General Algorithm

It is helpful to present the entire final algorithm. The six steps involved are:

1.

Construct moments. Loop over all the shell-pairs, generating moments up to and including ninth order, with a separate set for each type of scaling required for that type of shell-pair. Note that this part of the algorithm is only O(N) in cost.

2.

Convergence test. Loop over all www-theors for the present bra, finding for which shell-pairs the expansion will converge, and construct lists of those that pass and fail. This section (and those that follow) is O(N²).

3.

Find geometric parameters. Calculate the values of $\frac{AB \cdot DB}{DB \cdot DB}$, etc.

4.

Form ${\bf H}$ from the recurrence relation. This is performed once per m value of the class. There is a significant time saving if |AB|=0.

5.

Form ${\bf Hv}$. Required once per unique ${\bf Hv}$ product. Again there is a significant time saving if |AB|=0.

6.

Generate all (0)^(m)s, until a new ${\bf Hv}$ is required.