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Title:An improved empirical potential for the highly multi-reference sextuply bonded transition metal benchamrk molecule Cr2
Author(s):Dattani, Nikesh S.
Contributor(s):Li Manni, Giovanni; Tomza, Michał
Subject(s):Theory and Computation
Abstract:The ground electronic state of the chromium dimer dissociates into Cr\,($^7$S) + Cr\,($^7$S) and therefore the fragments are highly open shell systems with a total of 12 singly occupied orbitals among its constituent atoms. It is considered one of the most difficult homonuclear diatomics for \textit{ab initio} methods because of its highly multi-reference character. Therefore, every new multi-reference method must be tested against this benchmark system. However, the best empirical potential to compare with, has its own weaknesses. The photoelectron measurements of $v=0-9$ were fitted to a Morse potential (an old function which has only one parameter controlling the shape from $r_e$ to $D_e$), and also inverted using a semi-classical theory into a potential after combining these data with measurements from what were hypothesized to be $v=24-43$. This bridging of a {\raise.17ex\hbox{$\scriptstyle\sim$}} 2000\,cm$^{-1}$ gap in data back in 1993 was a valiant spectroscopic analysis. However since 1993, there have been enormous improvements in the field of potentiology. In 2011 a Morse/long-range (MLR) function successfully bridged a gap of more than 5000\,cm$^{-1}$ in experimental data$^a$, and in 2013 an experiment with $\pm$0.000\,02\,cm$^{-1}$ resolution confirmed that the 2011 MLR predicted the energy levels in the very center of this gap correctly within {\raise.17ex\hbox{$\scriptstyle\sim$}} 1\,cm$^{-1}$,$^b$. While \textit{ab initio} methods have very recently been able to predict differences in energy levels correctly to within 1\,cm$^{-1}$ for Li$_2$\,$^c$ and to a lesser extent for BeH$^d$, \textit{ab initio} methods have still not had this level of success for predicting binding energies. The MLR function not only has more flexibility than the original Morse function, but it also converges mathematically to the correct long-range limit expected by the state-of-the-art theory. Fitting the data to an MLR potential function in the Schr\"{o}dinger equation allows for a fully quantum mechanical treatment over the entire range of data. By avoiding a semi-classical treatment, and using this more flexible, more theoretically correct form, we improve the current best empirical potential. This vastly improves the experimental benchmarks against which emerging \textit{ab initio} methods are tested. However, the lack of data for Cr$_2$ is still a big problem, so further experimental work on Cr$_2$ is desperately needed. \tiny{$^a$Dattani \& Le\,Roy (2011) Journal of Molecular Spectroscopy, \textbf{268}, 119}, \tiny{$^b$Semczuk \textit{et al.} (2013) Physical Review A, \textbf{88}, 062510.}, \tiny{$^c$Dattani (2015)}, \tiny{$^d$Dattani (2015) Journal of Molecular Spectroscopy} \textbf{311}, 76.
Issue Date:2016-06-21
Publisher:International Symposium on Molecular Spectroscopy
Genre:Conference Paper/Presentation
Rights Information:Copyright 2016 by the authors
Date Available in IDEALS:2017-01-26

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