Accurate ab initio study of YbO

<p indent="0mm">Molecular systems composed of <italic>f</italic>-elements are the most challenging class of systems for quantum chemical calculations. This stems from the fact that <italic>f</italic>-elements have many valence orbitals [<italic>nf</italic>(<italic>n+</italic>1)<italic>d</italic>(<italic>n</italic>+2)<italic>s</italic>(<italic>n</italic>+2)<italic>p</italic> for each atom], many unpaired electrons, and hence many low-lying spin states, various chemical bonds and oxidation states, etc. All these imply that <italic>f</italic>-elements are strongly correlated systems of electrons. Moreover, the spatial locality and high angular momentum of 4<italic>f</italic> (and 5<italic>f</italic>) orbitals are extremely difficult to describe, as they require basis functions of high angular momenta for their spatial resolution. The situation is particularly challenging when the occupations of the <italic>f</italic>-orbitals experience changes during electronic transitions, which induce substantial differential dynamic correlation. On top of these factors, both scalar relativistic effect and spin-orbit coupling have to be accounted for accurately. As such, molecular systems composed of <italic>f</italic>-elements can only be accessed by multireference relativistic many-body methods that can handle relativistic effects as well as the static and dynamic components of the electron correlation in a balanced and adaptive manner, in conjunction with extended basis sets. Take YbO as an example. It is formally very simple because of its ionic structure Yb²⁺O²⁻. However, its ground state, whether 4<italic>f</italic>¹⁴ or 4<italic>f</italic>¹³<italic>σ</italic>¹, has long been under debate. While early <italic>ab initio</italic> investigations using the ECP-MRCISD method (effective core potential-based multireference configuration interaction with singles and doubles) showed that even the highest state of 4<italic>f</italic>¹³<italic>σ</italic>¹ is substantially lower than 4<italic>f</italic>¹⁴, later density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations predicted the opposite. While the latter is in line with experimental observations, the underlying accuracy of DFT and TD-DFT is not high enough for a final decision. Such discrepancies remain unresolved in the last <sc>15 years</sc> due to the lack of highly accurate multireference relativistic many-body methods. The situation has now changed, thanks to the advent of the SOiCI and iCISO methods, which are different combinations of the spin-separated exact two-component relativistic Hamiltonian (sf-X2C+so-DKH1) and the iterative configuration interaction (iCI) with selection and second-order perturbation theory (iCIPT2). In a nutshell, the sf-X2C Hamiltonian treats scalar relativistic effects to infinite order, whereas the so-DKH1 Hamiltonian treats spin-orbit coupling to first order. Given the fact that both the <italic>nf</italic>_5/2 and <italic>nf</italic>_7/2 spinors are radially very much the same as the scalar <italic>nf</italic> orbitals (i.e., spin-orbit coupling induced orbital relaxations are negligible), a perturbative treatment of spin-orbit coupling should be sufficient. This can be confirmed by the internal consistency between SOiCI and iCISO: the former accounts for partial orbital relaxations whereas the latter does not. On the other hand, iCIPT2 is a near-exact method for electron correlation. Therefore, SOiCI/iCISO is expected to provide benchmark results for <italic>f</italic>-elements. To verify this, the ionization potentials and excitation energies of the Yb atom and its cations are first calculated to compare with available experimental values. The results show that sf-X2C-iCIPT2 is near-exact in the treatment of both scalar relativity and electron correlation and that SOiCI and iCISO are hardly distinguishable from each other. Therefore, it can be concluded that the ground state of YbO is indeed 4<italic>f</italic>¹⁴. However, it is nearly degenerate with the lowest state of 4<italic>f</italic>¹³<italic>σ</italic>¹. The wavefunctions of 4<italic>f</italic>¹⁴ and 4<italic>f</italic>¹³<italic>σ</italic>¹ are analyzed in detail, to explain why the previous MRCISD calculations failed to predict the correct results.