Free-molecule potential field

The theory of chemical bonding is overwhelmed by a host of insurmountable obstacles the real orbitals and hybrids of LCAO have no physical, chemical or mathematically useful attributes - certainly not in the quantum-mechanical sense the distribution of electron density between atoms, in the form of spin pairs, is an overinterpretation of the empirical rules devised to catalogue chemical species the structures, assumed in order to generate free-molecule potential fields, are only known from solid-state diffraction experiments the assumption of directed bonds is a leap of faith, not even supported by crystal-structure analysis. The list is not complete. 

Once more, free-electron models correctly predict many qualitative trends and demonstrate the appropriateness of the general concept of electron delocalization in molecules. Free electron models are strictly one-electron simulations. The energy levels that are used to predict the distribution of several delocalized electrons are likewise one-electron levels. Interelectronic effects are therefore completely ignored and modelling the behaviour of many-electron systems in the same crude potential field is ndt feasible. Whatever level of sophistication may be aimed for when performing more realistic calculations, the basic fact of delocalized electronic waves in molecular systems remains of central importance... 

If the guest molecule is assumed to be confined, in the thermodynamic sense, within a particular cavity, if the internal vibrational and rotational states of the molecule are unaltered by occlusion, and if the potential field within a cavity is sufficiently uniform so that the movement of the molecule within the cavity can be represented as three-dimensional translation within the free volume of the cavity (), then the appropriate expression for the ratio of partition functions becomes simply... 

Since about 15 years, with the advent of more and more powerfull computers and appropriate softwares, it is possible to develop also atomistic models for the diffusion of small penetrants in polymeric matrices. In principle the development of this computational approach starts from very elementary physico-chemical data - called also first-principles - on the penetrant polymer system. The dimensions of the atoms, the interatomic distances and molecular chain angles, the potential fields acting on the atoms and molecules and other local parameters are used to generate a polymer structure, to insert the penetrant molecules in its free-volumes and then to simulate the motion of these penetrant molecules in the polymer matrix. Determining the size and rate of these motions makes it possible to calculate the diffusion coefficient and characterize the diffusional mechanism. 

This demonstrates that especially for systems with very flat potential energy surfaces of polar bonds, the interpretation of precise X-ray data has to be carried out very carefully and all possible perturbations of the environment must be taken into account. The comparison with the structures of free molecules is not appropriate. On the other hand, the theoretical model for the correct interpretation of such structures in polar mediums must be expanded for example, with the calculation of an Onsager solvent reaction field. 

In collaboration with experimental groups, we have recently studied some chlorinated-benzene crystals, 1,2,4,5-tetrachlorobenzene (TCB) [59] and 1,4-dichlorobenzene (DCB) [60], as well as solid tetracyanoethene (TCNE) [58]. In these studies we have used empirical atom-atom potentials, of exp-6 type [see Eq. (6)], which we have supplemented with the Coulomb interactions between fractional atomic charges. Lattice dynamics calculations have been performed by the harmonic method, with inclusion of intramolecular vibrations [70], see Eqs. (17) to (24). The normal modes of the free molecules have been calculated from empirical Valence Force Fields, using the standard CF-matrix method [101, 102]. The results of these calculations are used here to illustrate some phenomena occurring in more complex molecular crystals. These phenomena are well known the numerical results show their quantitative importance, in some specific systems. 

The control scheme that we have discussed does not require high-power lasers. The electric field of the light is weak enough that the levels of the system are not shifted by it. The laser induces transitions but these can be described as transitions between states of the free molecule. This is no longer the case when the laser is strong. The very potential on which the nuclei move can be altered by the external field because, if it is strong enough, its effect on the electrons can become comparable to the electrical field due to the nuclei or that of the other electrons. Once that happens a variety of other processes, such as non-resonant ionization,... 

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