TaN, a molecular system for probing $\mathcal{P},\mathcal{T}$-violating hadron physics

All-electron configuration interaction theory in the framework of the Dirac-Coulomb Hamiltonian has been applied to the TaN molecule, a promising candidate in the search for Beyond-Standard-Model physics in both the hadron and the lepton sector of matter. We obtain in the first excited {${}^3{\mathrm{\Delta }}_1$} state a $\mathcal{P},\mathcal{T}$-odd effective electric field of $36.0 \left[\frac{\rm GV}{\rm cm}\right]$,ascalar-pseudoscalar${\cal{P,T}}$-odd interaction constant of $32.8$ [kHz], and a nuclear magnetic-quadrupole moment interaction constant of $0.74$ [$\frac{{10}^{33}\text{Hz}}{e{\text{cm}}^2}$]. The latter interaction constant has been obtained with a new approach which we describe in detail. Using the same highly correlated all-electron wavefunctions with up to $2.5$ billion expansion terms, we obtain a parallel magnetic hyperfine interaction constant of $-2954$ [MHz] for the ${}^{181}\mathrm{T}\mathrm{a}$ nucleus, a very large molecule-frame electric dipole moment of $-4.91$ [Debye], and spectroscopic constants for the four lowest-lying electronic states of the molecule.