Real Molecular Shape

During recent decades the molecular theory of flexoelectricity in nematic liquid crystals was developed further by various authors. " In particular, explicit expressions for the flexocoefiicients were obtained using the molecular-field approximation taking into account both steric repulsion and attraction between the molecules of polar shape. The influence of dipole-dipole correlations and molecular flexibility was later considered. Recently flexoelectric coefficients have been calculated numerically using the mean-field theory based on a simple surface intermolecular interaction model. This approach allows us to take into consideration the real molecular shape and to evaluate the flexocoefiicients for mesogenic molecules of different structures including dimers with flexible spacers. 

This chapter is arranged as follows. In Section 1.2 we consider in more detail the dipolar and quadrupolar mechanisms of flexoelectricity, and in Section 1.3 we derive the general expressions for the flexocoefficients in terms of the direct pair correlation function. These results are used in Section 1.4 to obtain approximate expressions for the flexocoefficients in the molecular-field approximation taking into account both intermolecular repulsion and attraction. In that section we also consider the dependence of the flexocoefficients on the absolute value of the molecular dipole and on the orientation of the electric dipole with respect to the molecular long axes and the steric dipole. In Section 1.5 the effect of dipole-dipole correlations is analysed and in Section 1.6 we discuss the mean-field theory of flexoelectricity, which allows us to account for the real molecular shape. 

The molecular-statistical theory of flexoelectricity, presented in the previous sections, does not allow us to establish a direct relation between the flexocoefficients and the details of a particular molecular structure (except for permanent electric and steric dipoles) because the theory is based on simple model interaction potentials. A different version of the mean-field theory, which takes into consideration the real molecular shape, has recently been proposed by Ferrarini et This approach is based on the... 

The shape of the cavity has some effect on the molecular polarizabilities " - " however, the methods taking into account real molecular shapes are computationally expensive and are most appropriately utilized with accurate ab initio or density functional theory (DFT) approaches. " - " Even though spherical cavity is a crude approximation for most molecules, the predicted trends usually agree well with experiment and with the results of much more sophisticated and expensive methods. - ""... 

Over the span of two decades, molecular modeling has emerged as a viable and powerful approach to chemistry. Molecular mechanics calculations coupled with computer graphics are now widely used in lieu of tactile models to visualize molecular shape and quantify steric demands. Quantum chemical calculations, once a mere novelty, continue to play an ever increasing role in chemical research and teaching. They offer the real promise of being able to complement experiment as a means to uncover and explore new chemistry. 

Nevertheless, the use of spherical-cavity SCRF models finally led to a dead end, because no meaningful spherical cavities can be defined for non-spherical molecules. Even the attempt to overcome this problem by an extension of the Onsager model to ellipsoidal cavities did not really solve the problem, because this introduces additional fit parameters, while only a small portion of real molecules can still be considered as approximately ellipsoidal. Thus, the need for molecular-shaped SCRF models became more and more obvious. 

The optimal value for k is k = 1 for / = 0 and k = 2 for l = +oo. On the other hand, numerical simulations on real molecular systems seem to show that, depending on the charge and shape of the system, the optimal value for k is between k = 0 and k= 1/2. The discrepancy between theoretical arguments and numerical results might originate in the escaped charge problem, that is addressed in the following section. 

All of the information that was used in the argument to derive the >2/1 arrangement of nuclei in ethylene is contained in the molecular wave function and could have been identified directly had it been possible to solve the molecular wave equation. It may therefore be correct to argue [161, 163] that the ab initio methods of quantum chemistry can never produce molecular conformation, but not that the concept of molecular shape lies outside the realm of quantum theory. The crucial structure-generating information carried by orbital angular momentum must however, be taken into account. Any quantitative scheme that incorporates, not only the molecular Hamiltonian, but also the complex phase of the wave function, must produce a framework for the definition of three-dimensional molecular shape. The basis sets of ab initio theory, invariably constructed as products of radial wave functions and real spherical harmonics [194], take account of orbital shape, but not of angular momentum. 

Dunitz, J. D Filippini, G. and Gavezzotti, A. (2000). Molecular shape and crystal packing a study of C12H12 isomers, real and imaginary. Helvet. Chim. Acta, 83, 2317-35. [184]... 

Until recently, these ideas seemed to be too crazy to be sold to any truly serious scientist. These speculations passed away almost unnoticed with other equally cute but hardly practical suggestions of Daedalus . So it came later as a real surprise that, at least in this particular fantasy, the author had actually elaborated an original design of an unprecedented molecular shape and, moreover, had made the correct guess about the possibility of using graphite as a starting material for its construction ... 

The density functional method as applied by Tarazona to deal with classical fluids has been used to calculate the orientation of triatomic molecular fluids near the solid-liquid interface. The results give valuable suggestions about the effect of molecular shape on the orientation of real molecules such as liquid crystals near the solid-fluid interface. 

In the real synthesis systems, the surfactant effective packing parameter, g, are mainly affected by the following factors (1) charge, composition, molecular shape, and structure of surfactant, (2) the interactions between surfactant and inorganic species (e.g., charge-density matching), (3) reaction parameters and conditions concentration, pH, ion strength, temperature, etc. 

This is because stereochemistry nomenclature is merely a formal description of the real molecular structure. The correct spatial shape of the pharmacophore is not represented at all. A correct description of stereochemistry is possible with descriptors based on the three-dimensional structure only. Molecules can show the same pharmacophore (i. e., same three-dimensional arrangement of pharmacophore centers) but different chirality according to chirality nomenclature. 

Real-World Reading Link Have you ever rubbed two balloons in your hair to create a static electric charge on them If you brought the balloons together, their like charges would cause them to repel each other. Molecular shapes are also affected by the forces of electric repulsion. 

I use models (real or software) to help visualize common molecular shapes. 

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