This is parallel to the analogous question about the largest DFT calculation: What is the largest material that has been studied using density functional theory?

I assume we allow high performance computing (e.g local correlation, sparsity, parallelization, etc).


3 Answers 3



The local pair-natural orbital (DLPNO) based coupled cluster method have been managed to investigate large organic molecule and small proteins (linear C150H302 (452 atoms, >8800 basis functions) , Crambin with 644 atoms, and more than 6400 basis functions ,C350H902 (>1000 atoms, > 20000 basis functions)).

Riplinger, C., Sandhoefer, B., Hansen, A., & Neese, F. (2013). Natural triple excitations in local coupled cluster calculations with pair natural orbitals. The Journal of chemical physics, 139(13), 134101.

Riplinger, C., Pinski, P., Becker, U., Valeev, E. F., & Neese, F. (2016). Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory. The Journal of chemical physics, 144(2), 024109.

In recent years, considerable amount of effort has been made on developing linear scaling coupled cluster methods. These methods have been implemented in the electronic structure package ORCA which is developed by Max Planck Institute, Germany.

  • 1
    $\begingroup$ I think this will be pretty much the winner, The work of Frank Neese's group around DLPNO-CCSD(T) is pretty much a leap from "old fashioned CCSD(T)". (And all the other niceties of ORCA such as human readable output are also great.) $\endgroup$
    – DetlevCM
    Commented May 26, 2020 at 13:55
  • $\begingroup$ What would the answer be for models that do not apply any linear approximation? $\endgroup$
    – Mathews24
    Commented Mar 13, 2023 at 16:46

I’ll expand on this later but here is the abbreviated version.


The CTF code can do very large iterative CCSD and CCSDT using a dense spin-orbital formalism.

CCSD up to 55 (50) water molecules with cc-pVDZ http://solomonik.cs.illinois.edu/talks/molssi-monterey-may-2017.pdf

The 8-water CCSDT problem in Table 3 took 15 minutes on 1024 nodes of BG/Q and 21 minutes on 256 nodes of Edison. The strong scalability achievable for this problem is significantly better on Edison, increasing the number of nodes by four, BG/Q performs such a CCSDT iteration (using 4096 nodes) in 9 minutes while Edison computes it (using 1024 nodes) in 6 minutes.

“A massively parallel tensor contraction framework for coupled-cluster computations” https://www.sciencedirect.com/science/article/abs/pii/S074373151400104X https://www2.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-143.pdf https://apps.dtic.mil/dtic/tr/fulltext/u2/a614387.pdf


If nothing else, this shows how real the N^7 cost of CCSD(T) is. In 2005, ~80 electrons in ~1400 orbitals hit 6 TF/s. In 2019, ~220 electrons in ~1800 orbitals hit 9 PF/s with the same code. This is the same code running at similar efficiency, albeit for an order-of-magnitude less time, more than a decade later. 2.7^3 is not a small number...

The largest semidirect CCSD(T) using NWChem is CCSD(T) with 216 electrons / 1,776 basis functions (cc-pVTZ basis set), which achieved more than 9 petaflop/s on NERSC Cori (KNL). This is work led by PNNL to which I made a small software contribution.

This was the largest CCSD(T) calculation of its time (2005):

All of the calculations were performed with the NWChem suite of programs and Ecce (Extensible Computational Chemistry Environment), a problem-solving environment. The calculations were done on a massively parallel HP Linux cluster with Itanium-2 processors. The largest calculation performed was the CCSD(T) calculation on octane with 1468 basis functions (the aug-cc-pVQZ basis set). The perturbative triples (T) for octane took 23 h on 1400 processors, yielding 75% CPU efficiency and a sustained performance of 6.3 TFlops. Fourteen iterations were required for convergence of the CCSD, which took approximately 43 h on 600 processors.

J. Phys. Chem. A, 109 (31), 6934 -6938, 2005 - https://doi.org/10.1021/jp044564r

  • $\begingroup$ Thanks for providing the reference. It would be nice if you could provide me some resource (e.g. online course or books) to systematically learn parallel computing? $\endgroup$
    – Paulie Bao
    Commented May 25, 2020 at 19:08
  • $\begingroup$ It seems like the link to the CCSD(T) calculation in NWChem is not working. Where can I find that paper? $\endgroup$
    – KAJ226
    Commented Mar 6 at 17:05
  • $\begingroup$ i fixed the link, if you did not google the citation already $\endgroup$ Commented Mar 7 at 18:20

Localized natural orbitals methods allow tackling huge system sizes; some links were already given above. Of course, the accuracy remains sometimes a question in such methods: the methods rely on thresholds, which may not have always been converged! So you should keep in mind that these are not black-box tools like conventional coupled-cluster theory.

The biggest calculation I remember seeing is the monstrous 1023-atom, 44712-atomic-orbital LNO-CCSD(T)/def2-QZVP calculation on a lipid transfer protein by Nagy and Kállay in J. Chem. Theory Comput. 2019, 15, 10, 5275–5298 which they claim took just 18 days on 6 cores; this system is many times larger than the examples given so far.


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