Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group

Abstract

We have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies ͑in the sense of full configuration interaction, with 1-10 E h precision͒ in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.

Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds

“…Simple as it seems, this model system can be considered as specially stringent and demanding for electronic struc-ture theories [161][162][163][164]. Actually, Figure 6 presents the potential energy curve for a simultaneous stretching of all bonds; the DH forms behave poorly along the dissociation path compared with nearly-exact results, as it also happens with all other applied DFT-or MP2-based methods.…”

Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study

“…From previous studies, 3,4,6 one expects a huge degeneracy of the natural orbitals when the electrons are very localized about the nuclei, i.e., when λ N /a 1. Besides, the theory says that, in the thermodynamic limit, N → ∞, …”

“…12 DMRG works very efficiently also when other highly correlated methods fail, e.g., configuration interaction 13 is not applicable if the system size is too large and the standard coupled cluster singles and doubles plus perturbative triples becomes unstable in one dimension for large interatomic distances. 3 Nevertheless, even the very favorable numerical efficiency of DMRG is lost for a gapless (i.e., metallic) chain. In this case, also the Moller-Plesset perturbative approach is not straightforwardly applicable due to the numerical issues triggered by the vanishing small gap.…”

“…From previous studies, it is known that in the strongly correlated regime-i.e., for interatomic distances a larger than a certain critical distance a c -the ground state of the finite H chains is characterized by a huge degeneracy of the natural orbitals, 3,4 which leads to an almost uniform natural orbital population, narrowly dispersed around 1. 6 This behavior has to be contrasted with the weakly correlated regime (a < a c ) for which already the restricted Hartree-Fock reference-that yields either a doubly occupied or empty natural orbital-is quite accurate.…”

“…Indeed, it seems reasonable to model the H chain by including only the 1s orbitals and by neglecting the long-range tail of the Coulomb interaction, especially for large interatomic distances. As a consequence, the H chain has been intensively studied to benchmark ab initio approaches to strong electronic correlation [3][4][5][6] despite the fact that this atomic chain is not directly observable due to the well-known Peierls' instability.…”