Heßelmann A, Görling A (2011)
Publication Type: Journal article, Original article
Publication year: 2011
Original Authors: Hesselmann A., Görling A.
Publisher: American Institute of Physics (AIP)
Book Volume: 134
Article Number: 034120
Journal Issue: 3
DOI: 10.1063/1.3517312
A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples. © 2011 American Institute of Physics.
APA:
Heßelmann, A., & Görling, A. (2011). Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock. Journal of Chemical Physics, 134(3). https://dx.doi.org/10.1063/1.3517312
MLA:
Heßelmann, Andreas, and Andreas Görling. "Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock." Journal of Chemical Physics 134.3 (2011).
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