Intermolecular potentials square-well

The intermolecular potential consists of the sum of Eqs. (176), (177), (178), and (179). This simulation was done for 216 and 512 molecules but again only the autocorrelation functions for 512 molecules are discussed here. This potential is the strongest angular dependent potential we considered. The results from this potential indicate that it is slightly stronger than that in real liquid carbon monoxide. For example the mean square torque/TV2), for this simulation is 36 x 10-28 (dyne-cm)2 51 and the experimental value is 21 x 10-28 (dyne-cm)2. If this potential is taken seriously, then it should be pointed out that this small discrepancy in torques could be easily removed by using a smaller quadrupole moment. This would be a well justified step since experimental quadrupole moments for carbon monoxide range from 0.5 x 10-26 to 2.43 x 10-26 esu.49... 

The H-bond stretching frequency provides a measure of the curvature of the bottom of the well in the intermolecular potential. It is therefore instructive to point out that correlates fairly well with the interaction energy. These frequencies are rather small, on the order of 100 cm", and occur in the far-IR region of the spectrum. As a point of comparison, the stretching frequency of the C—F covalent bond typically appears at approximately 1000 cm". Since the force constant is proportional to the square of the frequency, one can say that the curvature of the H-bond potential is only some 1/100 that of the C —F bond. 

Fig. 2-1 Models of intermolecular potentials, (a) Forceless mass points (b) elastic hard spheres (c) elastic hard spheres with superposed central attractive forces (d) molecules with central finite repulsive and attractive forces (e) square-well model (f) point centers of inverse-power repulsion or attraction.

The intermolecular bead-bead interactions are represented by a single square well or single square shoulder potential as given in Eq. (2) ... 

Eqs 3.5 and 3.7 are easily evaluated by numerical quadrature for any assumed intermolecular potential-energy function uy. In a few simple cases, analytical results may be obtained and we consider here the case of the hard-core-square-well potential defined by... 

There is no strict equilibrium bond length R for the hard sphere or square well potentials, because there is no unique value of R at which the potential energy reaches a minimum. The square well, like the Morse potential, does have a dissociation energy. For intermolecular bonds, we shall label this dissociation energy (the well-depth) by e, rather than by D, which we use for dissociation of a chemical bond. 

The square well potential is another simplified intermolecular potential energy function that adds a shell with a constant, negative potential energy value to the hard sphere potential. 

Consider the intermolecular potential curve of a molecule represented on the one hand by the hard sphere model (with repulsive wall k, s = 2.4 A) and on the other by the square well model (with well between = 2.4 A... 

One model potential used for intermolecular forces combines the square well and an exponential... 

Fig. 9.1. A schematic representation of the radial distribution functions (above) and the respective potential functions (below) left, square well (full hues) and normal repulsive potential (dashed lines) center, attractive potential right, a complete intermolecular potential function.

Figure 9.16 The Square-Well Representation of the Intermolecular Potential of a Pair of Atoms.

The second simulation technique is molecular dynamics. In this technique, which was pioneered by Alder, initial positions of theparticles of a system of several hundred particles are assigned in some way. Displacements of the particles are determined by numerically simulating the classical equations of motion. Periodic boundary conditions are applied as in the Monte Carlo method. The first molecular dynamics calculations were done on systems of hard spheres, but the method has been applied to monatomic systems having intermolecular forces represented by the square-well and Lennard-Jones potential energy functions, as well as on model systems representing molecular substances. Commercial software is now available to carry out molecular dynamics simulations on desktop computers. ... 

There are other commonly employed intermolecular potentials such as square-well, Buckingham, and Coulomb similar to that of the L-J potential. 

A very simple but useful intermolecular potential is the so-called square well (cf. Fig. 3.6.3)... 

We shall now approximate the average intermolecular field acting on each element by a spherical square-well potential co (r) centered on the lattice point such that (cf. 7.3.1)... 

The rectangular form of the well, being cmde, nevertheless allows us to obtain a rather adequate description of local-order intermolecular forces arising in a liquid, which generally presents a state intermediate between solid body and gas. We emphasize that popular [13, 14] parabolic, cosine, or cosine-squared potential wells generally give poor description of the wideband... 

Figure 42. Form of the cosine-squared potential, in which a dipole vibrates (solid line). The horizontal dashed line marks the mean angular amplitude ( 45°) on the potential curve C/(0). Dotted curve denotes dimensionless intermolecular static electric field. For the chosen p value (p = 0.8) about 46% and 56% of the dipoles perform complete rotation, respectively, in the case of ordinary and heavy water. Upper horizontal line marks the value of the potential near edge of well. In the center of regions A the potential undergoes minimum (zero value) and the absolute value of static field-maximum.

---