We demonstrate the first application of the four-component relativistic extended-coupled-cluster (ECC) method, a variational approach, to determine the P , T -odd molecular electronic structure parameters necessary for high-precision spectroscopic measurements on ultracold molecules. We calculate the P , T -odd sensitivity parameters for two moderately heavy, laser-coolable diatomic molecules (SrH and SrF), as well as two relatively lighter open-shell molecules (CaH and CaF) in their ground electronic state, 2 Sigma 1/2. The hyperfine structure constants of 87Sr in the SrF and SrH molecules are also computed and compared with available experimental results to assess the accuracy of our calculations. Furthermore, we examine the roles of electron correlation, relativity, basis set, and virtual spinors in ECC calculations of the sensitivity parameters. Our study reveals that the ECC method is a reliable technique for studying P , T -odd properties of diatomic molecules such as CaH, CaF, SrH and SrF, yielding results in very good agreement with those obtained using two widely employed analytic approaches: the Z-vector technique and the linear expectation-value method within the relativistic single-reference coupled-cluster singles and doubles framework.

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