CheMPS2: a free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry

摘要

The density matrix renormalization group (DMRG) has become an indispensablenumerical tool to find exact eigenstates of finite-size quantum systems withstrong correlation. In the fields of condensed matter, nuclear structure andmolecular electronic structure, it has significantly extended the system sizesthat can be handled compared to full configuration interaction, without losingnumerical accuracy. For quantum chemistry (QC), the most efficientimplementations of DMRG require the incorporation of particle number, spin andpoint group symmetries in the underlying matrix product state (MPS) ansatz, aswell as the use of so-called complementary operators. The symmetries introducea sparse block structure in the MPS ansatz and in the intermediary contractedtensors. If a symmetry is non-abelian, the Wigner-Eckart theorem allows tofactorize a tensor into a Clebsch-Gordan coefficient and a reduced tensor. Inaddition, the fermion signs have to be carefully tracked. Because of thesechallenges, implementing DMRG efficiently for QC is not straightforward.Efficient and freely available implementations are therefore highly desired. Inthis work we present CheMPS2, our free open-source spin-adapted implementationof DMRG for ab initio QC. Around CheMPS2, we have implemented the augmentedHessian Newton-Raphson complete active space self-consistent field method, withexact Hessian. The bond dissociation curves of the 12 lowest states of thecarbon dimer were obtained at the DMRG(28 orbitals, 12 electrons,D$_{\mathsf{SU(2)}}$=2500)/cc-pVDZ level of theory. The contribution of $1s$core correlation to the $X^1\Sigma_g^+$ bond dissociation curve of the carbondimer was estimated by comparing energies at the DMRG(36o, 12e,D$_{\mathsf{SU(2)}}$=2500)/cc-pCVDZ and DMRG-SCF(34o, 8e,D$_{\mathsf{SU(2)}}$=2500)/cc-pCVDZ levels of theory.