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The Boyle temperature, TB, for an n-segment polymer in solution is the temperature where the second osmotic virial coefficient, A2, is zero. This characteristic is of interest for its connection to the polymer condensation critical temperature, particularly for n → ∞. TB can be measured experimentally or computed for a given model macromolecule. For the latter, we present and examine two approaches, both based on the Mayer-sampling Monte Carlo (MSMC) method, to calculate Boyle temperatures as a function of model parameters. In one approach, we use MSMC calculations to search for TB, as guided by the evaluation of temperature derivatives of A2. The second approach involves numerical integration of an ordinary differential equation describing how TB varies with a model parameter, starting from a known TB. Unlike general MSMC calculations, these adaptations are appealing because they neither invoke a reference for the calculation nor use special averages needed to avoid bias when computing A2 directly. We demonstrate these methods by computing TB lines for off-lattice linear Lennard-Jones polymers as a function of chain stiffness, considering chains of length n ranging from 2 to 512 monomers. We additionally perform calculations of single-molecule radius of gyration Rg and determine the temperatures Tθ, where linear scaling of R g 2 with n is observed, as if the polymers were long random-walk chains. We find that Tθ and TB seem to differ by 6% in the n → ∞ limit, which is beyond the statistical uncertainties of our computational methodology. However, we cannot rule out systematic error relating to our extrapolation procedure as being the source of this discrepancy. [ABSTRACT FROM AUTHOR]

We describe an extension of the ZENO program for polymer and nanoparticle characterization that allows for precise calculation of the virial coefficients, with uncertainty estimates, of polymeric structures described by arbitrary rigid configurations of hard spheres. The probabilistic method of virial computation used for this extension employs a previously developed Mayer-sampling Monte Carlo method with overlap sampling that allows for a reduction of bias in the Monte Carlo averaging. This capability is an extension of ZENO in the sense that the existing program is also based on probabilistic sampling methods and involves the same input file formats describing polymer and nanoparticle structures. We illustrate the extension's capabilities, demonstrate its accuracy, and quantify the efficiency of this extension of ZENO by computing the second, third, and fourth virial coefficients and metrics quantifying the difficulty of their calculation, for model polymeric structures having several different shapes. We obtain good agreement with literature estimates available for some of the model structures considered. [ABSTRACT FROM AUTHOR]

The virial equation of state (VEOS) provides a rigorous bridge between molecular interactions and thermodynamic properties. The past decade has seen renewed interest in the VEOS due to advances in theory, algorithms, computing power, and quality of molecular models. Now, with the emergence of increasingly accurate first-principles computational chemistry methods, and machine-learning techniques to generate potential-energy surfaces from them, VEOS is poised to play a larger role in modeling and computing properties. Its scope of application is limited to where the density series converges, but this still admits a useful range of conditions and applications, and there is potential to expand this range further. Recent applications have shown that for simple molecules, VEOS can provide first-principles thermodynamic property data that are competitive in quality with experiment. Moreover, VEOS provides a focused and actionable test of molecular models and first-principles calculations via comparison to experiment. This Perspective presents an overview of recent advances and suggests areas of focus for further progress. [ABSTRACT FROM AUTHOR]

Implementation of the harmonically mapped averaging (HMA) framework in the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is presented for on-the-fly computations of the energy, pressure, and heat capacity of crystalline systems during canonical molecular dynamics simulations. HMA has a low central processing unit and storage requirements and is straightforward to use. As a case study, the properties of the Lennard-Jones and embedded-atom model (parameterized for nickel) crystals are computed. The results demonstrate the higher efficiency of the new class compared to the inbuilt LAMMPS classes for calculating these properties. However, HMA loses its effectiveness in systems where diffusion occurs in the crystal, and an example is presented to allow this behavior to be recognized. In addition to its improved precision, HMA is less affected by small errors introduced by having a larger time step in molecular dynamics simulations. We also present an analysis of the effect of potential truncation on anharmonic properties, and show that artifacts of truncation on the HMA averages can be eliminated simply by shifting the potential energy to zero at the truncation radius. Full properties can be obtained by adding easily computed values for the lattice and harmonic properties using the untruncated potential. [ABSTRACT FROM AUTHOR]

In Paper I [J. R. Elliott, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 143, 114110 (2015)] of this series, a methodology was presented for computing the coefficients of a power series of the Helmholtz energy in reciprocal temperature, β, through density series based on cluster integral expansions. Previously, power series in β were evaluated by thermodynamic perturbation theory (TPT) using molecular simulation of a reference fluid. The present methodology uses cluster integrals to evaluate coefficients of the density expansion at each individual order of temperature. While Paper I [J. R. Elliott, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 143, 114110 (2015)] developed this methodology for square well (SW) spheres, the present work extends the methodology to Lennard-Jones (LJ) spheres, where the reference fluid is the Weeks-Chandler-Andersen potential. Comparisons of TPT coefficients computed from cluster integrals to those from molecular simulation show good agreement through third order in β when coefficients are expressed with effective approximants. Notably, the agreement for LJ spheres is much better than for SW spheres although fewer coefficients of the density series (B2–B5) are available than for SW spheres (B2–B6). The coefficients for Bi(β) of the reference fluid are shown to follow a simple relationship to the virial coefficients of hard sphere fluids, corrected for the temperature dependency of the equivalent hard sphere diameter. This lays the foundation for a correlation of the second virial coefficient of LJ spheres B2(β) that extrapolates to infinite order in temperature. This correlation of B2(β) provides a basis for estimating the low density limit of TPT coefficients at all orders in temperature, facilitating a recursive extrapolation formula to estimate TPT coefficients of fourth order and higher over the entire density range. The applicability of the resulting equation of state is demonstrated by computing the thermodynamic properties for LJ spheres and comparing to standard simulation results. [ABSTRACT FROM AUTHOR]

We report equilibrium molecular simulation data for the classical Lennard-Jones (LJ) model, covering all thermodynamic states where the crystal is stable, as well as fluid states near coexistence with the crystal; both fcc and hcp polymorphs are considered. These data are used to compute coexistence lines and triple points for equilibrium among the fcc, hcp, and fluid phases. All results are obtained with very high accuracy and precision such that coexistence conditions are obtained with one to two significant figures more than previously reported. All properties are computed in the limit of an infinite cutoff radius of the LJ potential and in the limit of an infinite number of atoms; furthermore, the effect of vacancy defects on the free energy of the crystals is included. Data are fit to a semi-empirical equation of state to within their estimated precision, and convenient formulas for the thermodynamic and coexistence properties are provided. Of particular interest is the liquid-vapor-fcc triple point temperature, which we compute to be 0.694 55 ± 0.000 02 (in LJ units). [ABSTRACT FROM AUTHOR]

The precision and accuracy of the anharmonic energy calculated in the canonical (NVT) ensemble using three different thermostats (viz., Andersen, Langevin, and Nosé-Hoover) along with no thermostat (i.e., microcanonical, NVE) are compared via application to aluminum crystals at ≈100 GPa for temperatures up to melting (4000 K) using ab initio molecular dynamics (AIMD) simulation. In addition to the role of the thermostat, the effect of using either conventional or the recently introduced harmonically mapped averaging (HMA) method is considered. The effect of AIMD time-step size Δt on the ensemble averages gauges accuracy, while for a given Δt, the stochastic uncertainty (computed using block averaging) provides the metric for precision. We identify the rate of convergence of block averages (with respect to block size) as an important issue in this context, as it imposes a minimum simulation length required to achieve reliable statistics, and it differs considerably among the methods. We observe that HMA with a Langevin thermostat in an NVT simulation shows the best performance, from the point of view of accuracy, precision, and simulation length. In addition, we introduce a novel HMA-based ensemble average for the temperature. In application to NVE simulations, the new formulation exhibits much smaller fluctuations compared to the conventional kinetic-energy approach; however, it provides only marginal improvement in uncertainty due to strong negative correlations exhibited by the conventional form (which acts to reduce its uncertainty but also slows convergence of the block averages). [ABSTRACT FROM AUTHOR]

Isothermal-isobaric Monte Carlo molecular simulation is used to measure the vapor-phase fugacity coefficients and equation of state of three fixed-charge models of water that are SPC/E, MSPC/E, and TIP3P. Findings reveal that the model show significant deviation from ideal-gas behavior, considerably more than seen experimentally, and a second-order virial treatment does not fully characterize the behavior.

Cluster integrals are evaluated for the coefficients of the combined temperature- and densityexpansion of pressure: Z = 1 + B2(β)η + B3(β)η² + B4(β)η³ + ..., where Z is the compressibility factor, η is the packing fraction, and the Bi(β) coefficients are expanded as a power series in reciprocal temperature, β, about β = 0. The methodology is demonstrated for square-well spheres with δ = [1.2-2.0], where δ is the well diameter relative to the hard core. For this model, the Bi coefficients can be expressed in closed form as a function of β, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the β series. Expanding the Bi coefficients in β provides a correspondence between the power series in density (typically called the virial series) and the power series in β (typically called thermodynamic perturbation theory, TPT). The coefficients of the β series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in β. These comparisons show good agreement at first order in β, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in β. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in β appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid. [ABSTRACT FROM AUTHOR]

The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone. [ABSTRACT FROM AUTHOR]

We calculated virial coefficients BN, 8 = N = 16, of the Lennard-Jones (LJ) model using both the Mayer-sampling Monte Carlo method and direct generation of configurations, with Wheatley's algorithm for summation of clusters. For N = 8, 24 values are reported, and for N = 9, 12 values are reported, both for temperatures T in the range 0.6 = T = 40.0 (in LJ units). For each N in 10 = N = 16, one to four values are reported for 0.6 = T = 0.9. An approximate functional form for the temperature dependence of BN was developed, and fits of LJ BN(T) based on this form are presented for each coefficient, 4 = N = 9, using new and previously reported data. [ABSTRACT FROM AUTHOR]