Potential, intermolecular anisotropy

In atom-atom potentials the anisotropy of the intermolecular potential, i.e., its dependence on the molecular orientations atom-atom potential in the form (15). It has been demonstrated by Sack (1964), Yasuda and Yamamoto (1971), and Downs et al. (1979) that analytic expressions can be derived for the expansion coefficients v rPP ) in (15) for atom-atom potentials (see Section II,A) with fM(rafi) = r dependence and by Briels (1980) that they can be derived for atom-atom interactions with exponential dependence... 

Surface SHG [4.307] produces frequency-doubled radiation from a single pulsed laser beam. Intensity, polarization dependence, and rotational anisotropy of the SHG provide information about the surface concentration and orientation of adsorbed molecules and on the symmetry of surface structures. SHG has been successfully used for analysis of adsorption kinetics and ordering effects at surfaces and interfaces, reconstruction of solid surfaces and other surface phase transitions, and potential-induced phenomena at electrode surfaces. For example, orientation measurements were used to probe the intermolecular structure at air-methanol, air-water, and alkane-water interfaces and within mono- and multilayer molecular films. Time-resolved investigations have revealed the orientational dynamics at liquid-liquid, liquid-solid, liquid-air, and air-solid interfaces [4.307]. 

The major reasons for using intrinsic fluorescence and phosphorescence to study conformation are that these spectroscopies are extremely sensitive, they provide many specific parameters to correlate with physical structure, and they cover a wide time range, from picoseconds to seconds, which allows the study of a variety of different processes. The time scale of tyrosine fluorescence extends from picoseconds to a few nanoseconds, which is a good time window to obtain information about rotational diffusion, intermolecular association reactions, and conformational relaxation in the presence and absence of cofactors and substrates. Moreover, the time dependence of the fluorescence intensity and anisotropy decay can be used to test predictions from molecular dynamics.(167) In using tyrosine to study the dynamics of protein structure, it is particularly important that we begin to understand the basis for the anisotropy decay of tyrosine in terms of the potential motions of the phenol ring.(221) For example, the frequency of flips about the C -C bond of tyrosine appears to cover a time range from milliseconds to nanoseconds.(222)... 

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. 

Basis set superposition error (BSSE) is a particular problem for supermolecule treatments of intermolecular forces. As two moieties with incomplete basis sets are brought together, there is an unavoidable improvement in the overall quality of the supermolecule basis set, and thus an artificial energy lowering. Various approximate corrections to BSSE are available, with the most widely used being those based on the counterpoise method (CP) proposed by Boys and Bemardi [3]. There are indications that potential energy surfaces corrected via the CP method may not describe correctly the anisotropy of the molecular interactions, and there have been some suggestions of a bias in the description of the electrostatic properties of the monomers (secondary basis set superposition errors). 

Since electrostatics dies off more slowly than dispersion, it is this repulsive correlation correction that remains at long distance. The authors left their results as a warning against attempts to simulate a true correlated intermolecular potential by supplementing the SCF interaction by dispersion alone. Another point is that there is a definite anisotropy to dispersion, as there is to other correlation components, that should not be ignored in construction of empirical potentials to model the interaction. 

The induced polarizability is also more complex to model especially for the big polyatomic molecules. Insufficient data concerning the interaction potentials are often a hindrance and make an accurate analysis less certain. To complicate matters even more, the anisotropy of the intermolecular interaction is often insufficiently known, or it is hard to account for even if it is known. 

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. 

S. L. Price and A. J. Stone, Mol. Phys., 47,1457 (1982). The Anisotropy of the CI2 CI2 Pair Potential as Shown by the Crystal Structure. Evidence for Intermolecular Bonding or Lone Pair Effects ... 

All intermolecular potentials are anisotropic to a certain extent. We need to consider anisotropy theoretically, first to define numerically the limits of the previously employed spherical approximation and second in an attempt to extend our simple theoretical tools to more complex potentials. 

Anisotropy of the repulsive core or of the attractive well, or both, can be treated in a similar manner, and as a practical example we will consider V-T transfer for an intermolecular potential composed of a spherical repulsive core surrounded by an anisotropic attractive well (such as dipole-dijjole interaction). We will further invoke an approximate localization of the relaxation interaction on the repulsive core, implying that the multipolar long-range forces do not directly influence the relaxation probability. This assumption is... 

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