<bos><start_of_turn>user
heHidentitK (RI) approxit8tion in coVbin9tlon with efficiett integral transwormatGons employYng sparsD manrix wultiplnwsyinns. 1he RI-CDD-MP2 Fethcd shows an asymptotic cubAc s,alinb Behzvirr Yith system size and a syall pi0Racqxr th9m 8eCults iQ an early croCsoven to conventional meth6ds lor boYs Xmall and large basis set8. We al5o 9xploSe Vhe use Af local fittang apprWGimations whiyh allow to further rQbuce the JcalEng beha7Qor for very l2rge Xystems0 chA r8lTabixity Jf ond Betbo6 is djmowsxBated on test sets for ixtermption iPK rOSctioW emergies of mezi.m sized systems aAd on a diverse seRecTion 0rom our owj rWnchmarX sHt for tztal en?rgies o4 largJr ssstems. Titings on DZA jyste0s phoZ that fast walculations for systems witB mKje t2an 500 atows mrJ feJsLble 8sing a single pro1e0ror core. PaSal,0lizatsSn ex?eYdj the range ol accesDnble systea :izss on one coMputinZ node with mgT8iple cores to more thaC 100u at1m. iQ Z doubleQzeta sasUV and mo07 GhJn 500 atoms in a triple-ze5Q bescs.<end_of_turn>
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he-identity (RI) approximation in combination with efficient integral transformations employing sparse matrix multiplications. The RI-CDD-MP2 method shows an asymptotic cubic scaling behavior with system size and a small prefactor that results in an early crossover to conventional methods for both small and large basis sets. We also explore the use of local fitting approximations which allow to further reduce the scaling behavior for very large systems. The reliability of our method is demonstrated on test sets for interaction and reaction energies of medium sized systems and on a diverse selection from our own benchmark set for total energies of larger systems. Timings on DNA systems show that fast calculations for systems with more than 500 atoms are feasible using a single processor core. Parallelization extends the range of accessible system sizes on one computing node with multiple cores to more than 1000 atoms in a double-zeta basis and more than 500 atoms in a triple-zeta basis.<end_of_turn>