Numerical Treatment of Perturbation Expressions

This section was intended to have a similar role in this chapter to that in Chapter 3 of the Sections 3.C, and 3.D, devoted to problems of time saving in SCF calculations. With the calculations of correlation energy, however, the situation is more complex because of a great number of different methods among which each has its own specific theoretical problems and, accordingly, it requires special tricks for accelerating the actual calculations. Since the most widely used methods, CI-SD and CEPA, have already been discussed in some detail in 

A typical (though not always unavoidable) first step in any proce-dure for the evaluation of correlation energy is the transformation of integrals over AO s (i.e. STO s, CGTF s and other possible basis set functions) with the indices V, X, and o to integrals over MO s with the indices i,j k and i  

If the number of basis set functions is n, the number of (ij kl) in-tegrals becomes n, Since the evaluation of each of the latter requires the manipulation with n integrals /U.V 7 6), the direct transformation according to eqn. (4.123) is extremely ineffective. Sutcliffe 

Essentially, the algorithm contains four steps in which partly transformed integrals are stepwise constructed according to the following scheme  

Making use of this algorithm requires of course to store the partly transformed integrals. It is profitable to store them in blocks ac- 

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