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 |
