The parallel hyperfine structure components is in agreement with [4]. The other data for the first excited A $^{2}$Σ + 1 / 2 state, listed in the Table III, were obtained for the first time. 

Finally, we would like to note that we have performed the most accurate to date electronic structure calculation of the lowest states of PbF and, as a result, have obtained the most reliable data for the spin-rotational Hamilto- nian constants. In this paper we have proposed solution of the problem of the sign mismatching in the perpen- dicular hyperfine structure constant. The new computed data for the spectroscopic constants better conform to the experimental results at present. The calculated ef- fective electric field on the electron is increased in the present study nearly by 10% compared to that in [2]. 

K.B. and A.P. are grateful to the Ministry of Education and Science of Russian Federation (Program for Develop- ment of Scientific Potential of High School) for the Grant No. 2.1.1/1136. A. T. and A.P. were supported by the RFBR grant 09–03–01034 

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