Empirical packing energy calculations

This work has shown that wide-angle X-ray scattering is a sensitive tool for evaluating the structure of non-crystalline polymers. The structure determination is only successfully approached by considering first the persistent conformation and then the packing which must to some extent be a consequence of such conformations. The method does not need to place any reliance on the semi-empirical conformational energy calculations. 

What can now be accomplished rather easily is the computer generation of many (a great many) crystal structures and the calculation of the packing energy and external vibrational entropy of each of them. In such an approach, only empirical potential energy schemes can be applied, due to the huge... 

DFT calculations of the structure of the molecularly adsorbed NO are in reasonable agreement with experiments, but overestimate the binding energy [197,198]. A barrier of 2.1 eV to dissociation is predicted by DFT, with the NO at the transition state nearly parallel to the surface and N and atoms in bridge sites [199]. This transition state geometry is similar to that of NO dissociation on other close-packed metal surfaces [200]. There is no global DFT PES so that all theoretical dynamics is based only on empirical model PES. 

The first assumjrtion is that the methods of molecular mechanics can be lied. Empirically calibiated potoitial functions that describe the internal structure of the polymer molecule and the intermolecular interactions are invoked. In addition, most of the work that has pursued structure and packing has been done by energy minimizatk>n. Thus die calculations are appropriate only for zero K. To stune dcgro this condition could be removed by using molecular dynamics. However there are some non-trivial complications in this approach and these wQI be discussed in a sqiarate section. 

The constants C and E in Eq. (3.1.89) have to be measured and up to now cannot be calculated based on a theory or by semi-empirical equations. E represents the energy needed to create a cavity in the dense packing of the liquid, that is, to push the molecules apart. Typically, E is of the order of magnitude of 10 kJ mol , for example, for water about 17 kJ mol in the range 0-100 °C. The strong decrease of ri with temperature is shown in Figure 3.1.18 for the example of water. 

Generally, several hundred unique crystal packings remain after optimization. They must then be evaluated with respect to either calculated physical properties such as density and lattice energy, or by means of empirical scoring functions ". ... 

---