CheMPS2: A free opensource spinadapted implementation of the density matrix renormalization group for ab initio quantum chemistry
Abstract
The density matrix renormalization group (DMRG) has become an indispensable numerical tool to find exact eigenstates of finitesize 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 socalled complementary operators. The symmetries introduce a sparse block structure in the MPS ansatz and in the intermediary contracted tensors. If a symmetry is nonabelian, the WignerEckart theorem allows to factorize a tensor into a ClebschGordan 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 opensource spinadapted implementation of DMRG for ab initio QC. Around CheMPS2, we have implemented the augmented Hessian NewtonRaphson complete active space selfconsistent 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_{SU(2)} = 2500)/ccpVDZ level of theory. The contribution of 1 s core correlation to the X^{1}Σ_{g}^{+} bond dissociation curve of the carbon dimer was estimated by comparing energies at the DMRG(36o, 12e, D_{SU(2)} = 2500)/ccpCVDZ and DMRGSCF(34o, 8e, D_{SU(2)} = 2500)/ccpCVDZ levels of theory.
 Publication:

Computer Physics Communications
 Pub Date:
 June 2014
 DOI:
 10.1016/j.cpc.2014.01.019
 arXiv:
 arXiv:1312.2415
 Bibcode:
 2014CoPhC.185.1501W
 Keywords:

 Density matrix renormalization group;
 Matrix product state;
 SU(2) spin symmetry;
 Abelian point group symmetry;
 Ab initio quantum chemistry;
 Condensed Matter  Strongly Correlated Electrons;
 Physics  Chemical Physics;
 Physics  Computational Physics
 EPrint:
 16 pages, 13 figures