Computer Time Saving in the SCF Procedure

As we have seen in the preceding section, considerable progress was achieved in the integral evaluation. Less attention was paid to hastening the SCF procedure itself. This is understandable because for current basis sets and molecules the integral time represents usually a dominant portion of the total time, unless some use is made of facilities and tricks noted in the preceding section. In such a 

Great difficulties with convergency are often encountered with o-pen shell systems for which even a combination of the techniques noted may be helpless. Such cases are called intrinsically divergent. Among methods which are applicable to these cases we note on the level shifting technique suggested by Guest and Saunders , The method was 

The crucial problem in the point (ii) - the construction of the Fock matrix - is a retrieval and effective manipulation of the integrals (av ,S ). Since all nonvanishing integrals must be read in from the tape or disk in each iteration, this manipulation may be very time consuming. Programs greatly differ on this point. From the discussion 211,219,227-229 follows that it is profitable to have 

The matrix elements (3,41) may be constructed if all three integrals are available at the same time. To achieve this, it is most profitable to compute them just in the order (ATlA ) (X AlV(r), ( S lvA). Otherwise, they must be reordered. The matrix elements P y Xg are then stored on a tape or disk together with the pair indices (/cv), (Xe ), They contribute to two G-matrix elements as follows  

The proper construction of the G matrix elements with respect to permutations of, v,X, (T indices in P and D is ensured by the terms (1 - I/2S) in the definitions of the P and matrices (note that Diuv and = Xer Atv) Only the nonequiva- 

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