  We investigate the properties of two interacting ultracold polar molecules
described as distinguishable quantum rigid rotors, trapped in a one-dimensional
harmonic potential. The molecules interact via a multichannel two-body contact
potential, incorporating the short-range anisotropy of intermolecular
interactions including dipole-dipole interaction. The impact of external
electric and magnetic fields resulting in Stark and Zeeman shifts of molecular
rovibrational states is also investigated. Energy spectra and eigenstates are
calculated by means of the exact diagonalization. The importance and interplay
of the molecular rotational structure, anisotropic interactions, spin-rotation
coupling, electric and magnetic fields, and harmonic trapping potential are
examined in detail, and compared to the system of two harmonically trapped
distinguishable atoms. Presented model and results may provide microscopic
parameters for molecular many-body Hamiltonians, and may be useful for the
development of bottom-up molecule-by-molecule assembled molecular quantum
simulators.
