Ensemble Generalized Kohn-Sham Theory: The Good, the Bad, and the Ugly

10.26434/chemrxiv.12846836.v2 ◽

2020 ◽

Author(s):

Tim Gould ◽

Leeor Kronik

Keyword(s):

Excited States ◽

Iterative Algorithm ◽

Open Systems ◽

Potential Operators ◽

Quantum Ensembles

Two important extensions of Kohn-Sham (KS) theory are generalized KS theory and ensemble KS theory. The former allows for non-multiplicative potential operators and greatly facilitates practical calculations with advanced, orbital-dependent functionals. The latter allows for quantum ensembles and enables the treatment of, e.g., open systems and excited states. Here, we combine the two extensions, both formally and practically, first via an exact yet complicated formalism, then via a computationally tractable variant that involves a controlled approximation of ensemble "ghost interactions" by means of an iterative algorithm. The resulting formalism is illustrated using selected examples. This opens the door to the application of generalized KS theory in more challenging quantum scenarios and to the improvement of ensemble theories for the purpose of practical and accurate calculations.

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Ensemble Generalized Kohn-Sham Theory: The Good, the Bad, and the Ugly

10.26434/chemrxiv.12846836.v3 ◽

2021 ◽

Author(s):

Tim Gould ◽

Leeor Kronik

Keyword(s):

Excited States ◽

Iterative Algorithm ◽

Open Systems ◽

Potential Operators ◽

Quantum Ensembles

Two important extensions of Kohn-Sham (KS) theory are generalized KS theory and ensemble KS theory. The former allows for non-multiplicative potential operators and greatly facilitates practical calculations with advanced, orbital-dependent functionals. The latter allows for quantum ensembles and enables the treatment of, e.g., open systems and excited states. Here, we combine the two extensions, both formally and practically, first via an exact yet complicated formalism, then via a computationally tractable variant that involves a controlled approximation of ensemble "ghost interactions" by means of an iterative algorithm. The resulting formalism is illustrated using selected examples. This opens the door to the application of generalized KS theory in more challenging quantum scenarios and to the improvement of ensemble theories for the purpose of practical and accurate calculations.

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Ensemble Generalized Kohn-Sham Theory: The Good, the Bad, and the Ugly

10.26434/chemrxiv.12846836.v1 ◽

2020 ◽

Cited By ~ 1

Author(s):

Tim Gould ◽

Leeor Kronik

Keyword(s):

Potential Theory ◽

Excited States ◽

Effective Potential ◽

Open Systems ◽

Potential Operators ◽

Optimized Effective Potential ◽

Quantum Ensembles

Two important extensions of Kohn-Sham (KS) theory are generalized KS theory and ensemble KS theory. The former allows for non-multiplicative potential operators and greatly facilitates practical calculations with advanced, orbital-dependent functionals. The latter allows for quantum ensembles and enables the treatment of, e.g., open systems and excited states. Here, we combine the two extensions, both formally and practically, first via an exact yet complicated formalism, then via a computationally tractable variant that involves a controlled approximation of ensemble "ghost interactions" by means of an approach inspired by optimized effective potential theory. The resulting formalism is illustrated using selected examples. This opens the door to the application of generalized KS theory in more challenging quantum scenarios and to the improvement of ensemble theories for the purpose of practical and accurate calculations.

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Vuv Spectra Y to Mo

International Astronomical Union Colloquium ◽

10.1017/s0252921100107808 ◽

1988 ◽

Vol 102 ◽

pp. 239

Author(s):

M.S.Z. Chaghtai

Keyword(s):

Excited States ◽

Spectral Analyses ◽

Vuv Spectra

Using R.D. Cowan’s computations (1979) and parametric calculations of Meinders et al (1982), old analyses are thoroughly revised and extended at Aligarh, of Zr III by Khan et al (1981), of Nb IV by Shujauddin et Chaghtai (1985), of Mo V by Tauheed at al (1985). Cabeza et al (1986) confirmed the last one largely.Extensive studies have been reported of the 1–e spectra, Zr IV (Rahimullah et al 1980; Acquista and Reader 1980), Nb V (Shujauddin et al 1982; Kagan et al 1981) and Mo VI (Edlén et al 1985). Some interacting 4p54d2levels of these spectra have been reported from our laboratory, also.Detailed spectral analyses of transitions between excited states have furnished complete energy values for J ≠ 1 levels of these spectra during 1970s and 80s. Shujauddin et al (1982) have worked out Nb VI and Tauheed et al (1984) Mo VII from our lab, while Khan et al (1981) share the work on Zr V with Reader and Acquista (1979).

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