A Scalar LMP2 Algorithm

Localize occupied molecular orbitals Create domains 

Compute screening quantities required for integral transformation Perform integral transformation generating ai bj) 

Begin LMP2 iterations Compute LMP2 residual Compute AT 

The various sparse arrays, including the two-electron integrals and the double-substitution amplitudes, will be handled by a sparse data representation that also provides support for parallel operations such as converting a replicated array to a distributed array and redistributing an array using a different distribution scheme a set of generalized contraction routines developed to perform contractions of these distributed sparse multidimensional arrays will be employed as well. 

In the following we will use a matrix notation for the double-substitution amplitudes, T,/, two-electron integrals, K,p and residual elements, R,y, where, for instance, T,y contains all the double-substitution amplitudes T for a fixed ij pair. Using the matrix notation is convenient in the discussion but does not reflect the actual data representation. The double-substitution amplitudes, integrals, and residual elements are stored as four-dimensional sparse arrays using the employed sparse data representation. In this representation, however, indices can be frozen for instance, freezing the indices i and / in the four-index array T with indices i, j, a, and b allows the sub-array T,y to be manipulated as a matrix. 

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