H.1 Recursive Algorithm to Calculate

is

where,

(H.6) |

The

(H.9) |

is defined in a manner identical to except that the left-connected system is comprised of the first blocks of (H.1). In terms of (H.4), the equation governing follows by setting and . Using the DYSON equation [(H.5)], one obtains

It should be noted that the last block is equal to the fully connected GREEN's function , which is the solution to (H.1). The full GREEN's function can be expressed in terms of the left-connected GREEN's function by considering (H.4) such that , and . By noting that the only non-zero block of is and using (H.5), one obtains

Both and are used for the calculation of the electron density, and so storing both sets of matrices will be useful. In view of the above equations, the algorithm to compute the diagonal blocks is given by the following steps