Intermolecular potentials pair additivity

Intermolecular potential functions have been fitted to various experimental data, such as second virial coefficients, viscosities, and sublimation energy. The use of data from dense systems involves the additional assumption of the additivity of pair interactions. The viscosity seems to be more sensitive to the shape of the potential than the second virial coefficient hence data from that source are particularly valuable. These questions are discussed in full by Hirschfelder, Curtiss, and Bird17 whose recommended potentials based primarily on viscosity data are given in the tables of this section. 

The intermolecular interactions are usually assumed to be pair-additive functions such as the Lennard-Jones 12-6 or 9-6 potentials or the Buckingham expontential-6 type of potentials and are parameterized using methods similar to those described in the previous paragraph to reproduce the crystallographic structure and the lattice energy. For the case of liquid systems the parameterization of non-bonded interactions can be done to reproduce the liquid densities and the heats of vaporization. 

Campbell, E. S., and Mezei, M., Use of a non-pair-additive intermolecular potential function to fit quantum-mechanical data on water molecule interactions, J. Chem. Phys. 67, 2338-2344 (1977). 

These are expressed in terms of scalar products between the unit axis system vectors on sites 1 and 2 (on different molecules) and the unit vector 6. from site 1 to 2. The S functions that can have nonzero coefficients in the intermolecular potential depend on the symmetry of the site. This table includes the first few terms that would appear in the expansion of the atom-atom potential for linear molecules. The second set illustrate the types of additional functions that can occur for sites with other than symmetry. These additional terms happen to be those required to describe the anisotropy of the repulsion between the N atom in pyridine (with Zj in the direction of the conventional lone pair on the nitrogen and yj perpendicular to the ring) and the H atom in methanol (with Z2 along the O—H bond and X2 in the COH plane, with C in the direction of positive X2). The important S functions reflect the different symmetries of the two molecules.Note that coefficients of S functions with values of k of opposite sign are always related so that purely real combinations of S functions appear in the intermolecular potential. 

Despite the serious limitations imposed by the economic restriction to fast irreversible quenches for small systems, there is, in each of the objectives cited above, the distinct compensatory advantage that virtually no restrictions are placed on the choice of the intermolecular potential (except that for economic reasons only it must at present be pairwise additive). Thus computer simulation can be used to assess the requirements in the pair potential for particular modes of behavior in glass formation in ... 

In Chapter 3 we discussed the calculation of the interaction between two particles by summing the intermolecular potential energies between all the molecules in one particle with all those in the other. This is often called the Hamaker or microscopic theory and assumes pair-wise additivity of the intermolecular potential energies. This implies that the potential associated with the interactions of a given molecule is independent of the presence of... 

The intermolecular potential energy of a pair of molecules i,j is represented as a fimction of the relative distance and the mutual orientations o> to,-. It is customary to consider the following contributions, which are supposed to be additive ... 

Strictly taken, a prerequisite for the discussion of cooperativity or nonadditivity requires the definition of the additive or noncooperative case [50]. Generally, in the field of intermolecular interaction, the additive model is a model based on the concept of pairwise additive interactions. For atomic clusters per definition, but also for molecular clusters, the use of pairwise additive interactions is almost always used in combination with the assumption of structurally frozen interaction partners. Even in cases of much stronger intermolecular interactions the concept of pair potentials modified to that of effective pair potentials is often used. Most of the molecular dynamics calculations of liquids and molecular solids take advantage of this concept. 

First, assume the intermolecular iiileraxtion potential from Equation 1.7- 8 to be a pair additive function ... 

Systems such as Ar2HCl and Ar2HF are of great interest, because they offer the hope of a spectroscopic determination of non-additive contributions to intermolecular potentials. Microwave spectra of these systems have been observed and infrared spectra are likely to be feasible. A complete solution of the dynamical problem for such systems is beyond our capabilities at present, but Hutson et al have carried out a preliminary study, investigating the hindered rotation of an HCl molecule under the influence of a (fixed) pair of Ar atoms. 

The second approach is to extend the simple two-parameter corresponding-states principle at its molecular origin. This is accomplished by making the intermolecular potential parameters functions of the additional characterization parameters /I, and the thermodynamic state, for example, the density p and temperature T. This can be justified theoretically on the basis of results obtained by performing angle averaging on a non-spherical model potential and by apparent three-body effects in the intermolecular pair potential. The net result of this substitution is a corresponding-states model that has the same mathematical form as the simple two-parameter model, but the definitions of the dimensionless volume and temperature are more complex. In particular the... 

The most successful corresponding-states theory for mixtures is called the van der Waals one-fluid theory. This theory was developed on a molecular basis by Leland and co-workers and follows from an expansion of the properties of a system about those of a hard sphere system. A hard-sphere system is one whose molecules only have repulsive intermolecular potentials with no attractive contributions. The starting equation for the development of the van der Waals one-fluid (known by the acronym VDW-1) theory is a rigorous statistical-mechanical result for the equation of state of a mixture of pair wise-additive, spherically symmetric molecules ... 

As ve stated earlier, it is possible to express all the thermodynamic properties of a liquid in terms of g(r), if we assume that the intermolecular potential is pair-wise additive. The thermodynamic energy is easily expressed in terms of g(r). e shall do this first by a physical argument and then by a formal approach. For a monatomic fluid, the total energy is given by... 

As usual, we assume that the intermolecular potential is pair-wise additive [Eq. (19)], and so becomes... 

In all molecular statistical calculations, the choice of a proper interaction potential is of crucial importance. Hard-core simulations [242-244,274,278,279,330] assume only repulsive forces between ellipsoidal particles, and fail to reflect realistic properties of the nematic phase [264, 269, 280, 281]. Therefore, attractive intermolecular potentials must be added. In most cases, an additive superposition of pair potentials is assumed in the calculations. Hybrid models use hard core repulsive potentials plus some attractive anisotropic potentials, for example, modified van der Waals models (e.g. 

---