A DFT + <i>U</i> Study on the Stability of Small Cu<sub>N</sub> Clusters (<i>N</i> = 3–6 Atoms): Calculation of Phonon Frequencies
Despite the interest in copper clusters, a consensus on their atomic structure is still lacking. The experimental observation of isolated clusters is difficult, and theoretical predictions vary widely. The latter is because one must adequately describe the closed shell of <i>d</i> electr...
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MDPI AG
2023-09-01
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| Series: | Condensed Matter |
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| Online Access: | https://www.mdpi.com/2410-3896/8/3/81 |
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| author | Luis A. Alcalá-Varilla Rafael E. Ponnefz-Durango Nicola Seriani Eduard Araujo-Lopez Javier A. Montoya |
| author_facet | Luis A. Alcalá-Varilla Rafael E. Ponnefz-Durango Nicola Seriani Eduard Araujo-Lopez Javier A. Montoya |
| author_sort | Luis A. Alcalá-Varilla |
| collection | DOAJ |
| description | Despite the interest in copper clusters, a consensus on their atomic structure is still lacking. The experimental observation of isolated clusters is difficult, and theoretical predictions vary widely. The latter is because one must adequately describe the closed shell of <i>d</i> electrons both in its short- and long-range effects. Herein, we investigate the stability of small copper clusters (Cu<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>N</mi></msub></semantics></math></inline-formula>, <i>N</i> = 3–6 atoms) using spin-polarized DFT calculations under the GGA approximation, the Hubbard <i>U</i> correction, and the van der Waals forces. We found that the spin-polarized and vdW contributions have little effect on the binding energies of the isomers. The inclusion of <i>U</i> represents the most relevant contribution to the ordering of the Cu<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>N</mi></msub></semantics></math></inline-formula> isomers, and our calculated binding energies for the clusters agreed with the experimental values. We also found that atomic relaxations alone are not enough to determine the stability of small copper clusters. It is also necessary to build the energy landscape or calculate the vibrational frequencies of the isomers. We found that the vibrational frequencies of the isomers were in the THz range and the normal modes of vibration were discrete. This approach is relevant to future studies involving isolated or supported copper clusters. |
| first_indexed | 2024-03-10T22:53:48Z |
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| last_indexed | 2024-03-10T22:53:48Z |
| publishDate | 2023-09-01 |
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| series | Condensed Matter |
| spelling | doaj.art-06a740b664c94c1cb9cdcb3f8653ae892023-11-19T10:07:59ZengMDPI AGCondensed Matter2410-38962023-09-01838110.3390/condmat8030081A DFT + <i>U</i> Study on the Stability of Small Cu<sub>N</sub> Clusters (<i>N</i> = 3–6 Atoms): Calculation of Phonon FrequenciesLuis A. Alcalá-Varilla0Rafael E. Ponnefz-Durango1Nicola Seriani2Eduard Araujo-Lopez3Javier A. Montoya4Departamento de Física y Electrónica, Universidad de Córdoba, Montería 230002, Córdoba, ColombiaDepartamento de Física y Electrónica, Universidad de Córdoba, Montería 230002, Córdoba, ColombiaCondensed Matter and Statistical Physics Section, The Abdus Salam ICTP, Strada Costiera 11, 34151 Trieste, ItalyGrupo de Modelado Computacional, Universidad de Cartagena, Cartagena de Indias 130001, Bolívar, ColombiaGrupo de Modelado Computacional, Universidad de Cartagena, Cartagena de Indias 130001, Bolívar, ColombiaDespite the interest in copper clusters, a consensus on their atomic structure is still lacking. The experimental observation of isolated clusters is difficult, and theoretical predictions vary widely. The latter is because one must adequately describe the closed shell of <i>d</i> electrons both in its short- and long-range effects. Herein, we investigate the stability of small copper clusters (Cu<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>N</mi></msub></semantics></math></inline-formula>, <i>N</i> = 3–6 atoms) using spin-polarized DFT calculations under the GGA approximation, the Hubbard <i>U</i> correction, and the van der Waals forces. We found that the spin-polarized and vdW contributions have little effect on the binding energies of the isomers. The inclusion of <i>U</i> represents the most relevant contribution to the ordering of the Cu<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>N</mi></msub></semantics></math></inline-formula> isomers, and our calculated binding energies for the clusters agreed with the experimental values. We also found that atomic relaxations alone are not enough to determine the stability of small copper clusters. It is also necessary to build the energy landscape or calculate the vibrational frequencies of the isomers. We found that the vibrational frequencies of the isomers were in the THz range and the normal modes of vibration were discrete. This approach is relevant to future studies involving isolated or supported copper clusters.https://www.mdpi.com/2410-3896/8/3/81copper clustersDFT + <i>U</i>van der WaalsHubbardphonon frequencies |
| spellingShingle | Luis A. Alcalá-Varilla Rafael E. Ponnefz-Durango Nicola Seriani Eduard Araujo-Lopez Javier A. Montoya A DFT + <i>U</i> Study on the Stability of Small Cu<sub>N</sub> Clusters (<i>N</i> = 3–6 Atoms): Calculation of Phonon Frequencies Condensed Matter copper clusters DFT + <i>U</i> van der Waals Hubbard phonon frequencies |
| title | A DFT + <i>U</i> Study on the Stability of Small Cu<sub>N</sub> Clusters (<i>N</i> = 3–6 Atoms): Calculation of Phonon Frequencies |
| title_full | A DFT + <i>U</i> Study on the Stability of Small Cu<sub>N</sub> Clusters (<i>N</i> = 3–6 Atoms): Calculation of Phonon Frequencies |
| title_fullStr | A DFT + <i>U</i> Study on the Stability of Small Cu<sub>N</sub> Clusters (<i>N</i> = 3–6 Atoms): Calculation of Phonon Frequencies |
| title_full_unstemmed | A DFT + <i>U</i> Study on the Stability of Small Cu<sub>N</sub> Clusters (<i>N</i> = 3–6 Atoms): Calculation of Phonon Frequencies |
| title_short | A DFT + <i>U</i> Study on the Stability of Small Cu<sub>N</sub> Clusters (<i>N</i> = 3–6 Atoms): Calculation of Phonon Frequencies |
| title_sort | dft i u i study on the stability of small cu sub n sub clusters i n i 3 6 atoms calculation of phonon frequencies |
| topic | copper clusters DFT + <i>U</i> van der Waals Hubbard phonon frequencies |
| url | https://www.mdpi.com/2410-3896/8/3/81 |
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