Intermolecular interactions, quadrupole

In this expression, the dipole dipole interactions are included in the electrostatic term rather than in the van der Waals interactions as in Eq. (9.43). Of the four contributions, the electrostatic energy can be derived directly from the charge distribution. As discussed in section 9.2, information on the nonelectrostatic terms can be deduced indirectly from the charge density. The polarizability a, which occurs in the expressions for the Debye and dispersion terms of Eqs. (9.41) and (9.42), can be expressed as a functional of the density (Matsuzawa and Dixon 1994), and also obtained from the quadrupole moments of the experimental charge density distribution (see section 12.3.2). However, most frequently, empirical atom-atom pair potential functions like Eqs. (9.45) and (9.46) are used in the calculation of the nonelectrostatic contributions to the intermolecular interactions. 

IV. Quadrupole Moments of Symmetric Systems and Their Manifestations in Intermolecular Interactions... 

The above simple picture of the attractive component of intermolecular forces is certainly not complete. Since a complete electrostatic description of a molecule usually requires the introduction of higher-order moments, one must also consider the potential energy due to dipole quadrupole interactions, quadrupole-quadrupole interactions, and interactions of moments of higher order. These lead to terms proportional to and so on. Obviously, the potential energy... 

We will now enter into a more detailed discussion on the determination of the molecular electric quadrupole moments from Eq. (II. 1). Quadrupole moments are important in the calculation of intermolecular interaction potentials > and as test quantities for quantum chemical calculations. Several quadrupole moments calculated according to Eq. (II. 1) from experimentally determined ground state rotational constants, g-values, and magnetic susceptibility anisotropies are listed in Table II. 1. Also listed for comparison are quadrupole moments calculated from empirically determined atom dipoles and from INDO-wavefunctions... 

Static ( eie)> polarization ( poi), van der Waals ( vdw)> and total interacting energies were calculated when a fluorine ion approaches the hexafluoroben-zene molecule perpendicular to the center of the aromatic ring. The obtained results point out the importance of the polarization component, which is similar to the electrostatic term in the 2.0 to 3.0 A range, the equihbrium distance for the fluoride aryl centroid complex is 2.6 A. The authors mention the importance of the quadrupole moment for understanding intermolecular interactions of aromatic system but they do not elaborate on this issue in this work. 

There is a third geometrical type, in which parallel aromatic molecules are parallel but not offset, i.e., face-to-face (FF) or eclipsed. For the electrostatic reasons just outlined, this is not an energy minimum for a pair of identical molecules in a symmetrical motif and is rarely observed. However, if the two aromatic molecules in a motif are different, with complementary electron distributions, the FF motif can be the energy minimum. One of the better-known instances of this is the intermolecular interaction between a hydrous arene and a perfluorous arene. Due to the opposite polarization of the C-H and C-F bonds, the molecular quadrupoles of CgHe and CgFe are oppositely signed, and so the electrostatic intermolecular stabilization between them is maximized with FF geometry. 

All transferable force fields discussed in Sect. 4.1 employ point charges to account for the molecular charge distribution, although a more accurate description of the electrostatics with higher multipole moments may be used. Hasse, Vrabec, and coworkers [102,109] proposed a set of simple united-atom force fields for more than 70 compounds of different classes that describe the intermolecular interactions using two LJ 12-6 sites plus a point dipole (15) or a point quadrupole (16). The potential... 

Quadrupole relaxation studies of the mobility of covalent compounds have almost exclusively dealt with the pure compounds and medium effects on halogen quadrupole relaxation are virtually unknown. Furthermore, we have seen in the above description of models of molecular motion in liquids and the interpretation of correlation times that the effect of specific intermolecular forces has in most cases been disregarded. For the understanding of the influence of different types of intermolecular interactions on molecular reorientation, systematic studies of quadrupole relaxation in liquid mixtures should be helpful. Halogen relaxation investigations of this type are nonexistent in the literature but a preliminary investigation in our... 

Even if most work has been performed on neat liquids the possibilities of the quadrupole relaxation method providing information on intermolecular interactions in multi-component systems have been recognized. It is expected that on complex formation the molecular mobility is slowed down but that for an anisotropic molecule the degree of slowing down of different reorientations depends on the mode of interaction. Except for the study by Huntress [58 61], cited above, on the system chloroform-benzene no such studies have been performed... 

Isosteric sorption heats of N2 and O2 obtained by SIM for Li,RE-LSX zeolite are shown in Figure 21 as dependences on sorption-phase concentration, n. The plots - AH vs. n for N2 and O2 exhibit three characteristic ranges (i) at c. ni 3 mol/kg, which reflects specific interactions of N2 and O2 quadrupoles with Li-b ions that may, in principle, occupy energetically different extra-framework sites (if) at c. (3S ni 6) mol/kg, which is governed by mostly non-specific van der Waals-type interactions, between gas molecules and the zeolite framework, and intermolecular interactions (Hi) at c. (65 w5 9) mol/kg, i.e., for n approaching... 

A more difficult situation exists when, in the free compounds, there are strong intermolecular interactions the perturbation of these interactions by complex formation can result in an increased NQI in a complex which contradicts the usual, simple prediction of an NQI reduction upon transition to a complex. Such situations are met in complexes of mercury halogenides such as HgBr2-dioxan and Hgl2-dioxan. More complete interpretation of the experimental results can be achieved if in a complex there is present a number of quadrupole nuclei this allows a comparison of shifts for each of them. In addition, there is often useful structural data available from X-ray diffraction. Finally for an estimation of a relative role of the various contributions to observable NQR frequency shifts, one can resort to theoretical calculations. 

---