Molecular crystals energy calculations

Figure 6.3 Cleaving a molecular crystal to calculate the surface energy of a solid.

Some consequences were discussed in Section I. If a pair of chemically identical (d-d) or nonidentical molecules ( f-D) are packed together, and this packing compared with the corresponding d-l or d-L pair, each for minimum total energy, there is no relation between the pair structures to enable them to be treated in a systematic way. Each case depends on the particular molecular composition and the particular atomic non-bonded radii which collectively are responsible for the surface shape of the molecule conceived as bounded by a hard surface. For each case it is of course possible to make calculations of packing energy and of optimum structure in the way now commonly followed for the packing in molecular crystals. Such calculations have not been reported so far as we are aware. 

Errors (/>(calc)-/>(expt)) in the predicted molecular crystal structures, calculated by minimizing the static lattice energy, starting from the experimental structure, for a model potential which includes a distributed multipole electrostatic model. The electrostatic term uses a DMA of a 6-31G SCF wave function, with all multipoles scaled by a factor of 0.9. The repulsion-dispersion potentials are taken from the literature (see text). The r.m.s. % error is calculated over the three cell edge lengths. Us is the calculated lattice energy, given at both the experimental and relaxed crystal structures. This can be compared with the experimental heat of sublimation AHsub (Chickos, 1987), where available. 

As already anticipated, the molecular surface we calculate is useful in describing condensed state properties. There is a steady linear relationship between Sn, and packing energy for organic crystals and the suiphoxide and suiphone compounds make no... 

M. A. Neumann and M.-A. Perrin, Energy Ranking of Molecular Crystals Using Density Functional Theory Calculations and an Empirical van der Waals Correction, J. Phys. Chem. B 109 (2005), 15531. 

The electrostatic energy of a molecular crystal can be evaluated with summation over the structure factors in Eq. (9.15). But to obtain the cohesive energy of a molecular crystal with such a summation, we would have to subtract the molecular electrostatic energies, which are implicitly included in the result. An alternative is to perform the calculation in direct space. 

Several issues remain to be addressed. The effect of the mutual penetration of the electron distributions should be analyzed, while the use of theoretical densities on isolated molecules does not take into account the induced polarization of the molecular charge distribution in a crystal. In the calculations by Coombes et al. (1996), the effect of electron correlation on the isolated molecule density is approximately accounted for by a scaling of the electrostatic contributions by a factor of 0.9. Some of these effects are in opposite directions and may roughly cancel. As pointed out by Price and coworkers, lattice energy calculations based on the average static structure ignore the dynamical aspects of the molecular crystal. However, the necessity to include electrostatic interactions in lattice energy calculations of molecular crystals is evident and has been established unequivocally. 

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