Intermolecular interactions anisotropicity

Milet, A., Korona, T., Moszynski, R., Kochanski, E., 1999, Anisotropic Intermolecular Interactions in Van der Waals and Hydrogen-Bonded Complexes What Can we Get from Density Functional Theory , J. Chem. Phys., Ill, 7727. 

In MOMs dimensionality is a major issue. As discussed back in Chapter 1, although all materials are structurally 3D, some of them exhibit physical properties with lower dimensionality, ID or 2D, mainly due to the pseudo-planar conformation of the molecules. In fact for bulk materials one cannot strictly use the terms ID or 2D because intermolecular interactions build anisotropic but indeed 3D networks. Hence, one is led to using the prehxes pseudo or quasi when referring to ID or 2D systems. However, ideal ID and 2D systems can be artihcially prepared exhibiting real ID and 2D properties, respectively, and we will hnd some examples of this in the next sections. 

The stress-optical behaviour of an elastomeric network of PDET is measured over a wide range of elongation ratios and temperatures. Theoretical calculations are carried out with the RIS model. For Act, no reasonable modification of the conformational energies or contributions to the anisotropic part of the polarizability tensor would achieve agreement between theory and experiments. The discrepancy between theoretical and experimental results may be qualitatively explained by intermolecular interactions. Agreement between theory and experiment is only obtained assuming the unlikely value of about + 4.2 kJ mol-1 for E(on). 

Jerry and Monnerie l " have proposed a modified theory of rubber elasticity which includes anisotropic intermolecular interactions U12 (favoring the alignment of neighbouring chain segments) in the form U,2 = ZUL(r12) PL(0i) PL(02), where r,2 is the intermolecular distance, 0X and 02 are the angles between the molecular axes... 

In conclusion, we note that for systems like HD-X, the intermolecular interactions become more anisotropic than for H2-X systems, because for HD the center of electronic charge and the center of mass do not coincide. The two centers differ by one sixth of the bond distance. Because the molecule rotates about the center of mass, new anisotropic terms appear in both the HD-X interaction potential and induced dipole components see Chapter 4 for details. 

Molecules generally interact with anisotropic forces. The accounting for the anisotropy of intermolecular interactions introduces substantial complexity, especially for the quantum mechanical treatment. We will, therefore, use as much as possible the isotropic interactions isotropic interaction approximation (IIA), where the Hamiltonian is given by a sum of two independent terms representing rotovibrational and translational motion. The total energy of the complex is then given by the sum of rotovibrational and translational energies. The state of the supermolecule is described by the product of rotovibrational and translational wavefunc-tions, with an associated set of quantum numbers r and t, respectively. 

If collisional systems involving one or more molecules are considered, the internal degrees of freedom of the molecule(s) (e.g., rotation, vibration) have to be taken into account. This often leads to cumbersome notations and other complications. Furthermore, we now have to deal with anisotropic intermolecular interactions which again calls for a significant modification of the formal theory. In that sense, this Chapter differs from the previous one but otherwise the reader will find here much the same material, techniques, etc., as discussed in Chapter 5. 

Practically all computations shown above were undertaken in the framework of the isotropic interaction approximation. For the examples considered, agreement of calculated and observed spectra was found. The most critical comparisons between theory and measurement were made for the H2-X systems whose anisotropy is relatively mild. Nevertheless, some understanding is desirable of what the spectroscopic effects of the anisotropy are. Furthermore, other important systems like N2-N2 and CO2-CO2 are more anisotropic than H2-X. The question thus remains as to what the spectroscopic significance of anisotropic interaction might be. In this Section, an attempt is made to focus on the known spectroscopic manifestations of the anisotropy of the intermolecular interaction. 

Milet A, Korona T, Moszynski R, Kochanski E (1999) Anisotropic intermolecular interactions in Van der Waals and hydrogen-bonded complexes What can we get from density functional calculations J Chem Phys 111 7727-7735... 

To see why this is the case, we first consider the portion of the response that arises from llsm. According to Equation (10), we can express (nsm(t) nsm(0)> in terms of derivatives of llsm with respect to the molecular coordinates. Since in the absence of intermolecular interactions the polarizability tensor of an individual molecule is translationally invariant, FIsm is sensitive only to orientational motions. Since the trace is a linear function of the elements of n, the trace of the derivative of a tensor is equal to the derivative of the trace of a tensor. Note, however, that the trace of a tensor is rotationally invariant. Thus, the trace of any derivative of with respect to an orientational coordinate must be zero. As a result, nsm cannot contribute to isotropic scattering, either on its own or in combination with flDID. On the other hand, although the anisotropy is also rotationally invariant, it is not a linear function of the elements of 11. The anisotropy of the derivative of a tensor therefore need not be zero, and nsm can contribute to anisotropic scattering. 

The main difference between the (3" structure compared to the / phase is the direction of the strong intermolecular interactions. Due to the smaller anion size the interaction directions are at 0°, 30°, and 60°, respectively, instead of face-to-face (90°) overlaps [335]. The more complicated interstack interaction results in a more anisotropic band structure with ID and 2D energy bands. There exists considerable disagreement between different band-structure calculations which might be caused by small differences in the transfer integral values [332, 335, 336]. One calculated FS based on the room temperature lattice parameters is shown in Fig. 4.27a [335]. Small 2D pockets occur around X and two ID open sheets run perpendicular to the a direction. In contrast, the calculation of [332] (not shown) revealed a rather large closed orbit around the F point. 

The liquid crystal state (LCS) shows order in one or two dimensions it lacks the three-dimensional long-range order of the crystalline state. LCS has characteristics intermediate between those of the crystalline and the disordered amorphous states. These phases are called liquid crystals because many of them can flow like ordinary liquids but they display-birefringence and other properties characteristic of crystalline soHds. In liquid crystal phases the molecules can move but the orientational order is conserved in at least ne direction. The LCS can be displayed by small molecules and by polymersj but in both cases a characteristic chemical structure is needed. The existence of the liquid crystal state is related to the molecular asymmetry and the presence of strong anisotropic intermolecular interactions (19-21). Thus, molecules with a rigid rod structure can form highly ordered... 

In the theory of electric properties of molecular systems in degenerate electronic states some unsolved problems remain. First, the problem of intermolecular interactions considering the degeneracy of the electronic states of the interacting molecules has not been solved completely. In this case, besides the lowering of the multipolarity of the interaction described in this paper, one can expect an essential contribution of anisotropic induction and dispersion interactions to different virial correction to the equations of state, refraction, and other electric characteristics of matter. 

Since the pressures applied to the crystals are, to a first approximation, unlikely to affect significantly the intramolecular geometry of the molecules, in the crystallographic refinements conducted in high pressure studies the intramolecular geometry is often constrained to that obtained from a suitable low temperature study. Limits on completeness of the data set also often lead to isotropic rather than anisotropic models for atomic displacements being necessary. In this context, the most useful information that can be obtained is on systematic trends in the behavior of different intermolecular interactions. 

The presence of the metal or insulator does not only add the molecule-substrate interaction as a formative influence, but can also alter the effective intermolecular interactions. For example, whereas the crystallisation of bulk tetraeene is governed by the attractive interaction between molecules in a particular relative orientation, the surface-confined molecules (on Ag( 111)) repel each other. The modification of the effective intermolecular interaction may originate both from substrate-mediation and from the intrinsically anisotropic molecular interaction potentials. As the possibly entropy-driven ordering of tetraeene on Ag(lll) shows, the modified interactions may introduce new ordering mechanisms at the interface. 

The good correlations observed between the relative rates of Table 17 and the chemical shifts of the protons in position 2 of protonated 4-substituted p n i-dines would indicate that the anisotropic contributions and the intermolecular interactions are substantially identical and that the major factor controlling both the chemical reactivity and the relative shielding of the hydrogen nuclei in the meta position to the substituent is the electron density in position 2 of the molecule. The slopes of the plots (Table 18) give a measure of the different selectivity, exclusively due to polar effects, and therefore a measure of the relative nucleophilici-ties of the free radicals involved. This interpretation is further supported by the linear correlations between the relative rates and the pKa of the 4-substituted P3nidines. 

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