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Author Bleiziffer, Patrick ♦ Schmidtel, Daniel ♦ Görling, Andreas
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ♦ INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY ♦ ELECTRON CORRELATION ♦ EVALUATION ♦ FLUCTUATIONS ♦ FREQUENCY DEPENDENCE ♦ HAMILTONIANS ♦ HARTREE-FOCK METHOD ♦ KERNELS ♦ STABILITY
Abstract The occurrence of instabilities, in particular singlet-triplet and singlet-singlet instabilities, in the exact-exchange (EXX) Kohn-Sham method is investigated. Hessian matrices of the EXX electronic energy with respect to the expansion coefficients of the EXX effective Kohn-Sham potential in an auxiliary basis set are derived. The eigenvalues of these Hessian matrices determine whether or not instabilities are present. Similar as in the corresponding Hartree-Fock case instabilities in the EXX method are related to symmetry breaking of the Hamiltonian operator for the EXX orbitals. In the EXX methods symmetry breaking can easily be visualized by displaying the local multiplicative exchange potential. Examples (N{sub 2}, O{sub 2}, and the polyyne C{sub 10}H{sub 2}) for instabilities and symmetry breaking are discussed. The relation of the stability conditions for EXX methods to approaches calculating the Kohn-Sham correlation energy via the adiabatic-connection fluctuation-dissipation (ACFD) theorem is discussed. The existence or nonexistence of singlet-singlet instabilities in an EXX calculation is shown to indicate whether or not the frequency-integration in the evaluation of the correlation energy is singular in the EXX-ACFD method. This method calculates the Kohn-Sham correlation energy through the ACFD theorem theorem employing besides the Coulomb kernel also the full frequency-dependent exchange kernel and yields highly accurate electronic energies. For the case of singular frequency-integrands in the EXX-ACFD method a regularization is suggested. Finally, we present examples of molecular systems for which the self-consistent field procedure of the EXX as well as the Hartree-Fock method can converge to more than one local minimum depending on the initial conditions.
ISSN 00219606
Educational Use Research
Learning Resource Type Article
Publisher Date 2014-11-28
Publisher Place United States
Journal Journal of Chemical Physics
Volume Number 141
Issue Number 20


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