7. Typical resource requirements

In this section, typical resource requirements for DMRG calculations are discussed. With \(L\) spatial orbitals and \(D\) virtual basis states, the algorithm has a theoretical scaling per sweep of

  • \(\mathcal{O}(L^4D^2 + L^3D^3)\) in CPU time
  • \(\mathcal{O}(L^2D^2)\) in memory
  • \(\mathcal{O}(L^3D^2)\) in disk

The block-sparsity and information compression due to the exploitation of symmetry have not been taken into account in these scalings! Ref. [TIMING] contains CPU time measurements for polyenes of increasing length, and demonstrates the scaling of CheMPS2 with \(L\).

7.1. N2/cc-pVDZ

The nitrogen dimer in the cc-pVDZ basis has an active space of 14 electrons in 28 orbitals. The exploited point group in the calculations was \(\mathsf{d2h}\), and the targeted state was \(X^1\Sigma_g^+\) at equilibrium bond length: 2.118 a.u. This system was first studied with DMRG in Ref. [NITROGEN]. The listed CheMPS2 timings are wall times per sweep (in seconds) on 16 Intel Xeon Sandy Bridge (E5-2670) cores @ 2.6 GHz. The calculation was performed on a single node, and needed ~ 6 Gb of memory.

\(D_{\mathsf{SU(2)}}\) Wall time per sweep (s) \(w_D^{disc}\) \(E_D\) (Hartree)
1000 117 9.9532e-07 -109.28209681
1500 279 3.7204e-07 -109.28214478
2000 529 1.7795e-07 -109.28216006
2500 1339 9.6998e-08 -109.28216623

7.2. H2O/Roos’ ANO DZ

Water in Roos’ ANO DZ basis has an active space of 10 electrons in 41 orbitals. The exploited point group in the calculations was \(\mathsf{c2v}\), and the targeted state was \(^1A_1\) at equilibrium geometry: O @ (0, 0, 0) and H @ (± 0.790689766, 0, 0.612217330) Angstrom. This system was first studied with DMRG in Ref. [WATER]. The listed CheMPS2 timings are wall times per sweep (in seconds) on 20 Intel Xeon Ivy Bridge (E5-2670 v2) cores @ 2.5 GHz. The calculation was performed on a single node, and needed ~ 64 Gb of memory.

\(D_{\mathsf{SU(2)}}\) Wall time per sweep (s) \(w_D^{disc}\) \(E_D\) (Hartree)
1000 820 8.6093e-08 -76.31468322
2000 4304 1.1262e-08 -76.31471043
3000 11872 2.8027e-09 -76.31471338
4000 23915 6.9927e-10 -76.31471401
[TIMING]
  1. Wouters and D. Van Neck, European Physical Journal D 68, 272 (2014), doi: 10.1140/epjd/e2014-50500-1
[NITROGEN]G.K.-L. Chan, M. Kallay and J. Gauss, Journal of Chemical Physics 121, 6110 (2004), doi: 10.1063/1.1783212
[WATER]
  1. K.-L. Chan and M. Head-Gordon, Journal of Chemical Physics 118, 8551 (2003), doi: 10.1063/1.1574318

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