Towards the "puzzle" of Chromium dimer Cr$_2$: predicting the Born-Oppenheimer rovibrational spectrum
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866909294375469056 |
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| author | Olivares-Pilón, Horacio Aguilar-Díaz, Daniel Turbiner, Alexander V. |
| author_facet | Olivares-Pilón, Horacio Aguilar-Díaz, Daniel Turbiner, Alexander V. |
| contents | The experimentally-observed non-trivial electronic structure of the Cr$_2$ dimer has made the calculation of its potential energy curve a theoretical challenge in the last decades. By matching the perturbation theory at small internuclear distances $R$ and the multipole expansion at large distances $R$ (supposedly both of asymptotic nature), and by adding a few Rydberg-Klein-Rees (RKR) turning points, extracted from experimental data by Casey-Leopold (1993), the analytic form of the potential energy curve for the ground state $X^1Σ^+$ of the Cr$_2$ dimer is found for the first time for the whole range of internuclear distances $R$. This has the form of a two-point Padé approximant and provides an accuracy of 3-4 decimal digits in 29 experimental vibrational energies. The resulting ground state $X^1Σ^+$ potential curve supports 19694 rovibrational states with a maximal vibrational number $ν_\text{max}=104$ at zero angular momentum and with a maximal angular momentum $L_\text{max}=312$ with energies $> 10^{-4}$ { hartree}, and additionally 218 weakly-bound states (close to the dissociation limit) with energies $< 10^{-4}$ { hartree}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_03259 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards the "puzzle" of Chromium dimer Cr$_2$: predicting the Born-Oppenheimer rovibrational spectrum Olivares-Pilón, Horacio Aguilar-Díaz, Daniel Turbiner, Alexander V. Chemical Physics Atomic and Molecular Clusters Atomic Physics Quantum Physics The experimentally-observed non-trivial electronic structure of the Cr$_2$ dimer has made the calculation of its potential energy curve a theoretical challenge in the last decades. By matching the perturbation theory at small internuclear distances $R$ and the multipole expansion at large distances $R$ (supposedly both of asymptotic nature), and by adding a few Rydberg-Klein-Rees (RKR) turning points, extracted from experimental data by Casey-Leopold (1993), the analytic form of the potential energy curve for the ground state $X^1Σ^+$ of the Cr$_2$ dimer is found for the first time for the whole range of internuclear distances $R$. This has the form of a two-point Padé approximant and provides an accuracy of 3-4 decimal digits in 29 experimental vibrational energies. The resulting ground state $X^1Σ^+$ potential curve supports 19694 rovibrational states with a maximal vibrational number $ν_\text{max}=104$ at zero angular momentum and with a maximal angular momentum $L_\text{max}=312$ with energies $> 10^{-4}$ { hartree}, and additionally 218 weakly-bound states (close to the dissociation limit) with energies $< 10^{-4}$ { hartree}. |
| title | Towards the "puzzle" of Chromium dimer Cr$_2$: predicting the Born-Oppenheimer rovibrational spectrum |
| topic | Chemical Physics Atomic and Molecular Clusters Atomic Physics Quantum Physics |
| url | https://arxiv.org/abs/2401.03259 |