In this article we present a concrete proposal for spin squeezing the ultracold ground state polar paramagnetic molecule OH, a system currently under fine control in the laboratory. In contrast to existing work, we consider a single, non-interacting molecule with angular momentum greater than $1/2$. Starting from an experimentally relevant effective Hamiltonian, we identify a parameter regime where different combinations of static electric and magnetic fields can be used to realize the single-axis twisting Hamiltonian of Kitagawa and Ueda [M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138 (1993)], the uniform field Hamiltonian proposed by Law et al. [C. K. Law, H. T Ng and P. T. Leung, Phys. Rev. A 63, 055601 (2001)], and a model of field propagation in a Kerr medium considered by Agarwal and Puri [G. S. Agarwal and R. R. Puri, Phys. Rev. A 39, 2969 (1989)]. To support our conclusions, we provide analytical expressions as well as numerical calculations, including optimization of field strengths and accounting for the effects of field misalignment. Our results have consequences for applications such as precision spectroscopy, techniques such as magnetometry, and stereochemical effects such as the orientation-to-alignment transition.
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