Towards the "puzzle" of Chromium dimer Cr$_2$: predicting the
Born-Oppenheimer rovibrational spectrum
- URL: http://arxiv.org/abs/2401.03259v1
- Date: Sat, 6 Jan 2024 17:00:12 GMT
- Title: Towards the "puzzle" of Chromium dimer Cr$_2$: predicting the
Born-Oppenheimer rovibrational spectrum
- Authors: Horacio Olivares-Pil\'on, Daniel Aguilar-D\'iaz and Alexander V.
Turbiner
- Abstract summary: The potential energy curve for the whole range of internuclear $R$ is found for the whole range of the Cr$vibration$$ dimer.
This has the form of a two-point Pade approximant and provides an accuracy of 3-4 decimal digits in 29 experimental vibrational energies.
- Score: 49.1574468325115
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The experimentally-observed non-trivial electronic structure of Cr$_2$ dimer
has made the calculation of the potential energy curve a theoretical challenge
in the last decades. By matching the perturbation theory at small internuclear
distances $R$, the multipole expansion at large distances $R$ (supposedly both
of asymptotic nature) and by adding a few RKR turning points, extracted from
experimental data, the analytic form for the potential energy curve for the
ground state $X^1\Sigma^+$ of the Cr$_2$ dimer is found for the whole range of
internuclear distances $R$. This has the form of a two-point Pade approximant
and provides an accuracy of 3-4 decimal digits in 29 experimental vibrational
energies. The resulting ground state $X^1\Sigma^+$ potential curve supports
19694 rovibrational states with a maximal vibrational number
$\nu_\text{max}=104$ 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.
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