Integral-direct algorithm

At SCF and MBPT(2) level, integral-direct approaches are now well established in order to overcome disk-space bottlenecks and allow treatment of molecules with more than 100 atoms and 1000 basis functions. Implementations of integral-direct algorithms within CC methods, however, have... 

Dirac equation one-electron relativistic quantum mechanics formulation direct integral evaluation algorithm that recomputes integrals when needed distance geometry an optimization algorithm in which some distances are held fixed... 

Evaluate the integrals. In a conventional algorithm, they are stored on disk and read in for each iteration. In a direct algorithm, integrals are computed a few at a time as the Fock matrix is formed. 

P PjV 2 (pp4>q)) [ qj / ) reading/writing to disk, it is desirable also to have direct algorithms for electron correlation method. Direct in this context means that the integrals are calculated as needed and then discarded. The need for integrals over MOs instead of AOs, however, makes the development of direct methods in electron correlation somewhat more complicated than at the HF level. Consider for example the MP2 energy expression." ... 

M. Schiitz and R. Lindh, An integral direct, distributed-data, parallel MP2 algorithm, Theor. Chim. Acta, 95 (1997), 13-34. 

Wilson170 provides a very clear and helpful survey of four-index transformation methods published before 1987. More recent work has focused attention on the sparsity of quantities in the AO basis. For example, Haser, Almlof, and Feyereisen have presented an integral-direct transformation algorithm which... 

A direct algorithm for contractions involving ab cd) integrals may be employed when storage and recovery of these integrals is not feasible. Here, components of Y are transformed into the atomic basis in their last two indices ... 

TURBOMOLE running on the DEC 5000/200 workstation. A full-direct algorithm, integral neglect threshold equal to 10 a.u. 

GAUSSIAN 90 running on CRAY Y-MP4/32. A full-direct algorithm, 14 MW of the core memory used, core orbitals not correlated. The numbers of integral evaluations are given in parentheses. 

An outline of the algorithm is shown in Figure 8.4. Like the replicated data algorithm from section 8.3, the distributed data algorithm is integral-direct. 

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