Multipole contributions intermolecular interactions

Examples of such approximate methods are the computation of intermolecular interaction energies in terms of experimental multipole moments of empirical atomic contributions. 

However, this formula, which expresses the dielectric constant of the medium in terms of the polarizability of an individual molecule, is only a rough approximation even for cubic crystals with the van der Waals forces acting between the isotropic molecules. For instance, the formula takes no account of spatial dispersion. Moreover, it does not take into account the contribution of the higher multipoles to the energy of the intermolecular interaction which is important at distances of the order of lattice constant. 

The book contains basic facts about the field of intermolecular interactions given in the language of perturbation theory, as well as the multipole expansion (including a lot of usefiil formulas for the electrostatic, induction, and dispersion contributions). This very well written book presents many important problems in a clear and comprehensive way. 

If the charge distribution is described by a set of distributed multipoles, as described in Section 4.2.3, the coulombic contributions to the intermolecular potential energy are calculated as multipole-multipole terms. The main disadvantage of even a rigorous distributed multipole model is that such a representation is still very localized, so that coulombic energies miss a large part of the penetration contribution. For use in a complete representation of intermolecular interactions, the dispersion, polarization, and repulsion terms must be evaluated separately by some semi-empirical or fiilly empirical method, for example the approximate atom-atom formulations of equations 4.38. 39. This approach has been extensively exploited by S. L. Price and coworkers over the years, in applications to molecular crystals [48]. 

Abstract We review two essential features of the intermolecular interaction energies (AE) computed in the context of quantum chemistry (QC) non-isotropy and non-additivity. Energy-decomposition analyses show the extent to which each comes into play in the separate AE contributions, namely electrostatic, short-range repulsion, polarization, charge-transfer and dispersion. Such contributions have their counterparts in anisotropic, polarizable molecular mechanics (APMM), and each of these should display the same features as in QC. We review examples to evaluate the performances of APMM in this respect. They bear on the complexes of one or several ligands with metal cations, and on multiply H-bonded complexes. We also comment on the involvement of polarization, a key contributor to non-additivity, in the issues of multipole transferability and conjugation. In the last... 

The results of energy partitioning in Li+... OH2 obtained with a number of different basis sets are listed in Table 3. Since intermolecular overlap is small in these kind of complexes (Table 1), we expect the electrostatic model to be a good approximation for classical contributions to the total energy of interaction. Indeed, ZlE cou is to a good approximation proportional to the dipole moment of the water molecule calculated with the same basis set. This can be seen even more clearly in Table 4 where zIEcou is compared with ion-dipole and ion-quadrupole energies obtained from the classical expression of the multipole expansion series 45,95-97) ... 

The potential outside the charge distribution and due to it is simply related to the moments, as is the interaction energy when an external field is applied.14 The multipole moments are thus very useful quantities and have been extensively applied in the theory of intermolecular forces, particularly at long range where the electrostatic contribution to the interaction may be expanded in moments. Their values are related to the symmetry of the system thus, for instance, a plane of symmetry indicates that the component of n perpendicular to it must be zero. Such multipoles are worth calculating in their own right. 

Later, a more concrete case of calculation of perturbing molecule 2 with a multipole moment Qtl on molecule 1 with the multipole moment is considered. Substituting in Eq. (226) an appropriate operator of intermolecular Coulomb interaction (Gray, 1968 Armstrong et al., 1968) and averaging over the orientations of the molecules, we find the following expression of the contribution in (t2) due to the direct Coulomb interaction ... 

This contribution to the total molecule/surface interaction is caused by the Coulomb interaction between the charge distributions of the ionic crystal and the adsorbed molecule or, stated differently, by the potential energy of the adsorbed molecule in the electrostatic field above the solid surface. In the theory of intermolecular forces, this interaction is generally expressed by means of a multipole expansion... 

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