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In large-scale quantum-chemical calculations the electron-repulsion integral(ERI) tensor rapidly becomes the bottleneck in terms of memory and disk space.When an external finite magnetic field is employed, this problem becomes evenmore pronounced because of the reduced permutational symmetry and the need towork with complex integrals and wave-function parameters. One way to alleviatethe problem is to employ a Cholesky decomposition (CD) to the complex ERIs overgauge-including atomic orbitals. The CD scheme establishes favourablecompression rates by selectively discarding linearly dependent productdensities from the chosen basis set while maintaining a rigorous and robusterror control. This error control constitutes the main advantage overconceptually similar methods such as density fitting which rely on employingpre-defined auxiliary basis sets. We implemented the use of the CD in theframework of finite-field (ff) Hartree-Fock and ff second-order M{\o}llerPlesset perturbation theory. Our work demonstrates that the CD compressionrates are particularly beneficial in calculations in the presence of a finitemagnetic field. The ff-CD-MP2 scheme enables the correlated treatment ofsystems with more than 2000 basis functions in strong magnetic fields within areasonable time span.

Cholesky decomposition of complex two-electron integrals over GIAOs: Efficient MP2 computations for large molecules in strong magnetic fields