Crystal structure calculation cluster method

Figure 8.50 A comparison of the performance of atom-atom potentials using the UNI method and PIXEL potentials in the description of the energy landscape for 133 naphthalene crystal structures. The experimental crystal structure is represented by a cluster of 5 points representing very similar structures with different unit cell settings. Energies are given on the abscissa in kJ mol The plot shows the usual way of representing the results of crystal structure calculations with the expectation that the most stable structure should be at the lowest energy and exhibit the highest density. (Reproduced with permission from The Royal Society of Chemistry).

Simulation of crystal structures using empirical interatomic potentials might be a powerful means of understanding experimentally observed properties of materials. Such an approach is nevertheless insufficient to predict unknown structures and their properties, since the determination of empirical potentials essentially requires information on the resultant crystal structures. The present method of deriving interatomic potentials from ab initio cluster calculations is basically free from experimental information. Although there still remain some empirical factors, such as the choice of reasonable cluster or the final selection of a potential out of some parameter sets [58],... 

Abstract. Geometrical parameters, total energy, heat of formation, energies of HOMO and LUMO orbitals, density of one-electron states (DOS) are determined by using of semi-empirical quantum chemistry PM3-method for isolated molecules Cn, dimers (Cn)2 and cuban-like clusters (Cn)8 for n = 20, 24, 28, 32. The results of calculations allow assuming the existence of polymerized cubic crystal structure on base of all considered small fullerenes. 

Theoretical cluster model MO calculations were used for the interpretation of these spectra. The DV-Xa method combined with realistic cluster approach (in which the model clusters were set up using available crystal structure information from diffraction experiments) proved to be a powerful tool to interpret the structural changes in the valence band spectrum due to the changes in the superstructure of the consisting PO4 tetrahedra. We found noticeable differences in the calculated spectra when the cluster geometry was changed, especially in the case of the hydrous and anhydrous pyrophosphate and similarly for the ring and spiral forms of the tetra-metaphosphate. 

The simplest crystal calculation consists of taking the atomic coordinates, cell data and space group for a crystal structure from an X-ray determination, building a static cluster of molecules to represent the crystal, and calculating all the interaction energies by some potential. This can be done by force field methods, Eq. (1.1.25) (time for one calculation a few milliseconds) or by Pixel, Eq. (1.1.34) (time for one calculation a few minutes). Figure 1.1.1 shows that the results are of comparable accuracy (remember that experimental values themselves are no more accurate than 5-10 kj mol-1). The UNI empirical force field [9] uses however about 100 parameters while the Pixel method uses only a few. 

Kantcrcvich L N 1988 An embedded-molecular-cluster method for calculating the electronic structure of point defects in ncn-metallic crystals. I. General theory J. Phys. C Solid State Phys. 21 5041... 

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