%0 Journal Article %1 :/content/aip/journal/jcp/139/15/10.1063/1.4825041 %A Bozkaya, Uğur %D 2013 %J The Journal of Chemical Physics %K chemistry mechanics physics quantum unread %N 15 %P 154105 %R http://dx.doi.org/10.1063/1.4825041 %T The extended Koopmans' theorem for orbital-optimized methods: Accurate computation of ionization potentials %U http://scitation.aip.org/content/aip/journal/jcp/139/15/10.1063/1.4825041 %V 139 %X The extended Koopmans' theorem (EKT) provides a straightforward way to compute ionization potentials (IPs) from any level of theory, in principle. However, for non-variational methods, such as Møller–Plesset perturbation and coupled-cluster theories, the EKT computations can only be performed as by-products of analytic gradients as the relaxed generalized Fock matrix (GFM) and one- and two-particle density matrices (OPDM and TPDM, respectively) are required J. Cioslowski, P. Piskorz, and G. Liu, J. Chem. Phys.107, 6804 (1997). However, for the orbital-optimized methods both the GFM and OPDM are readily available and symmetric, as opposed to the standard post Hartree–Fock (HF) methods. Further, the orbital optimized methods solve the N-representability problem, which may arise when the relaxed particle density matrices are employed for the standard methods, by disregarding the orbital Z-vector contributions for the OPDM. Moreover, for challenging chemical systems, where spin or spatial symmetry-breaking problems are observed, the abnormal orbital response contributions arising from the numerical instabilities in the HF molecular orbital Hessian can be avoided by the orbital-optimization. Hence, it appears that the orbital-optimized methods are the most natural choice for the study of the EKT. In this research, the EKT for the orbital-optimized methods, such as orbital-optimized second- and third-order Møller–Plesset perturbationU. Bozkaya, J. Chem. Phys.135, 224103 (2011) and coupled-electron pair theories OCEPA(0) U. Bozkaya and C. D. Sherrill, J. Chem. Phys.139, 054104 (2013), are presented. The presented methods are applied to IPs of the second- and third-row atoms, and closed- and open-shell molecules. Performances of the orbital-optimized methods are compared with those of the counterpart standard methods. Especially, results of the OCEPA(0) method (with the aug-cc-pVTZ basis set) for the lowest IPs of the considered atoms and closed-shell molecules are substantially accurate, the corresponding mean absolute errors are 0.11 and 0.15 eV, respectively.

@article{:/content/aip/journal/jcp/139/15/10.1063/1.4825041, abstract = {The extended Koopmans' theorem (EKT) provides a straightforward way to compute ionization potentials (IPs) from any level of theory, in principle. However, for non-variational methods, such as Møller–Plesset perturbation and coupled-cluster theories, the EKT computations can only be performed as by-products of analytic gradients as the relaxed generalized Fock matrix (GFM) and one- and two-particle density matrices (OPDM and TPDM, respectively) are required [J. Cioslowski, P. Piskorz, and G. Liu, J. Chem. Phys.107, 6804 (1997)]. However, for the orbital-optimized methods both the GFM and OPDM are readily available and symmetric, as opposed to the standard post Hartree–Fock (HF) methods. Further, the orbital optimized methods solve the N-representability problem, which may arise when the relaxed particle density matrices are employed for the standard methods, by disregarding the orbital Z-vector contributions for the OPDM. Moreover, for challenging chemical systems, where spin or spatial symmetry-breaking problems are observed, the abnormal orbital response contributions arising from the numerical instabilities in the HF molecular orbital Hessian can be avoided by the orbital-optimization. Hence, it appears that the orbital-optimized methods are the most natural choice for the study of the EKT. In this research, the EKT for the orbital-optimized methods, such as orbital-optimized second- and third-order Møller–Plesset perturbation[U. Bozkaya, J. Chem. Phys.135, 224103 (2011)] and coupled-electron pair theories [OCEPA(0)] [U. Bozkaya and C. D. Sherrill, J. Chem. Phys.139, 054104 (2013)], are presented. The presented methods are applied to IPs of the second- and third-row atoms, and closed- and open-shell molecules. Performances of the orbital-optimized methods are compared with those of the counterpart standard methods. Especially, results of the OCEPA(0) method (with the aug-cc-pVTZ basis set) for the lowest IPs of the considered atoms and closed-shell molecules are substantially accurate, the corresponding mean absolute errors are 0.11 and 0.15 eV, respectively.}, added-at = {2013-11-03T00:27:34.000+0100}, author = {Bozkaya, Uğur}, biburl = {https://www.bibsonomy.org/bibtex/2a29497cb6417187340e500b8920f060d/drmatusek}, doi = {http://dx.doi.org/10.1063/1.4825041}, eid = {154105}, interhash = {7d5ba75f7271dc4c1847a15082074941}, intrahash = {a29497cb6417187340e500b8920f060d}, journal = {The Journal of Chemical Physics}, keywords = {chemistry mechanics physics quantum unread}, month = oct, number = 15, pages = 154105, timestamp = {2013-11-03T00:27:34.000+0100}, title = {The extended Koopmans' theorem for orbital-optimized methods: Accurate computation of ionization potentials}, url = {http://scitation.aip.org/content/aip/journal/jcp/139/15/10.1063/1.4825041}, volume = 139, year = 2013 }