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Author Roemelt, Michael
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword ATOMIC AND MOLECULAR PHYSICS ♦ ALGORITHMS ♦ BORN-OPPENHEIMER APPROXIMATION ♦ DENSITY MATRIX ♦ EIGENFUNCTIONS ♦ EIGENVALUES ♦ EXCITED STATES ♦ G VALUE ♦ GROUND STATES ♦ HAMILTONIANS ♦ L-S COUPLING ♦ MAGNETIC FIELDS ♦ MATRIX ELEMENTS ♦ MEAN-FIELD THEORY ♦ MOLYBDENUM COMPLEXES ♦ RELATIVISTIC RANGE ♦ RENORMALIZATION ♦ SPIN ♦ TENSORS ♦ TRIPLETS ♦ WAVE FUNCTIONS
Abstract Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
ISSN 00219606
Educational Use Research
Learning Resource Type Article
Publisher Date 2015-07-28
Publisher Place United States
Journal Journal of Chemical Physics
Volume Number 143
Issue Number 4


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