Intermolecular interactions physical interpretation

Now the author would like to reconunend the reader to study the multipole expansion concept (Appendix X on p. 1038, also cf. Chapter 12, p. 624). 

In other words, multipole expansion describes the intermolecular interaction of two non-spherically symmetric, distant objects by the interaction of deviations (multipoles) from spherical symmetry. 

To prepare ourselves for the application of the multipole expansion, let us introduce two Cartesian coordinate systems with x and y axes in one system parallel to the corresponding axes in the other system, and with the z axes collinear (see Fig. X.1 on p. 1039). One of the systems is connected to molecule A, the other one to molecule B, and the distance between the origins is R ( intermolecular distance ). 

The very fact that we use closed sets (like the spheres) in the theory, indicates that in the polarization approximation we are in no man s land between the quantum and classical worlds. 

In the square brackets we can recognize the multipole moment operators for the total molecules calculated in their coordinate systems 

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The moments of a charge distribution provide a concise summary of the nature of that distribution. They are suitable for quantitative comparison of experimental charge densities with theoretical results. As many of the moments can be obtained by spectroscopic and dielectric methods, the comparison between techniques can serve as a calibration of experimental and theoretical charge densities. Conversely, since the full charge density is not accessible by the other experimental methods, the comparison provides an interpretation of the results of the complementary physical techniques. The electrostatic moments are of practical importance, as they occur in the expressions for intermolecular interactions and the lattice energies of crystals. 

Thus, we obtain the energy of the supersystem, EAB, from which it is possible to extract exact energies EA and EB for systems A and B and to obtain the expression for the interaction energy up to a particular order of the perturbation expansion. It was not the aim of this chapter to present the details of the MB-RSPT treatment of intermolecular interactions but rather to point out the fundamental ideas involved. Detailed derivation and explicit formulas as well as the physical interpretation of individual terms are presented in Refs.138,139 ... 

Contrary to the previously described supermolecular approach, perturbation theory treatment allows for the partition of the interaction energy into physically interpretable components. The most frequently used method for this purpose is symmetry-adapted perturbation theory (SAPT) [13]. More recently, great effort has also been invested in the development of DFT-SAPT [14-16], In the present contribution, we use the variational-perturbational scheme [17-20], In this approach, the intermolecular interaction energy components are determined based on the wave functions of the subsystems evaluated in the dimer-centered basis set. Thus, both interaction energy and its components are BSSE-free. More details about this scheme can be found elsewhere [21-23]. The total intermolecular interaction energy at the MP2 level of theory can be expressed as follows ... 

Based on the premise that a useful description of molecular structure represents the molecule in a surrounding of other structures, Kier and Hall developed the encounter concept to provide a theoretical basis for the interpretation of the molecular connectivity indices (Kier and Hall, 2000 2001). According to this concept, the measurement of a physical (or biological) property reflects the collective influence of the encounters between each molecule and other molecules in its direct environment. In the light of this theoretical concept, the interpretation of the value is that it encodes the relative accessibility of a bond to encounter another bond in another molecule, the resultant encounter which may lead to an intermolecular interaction. The term accessibility is defined as the topological and electronic availability of one bond to engage in some interaction with another bond. 

Abstract. A comparative investigation of C6o fiillerene solubility and donor force of alkyl derivatives of benzene has been performed. Based on the found correlation, which was determined by current methods, between C6o solubility and donor force of solvents, it has been concluded that the process of Cgo dissolution in aromatic hydrocarbons is a process of intermolecular interaction combined with charge-transfer and formation of complexes of the donor-acceptor type. The agreement between a series of physical and chemical phenomena (factors, properties) observed in studies of C60 solubility and a number of existing criteria which allow the phenomena to be interpreted as a manifestation of the charge-transfer interaction substantiates our conclusion. 

An up-to-day and exhaustive discussion of the computational aspects of ab initio calculations of intermolecular interactions for small to medium size molecules can be found in [12]. In this work, we shall be mostly concerned with the weak interactions occurring between closed-shell molecules in the VdW region, and with the physical interpretation of the different components of the interaction. Almost the whole totality of the experimental data in this region refers in fact to VdW molecules [8, 9, 20, 21],... 

In the present work, for simplicity, we consider the evaluation of all terms at the Hartree-Fock level and for closed-shell molecular ground states. The admission of correlation effects changes neither the essential framework of the theory nor the physical interpretation of the intermolecular interactions. 

Abstract - The crucial details for the interpretation of spatial structures and intermolecular interactions of peptides and proteins could be revealed by proper combination of physical and chemical techniques. The paper presents the results of the combined approach for the evaluation of the conformation in solution of honey-bee venom component apamin (18 membered polypeptide), of three dimensional structure of Central Asian cobra neurotoxin II (61 amino acid residues), and of the topography of its binding site with acetylcholine receptor Torpedo Marmorata. 

In Sections 4.1 and 4.2 we discussed the fact that the electric moments of molecules play an important role in the description of the intermolecular forces between two molecules separated by a large distance. Their contribution to the interaction energy is of purely classical, i.e. electrostatic nature. Here, we want to show now that also the contribution from quantum mechanical dispersion or London forces, i.e. the dispersion energy E, can be related to molecular properties of the two interacting molecules. In particular, we will see that it is related to the frequency-dependent polarizabilities, which is in line with the physical interpretation of the dispersion forces as arising from the interaction of induced dipole moments, which implies that both charge distributions are perturbed by their interaction. 

The first term on the right-hand side of Equation 7.62 describes (within the subset of space) the transition due to the intermolecular interaction alone. The physical interpretation ofthe second term may be regarded in the following manner. Recalling that V is the full (intra- and intermolecular) interaction, the diagonal transition matrix element of R E) may evidently be written in the form... 

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