Rotational splittings in diatomic molecules of interest to searches for new physics

Diatomic molecules with an energetically low-lying $^3 Δ_1$ state are attractive platforms to detect new physics beyond the Standard Model, such as parity- and time-reversal violating phenomena. One of the advantages of using a $^3 Δ_1$ state is its tiny $Λ$-splitting due to the coupling between the electronic and rotational angular momenta, which facilitates polarizing the molecules in small external electric fields. Theoretical estimation of the magnitude of the $Λ$-splitting is helpful for planning new experiments. In this study, we present a theoretical model to calculate the $Λ$-splitting. Our model integrates the relativistic four-component wavefunction and the traditional rotational Hamiltonian based on Hund's case (a). The multireference character of the wavefunction is taken into account. Our calculations for PtH and ThF$^+$ molecules qualitatively agree with experiment. The $Λ$-splitting of TaO$^+$ for the rotational ground state is predicted to be around 9 kHz. This tiny splitting can reduce the systematic uncertainty, but in a practical experiment, it may cause depolarization during rotation ramp-up.