We model the binding energies of rovibrational levels of the RbYb molecule using experimental data from two-color photoassociation spectroscopy in mixtures of ultracold ${}^{87}$Rb with various Yb isotopes. The model uses a theoretical potential based on state-of-the-art ab initio potentials, further improved by least-squares fitting to the experimental data. We have fixed the number of bound states supported by the potential curve, so that the model is mass scaled, that is, it accurately describes the bound-state energies for all measured isotopic combinations. Such a model enables an accurate prediction of the $s$-wave scattering lengths of all isotopic combinations of the RbYb system. The reduced mass range is broad enough to cover the full scattering lengths range from $$-${}$\infty${}$ to $+$\infty${}$. For example, the ${}^{87}$Rb${}^{174}$Yb system is characterized by a large positive scattering length of $+880(120)$ a.u., while ${}^{87}$Rb${}^{173}$Yb has $a=$-${}626(88)$ a.u. On the other hand ${}^{87}$Rb${}^{170}$Yb has a very small scattering length of $$-${}11.5(2.5)$ a.u. confirmed by the pair's extremely low thermalization rate. For isotopic combinations including ${}^{85}$Rb the variation of the interspecies scattering lengths is much smoother ranging from $+39.0(1.6)$ a.u. for ${}^{85}$Rb${}^{176}$Yb to $+230(12)$ a.u. in the case of ${}^{85}$Rb${}^{168}$Yb. Hyperfine corrections to these scattering lengths are also given. We further complement the fitted potential with interaction parameters calculated from alternative methods. The recommended value of the van der Waals coefficient is ${C}_{6}=2837(13)$ a.u. agrees with but is more precise than the current state-of-the-art theoretical predictions [M. S. Safronova, S. G. Porsev, and C. W. Clark, Phys. Rev. Lett. 109, 230802 (2012)].

Different generalized Douglas-Kroll transformed Hamiltonians (DKn, n=1, 2,…,5) proposed recently by Hess et al. are investigated with respect to their performance in calculations of the spin–orbit splittings. The results are compared with those obtained in the exact infinite-order two-component (IOTC) formalism which is fully equivalent to the four-component Dirac approach. This is a comprehensive investigation of the ability of approximate DKn methods to correctly predict the spin–orbit splittings. On comparing the DKn results with the IOTC (Dirac) data one finds that the calculated spin–orbit splittings are systematically improved with the increasing order of the DK approximation. However, even the highest-order approximate two-component DK5 scheme shows certain deficiencies with respect to the treatment of the spin–orbit coupling terms in very heavy systems. The meaning of the removal of the spin-dependent terms in the so-called spin-free (scalar) relativistic methods for many-electron systems is discussed and a computational investigation of the performance of the spin-free DKn and IOTC methods for many-electron Hamiltonians is carried out. It is argued that the spin-free IOTC rather than the Dirac-Coulomb results give the appropriate reference for other spin-free schemes which are based on approximate two-component Hamiltonians. This is illustrated by calculations of spin-free DKn and IOTC total energies, r−1 expectation values, ionization potentials, and electron affinities of heavy atomic systems.

The present study is devoted to the combined experimental and theoretical description of the photophysical properties and photodegradation of the new boron-dipyrromethene (BODIPY) derivatives obtained recently for biomedical applications, such as bacteria photoinactivation (Piskorz et al., Dyes and Pigments 2020, 178, 108322). Absorption and emission spectra for a wide group of solvents of different properties for the analyzed BODIPY derivatives were investigated in order to verify their suitability for photopharmacological applications. Additionally, the photostability of the analyzed systems were thoroughly determined. The exposition to the UV light was found first to cause the decrease in the most intensive absorption band and the appearance of the hypsochromically shifted band of similar intensity. On the basis of the chromatographic and computational study, this effect was assigned to the detachment of the iodine atoms from the BODIPY core. After longer exposition to UV light, photodegradation occurred, leading to the disappearance of the intensive absorption bands and the emergence of small intensity signals in the strongly blue-shifted range of the spectrum. Since the most intensive bands in original dyes are ascribed to the molecular core bearing the BF₂ moiety, this result can be attributed to the significant cleavage of the BF₂ ring. In order to fully characterize the obtained molecules, the comprehensive computational chemistry study was performed. The influence of the intermolecular interactions for their absorption in solution was analyzed. The theoretical data entirely support the experimental outcomes.

Very accurate quantum mechanical calculations of the pure vibrational spectrum of the molecular ion are reported and compared with newly obtained pure vibrational transitions extracted from the available experimental data. The calculations are performed without assuming the Born-Oppenheimer approximation regarding separability of the nuclear and electronic motions and include the first order relativistic mass-velocity and Darwin corrections. For the two lowest transitions, whose experimental energies are established with the highest precision, the calculated and the experimental results show very good agreement.

Variational calculations employing explicitly correlated Gaussian functions and explicitly including the nuclear motion [i.e., without assuming the Born-Oppenheimer (BO) approximation] have been performed to determine the lowest singlet transition energy in the ${}^9\mathrm{Be}$ atom. The non-BO wave functions were used to calculate the ${\alpha }^2$ relativistic corrections ($\alpha =1/137.035999679$). With those corrections and with the ${\alpha }^3$ and ${\alpha }^4$ QED corrections determined previously by others, we obtained $54677.35{\mathrm{cm}}^{-1}$ for the $3{}^{1}S\to 2{}^{1}S$ transition energy. This result falls within the error bracket for the experimental transition of $54677.26(10){\mathrm{cm}}^{-1}$. This is the first time an electronic transition of Be has been calculated from first principles with the experimental accuracy.