Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory
Electron density is used to compute Shannon entropy. The deviation from the Hartree–Fock (HF) of this quantity has been observed to be related to correlation energy. Thus, Shannon entropy is here proposed as a valid quantity to assess the quality of an energy density functional developed w...
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| Format: | Article |
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MDPI AG
2018-05-01
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| Series: | Computation |
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| Online Access: | http://www.mdpi.com/2079-3197/6/2/36 |
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| author | Claudio Amovilli Franca Maria Floris |
| author_facet | Claudio Amovilli Franca Maria Floris |
| author_sort | Claudio Amovilli |
| collection | DOAJ |
| description | Electron density is used to compute Shannon entropy. The deviation from the Hartree–Fock (HF) of this quantity has been observed to be related to correlation energy. Thus, Shannon entropy is here proposed as a valid quantity to assess the quality of an energy density functional developed within Kohn–Sham theory. To this purpose, results from eight different functionals, representative of Jacob’s ladder, are compared with accurate results obtained from diffusion quantum Monte Carlo (DMC) computations. For three series of atomic ions, our results show that the revTPSS and the PBE0 functionals are the best, whereas those based on local density approximation give the largest discrepancy from DMC Shannon entropy. |
| first_indexed | 2024-12-14T14:00:49Z |
| format | Article |
| id | doaj.art-6d6be582580d4ec6ad8d94ffe9cdd782 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-12-14T14:00:49Z |
| publishDate | 2018-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-6d6be582580d4ec6ad8d94ffe9cdd7822022-12-21T22:58:43ZengMDPI AGComputation2079-31972018-05-01623610.3390/computation6020036computation6020036Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham TheoryClaudio Amovilli0Franca Maria Floris1Dipartimento di Chimica e Chimica Industriale, University of Pisa, Via Giuseppe Moruzzi 13, 56124 Pisa, ItalyDipartimento di Chimica e Chimica Industriale, University of Pisa, Via Giuseppe Moruzzi 13, 56124 Pisa, ItalyElectron density is used to compute Shannon entropy. The deviation from the Hartree–Fock (HF) of this quantity has been observed to be related to correlation energy. Thus, Shannon entropy is here proposed as a valid quantity to assess the quality of an energy density functional developed within Kohn–Sham theory. To this purpose, results from eight different functionals, representative of Jacob’s ladder, are compared with accurate results obtained from diffusion quantum Monte Carlo (DMC) computations. For three series of atomic ions, our results show that the revTPSS and the PBE0 functionals are the best, whereas those based on local density approximation give the largest discrepancy from DMC Shannon entropy.http://www.mdpi.com/2079-3197/6/2/36Shannon entropydensity functional theoryQuantum Monte Carloelectronic structure of atoms |
| spellingShingle | Claudio Amovilli Franca Maria Floris Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory Computation Shannon entropy density functional theory Quantum Monte Carlo electronic structure of atoms |
| title | Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory |
| title_full | Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory |
| title_fullStr | Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory |
| title_full_unstemmed | Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory |
| title_short | Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory |
| title_sort | shannon entropy in atoms a test for the assessment of density functionals in kohn sham theory |
| topic | Shannon entropy density functional theory Quantum Monte Carlo electronic structure of atoms |
| url | http://www.mdpi.com/2079-3197/6/2/36 |
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