Relativistic Cholesky-decomposed density matrix MP2

Benjamin Helmich-Paris*, Michal Repisky, Lucas Visscher

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

221 Downloads (Pure)


In the present article, we introduce the relativistic Cholesky-decomposed density (CDD) matrix second-order Møller-Plesset perturbation theory (MP2) energies. The working equations are formulated in terms of the usual intermediates of MP2 when employing the resolution-of-the-identity approximation (RI) for two-electron integrals. Those intermediates are obtained by substituting the occupied and virtual quaternion pseudo-density matrices of our previously proposed two-component (2C) atomic orbital-based MP2 (Helmich-Paris et al., 2016) by the corresponding pivoted quaternion Cholesky factors. While working within the Kramers-restricted formalism, we obtain a formal spin-orbit overhead of 16 and 28 for the Coulomb and exchange contribution to the 2C MP2 correlation energy, respectively, compared to a non-relativistic (NR) spin-free CDD-MP2 implementation. This compact quaternion formulation could also be easily explored in any other algorithm to compute the 2C MP2 energy. The quaternion Cholesky factors become sparse for large molecules and, with a block-wise screening, block sparse-matrix multiplication algorithm, we observed an effective quadratic scaling of the total wall time for heavy-element containing linear molecules with increasing system size. The total run time for both NR and 2C calculations was dominated by the contraction to the exchange energy. We have also investigated a bulky Te-containing supramolecular complex. For such bulky, three-dimensionally extended molecules the present screening scheme has a much larger prefactor and is less effective.

Original languageEnglish
Pages (from-to)38-46
Number of pages9
JournalChemical Physics
Early online date14 Nov 2018
Publication statusPublished - 1 Feb 2019


B.H.-P. acknowledges gratefully financial support from the German Research Foundation DFG (Grant No. HE 7427/1-1) and from the Netherlands Organisation for Scientific Research NWO by a Veni fellowship (Grant No. 722.016.011). M.R. acknowledges financial support by the Research Council of Norway through its Centres of Excellence scheme, project number 262695. Computer time at the Dutch national super computer Cartesius granted by the NWO is very much appreciated. B.H.-P. would like to thank Georgi L. Stoychev for discussions on automatized auxiliary basis sets and Florian Weigend and Uwe Huniar for providing generous support on 2C Hartree-Fock calculations with Turbomole. Appendix A

FundersFunder number
German Research Foundation DFGHE 7427/1-1
Netherlands Organisation for Scientific Research NWO722.016.011
Norges forskningsråd262695


    Dive into the research topics of 'Relativistic Cholesky-decomposed density matrix MP2'. Together they form a unique fingerprint.

    Cite this