Examples and Scaling

A series of homologous molecules H-(-C=C-)-nH with n = 3, 5, 10, 13, and 15 are examined. The advantage of the divide-and-conquer method over the conventional KS 

Basis effects energy and kinetic energy (in hartree) for H-(-C=C-)-jH. A (ij/klm) basis set means that each contributing H atom contributes i s-type atomic orbitals and j p-type atomic orbitals and each contributing C atom contributes k s-type atomic orbitals, 1 p-type atomic orbitals, and m d-type atomic orbitals. 

First neighbors and second neighbors as buffer atoms 

The results are reported in Table 5. The divide-and-conquer energies E(DC) are given relative to their corresponding KS values E(KS). Compared with E(KS), E(DC) is higher in all cases. The difference of E(DC) - E(KS) increases as n increases. An interesting trend is found among the energy differences. When a pair of C atoms are added the difference of E(DC) - E(KS) increases by about 2 millihartree, that is, by 1 millihartree per C atom. This relative error to the KS values will diminish when the method is applied to chemical reactions or to the determination of relative stabilities. The error per C atom is of course very basis-set-dependent and bond-type dependent. 

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Of course, we don t very often react such large quantities as a whole mole in the laboratory, we have to scale it down, just as you may have to do in following a recipe in the kitchen. If the recipe is for four people and there are only two of you, you divide all the quantities of ingredients by two. The same is true of chemical recipes. Let us look at the last example and scale it down to /loth scale. 

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