Basics of Integral Computation

The two-electron integrals arise in the evaluation of matrix elements between Slater determinants of a two-electron operator of the form 

We will use the shorthand notation fuv pk) to represent the integral (0 vl pp(pk) from Eq. 7.3, where ji, v, p, and k label real, spatial atomic orbitals. 

In practice, integral screening is employed before the integrals are computed. The screening is performed using the Schwarz inequality 

In the remainder of this chapter we will discuss different ways to parallelize the computation of the two-electron integrals with focus on how to achieve load balance. Two-electron integral computation in a quantum chemistry code is often performed in the context of a procedure such as Fock matrix formation or two-electron integral transformation, but we here consider the integral computation separately to specifically concentrate on strategies for distributing the work. Examples of parallel two-electron integral computation in quantum chemical methods are discussed in chapters 8,9, and 10. 

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