A 2x2 System

We may write H as two terms, the first a part that is a polynomial function of S and the second a sort of remainder. 

we see in this simple case that the closeness of the approximation depends upon the size the second term in Eq. (35) whether it is really a small perturbation upon the system. With these matrices the approximation would be good only if the two diagonal elements of H are close in value. The 2x2 case is rather special, however, and we give further more complicated examples. 

For naphthalene we examine the H and S matrices based upon the both the HLSP functions and the standard tableaux functions for the system. In both cases we include the non-ionic structures, only. This will give a picture of how the situation compares for the two sorts of basis functions. In both cases, of course, the dimensions of the matrices are 42x42, the number of non-ionic Rumer diagrams for a naphthalene structure. Some statistics concerning the commutator are shown in Table 6. It is clear that, 

When an ST03G AO basis full VB calculation of CH4 is carried out, there are 1716 singlet standard tableaux functions all together. When these are combined into functions of symmetry Mi the number of independent linear combinations is reduced to 164. Thus the symmetry factored H and S matrices are 164x164. We show the statistics for the HS—SH matrix for standard tableaux functions in Table 7. The statistics for HLSP functions are not available in this case. It is immediately obvious that the numbers 

---

Consider a 2x2 system for which at steady-state the gains are /fy. We may write ... 

It can be demonstrated that in the case of a 2x2 system the elements in the steady state RGA can be calculated by the following relation ... 

Avoid very interactive loops, as RGA element close to 0.5 in a 2x2 system. 

---