Lattice energy electrostatic calculation

Calculation of the Electrostatic Energy of Lattice Breakup In 1919, Max Bom proposed a method for calculating the energy necessary to draw apart a pair of ions from a crystal lattice to infinite distance against electrostatic attraction forces. The equation derived by Bom gives for the lattice energy of a NaCl crystal the value -762kJ/mol (i.e., a value close to the experimental value of the heat of breakup that we had mentioned). 

Voogd, J., J. L. Derissen, and F. B. van Duijneveldt. 1981. Calculation of Proton-Transfer Energies and Electrostatic Lattice Energies of Various Amino Acids and Peptides Using CNDO/2 and Ab Initio SCF Methods. J. Am. Chem. Soc. 103, 7701-7706. 

Of interest is the relative contribution of the electrostatic interactions to the total calculated lattice energy. Some of the results are reproduced in Fig. 9.3 (Coombes and Price 1995). It is clear that the contribution increases rapidly for the more polar molecules, and can be pronounced. For formamide, the electrostatic contribution is more than 100% of the lattice energy, as the repulsive and the van der Waals r 6 forces are of approximately equal magnitude and sum to a small, opposite, contribution. 

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. 

A number of techniques have been employed to model the framework structure of silica and zeolites (Catlow Cormack, 1987). Early attempts at calculating the lattice energy of a silicate assumed only electrostatic interactions. These calculations were of limited use since the short-range interactions had been ignored. The short-range terms are generally modelled in terms of the Buckingham potential,... 

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

For compounds that are ionic rather than molecular solids, AHf can be calculated by appropriately combining the heats of formation of the gas phase ions (computed or experimental) with the lattice energy (converted to enthalpy [91]). We have developed formulas for lattice energies in terms of properties of the electrostatic potentials on the anions surfaces [92], for any of three possible cations NH4+, Na+ and K+. 

The determination of the Madelung constant for a crystal structure requires the evaluation of electrostatic self-potentials of the structure. Any lattice energy can also be expressed using lattice site self-potentials (which is what Ewald actually calculated) ... 

Hirshfeld, F. L. and Mirsky, K. (1979). The electrostatic term in lattice-energy calculations acetelene, carbon dioxide and cyanogen. Acta Crytallogr A, 35, 366-70. [166]... 

At first glance, calculation of the lattice energy of a crystal may seem simple just take every pair of ions and calculate the sum of the electrostatic energy between each pair, using the equation below. 

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