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# Partial AO Algorithms

To minimize the computational requirements (in particular the disk-space requirements) in large-scale CC calculations, AO based algorithms have been implemented for those terms which in the MO representation require the {$\langle ab||cd\rangle$} integrals involving four virtual indices.

Partial AO algorithms are available in CFOUR for energy (as well as first- and second-derivative and response-theory) calculations at MP2, MP3, MP4 and all CC levels up to CCSD(T) for all types of reference functions. No AO algorithms are available for CCSDT calculations.

The use of AO based AO algoritms is enforced via the keyword ABCDTYPE=AOBASIS

It is recommended to use AO based algorithm in all CCD, QCISD, CCSD, and CCSD(T) calculations to minimize the computational effort

Substantial saving of computation time can be obtained by using in addition the AO_LADDERS=SPARSE_AO keyword. If set the program uses a sparse matrix algorithm which first rearranges the integral matrix in order to get "well-occupied" and "very sparse" blocks. "Well-occupied" blocks will be multiplied by matrix multiplication while in "very sparse" blocks only the non-zero elements are considered. The computational time is further reduced using symmetrized and anti-symmetrized integral and amplitude matrices in the multiplication. This is the fastest way to perform energy, first- or second-derivative calculations on CCSD level. Since the algorithm is new, it is not set as default for the time being. It does not work with MPI parallel mode, but efficiently uses OpenMP up to four cores.