Effective Algorithms of the RI Approximation for the CIS Method: an Example of Application of the High-Memory Strategy in the Ab Initio Calculations

Maksim D. Zhukov; Ilya O. Glebov

doi:10.14529/jsfi260101

Authors

Maksim D. Zhukov Chemistry Department, Lomonosov Moscow State University, Moscow, Russia https://orcid.org/0009-0001-6065-3623
Ilya O. Glebov Chemistry Department, Lomonosov Moscow State University, Moscow, Russia https://orcid.org/0000-0002-2262-1778

DOI:

https://doi.org/10.14529/jsfi260101

Keywords:

Configuration interaction, resolution of identity, ab initio, electronic repulsion integrals, Davidson diagonalization

Abstract

Two variants of the CIS methods with the RI approximation have been implemented. Both methods employ the high-memory strategy: the first, RI-CIS(1), is based on the full storage of the decomposed electronic repulsion integrals (ERI) tensor and CIS Hamiltonian, while the second, RI-CIS(2), stores only the decomposed ERI tensor. Both variants of the RI-CIS were tested for parallelism, performance, and precision. The results are compared with the default CIS method and RIJCOSX approximation. The considered methods demonstrate higher performance compared to their analogs and higher precision compared to the RIJCOSX approximation. Even the worse scaling of the RI methods did not lead to the lower performance in the conducted test calculations. The reported algorithms show that the performance of the quantum chemistry calculations is limited not only by the CPU power but also by the availability of RAM. The large volume of available memory can significantly increase the speed of the calculation by employing more effective but memory-consuming algorithms.

References

Shavitt, I.: The history and evolution of configuration interaction. Molecular Physics 94(1), 3–17 (May 1998). https://doi.org/10.1080/002689798168303

Adamo, C., Jacquemin, D.: The calculations of excited-state properties with Time-Dependent Density Functional Theory. Chem. Soc. Rev. 42(3), 845–856 (2013). https://doi.org/10.1039/c2cs35394f

Beebe, N.H.F., Linderberg, J.: Simplifications in the generation and transformation of two-electron integrals in molecular calculations. International Journal of Quantum Chemistry 12(4), 683–705 (Oct 1977). https://doi.org/10.1002/qua.560120408

Vahtras, O., Almlöf, J., Feyereisen, M.: Integral approximations for LCAO-SCF calculations. Chemical Physics Letters 213(5–6), 514–518 (Oct 1993). https://doi.org/10.1016/0009-2614(93)89151-7

Glebov, I.O., Poddubnyi, V.V.: An effective algorithm of the Hartree–Fock approach with the storing of two-electron integrals in the resolution of identity approximation. Russian Journal of Physical Chemistry A 98(4), 617–625 (Apr 2024). https://doi.org/10.1134/s0036024424040101

Weigend, F.: A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency. Physical Chemistry Chemical Physics 4(18), 4285–4291 (Aug 2002). https://doi.org/10.1039/b204199p

Neese, F.: The ORCA program system. WIREs Computational Molecular Science 2(1), 73–78 (Jun 2011). https://doi.org/10.1002/wcms.81

Neese, F.: Software update: the ORCA program system, version 4.0. WIREs Computational Molecular Science 8(1) (Jul 2017). https://doi.org/10.1002/wcms.1327

Neese, F., Wennmohs, F., Hansen, A., Becker, U.: Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. a ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange. Chemical Physics 356(1–3), 98–109 (Feb 2009). https://doi.org/10.1016/j.chemphys.2008.10.036

Almlöf, J., Faegri, K., Korsell, K.: Principles for a direct SCF approach to LICAO–MO abinitio calculations. Journal of Computational Chemistry 3(3), 385–399 (Sep 1982). https://doi.org/10.1002/jcc.540030314

Weigend, F., Häser, M., Patzelt, H., Ahlrichs, R.: RI-MP2: optimized auxiliary basis sets and demonstration of efficiency. Chemical Physics Letters 294(1–3), 143–152 (Sep 1998). https://doi.org/10.1016/s0009-2614(98)00862-8

Aquilante, F., Malmqvist, P.Å., Pedersen, T.B., et al.: Cholesky decomposition-based multiconfiguration second-order perturbation theory (CD-CASPT2): Application to the spinstate energetics of CoIII(diiminato)(NPh). Journal of Chemical Theory and Computation 4(5), 694–702 (Apr 2008). https://doi.org/10.1021/ct700263h

Folkestad, S.D., Kjønstad, E.F., Koch, H.: An efficient algorithm for Cholesky decomposition of electron repulsion integrals. The Journal of Chemical Physics 150(19) (May 2019). https://doi.org/10.1063/1.5083802

Davidson, E.R.: The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. Journal of Computational Physics 17(1), 87–94 (Jan 1975). https://doi.org/10.1016/0021-9991(75)90065-0

Crouzeix, M., Philippe, B., Sadkane, M.: The Davidson Method. SIAM Journal on Scientific Computing 15(1), 62–76 (Jan 1994). https://doi.org/10.1137/0915004

Weigend, F.: Accurate Coulomb-fitting basis sets for H to Rn. Physical Chemistry Chemical Physics 8(9), 1057 (2006). https://doi.org/10.1039/b515623h

Glebov, I.O., Kozlov, M.I., Poddubnyy, V.V.: Comparison of the Coulomb and non-orthogonal approaches to the construction of the exciton Hamiltonian. Computational and Theoretical Chemistry 1153, 12–18 (Apr 2019). https://doi.org/10.1016/j.comptc.2019.02.010

Glebov, I.O., Poddubnyy, V.V., Khokhlov, D.V.: Perturbative expansion of non-orthogonal product approach for charge transfer states. The Journal of Physical Chemistry A 126(34), 5800–5813 (Apr 2022). https://doi.org/10.26434/chemrxiv-2022-9jb6k

Glebov, I.O., Poddubnyy, V.V., Khokhlov, D.: Perturbation theory in the complete degenerate active space (CDAS-PT2). The Journal of Chemical Physics 161(2) (Jul 2024). https://doi.org/10.1063/5.0211210

Valeev, E.F.: Libint: A library for the evaluation of molecular integrals of many-body operators over Gaussian functions. http://libint.valeyev.net/ (2025), version 2.11.2

Pritchard, B.P., Altarawy, D., Didier, B., et al.: New basis set exchange: An open, up-todate resource for the molecular sciences community. Journal of Chemical Information and Modeling 59(11), 4814–4820 (Oct 2019). https://doi.org/10.1021/acs.jcim.9b00725

Feller, D.: The role of databases in support of computational chemistry calculations. Journal of Computational Chemistry 17(13), 1571–1586 (Oct 1996). https://doi.org/10.1002/(sici)1096-987x(199610)17:13<1571::aid-jcc9>3.0.co;2-p

Schuchardt, K.L., Didier, B.T., Elsethagen, T., et al.: Basis set exchange: A community database for computational sciences. Journal of Chemical Information and Modeling 47(3), 1045–1052 (Apr 2007). https://doi.org/10.1021/ci600510j

Craig, N.C., Groner, P., McKean, D.C.: Equilibrium structures for butadiene and ethylene: Compelling evidence for π-electron delocalization in butadiene. The Journal of Physical Chemistry A 110(23), 7461–7469 (May 2006). https://doi.org/10.1021/jp060695b

Bode, B.M., Gordon, M.S.: Macmolplt: a graphical user interface for GAMESS. Journal of Molecular Graphics and Modelling 16(3), 133–138 (Jun 1998). https://doi.org/10.1016/s1093-3263(99)00002-9