Density functional elongation method

Finally, we mention that density-functional methods have also been used in studying much more complex systems than simple crystals. A recent example is the study of Galli et al.90 who studied the microfracture in an a-SiC. Thereby, they modelled the system as consisting of periodically repeated units of 128 atoms. After optimizing the structure of this, they increased one of the unit-cell lengths and monitored the positions of the atoms as a function of this elongation until a fracture occurred. Despite this simple description it should be stressed that such calculations are very complicated and represent some of the most sophisticated ones that at present can be carried through with density-functional methods. 15... 

In their first density-functional studies based on this method, Aoki et a/. considered chains of weakly interacting units, i.e. an aperiodic chain of H2 units as well as chains of hydrogen-bonded units. As an illustration of the effectiveness of their approach we discuss here briefly their results for a chain of water molecules, (H20) . In Figure 10 we show the computer-time consumption as a function of n for three different studies based on the elongation method (they differ in the definition of the initial unit) in comparison with the time for a standard density-functional calculation where the full system is treated for any n. Figure 11 shows the interaction energy defined as... 

Figure 10 CPU time used in studying a (H20) cluster as a function of n with either a standard density-functional method (upper curve) or the elongation method (the three lower curves). For the elongation method three different initial structures were chosen leading to the three different curves. The data are from ref. 40...

Aoki, Y, Suhai, S., Imamura, A. An efficient cluster elongation method in density functional theory and its application to poly-hydrogen-bonding molecules. J. Chem. Phys. 101, 10808-10823 (1994)... 

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