Density-matrix renormalization-group algorithms with nonorthogonal orbitals and non-Hermitian operators, and applications to polyenes.
We describe the theory and implementation of two extensions to the density-matrix renormalization-group (DMRG) algorithm in quantum chemistry: (i) to work with an underlying nonorthogonal one-particle basis (using a biorthogonal formulation) and (ii) to use non-Hermitian and complex operators and complex wave functions, which occur naturally in biorthogonal formulations. Using these developments, we carry out ground-state calculations on ethene, butadiene, and hexatriene, in a polarized atomic-orbital basis. The description of correlation in these systems using a localized nonorthogonal basis is improved over molecular-orbital DMRG calculations, and comparable to or better than coupled-cluster calculations, although we encountered numerical problems associated with non-Hermiticity. We believe that the non-Hermitian DMRG algorithm may further become useful in conjunction with other non-Hermitian Hamiltonians, for example, similarity-transformed coupled-cluster Hamiltonians.
Chan
Garnet Kin-Lic
GK
Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, USA. gc238@cornell.edu
Van Voorhis
Troy
T
D000465:Algorithms; D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D011090:Polyenes / Q000737:chemistry*; D011789:Quantum Theory
D011090:Polyenes