Rydberg states of ZnAr complex

Abstract

Ab initio potential energy curves (PECs) of electronic states of ZnAr complex are calculated up to Rydberg state correlating with the $\left(4s6s\right){}^1{S}_0$ asymptote of Zn atom. Analysis of various sources of errors of presented calculations is performed including finite basis set size, deficiencies in inclusion of the electron correlation and relativistic effects, and size-inconsistency errors of the multireference second-order perturbation theory. In particular, it is emphasised that the inclusion of the midbond bases substantially improves the convergence rate of the binding energies with respect to the basis set size not only for the van der Waals ground state of ZnAr complex, but also it is the case for the excited states including the Rydberg ones. Wherever it is possible, the comparison with the experimental data and other theoretical results is presented. Properties of the double-well PECs of the Σ Rydberg states are interpreted within the simplified theory, in which, the appearance of the energy barrier and, partially, of the outer well originates from the low-energy scattering of the Rydberg electron on the Ar atom.

GRAPHICAL ABSTRACT

Keywords:

• Van der Waals complex
• diatomic molecule
• Rydberg states
• undulations of potential energy curves
• ab initio calculations
• accuracy of ab initio methods
• midbond basis functions

Acknowledgements

This paper is dedicated to the memory of Professor Lutosław Wolniewicz.

Disclosure statement

The authors report there are no competing interests to declare.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1 Quantum number $\mathrm{\Omega }=|M_S+M_L|$ corresponds to the projection of the total electronic angular momentum on the molecular axis and the superscripts $0^{\pm }$ identify the $\mathrm{\Omega }=0$ states that do not change $(+)$ or invert $(-)$ their sign under the reflection with respect to the plane containing molecular axis.

2 This ‘diabatisation’ led to irregularities of PEC within inner well of $\left(4d6s\right){}^1\mathrm{\Sigma }$ state in the case of calculations with I-III and I'-III' bases. Therefore, we have not performed such reorderings in the case of $\left(4s5p\right){}^1\mathrm{\Sigma }$ and $\left(4s6s\right){}^1\mathrm{\Sigma }$ states obtained with III-332, III-33211 and III-a5Z bases.

3 The spin-free PECs of ZnAr complex obtained with I-III and I'-III' basis sets can be found in SM (Figures S1–S8).

4 Spectroscopic characteristics, i.e. $R_e$, $D_e$ and ${\omega }_e^{\left[f\right]}$, obtained with MS-CASPT2 and CCSD(T) methods for all the considered states of ZnAr complex and with all the basis sets of Table 1 are collected in SM (Tables S6–S14 and Figures S9–S12). Deviations from the general trends of changes of the values of $R_e$, $D_e$ and ${\omega }_e^{\left[f\right]}$ obtained with different basis sets may be attributed to the avoided crossings (SM, Figure S15).

5 Figure 4 in main text and the Figures S9–S12 in SM present the patterns of convergence of the inner-well spectroscopic characteristics $R_e,D_e,{\omega }_e^{\left[f\right]}$ of the individual states.

6 Figures S13–S14 in SM present the patterns of convergence of $R_b$, $E_b$, $R_e^{\mathrm{o}\mathrm{u}\mathrm{t}}$, $D_e^{\mathrm{o}\mathrm{u}\mathrm{t}}$ for the individual Σ Rydberg states.

7 Tables S6–S8 in SM collect the values of $R_e,D_e,{\omega }_e^{\left[f\right]}$ plotted in Figure 4.

8 Consult Figures S1–S4 and Table S9 in SM.

9 Tables S4 and S5 in SM present results of atomic MS-CASPT2/RASSI-SO calculations.

10 Consult Table S6 in SM.

11 See also Ref. [96].

12 PEC of $B{}^{3}1\left(4p{}^3{P}_1\right)$ state is presented in Figure S16 in SM.

13 In particular, the values of well depth $D_e$ of $\left(4s4p\right){}^1\mathrm{\Pi }$ state are 644 cm${}^{-1}$ and 677 cm${}^{-1}$ for II' and III-a5Z bases, respectively (Table S10 in SM).

14 This is estimated by the difference of 7 cm${}^{-1}$ between well-depth $D_e$ values obtained with MS-CASPT2 method for II' and III-a5Z bases (Table S10 in SM).

15 Figure 2 and Figure S17 in SM present classically accessible regions for Rydberg electrons and $e-$Ar scattering length $A_s\left(k_R\right)$, respectively.

16 Compare also with $\mathrm{\Delta }{E}_s\left(R\right)$ presented in Figure 13 (and in Figure S18 of SM) calculated for the highest Rydberg states of ZnAr complex considered here.

Additional information

Funding

This work was supported by the National Science Centre Poland under grant number UMO-2015/17/B/ST4/04016.