Intermolecular Pair Potential Research Articles

A journey toward the heaven of chemical fidelity of intermolecular force fields

AbstractAlongside the evolution of density functional theory into a new era led by the dispersion‐corrected hybrid density functional theory approaches, formulation of a new generation of intermolecular potentials has also taken the center stage. An ideal potential formulation should desirably possess simplicity of functional forms, physically meaningful parameters, separability of various terms into atomic‐level contributions, computational tractability, ability to capture non‐additivity of interactions, transferability across different chemical species, and crucially, chemical fidelity in terms of reproducing the benchmark data. The Lennard‐Jones potential, one of the popular intermolecular pair potentials for performing large‐scale simulations fails to capture the intricate features of molecular interactions. Woven around the central theme of anisotropy in the nature of intermolecular interactions, herein, we describe various landmark contributions in the quest for chemical fidelity of empirical potential formulations that include (i) incorporation of the anisotropic nature of exchange‐repulsion and dispersion contributions, (ii) multipolar description of the dispersion terms, (iii) damping functions to provide an accurate description of the asymptotes, and (iv) transferability of intermolecular interaction terms. We illustrate the nuances of intermolecular force field development in the context of modeling the non‐covalent interactions governing the (i) binding of atoms and molecules with carbon nanostructures, (ii) molecular aggregates of polycyclic aromatic hydrocarbons, and (iii) interlayer interactions in layered nanostructures. We exemplify the hierarchy of empirical potentials by depicting them on the various rungs of the Jacob's ladder equivalent of density functional theory for the intermolecular force fields. Finally, we discuss some possible futuristic directions in intermolecular force field development.This article is categorized under: Structure and Mechanism > Computational Materials Science Software > Molecular Modeling Molecular and Statistical Mechanics > Molecular Interactions

Algebraic second virial coefficient of the Mie m - 6 intermolecular potential based on perturbation theory.

We propose several simple algebraic approximations for the second virial coefficient of fluids whose molecules interact by a generic Mie m - 6 intermolecular pair potential. In line with a perturbation theory, the parametric equations are formulated as the sum of a contribution due to a reference part of the intermolecular potential and a perturbation. Thereby, the equations provide a convenient (low-density) starting point for developing equation-of-state models of fluids or for developing similar approximations for the virial coefficient of (polymeric-)chain fluids. The choice of Barker and Henderson [J. Chem. Phys. 47, 4714 (1967)] and Weeks, Chandler, and Andersen [Phys. Rev. Lett. 25, 149 (1970); J. Chem. Phys. 54, 5237 (1971); and Phys. Rev. A 4, 1597 (1971)] for the reference part of the potential is considered. Our analytic approximations correctly recover the virial coefficient of the inverse-power potential of exponent m in the high-temperature limit and provide accurate estimates of the temperatures for which the virial coefficient equals zero or takes on its maximum value. Our description of the reference contribution to the second virial coefficient follows from an exact mapping onto the second virial coefficient of hard spheres; we propose a simple algebraic equation for the corresponding effective diameter of the hard spheres, which correctly recovers the low- and high-temperature scaling and limits of the reference fluid's second virial coefficient.

Ab Initio Intermolecular Potential Energy Surfaces and Cross Second Virial Coefficients for the Dimer N2-NO.

Ab initio intermolecular potential energy surfaces (PES) of N2-NO have been constructed at the level of theory CCSD(T) with the augmented correlation-consistent basis sets aug-cc-pVmZ (with m = 2, 3, 4). The nitrogen in the closed-shell electronic configuration X1Σ+ and nitric oxide in the open-shell electronic configuration A2Σ+ were employed to calculate ab initio intermolecular interaction energies. The two new ab initio 5-site intermolecular pair potentials at the theoretical level CCSD(T)/aug-cc-pVmZ (with m = 4, 24) were developed appropriately and are suitable for N2-NO dimer by using the nonlinear least-squares fitting method combining MIO and Levenberg–Marquardt algorithms. The correlation quality of these two potentials was found to be very good with R2 values in the range of 0.98372 to 0.99775. The cross second virial coefficients B12(T) of the N2-NO dimer were calculated in the temperature range of 100 to 470 K using the two ab initio 5-site potentials. The discrepancies between the calculated results and the experimental data can be acceptable.

Maxwell factors for gaseous 2.3.3.3-tetrafluoropropene and cis-1.3.3.3-tetrafluoropropene at zero density

In this study we focused on the Maxwell factor of fluorinated propene isomers 2.3.3.3-tetrafluoropropene and cis-1.3.3.3-tetrafluoropropene last years receiving considerable attention as the next generation of refrigerants. Fluorinated propene isomers contain carboncarbon double bound. The advantage of both refrigerants is a low global warming potential value of 4 and 6 respectively. This paper deals with the temperature dependence of thermal conductivity in the limit of zero density for dilute gases. A theoretically based correlation formalism has been examined according to the kinetic theory of Mason–Monchik–Parker using a set of trial functions and related to the translational and integral effective collisions that incorporate the information concerning intermolecular pair potential and binary collisions. The results have correlated using the Maxwell factor. The analysis of quantities for practical purposes which are related to the thermal conductivity and viscosity has been made.

Structural–Dynamic Phase Transitions in Petroleum Disperse Systems

Using the techniques of proton nuclear magnetic resonance (1H NMR) relaxometry and near-infrared spectroscopy, a multiextremun nature of dependencies of physicochemical properties, fractality, and quantization of changes in 1H NMR parameters that determine phase transitions between types of petroleum disperse systems in the order: Hydrocarbons ⇔ Crude oil ⇔ Atmospheric residue ⇔ Vacuum residue ⇔ Asphalt ⇔ Carbenes ⇔ Coke, has been experimentally established. A model of structural–dynamic transitions, associated with a change in the intermolecular pair potential characterized by a number of minima is proposed.

Calculation of cross second virial coefficients using ab initio intermolecular potential energy surfaces for dimer H2-N2

The ab initio intermolecular pair potentials of dimer H2-N2 were calculated from all constructed orientations, using the level of the theory CCSD(T) and basis sets aug-cc-pVmZ (m = 2, 3, 4, 23, 24, 34). The complete basis sets limit aug-cc-pVmZ (m = 23, 24, 34) were extrapolated by ab initio interaction energies at the level of the theory CCSD(T) with correlation-consistent basis sets aug-cc-pVmZ (m = 2, 3, 4). Then the quantum mechanical results were used for developing two new 5-site intermolecular potential functions by fitting ab initio intermolecular energies of dimer H2-N2. The ab initio fitted intermolecular potentials are used in standard thermodynamic relationships to get the cross second virial coefficients B12(T) of the hydrogen-nitrogen mixture. The calculated results are in good agreement with the experimental data.

Calculation of second virial coefficients using ab initio intermolecular pair potentials for F2-F2 and H2-F2 dimers

The ab initio intermolecular pair potentials of dimers F2-F2 and H2-F2 were calculated from all constructed orientations, using the level of theory CCSD(T) and basis sets aug-cc-pVmZ (m=2, 3, 23). The complete basis set limit aug-cc-pV23Z was extrapolated by ab initio interaction energies at the level of theory CCSD(T) with two basis sets aug-cc-pVmZ (m=2, 3). Then the quantum mechanical results were used for constructing two new 5-site potential functions by fitting ab initio energies of dimers F2-F2 and H2-F2. The correlation between ab initio and the fitted ab initio energies of 5-site pair potentials for dimers F2-F2 and H2-F2 is appeared by fitness values R2 in range 0.99749–0.99997. The fitted potentials were used in standard thermodynamic relations to obtain the second virial coefficients and the results were compared to experimental data.

A Coarse-Grained Model of Stratum Corneum Lipids: Free Fatty Acids and Ceramide NS.

Ceramide (CER)-based biological membranes are used both experimentally and in simulations as simplified model systems of the skin barrier. Molecular dynamics studies have generally focused on simulating preassembled structures using atomistically detailed models of CERs, which limit the system sizes and time scales that can practically be probed, rendering them ineffective for studying particular phenomena, including self-assembly into bilayer and lamellar superstructures. Here, we report on the development of a coarse-grained (CG) model for CER NS, the most abundant CER in human stratum corneum. Multistate iterative Boltzmann inversion is used to derive the intermolecular pair potentials, resulting in a force field that is applicable over a range of state points and suitable for studying ceramide self-assembly. The chosen CG mapping, which includes explicit interaction sites for hydroxyl groups, captures the directional nature of hydrogen bonding and allows for accurate predictions of several key structural properties of CER NS bilayers. Simulated wetting experiments allow the hydrophobicity of CG beads to be accurately tuned to match atomistic wetting behavior, which affects the whole system, since inaccurate hydrophobic character is found to unphysically alter the lipid packing in hydrated lamellar states. We find that CER NS can self-assemble into multilamellar structures, enabling the study of lipid systems more representative of the multilamellar lipid structures present in the skin barrier. The coarse-grained force field derived herein represents an important step in using molecular dynamics to study the human skin barrier, which gives a resolution not available through experiment alone.

Complete equation of state for shocked liquid nitrogen: Analytical developments.

The thermodynamic response of liquid nitrogen has been studied extensively, in part, due to the long-standing interest in the high pressure and high temperature dissociation of shocked molecular nitrogen. Previous equation of state (EOS) developments regarding shocked liquid nitrogen have focused mainly on the use of intermolecular pair potentials in atomistic calculations. Here, we present EOS developments for liquid nitrogen, incorporating analytical models, for use in continuum calculations of the shock compression response. The analytical models, together with available Hugoniot data, were used to extrapolate a low pressure reference EOS for molecular nitrogen [R. Span et al., J. Phys. Chem. Ref. Data 29, 1361 (2000)] to high pressures and high temperatures. Using the EOS presented here, the calculated pressures and temperatures for single shock, double shock, and multiple shock compression of liquid nitrogen provide a good match to the measured results over a broad range of P-T space. These calculations provide the first comparison of EOS developments with recently measured P-T states under multiple shock compression. The present EOS developments are general and are expected to be useful for other liquids that have low pressure reference EOS information available.

QSPR-Modeling for the Second Virial Cross-Coefficients of Binary Organic Mixtures

The second virial cross-coefficient is an important characteristic of the pair intermolecular interactions that describes solely the heterogeneous interactions. In the current study, the authors made the first attempt to develop rigorous QSPR models for analysis and prediction of the second virial cross-coefficient. Novel descriptors to describe pair intermolecular interactions were implemented. Statistical characteristics of the obtained models showed high performance. Prediction errors are comparable to the errors of data. Theoretically predicted values of the second virial cross-coefficient may be used to derive PVT-properties of mixtures at the different temperatures as well as to calculate intermolecular pair potential.

A corresponding-states framework for the description of the Mie family of intermolecular potentials

The Mie (λr, λa) intermolecular pair potential has been suggested as an alternative to the traditional Lennard–Jones (12–6) potential for modelling real systems both via simulation and theory as its implementation leads to an accuracy and flexibility in the determination of thermophysical properties that cannot be obtained when potentials of fixed range are considered. An additional advantage of using variable-range potentials is noted in the development of coarse-grained models where, as the superatoms become larger, the effective potentials are seen to become softer. However, the larger number of parameters that characterise the Mie potential (λr, λa, σ, ϵ) can hinder a rational study of the particular effects that each individual parameter have on the observed thermodynamic properties and phase equilibria, and higher degeneracy of models is observed. Here a three-parameter corresponding states model is presented in which a cohesive third parameter α is proposed following a perturbation expansion and assuming a mean-field limit. It is shown that in this approximation the free energy of any two Mie systems sharing the same value of α will be the same. The parameter α is an explicit function of the repulsive and attractive exponents and consequently dictates the form of the intermolecular pair potential. Molecular dynamics simulations of a variety of Mie systems over a range of values of α are carried out and the solid–liquid, liquid–vapour and vapour–solid phase boundaries for the systems considered are presented. Using the simulation data, we confirm that systems of the same α exhibit conformal phase behaviour for the fluid-phase properties as well as for the solid–fluid boundary, although larger differences are noted in the solid region; these can be related to the approximations in the definition of the parameter. Furthermore, it is found that the temperature range over which the vapour–liquid envelope of a given Mie system is stable follows a linear dependency with α when expressed as the ratio of the critical–point temperature to the triple–point temperature. The limit where potentials of the Mie family will not present a stable fluid envelope is predicted in terms of the parameter α and the result is found to be in excellent agreement with previous studies. This unique relation between the fluid range and the cohesive parameter α is shown to be useful to limit the pairs of Mie exponents that can be used in coarse-grained potentials to treat real systems in order to obtain temperature ranges of stability for the fluid envelope consistent with experiment.

Adding flexibility to the "particles-on-a-sphere" model for large-amplitude motion: POSflex force field for protonated methane.

The so-called "particles-on-a-sphere" (POS) model has been introduced a while ago in order to describe in simple terms large-amplitude motion of polyatomic hydrides, XH(n). The POS model of protonated methane, CH₅⁺, has been shown to capture well the essence of the fluxional nature of this enigmatic floppy molecule. Here, we extend this model to the POSflex force field by adding flexibility to the C-H bonds, which are constrained to a common fixed bond length in the original model. This makes the present model extremely efficient for computer simulation, including path integral molecular dynamics in order to assess the crucial quantum effects on nuclear motion at low temperatures. Moreover, the POSflex force field can be conveniently used to study microsolvation effects upon combining it with intermolecular pair potentials to account for solute-solvent interactions. Upon computing static properties as well as thermal and quantum fluctuation effects at ambient and low temperatures, respectively, it is shown that the POSflex model is very well suited to describe the structural properties of bare CH₅⁺, including hydrogen scrambling and thus fluxionality in the first place. The far- to mid-infrared spectrum up to the bending band is roughly described, whereas the model fails to account for the well-structured stretching band by construction.

An improved kinetic theory approach for calculating the thermal conductivity of polyatomic gases

A new kinetic theory approach for calculating the thermal conductivity of a dilute polyatomic gas from the intermolecular pair potential is presented. The contributions due to internal degrees of freedom have been separated into a classical rotational and a quantum-mechanical vibrational part. Assuming that the vibrational states of the molecules do not significantly influence the collision trajectories, and that vibrationally inelastic and vibrationally resonant collisions are rare, we have obtained a simple self-diffusion mechanism for the vibrational contribution to the thermal conductivity. For non-polar gases like methane or nitrogen, the new approach yields thermal conductivity values that are very close to those obtained with the previously used kinetic theory approach. However, for polar gases like hydrogen sulphide and water vapour, the values obtained with the new scheme are much closer to the most accurate experimental data.

Application of Tao–Mason equation of state to light fluids

A statistically-based equation of state (EOS) proposed by Tao and Mason was applied to four light fluids including 4He, Ne, H2 and CH4. The best intermolecular pair potentials were taken to evaluate the second virial coefficients of four aforecited systems. For CH4 and Ne the first quantum correction, and for He and H2, up to the second quantum correction were performed on the classical second virial coefficient. The calculated second virial coefficients were applied to Tao–Mason (TM) EOS to predict the density of four systems in both subcritical and supercritical regions. Agreement with experiment was excellent for all four systems.

Solubility of CO2 in (Water + Acetone): Correlation of Experimental Data and Predictions from Molecular Simulation

The correlation and prediction of the solubility of gases in (nonelectrolyte as well as in electrolyte) aqueous/organic solvent mixtures is an important topic in many areas of chemical engineering. Despite the importance of that field, comparatively little attention has been given to that area in both classical thermodynamics (i.e., correlation methods that are based on semiempirical expressions for the excess Gibbs energy) and molecular simulation (where gas solubility can be predicted from intermolecular pair potentials). In the work presented here, recently published experimental data for the solubility of carbon dioxide in aqueous solutions of acetone (covering temperatures from 313 to 395 K at pressures ranging up to about 9 MPa) are used for testing a semiempirical, classical method (for the correlation of such gas solubility phenomena) as well as the Gibbs ensemble Monte Carlo method (GEMC) (for predicting the solubility of carbon dioxide in aqueous solutions of acetone from published intermolecula...

Solvent induced shifts of fundamental vibrational frequency and first overtone of CO + Ar solution. Monte-Carlo simulation

CO/Ar solutions in composition range from 0.044 to 0.188 mol fraction of carbon monoxide have been simulated by Monte-Carlo calculation within NPT ensemble. The simulations have been carried out at different values of temperature and pressure. The intermolecular pair potentials depend on the CO vibrational quantum number v, which is vital for the solvent induced frequency shift calculations. The results of these calculations were compared with a few available data of spectroscopic measurements. An analysis of the contributions of different intermolecular interaction types to internal energy and CO vibrational red and blueshift is made. As it follows from simulation results there is a possibility to change the solvent induced shift from red to blue by solution composition variation.

Molecular dynamics in arbitrary geometries: Parallel evaluation of pair forces

A new algorithm for calculating intermolecular pair forces in molecular dynamics (MD) simulations on a distributed parallel computer is presented. The arbitrary interacting cells algorithm (AICA) is designed to operate on geometrical domains defined by an unstructured, arbitrary polyhedral mesh that has been spatially decomposed into irregular portions for parallelisation. It is intended for nano scale fluid mechanics simulation by MD in complex geometries, and to provide the MD component of a hybrid MD/continuum simulation. The spatial relationship of the cells of the mesh is calculated at the start of the simulation and only the molecules contained in cells that have part of their surface closer than the cut-off radius of the intermolecular pair potential are required to interact. AICA has been implemented in the open source C++ code OpenFOAM, and its accuracy has been indirectly verified against a published MD code. The same system simulated in serial and in parallel on 12 and 32 processors gives the same results. Performance tests show that there is an optimal number of cells in a mesh for maximum speed of calculating intermolecular forces, and that having a large number of empty cells in the mesh does not add a significant computational overhead.

Molecular-based equation of state for TIP4P water

Using a theoretically justified decomposition of realistic intermolecular pair potentials into a short-range reference model and a perturbation part, one obtains the Helmholtz free energy in a form made up of several terms, each originating from a different type of interaction. Using a primitive model to estimate the properties of the short-range reference in an analytic form, this decomposition has been used to derive an equation of state of TIP4P water using the vapor-liquid equilibrium data to adjust its parameters. It is shown that the equation reproduces the thermodynamic properties of TIP4P water reasonably well including the temperature density maximum.

Protein–Protein Interactions in Complex Cosolvent Solutions

The effects of various kosmotropic and chaotropic cosolvents and salts on the intermolecular interaction potential of positively charged lysozyme is evaluated at varying protein concentrations by using synchrotron small-angle X-ray scattering in combination with liquid-state theoretical approaches. The experimentally derived static structure factors S(Q) obtained without and with added cosolvents and salts are analysed with a statistical mechanical model based on the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential, which accounts for repulsive and attractive interactions between the protein molecules. Different cosolvents and salts influence the interactions between protein molecules differently as a result of changes in the hydration level or solvation, in charge screening, specific adsorption of the additives at the protein surface, or increased hydrophobic interactions. Intermolecular interaction effects are significant above protein concentrations of 1 wt %, and with increasing protein concentration, the repulsive nature of the intermolecular pair potential V(r) increases markedly. Kosmotropic cosolvents like glycerol and sucrose exhibit strong concentration-dependent effects on the interaction potential, leading to an increase of repulsive forces between the protein molecules at low to medium high osmolyte concentrations. Addition of trifluoroethanol exhibits a multiphasic effect on V(r) when changing its concentration. Salts like sodium chloride and potassium sulfate exhibit strong concentration-dependent changes of the interaction potential due to charge screening of the positively charged protein molecules. Guanidinium chloride (GdmCl) at low concentrations exhibits a similar charge-screening effect, resulting in increased attractive interactions between the protein molecules. At higher GdmCl concentrations, V(r) becomes more repulsive in nature due to the presence of high concentrations of Gdm(+) ions binding to the protein molecules. Our findings also imply that in calculations of thermodynamic properties of proteins in solution and cosolvent mixtures, activity coefficients may not generally be neglected in the concentration range above 1 wt % protein.

Prediction of the thermophysical properties of pure neon, pure argon, and the binary mixtures neon-argon and argon-krypton by Monte Carlo simulation using ab initio potentials.

Gibbs ensemble Monte Carlo simulations were used to test the ability of intermolecular pair potentials derived ab initio from quantum mechanical principles, enhanced by Axilrod-Teller triple-dipole interactions, to predict the vapor-liquid phase equilibria of pure neon, pure argon, and the binary mixtures neon-argon and argon-krypton. The interaction potentials for Ne-Ne, Ar-Ar, Kr-Kr, and Ne-Ar were taken from literature; for Ar-Kr a different potential has been developed. In all cases the quantum mechanical calculations had been carried out with the coupled-cluster approach [CCSD(T) level of theory] and with correlation consistent basis sets; furthermore an extrapolation scheme had been applied to obtain the basis set limit of the interaction energies. The ab initio pair potentials as well as the thermodynamic data based on them are found to be in excellent agreement with experimental data; the only exception is neon. It is shown, however, that in this case the deviations can be quantitatively explained by quantum effects. The interaction potentials that have been developed permit quantitative predictions of high-pressure phase equilibria of noble-gas mixtures.