## 4 Results and Discussions
Figure 2: Radial parts of partial harmonics of SC series of H atom 1s wave function found via a solution of Hatree-Fock equations in the molecular axis of reference: (**a**) SC expansion into series (1) with \(l\leq 60\); and (**b**) SC expansion into series (1) with \(l\geq 8\). agreement with the form of radial parts of the partial harmonics of SC expansion of the wave function of H atom 1s state (see Figure 2b). It can be concluded that the influence of the ligand field with the charge \(Z_{L}=1\) on radial parts of the partial harmonics of SC expansion of \(2\sigma-\)MO with orbital moments \(l\geq 8\) is decisive. Thus, in accordance with the procedure proposed above (see Section 2.2) the crosslinking of MO (1) with ligand functions \(\psi_{\mu l_{0}}^{n\gamma_{L}}(r)\) is done starting from \(l_{0}=8\). A significant influence of the higher harmonics of the SC expansion on the energy characteristics of the molecular system is observed with the growth of the ligand \(Z_{L}\) charge. To estimate this effect, the calculation of the total energy of the electron configuration \(1\sigma^{2}2\sigma^{2}3\sigma^{2}1\pi^{4}\) is performed depending on the charge \(Z_{L}\) which varied within the range of \(Z_{L}=2\div 5\) (instead of case \(Z_{L}=1\)). The results obtained for the total energies are given in Table 2.  
The values of the total energies on the basis of MO with SC expansion limited to \(l\leq 4\) are given in column (a) of Table 2. The calculation results accounting the ligand functions with expansion up to \(l=60\) are given in the column (b) of Table 2.  
It is obvious that higher harmonics of the SC expansion of MO begin to significantly affect the energy characteristics of the molecular system. The calculation results of the MO electron state \(1\sigma^{2}2\sigma^{2}3\sigma^{2}1\pi^{4}\) show that this iterative scheme solves the main problem of the SC methods. That is the description of MO behavior in the area of ligand nuclei. It is also evident that with increasing the ligand charge, the contribution of the higher harmonics of MO, taken into account by this SC approach, increases substantially. Thus, the represented iterative scheme of the SC calculation of MO becomes effective when studying molecules with nonhydrogen ligands. The results of the research show that taking into account the higher harmonics of the expansion of the wave functions of the ligands electron shells is a necessary condition in performing calculations in the SC representation for obtaining accurate energy characteristics of molecular systems. The possibilities of obtaining the excited states represented by the iterative scheme are considered on the example of ionization of \(\sigma\) symmetry shells of HF molecule ground state. Table 3 displays the results of accounting the ligand functions with MO expansion up to \(l=60\). Energy characteristics of the electron configurations: \(1\sigma\equiv 1\sigma^{1}2\sigma^{2}3\sigma^{2}1\pi^{4}\); \(2\sigma\equiv 1\sigma^{2}2\sigma^{1}3\sigma^{2}1\pi^{4}\); \(3\sigma\equiv 1\sigma^{2}2\sigma^{2}3\sigma^{1}1\pi^{4}\) are given as the results. Obtaining the ionized states in the \(\ll\)Z + 1\(\Rightarrow\) approximation of MC approach requires a special charge increase of the chosen core of the molecular system, which corresponds to the creation of a vacancy. Such an artificial technique is used in connection with the absence of the possibility of directional ionization of the electron shell. Unified approach to the calculation of any states is in the proposed iterative scheme. It ensures the possibility of ionization of any electronic shell. \begin{table}
\begin{tabular}{l l l} \hline \(Z_{L}\) & Total Energy (a) & Total Energy (b) \\ \hline
2 & \(-101.0902\) & \(-101.0951\) \\
3 & \(-102.8639\) & \(-102.9189\) \\
4 & \(-105.1593\) & \(-105.4553\) \\
5 & \(-107.7773\) & \(-108.5403\) \\ \hline \end{tabular}
\end{table} 
Table 2: Total energy of the electron state is \(1\sigma^{2}2\sigma^{2}3\sigma^{2}1\pi^{4}\) (in atomic units).