Density-matrix renormalization-group algorithms with nonorthogonal orbitals and non-Hermitian operators, and applications to polyenes

Journal Article · Sun May 22 04:00:00 EDT 2005 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.1899124· OSTI ID:20722244

Chan, Garnet Kin-Lic; Van Voorhis, Troy ^[1]

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1. Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301 (United States)

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.

• OSTI ID: 20722244
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 20 Vol. 122; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
BUTADIENE
DENSITY MATRIX
ETHYLENE
GROUND STATES
HAMILTONIANS
HERMITIAN OPERATORS
MOLECULAR ORBITAL METHOD
RENORMALIZATION
WAVE FUNCTIONS