Crystal sublimation energy

The packing energy of an organic crystal can be easily calculated by a lattice sum over pairwise interactions. The potential parameters for these calculations are summarized in Table 15. The packing energy is usually a quite accurate estimate of the crystal sublimation energy. 

In CVFF partial charges and van der Waals terms were derived from a simultaneous least squares fitting to crystal sublimation energies, and although similar in magnitude to ESP charges (HF/6-31G ) they are not directly comparable. 

The group oxidation state of +5 is too high to allow the formation of simple ionic salts even for Nb and Ta, and in lower oxidation states the higher sublimation energies of these heavier metals, coupled with their ease of oxidation, again militates against the formation of simple salts of the oxoacids. As a consequence the only simple oxoanion salts are the sulfates of vanadium in the oxidation states +3 and +2. These can be crystallized from aqueous solutions as hydrates and are both strongly... 

The atoms of any metal adhere together to form a crystal because of the forces of attraction between them to remove an atom from the surface requires a definite amount of work, characteristic of the metal this is called the sublimation energy. ... 

However, the obscure choice of frequencies in the visible and UV regions in the original calculations may have been guided by a desire to fit experimental heats. In fact, the Debye rotational and translational crystal frequencies relate to sublimation energies of the lattice, and, together with internal molecular vibrations, can be used to calculate thermodynamic functions (16). An indirect connection between maximum lattice frequencies (vm) and heats of formation may hold because the former is inversely related to interatomic dimensions (see Section IV,D,1) ... 

Several computations of the total surface energy (per unit area) Us start from the experimental value of the sublimation energy, Ls, of the crystal. When it is remembered that the intensity of interatomic forces frequently is derived from thisZ,S) the direct use of the experimental data does not appear to be a serious drawback. On the other hand, this approach does not differentiate between different crystal faces and can give only an averaged value for all of these. 

Malta and co-workers [41] conclude that stability of the molecules investigated is explained partially in terms of the energy that is necessary to disrupt the encasing network of these H-H bond paths. These interactions must be ubiquitous, and their stabilization energies contribute to the sublimation energies of hydrocarbon molecular crystals. 

Most ot the enthalpies associated with steps in the cycle can be estimated, to a greater or less accuracy, by experimental methods. The lattice energy, however, is almost always obtained theoretically rather than from experimental measurement. It might be supposed that the "enthalpy of dissociation of a lattice coukl be measured in the same way as the enthalpy of atomization of the metal and nonmctal, that is, by heating the crystal and determining how much energy is necessary to dissociate it into ions. Unfortunately, this is experimentally very difficult When a crystal sublimes (AHj), the result is not isolated gaseous ions but ion pairs and other clusters. For this reason it is necessary to use Eq. 4.13 or some more accurate version of It. Wc can then use the Bom-Haber cycle to check the accuracy of our predictions if we can obtain accurate data on every other step in the cycle Values computed from the Bom-Haber cycle are compared with those predicted by Eq. 4.13 and its modifications in Table 4.3. 

Similar small but significant deviations of the carbon atoms from a planar conformation have been found in chrysene (10) and in 20-methylcholanthrene (12) (Iball and MacDonald, 1960). The deformation energies for these molecules (0-025-0-040 and 0-155-0-260 kcal mole-1 respectively Ali and Coulson, 1959) are of the order of one-hundredth of the sublimation energy and serve to demonstrate that the small out-of-plane deviations found by Iball and his associates could easily arise in the process of packing the separate molecules into the crystal. 

Atoms in the bulk simple cubic crystal have the six nearest neighbors and 12 second-nearest neighbors shown in the upper right figure for a total binding energy of 6cj>i + 122- Each bond is shared between two atoms. Hence, the mean sublimation energy of the crystal is one-half that value, or... 

Per unit volume of the crystal, the mean sublimation energy of a simple cubic structure with lattice parameter a is Eq. 2.22 divided by a3. Compare this with adatoms adsorbed on a smooth face, which have one nearest neighbor and four second-nearest neighbors. Their binding energy is thus significantly lower ((J>1 +4(1)2). 

According to expression (1.15), sublimation energy Ls of the crystal. The atomic area to can be calculated from the molar volume vm as follows ... 

Evidently AGS,in = AGfa, + AG, v. The free energy of solution, AG i , is obtained from the molar solubility s, ACJ = —RT In s the quantity AGi aii is the lattice energy of the crystal, obtainable as the sublimation energy. AG i is often small because the interaction energy within the solid is comparable with the energy of interaction between solute and solvent. We will return to solvation energies... 

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