Slater determinant quadruply

How are the additional determinants beyond the HF constructed With N electrons and M basis functions, solution of the Roothaan-Hall equations for the RHF case will yield N/2 occupied MOs and M — N/2 unoccupied (virtual) MOs. Except for a minimum basis, there will always be more virtual than occupied MOs. A Slater detemfinant is determined by N/2 spatial MOs multiplied by two spin functions to yield N spinorbitals. By replacing MOs which are occupied in the HF determinant by MOs which are unoccupied, a whole series of determinants may be generated. These can be denoted according to how many occupied HF MOs have been replaced by unoccupied MOs, i.e. Slater determinants which are singly, doubly, triply, quadruply etc. excited relative to the HF determinant, up to a maximum of N excited electrons. These... 

In the Cl expansion (48) we only include those doubly substituted Slater determinants that are obtained from 0 if one replaces < r and R by and / . We include as well quadruply substituted determinants i. e. obtained from 0 on substituting rx, and 6-fold substituted determinants etc. We do not, however r ard the coefficients of these higher than doubly substituted determinants as free variational parameters, but we make a... 

Let us continue throwing away determinants. This time, however, we have to make a compromise i.e.. some of the Slater determinants are arbitrarily considered not to be important (which will worsen the results, if they are rejected). Which of the determinants should be considered as not important The general opinion in quantum chemistry is that the multiple excitations are less and less important (when the multiplicity increases). If we take only the singly, doubly, triply, and quadruply excited determinants, the number of determinants will reduce to 25000 and we will obtain 99% of the approximate correlation energy defined above. If we take the singly and doubly excited determinants only, there are only 360 of them, and 94% of the correlation effect is obtained. This is why this Cl Singles and Doubles (CISD) method is used so often. 

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