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We examine the low-energy spectrum and polarisation of the dipole moments oftwo static polar molecules under the influence of an external dc electric fieldand their anisotropic dipole-dipole interaction. We model the molecules asquantum rigid rotors to take their rotational degrees of freedom into account,and consider a selection of linear, symmetric and asymmetric top molecules. Weprovide a comprehensive examination of the energy spectra and polarisation ofthe dipoles for varying inter-molecular separation and direction of theelectric field, and find that the properties of the molecules depend stronglyon the field's direction at short separations, showing the importance ofaccounting for molecular rotation. Our results provide important insight intoapplications of cold molecules for quantum computation and molecular dipolargases.

Rotational properties of two interacting cold polar molecules: linear, symmetric, and asymmetric tops