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An analytical implementation of static dipole polarizabilities within the generalized Kohn–Sham semicanonical projected random phase approximation (GKS-spRPA) method for spin-restricted closed-shell and spin-unrestricted open-shell references is presented. General second-order analytical derivatives of the GKS-spRPA energy functional are derived using a Lagrangian approach. By resolution-of-the-identity and complex frequency integration methods, an asymptotic [Formula: see text] scaling of operation count and [Formula: see text] scaling of storage is realized, i.e., the computational requirements are comparable to those for GKS-spRPA ground state energies. GKS-spRPA polarizabilities are assessed for small molecules, conjugated long-chain hydrocarbons, metallocenes, and metal clusters, by comparison against Hartree–Fock (HF), semilocal density functional approximations (DFAs), second-order Møller–Plesset perturbation theory, range-separated hybrids, and experimental data. For conjugated polydiacetylene and polybutatriene oligomers, GKS-spRPA effectively addresses the “overpolarization” problem of semilocal DFAs and the somewhat erratic behavior of post-PBE RPA polarizabilities without empirical adjustments. The ensemble averaged GKS-spRPA polarizabilities of sodium clusters (Na n for n = 2, 3, …, 10) exhibit a mean absolute deviation comparable to PBE with significantly fewer outliers than HF. In conclusion, analytical second-order derivatives of GKS-spRPA energies provide a computationally viable and consistent approach to molecular polarizabilities, including systems prohibitive for other methods due to their size and/or electronic structure.
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Natural transition orbitals for complex two‐component excited state calculations
Abstract While the natural transition orbital (NTO) method has allowed electronic excitations from time‐dependent Hartree‐Fock and density functional theory to be viewed in a traditional orbital picture, the extension to multicomponent molecular orbitals such as those used in relativistic two‐component methods or generalized Hartree‐Fock (GHF) or generalized Kohn‐Sham (GKS) is less straightforward due to mixing of spin‐components and the inherent inclusion of spin‐flip transitions in time‐dependent GHF/GKS. An extension of single‐component NTOs to the two‐component framework is presented, in addition to a brief discussion of the practical aspects of visualizing two‐component complex orbitals. Unlike the single‐component analog, the method explicitly describes the spin and frequently obtains solutions with several significant orbital pairs. The method is presented using calculations on a mercury atom and a CrO2Cl2complex.
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- PAR ID:
- 10457608
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Journal of Computational Chemistry
- Volume:
- 41
- Issue:
- 16
- ISSN:
- 0192-8651
- Page Range / eLocation ID:
- p. 1557-1563
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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