure data of aqueous bovine serum albumin (BSA)-NaCl solutions in the one-component assumption. Considering the experimental error, the correlation results are good, with only one regressed parameter (disperse energy parameter ?). The deviation of correlation is discussed in detail. A concept of effective diameter, which obviously can decrease the deviation of correlation, is given.     

The virial coefficients of hard hypersphere binary mixtures

The third, fourth and fifth virial coefficients of hard hypersphere binary mixtures with dimensionality d = 4, 5 have been calculated for size ratios R ≥ 0.1, R = ≡ σ₂₂/σ₁₁, where σ _ii is the diameter of component i. The composition independent partial virial coefficients have been evaluated by Monte Carlo integration of the corresponding Mayer modified star diagrams. The results are compared with the predictions of Santos, S., Yuste, S. B., and Lopez de Haro, M., 1999, Molec. Phys., 96, 1 of the equation of state of a multicomponent mixture of hard hyperspheres, and the good agreement gives strong support to the validity of that recipe.     

Comment on: An intermolecular potential for nitrogen from a multi-property analysis

A paper by Cappelletti et al. (1998, Molec. Phys. 93, 485) utilizes classical trajectory effective cross-sections to predict the rotational collision number for nitrogen gas. It is suggested that use of the rotational heat capacity, rather than the total internal heat capacity, will give a more meaningful conversion of the cross-sections into relaxation time. In addition, an error in the formula for first-order collision number is corrected.     

The absorption spectrum of diatomic calcium between 120 and 20 nm

The vacuum ultraviolet absorption spectrum of Ca₂ has been extended down to 20?nm by using the same techniques as those described by Nzohabonayo et al. [2003, Molec. Phys., 101, 2917]. All the new states observed are Rydberg states giving three new ionization limits at 13.76?eV, 17.99?eV and a third one higher than 33?eV.     

The wavefunction of the complex coordinate method

We show for a model system previously studied by Moiseyev et al. (1978, Molec. Phys., 36, 1613) how, with a basis of sufficient flexibility, the wave-function of the complex coordinate method can approach the function which can be directly obtained from a numerical integration of the wave equation with a complex coordinate and a complex energy. Diagrams of the complex wavefunction are used to visualize its behaviour in the short and long range regions, and the attenuation (localization) produced by the rotation.     

Interplay between elastic fields due to gravity and a partial dislocation for a hard-sphere crystal coherently grown under gravity: driving force for defect disappearance

We previously observed that an intrinsic staking fault shrunk through a glide of a Shockley partial dislocation terminating its lower end in a hard-sphere crystal under gravity coherently grown in ?001? by Monte Carlo simulations [Mori et al., Molec. Phys. 105, 1377 (2007)]; it was an answer to a one-decade long standing question why the stacking disorder in colloidal crystals reduced under gravity [Zhu et al., Nature 387, 883 (1997)]. Here, we present an elastic energy calculation; in addition to the self-energy of the partial dislocation [Mori et al., Prog. Theor. Phys. Suppl. 178, 33 (2009)] we calculate the cross-coupling term between elastic field due to gravity and that due to a Shockley partial dislocation. The cross-term is an increasing function of the linear dimension R over which the elastic field expands, showing that a driving force arises for the partial dislocation moving toward the upper boundary of a grain.     

Virial coefficients and equations of state for mixtures of hard discs,hard spheres and hard hyperspheres

The composition-independent virial coefficients of a d-dimensional binary mixture of (additive) hard hyperspheres following from a recent proposal for the equation of state of the mixture (Santos, A., Yuste, S. B., and López de Haro, M., 1999, Molec. Phys., 96, 1) are examined. Good agreement between theoretical estimates and available exact or numerical results is found for d = 2, 3, 4 and 5, except for mixtures whose components are very disparate in size. A slight modification that remedies this deficiency is introduced and the resummation of the associated virial series is carried out, leading to a new proposal for the equation of state. The case of binary hard sphere mixtures (d = 3) is analysed in some detail.     

Thermal diffusion in binary mixtures containing molecular gases. III. The temperature dependence of αT

A recent expression for the thermal diffusion factor α_T for binary atom-molecule mixtures, which includes a full range of inelastic collisional contributions [McCourt, F. R. W., 2003, Molec. Phys., 101, 2181] has been utilized to calculate its temperature dependence for equimolar N₂-He, Ne, Ar mixtures and for an equimolar CO₂-Ar mixture. Accurate classical trajectory values for the effective cross-sections entering into the expression for α_T, obtained for the most reliable potential energy surfaces available, have been employed in the calculations. Good agreement has been attained with experiment for all four binary mixtures, including the decrease of α_T with increase in temperature observed for CO₂-Ar mixtures, heretofore considered to be anomalous.     

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r12-)MR-CI. VI. The helium dimer (He2) revisited

A recent computation of the helium dimer interaction potential for intermediate distances (2 ≤ R/a₀ ≤ 15) using the (explicitly correlated) r₁₂-MR-ACPF (averaged coupled-pair functional) method [GDANITZ, R. J., 1999, Molec. Phys., 96, 1423] is extended to larger basis sets. Calculations including a large atom centred [11 s8p6d5f4g3h2ilk] set show that the convergence of the energy with respect to enlargement of the basis set has previously been considerably underestimated. The extension of the P_k potential (292.75 ± 0.01, ?10.980 ± 0.004 and ?4.620 = ± 0.002 K at R = 4, 5.6 and 7 _a0) to distances between 2.5 and 15_a0 (P_k?)is close to a recent potential of van Mourik and Dunning [1999, J. Chem. Phys., 111, 9248] and it is believed to be the most accurate available. It gives rise to ⁴He₂ molecular constants of (R) = 46.4 ± 1.4 Å and D₀ = 1.67 ± 0.11 mK.