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Potential energy and spectroscopic constants for the X\(^2 \sum^+ _\mu\) ground state of a;, were calculated by configuration-interaction (Cl) methods, using large basis sets with polarization and diffuse functions. From these CI wavefunctions, the isotropic (a\(_{iso}\)) and dipolar (A\(_{dip}\)) components of the hyperfine coupling constant were obtained. The effects of various s, p basis sets, polarization and diffuse functions, as well as the influence of reference configurations and configuration selection thresholds were investigated. The best values obtained are 35·31 G for a\(_{iso}\) and 29·440 for A\(_{dip}\)• tobe compared with experimental values of 37 ± 1 G and 32 ± 1 G, respectively. It is shown that the contributions to a1so of the K and L shells are opposite in sign, differing by about 4 G. Upon vibrational averaging, both a\(_{iso}\) and A\(_{dip}\) move towards smaller values as v increases. An adiabatic electron affinity of 2·46eV was obtained for CL\(_2\) , and a vertical electron detachment energy of 3·71 eV for Cl;.