Intermolecular potentials thermodynamic properties from

In the present paper we review recent advances in the symmetry-adapted perturbation theory calculations of interaction potentials and interaction-induced properties. We will give a brief description of the theoretical methods needed on the route from the intermolecular potential and properties to rovibrational spectra and collision-induced Raman spectra. We also discuss applications of the interaction potentials and interaction-induced polarizabilities to compute (thermodynamic and dielectric) second virial coefficients. Finally, we illustrate these theoretical approaches on several examples from our own work. 

Computing thermodynamic properties is the most important validation of simulations of solutions and biophysical materials. The potential distribution theorem (PDT) presents a partition function to be evaluated for the excess chemical potential of a molecular component which is part of a general thermodynamic system. The excess chemical potential of a component a is that part of the chemical potential of Gibbs which would vanish if the intermolecular interactions were to vanish. Therefore, it is just the part of that chemical potential that is interesting for consideration of a complex solution from a molecular basis. Since the excess chemical potential is measurable, it also serves the purpose of validating molecular simulations. 

The electrostatic part, Wg(ft), can be evaluated with the reaction field model. The short-range term, i/r(Tl), could in principle be derived from the pair interactions between molecules [21-23], This kind of approach, which can be very cumbersome, may be necessary in some cases, e.g. for a thorough analysis of the thermodynamic properties of liquid crystals. However, a lower level of detail can be sufficient to predict orientational order parameters. Very effective approaches have been developed, in the sense that they are capable of providing a good account of the anisotropy of short-range intermolecular interactions, at low computational cost [6,22], These are phenomenological models, essentially in the spirit of the popular Maier-Saupe theory [24], wherein the mean-field potential is parameterized in terms of the anisometry of the molecular surface. They rely on the physical insight that the anisotropy of steric and dispersion interactions reflects the molecular shape. 

The starting point is an expression for the intermolecular potential energy, Ul, for two solute particles, i and j, distance r apart in solution. From this expression it is theoretically possible to calculate the thermodynamic properties of the solution. The quantitative link is provided by the radial distribution function, g(r), which provides information concerning the distribution of particles in solution. 

Detailed calculations on the condensed phases of biphenyl have been carried out by the variable shape isothermal-isobaric ensemble Monte Carlo method. The study employs the Williams and the Kitaigorodskii intermolecular potentials with several intramolecular potentials available from the literature. Thermodynamic and structural properties including the dihedral angle distributions for the solid phase at 300 K and 110 K are reported, in addition to those in the liquid phase. In order to get the correct structure it is necessary to carry out calculations in the isothermal-isobaric ensemble. Overall, the Williams model for the intermolecular potential and Williams and Haigh model for the intramolecular potential yield the most satisfactory results. In contrast to the results reported recently by Baranyai and Welberry, the dihedral angle distribution in the solid state is monomodal or weakly bimodal. There are interesting correlations between the molecular planarity, the density and the intermolecular interaction. 

Equations (3.2) and (3.3) relate intermolecular interactions to measurable solution thermodynamic properties. The excess chemical potential is obtained from... 

In a recent study, a new model of fluids was described by using the generalized van der Waals theory. Actually, van der Waals over 100 years ago suggested that the structure and thermodynamic properties of simple fluids could be interpreted in terms of neatly separate contributions from intermolecular repulsions and attractions. A simple cubic equation of state was described for the estimation of the surface tension. The fluid was characterized by the Lennard-Jones (12-6) potential. In a recent study the dependence of surface tension of liquids on the curvature of the liquid-vapor interface has been described. ... 

One simple universal equation applies to all substances, requiring no substance-specific parameters. However, for most real states, the ideal-gas equation is inadequate, and real-fluid properties are obtained by adding to the ideal-gas equation the contribution of intermolecular potential in the form of deviation functions, also called residual functions. A major objective of Section 4.2 is to derive the deviation functions from the equation of state of the substance. Because the ideal-gas properties are known, to And the deviation function is as good as finding the state function of a real substance. In this way the ideal-gas equation is used universally in all equation-of-state calculations of thermodynamic functions. 

A general method of predicting the effective molecular diameters and the thermodynamic properties for fluid mix-tures based on the hard-sphere expansion conformal solution theory is developed. The method of Verlet and Weis produces effective hard-sphere diameters for use with this method for those fluids whose intermolecular potentials are known. For fluids with unknown potentials, a new method has been developed for obtaining the effective diameters from isochoric behavior of pure fluids. These methods have been extended to polar fluids by adding a new polar excess function, to account for polar contributions in a mixture. A new set of pseudo parameters has been developed for this purpose. The calculation of thermodynamic properties for several fluid mixtures including CH —C02 has been carried out successfully. 

Physically, the dependence of the ion-induced nucleation rate of a substance on the sign of the ion charge must arise from some asymmetry in the molecular interactions. Such asymmetry should, in principle, manifest itself in a sign dependence of the relevant thermodynamic quantities such as the surface tension. To account for the ion charge preference in ion-induced nucleation requires a statistical mechanical theory, which assumes an intermolecular potential as the fundamental information required to evaluate the relevant thermodynamic properties. 

Van der Waals interactions, or noncovalent-bonded interactions, play an essential role of intermolecular interaction potentials in condensed matter physics, materials chemistry, and structural biology. These interactions are crucial for understanding and predicting the thermodynamic properties of liquids and solids [1], the energy transfers among molecular complexes [2], and the conformational tertiary structures of nanostructures. Intermolecular bonds do not originate from sharing of electrons... 

Although successful in many applications, the RISM approximation suffers from a number of major defects. First, it is not the best choice to calculate the equation of state, and the results that are obtained are thermodynamically inconsistent. Secondly, calculated structural properties show an unphysical dependence on the presence of auxiliary sites, i.e., on sites that label points in a molecule but contribute nothing to the intermolecular potential. Thirdly, use of the RISM approximation leads to trivial and incorrect results for certain quantities descriptive of angular correlations in the fluid. ... 

In molecular force fields, the interaction energy between sites can be divided into contributions from intramolecular and intermolecular interactions. The significance of the different contributions to the force field varies depending on the required application. E.g., for industrial engineering applications, simple models with a low computational cost are required that are nonetheless able to predict accurately thermodynamic properties. Numerous force fields of varying complexity are currently available. The simplest force fields include only potentials that describe the intermolecular interactions and are frequently used for small molecules. More complex force fields include intramolecular interactions that are necessary for the simulation of larger molecules such as polymers. 

The Nath, Escobedo, and de Pablo (NERD) force field [100,131-133] was developed to provide accurate predictions of thermodynamic properties. It is currently available for linear [100] and branched alkanes [131,133] as well as for alkenes [132]. It has a similar functional form as the TraPPE-UA force field, but bond stretching is included. This interaction and angle bending are represented by harmonic potentials [(20) and (22)]. The torsional potential is of the form of (25), neglecting cross terms. The U 12-6 potential (6) is used to describe the intermolecular and intramolecular interactions between sites that are separated by more than three bonds. The LJ parameters were obtained from fits to experimental values of liquid density and second virial coefficient. Saturated liquid densities from the NERD force field are in good... 

Equations of state are used in engineering to predict the thermodynamic properties in particular the phase behaviour of pure substances and mixtures. However, since there is neither an exact statistical-mechanical solution relating the properties of dense fluids to their intermolecular potentials, nor detailed information available on intermolecular potential functions, all equations of state are, at least partially, empirical in nature. The equations of state in common use within both industry and academia are described elsewhere in this book and can be arbitrarily classified as follows (1), cubic equations derived from the observation of van der Waals that are described in Chapter 4 (2), those based on the virial equation discussed in Chapter 3 (3), equations based on general results obtained from statistical mechanics and computer simulations mentioned in Chapter 8 and (4), those obtained by selecting, based on statistical means, terms that best represent the available measurements obtained from a broad range of experiments as outlined in Chapter 12. The methods used for mixtures are also alluded to in these chapters and in Chapter 6. 

A subset of predictive procedures is formed when a limited set of measurements of some physical property for a particular fluid, either microscopic or macroscopic, has been performed for which a rigorous theory exists, but which is devoid of approximations or contains approximations that are well-characterized. The theory may then be used to allow the available measurements on one prtq erty to be used to predict another for which no measurements are available. This may be done either directly through an explicit theoretical relationship between the prq>erties, or through the intermediacy of an intermolecular potential derived from data on one property. In the first case it is unlikely that the temperature range of the prediction can exceed that of the original measurements, whereas in the latter case it is possible that new thermodynamic states may be treated. The scheme is predictive in the sense that no information on the property to be evaluated is required an example of such a procedure is the evaluation of the thermal conductivity of monatomic gases from the viscosity, which is discussed in Chapters 4 and 11. 

Most of the information about purely 2D fluids has been obtained from computer simulations or from the application of theories commonly used in the three-dimensional case. In this subsection, we will summarize the most important studies and results about the properties of the 2D Lermard-Jones system, which is the most widely used model. The 2D L-J system is defined through the intermolecular potential given in Eq. (12), where now the distance is considered only in two dimensions, the L-J parameters a and real fluid. In both computer simulations and theories, the thermodynamic properties are commonly expressed in reduced (adimensional) units, marked with a superscript, which are related to the real imits through the L-J parameters as follows ... 

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