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cluded 1 s to 4 f electrons of Pb (68 core electrons). In addition the 5 s , 5 p and 5 d shells of Pb (treated explicitly with the used GRECP) were frozen. All the electrons of fluorine were treated explicitly. The resulting configura- tions were: 6 s $^{2}$6 p 2 for Pb and 1 s $^{2}$2 s $^{2}$2 p 5 for F. For Pb we used generalized correlation atomic basis set [15, 16] (15 s 16 p 12 d 9 f )/[5 s 7 p 4 d 2 f ] and GRECP from the paper [16]. For F we used the ANO-I (14 s 9 p 4 d 3 f )/[4 s 3 p 2 d 1 f ] atomic basis from the MOLCAS 4.1 library [17]. 

By means of the complete active space self-consistent field method the molecular orbitals were received. Molec- ular symmetry was treated by using the C 2 v point group classification scheme. The next step was to apply the spin-orbit direct configuration interaction (SODCI) ap- proach [18–20] (modified in [21] to account for spin-orbit interaction in configuration selection procedures). The main idea of this method is to use selected singly and doubly excited configurations with respect to some mul- ticonfigurational reference states within the second order perturbation theory. After that the SODCI approach is employed on the space of all the selected configurations. 

In the present work we calculated four lowest states, which belonged to the configurations [...] σ $^{2}$π$_{1}$$_{/}$$_{2}$ ( $^{2}$Π$_{1}$$_{/}$$_{2}$ ), [...] σ $^{2}$π$_{3}$$_{/}$$_{2}$ ( $^{2}$Π$_{3}$$_{/}$$_{2}$ ), [...] σ $^{2}$σ ′ (A $^{2}$Σ + 1 / $_{2}$) and [...] σ $^{2}$σ ′′ (B $^{2}$Σ + 1 / $_{2}$). Here σ is mainly formed from the 6 s basis function of Pb, π$_{1}$$_{/}$$_{2}$ and π$_{3}$$_{/}$$_{2}$ are mainly made from 6 p$_{x}$ and 6 p$_{y}$ functions of Pb. The orbitals σ ′ and σ ′′ are formed from the 6 p$_{z}$ and 7 s functions of Pb, respectively. 

One of the main goals of the present paper was to draw potential curves for the ground and three lowest excited states. Therefore, we made calculations for sev- eral internuclear distances (from 3.8 a.u. to 4.2 a.u.) near the ground state equilibrium distance ( R e = 2 . 0575 ˚ A ≈ 4 . 0 a . u . ). 

Equilibrium internuclear distances, vibrational con- stants, T e and dipole moments for four lowest states of PbF molecule can be found in Table I (the most pre- cise data, with 0.00005 treshold, are pointed out for the D ( R )). The PbF properties could be divided into two groups: valence and core ones. The parallel and per- pendicular G -factor components, the electronic dipole molecule moment D(R) or Ω–doubling constant could be related to the valence properties. However, such prop- erties as E eff , A$_{⊥}$ , A$_{‖}$ , anapole moment constant W$_{P}$ or T -odd interaction constant W$_{P,T}$ could be referred to the core ones. Mainly all these properties were calcu- lated for the ground and first excited states at the point 4.0 a.u., which is close to the equilibrium distance. In the core region one should make a four-component rela- tivistic calculation. However, we have performed calcula- tions on two-component orbitals by means of pseudopo- tential and, therefore, have to apply a restore procedure for four-component orbitals from two-component ones at the next stage. For this purpose the nonvariational one-centre restoration method developed in [14, 22–26] 

is employed. One can find the calculated parameters of the spin-rotational Hamiltonian, H$_{sr}$ , in Table III for the $^{2}$Π$_{1}$$_{/}$$_{2}$ and A $^{2}$Σ + 1 / 2 state, respectively (where (a) and (b) of [1] correspond to the minimal and maximal spin- orbital mixing). Finally, in Table II the matrix element values of Ω–doubling constant Δ divided by 2 / 2 MR 2 (Δ / 2B $^{′}$(R)) and electronic dipole moments are listed for five investigated points and for two electronic states of the molecule. 

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According to the data pointed out in Table I, T e values are in good agreement with the experimental data. The obtained equilibrium distance, R e , have slightly higher value than in the experiment, whereas the presently ob- tained vibrational constants are in much better agree- ment with the experiment comparing to those from [2]. Note that the dipole moment D ( R ) value for the ground state are nearly the same to those obtained in [2], whereas they are decreased approximately two times for the ex- cited state. All data in Table II obtained for D(R) and Ω-doubling constant have been calculated with the 0.0005 threshold. But we should note that we have computed these parameters for point 4.0 a.u. more accurately with 0.00005 threshold. For Ω-doubling these values are -0.361 and 1.46 for the $^{2}$Π$_{1}$$_{/}$$_{2}$ and A $^{2}$Σ + 1 / 2 states, respectively. 

Let us thoroughly examine the data obtained in Ta- ble III. First of all we would like to discuss the results for the ground state. The first point to note is that the A$_{‖}$ value is in the fault bounds, meantime the G$_{‖}$ value is increased in two times according to [2]. The effective field constant W$_{d}$ obtained is the best datum to-date, the anapole moment constant W$_{P}$ and T -odd interac- tion constant W$_{P,T}$ increased their values nearly by 50%. The most interesting result concerns the perpendicular hyperfine structure constant A$_{⊥}$ . The sign of the ob- tained value exactly agree with those in previous works [1, 2]. Since the constants of the H$_{sr}$ such as A$_{⊥}$ , G$_{⊥}$ , Ω-doubling are determined by the off-diagonal matrix el- ement, it is important to fix the phase factors for the wave functions to get the consistent signs of those ma- trix elements. In our calculations the phase factor is the 

