Lattice-energy calculations

Values for the partial charges of atoms can be derived from quantum mechanical calculations, from the molecular dipole moments and from rotation-vibration spectra. However, often they are not well known. If the contribution of the Coulomb energy cannot be calculated precisely, no reliable lattice energy calculations are possible. 

The early agreement between calculated and experimental heats for fluorides was fortuitous because the high value given to D(F2) was compensated by the large electron affinity value [A/f F ) = lD(Ft) -.EA(F)]. The drop in value of AH°(F >) over the years (see Table I) vitiates some of the more elaborate lattice-energy calculations and Ka-pustinskii s semiempirical method seems adequate (138), but see reference (126). 

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. 

The same result was obtained by Alberti and Vezzalini [70] using lattice energy calculations. 

C03 (g). The lattice energy calculations of Lennard-Jones and Dent1, 2 on the carbonates of zinc, cadmium, calcium, and magnesium yield, for C03 (g), Qf = — 75 10. 

A simpler approach to lattice energy calculations was suggested by the Russian chemist Kapustinskii. His expression ... 

The situation with respect to the photobehavior of 7-chlorocoumarin is interesting (Fig. 11). There are two reaction pathways in this crystal one that favors the formation of the vyn-IIII isomer arising from reaction between the transla-tionally related molecules with a center-to-center distance of 4.54 A and another that would yield the anti-HT dimer, corresponding to the reaction between the centrosymmetrically related molecules, the center-to-center distance being 4.12 A. Experiment clearly shows that only the yy -HH dimer is obtained—not the one that would correspond to the path of least motion. This is supported by the results of the lattice energy calculations. The implication is that the shape of the free volume is anisotropic, with the larger volume or extension in the direction of the translational periodicity of 4.54 A. 

Similarly, competition experiments on the aminobenzonitrile isomers 62-64 showed 62 > 63 > 64 preferences towards host 1 [66], In this case, complexing selectivity was also concentration dependent. Lattice energy calculations performed for the crystallographically obtained models agreed well with the results of the competition experiments. Additionally, when there were no pronounced selectivity differences, both hosts were included in the host framework. 

The spectrum of the unstable diatomic CuF molecule has been observed at high temperatures, from the vapor above molten copper(II) fluoride (10), but no evidence for the solid material has been obtained, even after rapid quenching to room temperature. Lattice energy calculations, assuming that CuF would have the rock-salt structure, show that the disproportionation... 

Coefficients for lattice energy calculations with WMIN and 631G electrostatic potential charges ... 

The lattice energies calculated using this equation are compared with those obtained from the Born-Haber cycle in Table 4.2.4. 

They compare heats of formation of A-metal and B-metal compounds by selecting pairs of ions (one A and one B) of the same charge and of very similar ionic radii. In such cases the lattice energies calculated on the simple ionic model will be very similar. B-metal ions cannot be assigned constant radii to the same extent that this is possible for A-metal ions,... 

At the right-hand side of Fig. 5, a comparison is made between two A-metal ions, Sr2+ and Caa+ (radii 1.13 and 0.99 A). Here the difference in radii is much greater than in any of the A/B pairs with which we have been concerned. However, the differences between one anion and another are now a good deal smaller moreover, these differences agree very well with values calculated on the basis of the differences in ionic size alone. The theoretical predictions given by ionic lattice-energy calculations are shown as circles to the left of the Sr/Ca points. 

Lattice energy calculations can assist in assessment of which cations are to be chosen in the zeolite lattice or channels in order to stabilize the structure. 

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