Using an approach based upon a set of auxiliary many-electron wavefunctions we present a rigorous derivation of spin-orbit coupling (SOC) within the framework of linear-response time-dependent density functional theory (LR-TDDFT). Our method is based on a perturbative correction of the non-relativistic collinear TDDFT equations using a Breit-Pauli spin-orbit Hamiltonian. The derivation, which is performed within both the Casida and Sternheimer formulations of LR-TDDFT, is valid for any basis set. The requirement of spin noncollinearity for the treatment of spin-flip transitions is also discussed and a possible alternative solution for the description of these transitions in the collinear case is also proposed. Our results are validated by computing the SOC matrix elements between singlet and triplet states of two molecules, formaldehyde and acetone. In both cases, we find excellent agreement with benchmark calculations performed with a high level correlated wavefunction method.
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14 April 2014
Research Article|
April 09 2014
Derivation of spin-orbit couplings in collinear linear-response TDDFT: A rigorous formulation
Felipe Franco de Carvalho;
Felipe Franco de Carvalho
1
Laboratory of Computational Chemistry and Biochemistry
, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Switzerland
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Basile F. E. Curchod;
Basile F. E. Curchod
1
Laboratory of Computational Chemistry and Biochemistry
, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Switzerland
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Thomas J. Penfold;
Thomas J. Penfold
2
SwissFEL
, Paul Scherrer Inst, CH-5232 Villigen, Switzerland
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Ivano Tavernelli
Ivano Tavernelli
a)
1
Laboratory of Computational Chemistry and Biochemistry
, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Switzerland
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a)
Electronic mail: ivano.tavernelli@epfl.ch
J. Chem. Phys. 140, 144103 (2014)
Article history
Received:
February 05 2014
Accepted:
March 19 2014
Citation
Felipe Franco de Carvalho, Basile F. E. Curchod, Thomas J. Penfold, Ivano Tavernelli; Derivation of spin-orbit couplings in collinear linear-response TDDFT: A rigorous formulation. J. Chem. Phys. 14 April 2014; 140 (14): 144103. https://doi.org/10.1063/1.4870010
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