Electronic spectra of ytterbium fluoride from relativistic electronic structure calculations

We report an investigation of the low-lying excited states of the YbF molecule-a candidate molecule for experimental measurements of the electron electric dipole moment-with 2-component based multi-reference configuration interaction (MRCI), equation of motion coupled cluster (EOM-CCSD) and the extrapolated intermediate Hamiltonian Fock-space coupled cluster (XIHFS-CCSD). Specifically, we address the question of the nature of these low-lying states in terms of configurations containing filled or partially-filled Yb 4f shells. We show that while it does not appear possible to carry out calculations with both kinds of configurations contained in the same active space, reliable information can be extracted from different sectors of Fock space-that is, by performing electron attachment and detachment IHFS-CCSD and EOM-CCSD calculation on the closed-shell YbF+ and YbF− species, respectively. From these calculations we predict Ω = 1/2, 3/2 states, arising from the 4f13σ26s, 4f145d1/6p1, and 4f135d1σ16s configurations to be able to interact as they appear in the same energy range around the ground-state equilibrium geometry. As these states are generated from different sectors of Fock space, they are almost orthogonal and provide complementary descriptions of parts of the excited state manifold. To obtain a comprehensive picture, we introduce a simple adiabatization model to extract energies of interacting Ω = 1/2, 3/2 states that can be compared to experimental observations.

tial energy curves, including spectroscopic parameters, and dipole moments-both transition dipole moments (TDM) and permanent electric dipole moments (PEDM)-for different basis set sizes are presented. Subsequently, the problem of the relative position of the f 13 and f 14 states is addressed and its basis set dependence. Lastly, transition dipole moments are listed. Section 3 contains the potential energy curves and spectroscopic parameters for different basis set sizes applying the Fock space coupled cluster method and spectroscopic parameters for the states after adiabatic mixing as presented in the main text. An extended list of equation-of-motion coupled cluster transition energies for the Yb + is listed in section 4.
This section also contains EOM-CCSD potential energy curves for different basis set sizes.
Finally, in section 6 Franck-Condon factors for potentials stemming from the different methods are depicted and compared. Additional figures (orbital pictures, basis set convergence) can be found in the first version of this manuscript on arXiv. 1 1 Orbitals

Orbital energies
In this part the orbital energies obtained by AOC-SCF for several internuclear separations are shown.  Figure S1: Orbital energies for different bond distances. Blue, green, and red are occupied, partially filled, and virtual orbitals, respectively.

Diatomic orbitals -equilibrium distance
This section contains orbitals of the YbF diatomic for a internuclear distance close to the ground state equilibrium one.               Figure S9 shows the combined potentials energy curves for larger bond distances.    3.2 Open f-shell -potential energy curves   Figure S12: XIHFS-CCSD PECs for (1h,0p) sector starting from the anion reference for the quadruple zeta basis sets, extrapolation using the results in figure S11

Spectroscopic quantities after mixing
We extracted the spectroscopic quantities for the adiabatized potentials shown in the main text and listed them here.
Table S15: Spectroscopic constants for the different electronic states (Ω = 1/2, 3/2, 5/2) obtained by EOM-CCSD for the (0h,1p) sector using different basis set sizes. Vibrational constant (ω e ), anharmonicty constant (ω e χ e ), and transition energy (T e ), are given in cm −1 , the equilibrium bond distance (r e ) inÅ.    Figure S16 shows the PECs for longer bond distances.  Table S17: Spectroscopic constants for excited states with Ω = 1/2, 3/2, 5/2, starting from 18000 cm −1 for different methods using the values after extrapolation to the basis set limit. Transition energy (T e ), vibrational constant (ω e ), and anharmonicty constant (ω e χ e ) are given in cm −1 , the equilibrium bond distance (r e ) inÅ. Experimental transitions that were not assigned(n.a.) are also listed.   Additionally, there is more uncertainty with regards to the position of the potential energy curves, as configuration interaction is not size consistent and we observe transition in the range from 14000 to 19000 cm −1 for these states. The states are more dense is this case, which is expected as states of the Yb(4f 13 [F • 7/2 ]5d 1 σ 1 6s )F configuration are included, which