Thermodynamic Perturbation Research Articles

Solvation Free Energy Calculations: The Combination between the Implicitly Polarized Fixed-charge Model and the Reference Potential Strategy.

The IPolQ-Mod charges, which are the average of two charge sets fitted in vacuum state and condensed phase, take account of polarization effect implicitly in the solvation free energy calculation. However, the performance of the IPolQ-Mod charges sensitively depends on the QM levels used to generate the electrostatic potential from which the charges are fitted. In addition, the forces on atoms are not accurate theoretically in the molecular dynamics (MD) simulation as the solvent only feels the electrostatic potential of a half-polarized density of the solute according to the derivation of the IPolQ-Mod charges. To study these issues in detail, the IPolQ-Mod charges are combined with the reference potential (RP) strategy to predict the solvation free energies in the present study. It is found that the thermodynamic perturbation (TP) corrections utilizing total energy difference and interaction energy difference are almost the same and free of bias. The solvation free energies estimated by the RP method match very well with those obtained by applying IPolQ-Mod charges into MD simulation directly. By means of the RP strategy, the performances of the IPolQ-Mod charges with the change of the strength of the exact HF exchange in several DFT functionals are determined effectively. Although the "optimal" strengths are found in B3LYP and LC-ωPBE, the improvements over the default strength are not too much. In addition to the IPolQ-Mod charges, other charge models like bond charge correction (BCC) charges could also be combined with the RP strategy to study the thermodynamic properties like solvation free energy. © 2019 Wiley Periodicals, Inc.

On the liquid–vapour coexistence curve in a Lennard–Jones fluid

A hard-core double Yukawa potential is taken as an approximation of the Lennard–Jones (LJ) potential. Using first-order thermodynamic perturbation theory with a hard-sphere fluid as the reference system, the equation of state of the hard-core double Yukawa fluid is derived analytically. Adjusting the hard-core diameter with the Barker and Henderson prescription to account for the repulsive part of the LJ potential, the liquid–vapour coexistence curve of the LJ fluid is computed with such equation of state. The results are compared with simulation data for the LJ fluid and very good agreement is observed.

A doubly associated reference perturbation theory for water

In this work we develop a new classical perturbation theory for water which incorporates the transition to tetrahedral symmetry in both the dispersion and hydrogen bonding contributions to the free energy. This transition is calculated self-consistently using Wertheim's thermodynamic perturbation theory. However, since the reference fluid structure to the hydrogen bonding theory itself depends on hydrogen bonding, the theory represents an approach which goes beyond perturbation theory. The theory is shown to accurately represent the thermodynamics of pure water. It is demonstrated that the new theory can reproduce the anomalous density maximum as well as minima in the isothermal compressibility and isobaric heat capacity.

Role of the soft-core repulsion upon the prediction of characteristic curves with PC-SAFT

In this work, the role of the soft-core repulsion upon the capability of the perturbed chain-statistical fluid association theory (PC-SAFT) of predicting coherent Brown's ideal curves (Amagat, Boyle, and Charles) was analyzed. The soft-core repulsion was introduced by using two different theoretical approaches to define the effective diameter into the Barker and Henderson thermodynamic perturbation theory (TPT). The Brown's characteristic curves were predicted for seven pure components, representing spherical, planar, and non-spherical molecules. For all modeled components (i.e., independent of the molecular size) the soft-core repulsion included into the original effective diameter of PC-SAFT fails to predict physically coherent Amagat curves, and this original diameter should be used with caution to perform calculations at extreme conditions of temperature and pressure. On the contrary, the soft-core model resulting of combining the Boltzmann factor criterion (BFC) approach and the generalized Lennard-Jones (GLJ) potential gives as a result a simple, analytical, and temperature-dependent effective diameter, which permitted to trace physically coherent Brown's characteristic curves with this equation of state (EoS). Finally, the BFC effective diameter was used to determine the effect of varying the intermolecular potential steepness (or softness) upon the Brown's characteristic curves, producing Amagat envelopes that increased at higher steepness (i.e., less softness), while the contrary behavior was found for both the Boyle and Charles curves.

On-the-fly machine learning force field generation: Application to melting points

An efficient and robust on-the-fly machine learning force field method is developed and integrated into an electronic-structure code. This method realizes automatic generation of machine learning force fields on the basis of Bayesian inference during molecular dynamics simulations, where the first principles calculations are only executed, when new configurations out of already sampled datasets appear. The developed method is applied to the calculation of melting points of Al, Si, Ge, Sn and MgO. The applications indicate that more than 99 \% of the first principles calculations are bypassed during the force field generation. This allows the machine to quickly construct first principles datasets over wide phase spaces. Furthermore, with the help of the generated machine learning force fields, simulations are accelerated by a factor of thousand compared with first principles calculations. Accuracies of the melting points calculated by the force fields are examined by thermodynamic perturbation theory, and the examination indicates that the machine learning force fields can quantitatively reproduce the first principles melting points.

Zero-temperature limit and statistical quasiparticles in many-body perturbation theory

The order-by-order renormalization of the self-consistent mean-field potential in many-body perturbation theory for normal Fermi systems is investigated in detail. Building on previous work mainly by Balian and de Dominicis, as a key result we derive a thermodynamic perturbation series that manifests the consistency of the adiabatic zero-temperature formalism with perturbative statistical mechanics---for both isotropic and anisotropic systems---and satisfies at each order and for all temperatures the thermodynamic relations associated with Fermiliquid theory. These properties are proved to all orders.

Extension of Wertheim's thermodynamic perturbation theory to include higher order graph integrals.

This work extends Wertheim's Thermodynamic Perturbation Theory (TPT) to include dimer-dimer graphs, i.e., we extend the theory beyond the so-called single-chain approximation. The theory is referred to as thermodynamic perturbation dimer theory. We provide a graph-theoretical derivation of the additional dimer-dimer term and resum the graphs in terms of 3- and 4-particle correlation functions. It is shown how orientationally averaged (hard-sphere) correlation functions can be obtained by Monte Carlo simulation. The 4-particle correlation function, which arises from the additional order term, is adjusted to results of molecular (hard-sphere) dimer fluid simulations. A new equation of state for linear, flexible hard chain fluids is obtained. The predictions of the compressibility factor and the second virial coefficient of the new theory show a better agreement to results from molecular simulations compared as compared to TPT1 and TPT2. We compare the results of the derived theories with simulated data of chains with length ν = 4, 8, 16, and 64 and show that simply considering higher orders of the regular TPT is not sufficient to describe the low-density behavior of longer chains.

Calculation of electrical resistivity of Na-based liquid binary alkali alloys

Electrical resistivity, ρ, for Na-based liquid alkali binary alloys namely NaxK1−x, NaxRb1−x, NaxCs1−x and NaxLi1−x are calculated using the extended Ziman's formula developed by Faber and Ziman. Form factor, Vij(q), and partial structure factor, Sij(q), are the main ingredients of this calculation. For Vij(q), we have chosen Bretonnet-Silbert (BS) pseudo-potential with Ichimaru-Utsumi (IU), and Vashishta-Singwi (VS) local field correction functions. For Sij(q), we have chosen linearized Weeks-Chandler-Andersen (LWCA) thermodynamic perturbation theory. From the comparison of the calculated results of ρ with available experimental data and other theoretical values, a good qualitative consistency is found except for liquid NaxLi1−x alloys. We observe that VS local field correction function along with LWCA theory provides much better results than those obtained with IU local field correction near melting point at the liquid state. Calculated results at temperatures far from the melting curve are deviated much from experimental data. Explanation behind this discrepancy requires a further study with more sophisticated theory.

On the solvation force of water-like fluid models with square-well attraction and site–site association in slit-like pores: density functional approach

The solvation force of the water-like fluid models with square-well attraction and site–site chemical association confined to slit-like pores has been explored. Theoretical procedure is based on the application of the density functional approach with mean-field approximation for the attractive interparticle interactions. The chemical association effects are treated by using the first-order thermodynamic perturbation theory of Wertheim. Trends of behaviour of the solvation force are put in correspondence with the distribution of molecules in the pores and with the average density of the adsorbate. Moreover, the distribution of non-bonded species on pore width is described. The influence of the width of the square-well and of the gas–solid attraction is discussed. A comparison of theoretical predictions with computer simulations results for water models in slit-like pores is performed.

First-principles study of the melting temperature of MgO

Using first-principles only, we calculate the melting point of MgO, also called periclase or magnesia. The random phase approximation (RPA) is used to include the exact exchange as well as local and non-local many-body correlation terms, in order to provide high accuracy. Using the free energy method, we obtain the melting temperature directly from the internal energies calculated with DFT. The free energy differences between the ensembles generated by the molecular dynamics simulations are calulated with thermodynamic integration or thermodynamic perturbation theory. The predicted melting temperature is $T_m^\text{RPA} =3043\pm 86$ K, and the values obtained with the PBE and SCAN functionals are $T_m^\text{PBE} = 2747 \pm 59$ K and $T_m^\text{SCAN} = 3032\pm 53 $ K.

Bond cooperativity and ring formation in hydrogen fluoride thermodynamic properties: A two-density formalism framework.

In this work, we develop a thermodynamic perturbation theory using a two-density formalism framework to model the bond cooperativity effect for associating hard sphere and Lennard-Jones fluids. The theory predictions are compared with Monte Carlo simulation results and they are in excellent agreement. We incorporate bond angle dependent ring formation into the theory to calculate hydrogen fluoride thermodynamic properties. The liquid density and vapor pressure obtained by the theory are in good agreement with the experimental data. Comparing the thermo-physical properties of hydrogen fluoride calculated by this theory with previous studies reveals the importance of bond angle dependent ring formation and cooperative hydrogen bonding to capture its anomalous behavior especially in the vapor phase. The cooperativity ratio obtained in our model is close to the values reported by previous quantum studies.

A complete integral equation theory for accurate thermodynamics of chain molecules

An integral equation theory is developed for n-alkane chains ranging in carbon number from eight to infinity through an adaptation of the polymer referenced interaction site model (PRISM). Thermodynamic perturbation theory (TPT) is adapted as the basis for expressing the equation of state through the coupling parameter expansion (CPE) as an extension of the theory developed by Ramana et al. for spherical molecules. The key feature of PRISM theory is the assumption that all pair correlations for a given site type are equivalent, regardless of whether they appear at the end of the chain or in the middle. The present analysis assumes that the PRISM result represents the average over all sites in the chain. The site-site interaction energies are then implemented through a weighted average based on their frequency of occurrence. The CPE is demonstrated through the fourth order in temperature, although higher order terms are accessible in principle. An advantage of the TPT representation is that convergence need be achieved only once for each chain length and density, then the TPT coefficients can be tabulated and interpolated for future reference. This approach moderates difficulties with molecular simulation of fully equilibrated long chains and uncertainty in the estimation of higher order TPT coefficients. Step potentials are used as the basis for validating and refining the theory using published simulation results for n-alkanes through 80 carbons. We find that the first order TPT contribution is fairly accurate regardless of conformational details but the second order TPT contribution is remarkably sensitive to conformation. We can obtain accurate characterization of the second order contribution by varying the stiffness parameter of the semi-flexible chain model. Higher order TPT contributions follow from the second order result. The theory would not be “complete,” however, without accurate characterization of the TPT reference contribution, which simultaneously impacts the first order contribution. We combine the compressibility route with a Yukawa closure to accurately characterize the reference fluid thermodynamics as a function of density, chain length, and bond length. Altogether, the result is an accurate model of all contributions to chain molecular thermodynamics, including the underlying fluid structure. A sample application is demonstrated by generating the phase diagrams through 80 carbons. It is observed that the flatness near the critical region is reproduced by including the higher order TPT contributions, but the impact of higher order contributions in the critical region is diminished for 80 carbon chains.

Theoretical equations of state for a charged fluid.

In this article, we present a molecular thermodynamic study of a system of N particles contained within a volume V and interacting via a hard-core pair potential with an attractive interaction according to the Wolf model for charged systems. This variable-range potential is characterized by three parameters: the repulsive hard-core diameter σ, the energy-well depth ϵ, and the inverse range α; a fourth parameter of the model is a cut-off distance xc that depends on α according to the relation xc = 2/α. Two equations of state (EOSs) are presented and derived from thermodynamic perturbation theory and Monte Carlo (MC) simulation data. The first EOS is given by the standard Zwanzig's high-temperature expansion of the Helmholtz free energy, where the first three perturbation terms a1, a2, and a3 were obtained from MC simulations in the canonical ensemble (NVT) and parameterized as functions of α and the reduced density of particles ρ* = Nσ3/V. The second EOS was obtained from the discrete perturbation theory applied to a discrete representation of the Wolf potential. Results for pressures, internal energies, and isochoric heat capacities are compared to the MC computer simulation data of the Wolf system, including vapor-liquid coexistence curves, for different values of α. Overall, both EOSs give a very good representation of the thermodynamic properties of the Wolf fluid when 0.3 ≤ α ≤ 1.0 and 0.05 ≤ ρ* ≤ 0.8. Since the Yukawa fluid can reproduce information of screened ionic interactions, we discuss the equivalence between the Wolf and Yukawa fluids in the context of equivalent systems in liquid theory.

A new equation of state for homo-polymers in dissipative particle dynamics.

A chain-revised Groot-Warren equation of state (crGW-EOS) was developed and tested to describe systems of homo-oligomeric chains in the framework of dissipative particle dynamics (DPD). First, thermodynamic perturbation theory is applied to introduce correction terms that account for the reduction in pressure with an increasing number of bonds at constant bead number density. Then, this EOS is modified by introducing a set of switching functions that yields an accurate second virial coefficient in the low-density limit. The crGW-EOS offers several improvements over the revised Groot-Warren equation of state and Groot-Warren equation of state for chain molecules. We tested the crGW-EOS by using it to predict the pressure of oligomeric systems and the B2 virial coefficient of chain DPD particles for a range of bond lengths. Additionally, a method is developed for determining the strength of cross-interaction parameters between chains of different compositions and sizes and for thermal and athermal mixtures. We explored how different levels of coarse-graining affect the upper-critical solution temperature.

A resummed thermodynamic perturbation theory for positive and negative hydrogen bond cooperativity in water

In this paper a resummed thermodynamic perturbation theory is developed which accounts for both positive and negative hydrogen bond cooperativity in water. The theory is developed in Wertheim’s multi-density statistical mechanics. We demonstrate that the hydrogen bonded structure of water is controlled by positive hydrogen bond cooperativity in homodromic hydrogen bonded clusters. Inclusion of negative anti-cooperativity in antidromic hydrogen bonded structures has little effect on the underlying hydrogen bond structure of liquid water. The resummed perturbation theory is shown to give hydrogen bond statistics consistent with first principles ab initio molecular dynamics simulations. In addition, the theory is shown to be in good agreement with experiment in the prediction of the average number of hydrogen bonds per water molecule in a liquid at ambient conditions. Finally, we develop a full thermodynamic model for water by including contributions to the free energy for isotropic square well attractions. We demonstrate that the model gives good representation of saturated liquid density, hydrogen bonding and vapor pressure. In addition, we show the full model predicts the anomalous minima in isothermal compressibility and isobaric heat capacity.

Statistical theory of fluids with a complex electric structure: Application to solutions of soft-core dipolar particles

Based on the thermodynamic perturbation theory (TPT) and the random phase approximation (RPA), we present a statistical theory of solutions of electrically neutral soft molecules, every of which is modelled as a set of sites that interact with each other through the potentials, presented as the sum of the Coulomb potential and arbitrary soft-core potential. As an application of our formalism, we formulate a general statistical theory of solution of the soft-core dipolar particles. For the latter, we obtain a new analytical relation for the screening function. As a special case, we apply this theory to describing the phase behavior of a solution of the dipolar particles interacting with each other in addition to the electrostatic potential through the repulsive Gaussian potential – Gaussian core dipolar model (GCDM). Using the obtained analytic expression for the total free energy of the GCDM, we obtain the liquid-liquid phase separation with an upper critical point. The developed formalism could be used as a general framework for the coarse-grained description of thermodynamic properties of solutions of macromolecules, such as proteins, betaines, polypeptides, etc.

Thermodynamic properties of CH4, CCl4 and CF4 on the melting line. Theory and computer simulation

Thermodynamic properties of the condensed phases of methane CH4, carbon tetrafluoride CF4 and carbon tetrachloride CCl4 on the melting line and in the high-pressure region were studied using the equations of state developed earlier for methane in the framework of the thermodynamic perturbation theory. We also present the results of Monte Carlo computer simulations of fcc phases of methane, carbon tetrachloride, and of the monoclinic tetrafluoromethane phase using a potential model that takes into account both the central and octupole–octupole interaction. The contribution of the octupole–octupole interaction to the thermodynamic properties of crystals are evaluated. The simulation results are compared with the available experimental data on the sublimation and melting lines, as well as to results of previous calculations based on the equations of state.

Analytic results for the three- and four-particle correlation functions of the fluid of hard disks.

Analytic expressions for the three- and four-particle correlation functions of the hard disk fluid in terms of geometric functionals have been derived using the combined geometric/thermodynamic idea of Boublik [Fluid Phase Equilib. 316, 1 (2012)]. To assess the approximate result, extensive Monte Carlo simulations were performed to obtain the triplet correlation function, g3, over a wide range of densities. We then focussed on the rolling contact configurations that are required in the second-order thermodynamic perturbation theory of patchy colloid models. The analytic approximation is shown to perform very well, and the simulation data have therefore been parametrized using Boublik's functional form for their subsequent use.

Surface charge modulation of sulfobetaine micelles by interaction with different anions: A dynamic light scattering study

This work reports a Dynamic Light Scattering study on aqueous micelles formed by tetradecyl dialkylammonium propanesulfonate surfactants (sulfobetaines; with alkyl = methyl, ethyl, n‑propyl and n‑butyl) within a range of surfactant concentrations (0.01–0.40 M) both in pure water and in the presence of various concentrations of NaBr, NaOH and NaClO4 (0.02–0.50 M NaBr; 0.10–1.00 M NaOH; 0.005–0.50 M NaClO4). From values of diffusion coefficients, D, we obtained micellar hydrodynamic radii, Rh, by application of the Stokes-Einstein relation. Plots of D vs. sulfobetaine concentrations can be qualitatively explained with a model based on a linear interaction theory, which allowed to separate thermodynamic and hydrodynamic perturbations to D. Results show that: i) formally neutral sulfobetaine micelles become negatively charged by preferential interaction with strongly interacting, “soft” anions; ii) the surface negative charge increases with the hydrophobicity of the anions; iii) bulkier alkyl substituents on the sulfobetaine head groups lead to less charged, less hydrated aggregates, which result in opposite perturbations to D; (iv) highly hydrated, high charge density hydroxide ions lead to an increase of micellar sizes through a disc-like growth pattern.

Diagnosing Ocean Feedbacks to the BSISO: SST‐Modulated Surface Fluxes and the Moist Static Energy Budget

AbstractThe oceanic feedback to the atmospheric boreal summer intraseasonal oscillation (BSISO) is examined by diagnosing the sea surface temperature (SST) modification of surface fluxes and moist static energy on intraseasonal scales. SST variability affects intraseasonal surface latent heat (LH) and sensible heat (SH) fluxes, through its influence on air‐sea moisture and temperature gradients (∆q and ∆T, respectively). According to bulk formula decomposition, LH is mainly determined by wind‐driven flux perturbations, while SH is more sensitive to thermodynamic flux perturbations. SST fluctuations tend to increase the thermodynamic flux perturbations over active BSISO regions, but this is largely offset by the wind‐driven flux perturbations. Enhanced surface fluxes induced by intraseasonal SST anomalies are located ahead (north) of the convective center over both the Indian Ocean and the western Pacific, favoring BSISO northward propagation. Analysis of budgets of column‐integrated moist static energy (⟨m⟩) and its time rate of change (∂⟨m⟩/∂t) shows that SST‐modulated surface fluxes can influence the development and propagation of the BSISO, respectively. LH and SH variability induced by intraseasonal SSTs maintain 1–2% of ⟨m⟩ day−1 over the equatorial western Indian Ocean, Arabian Sea, and Bay of Bengal but damp about 1% of ⟨m⟩ day−1 over the western North Pacific. The contribution of intraseasonal SST variability to ∂⟨m⟩/∂t can reach 12–20% over active BSISO regions. These results suggest that SST variability is conducive, but perhaps not essential, for the propagation of convection during the BSISO life cycle.