CheMPS2: A free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry
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The density matrix renormalization group (DMRG) has become an indispensable
numerical tool to find exact eigenstates of finite-size quantum systems with
strong correlation. In the fields of condensed matter, nuclear structure and
molecular electronic structure, it has significantly extended the system sizes
that can be handled compared to full configuration interaction, without losing
numerical accuracy. For quantum chemistry (QC), the most efficient
implementations of DMRG require the incorporation of particle number, spin and
point group symmetries in the underlying matrix product state (MPS) ansatz, as
well as the use of so-called complementary operators. The symmetries introduce
a sparse block structure in the MPS ansatz and in the intermediary contracted
tensors. If a symmetry is non-abelian, the Wigner-Eckart theorem allows to
factorize a tensor into a Clebsch-Gordan coefficient and a reduced tensor. In
addition, the fermion signs have to be carefully tracked. Because of these
challenges, implementing DMRG efficiently for QC is not straightforward.
Efficient and freely available implementations are therefore highly desired. In
this work we present CheMPS2, our free open-source spin-adapted implementation
of DMRG for ab initio QC. Around CheMPS2, we have implemented the augmented
Hessian Newton-Raphson complete active space self-consistent field method, with
exact Hessian. The bond dissociation curves of the 12 lowest states of the
carbon 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 carbon
dimer 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.