## 2 Materials and Methods  
### Basic Equation of Iteration Scheme  
Integro-differential equations underlie the iterative scheme of obtaining radial parts of MO. They are the generalization of Hatree-Fock equation first recorded for an atom [27]. The equations were obtained on the basis of minimizing the energy functional in the Born-Oppenheimer approximation [28] for the wave function on N-electron molecular system \(\Psi=(N! )^{-1/2}det\|\phi_{n\gamma}\|\), represented as antisymmetrized product of one-electron MO \(\phi_{n\gamma}\). After the variation procedure we obtain a set of coupled integro-differential Hartree-Fock equations systems each of which corresponds to a certain MO \(n\gamma\) of molecule electron configuration. In this case, the single-electron MO \(\phi_{n\gamma}\), in the nonrelativistic SC representation, has the form [6]:  
\[\Phi_{n\gamma\mu}(r,\vartheta,\varphi)=\frac{1}{r}\sum_{l}P_{l}^{n\gamma}(r)Y _{l}^{\mu}(\vartheta,\varphi), \tag{1}\]  
where \(P_{l}^{n\gamma}(r)\) is the radial and \(Y_{l}^{\mu}(\vartheta,\varphi)\) is the angular part of \(l\), the symmetry partial harmonic of MO with the fixed (for a linear molecule) value of the \(\mu\), the projections of angular momentum to the quantization axis \(OZ\) (molecule axis); \(n\) is the main quantum number; \(\gamma\) is the symmetry of MO; and \(r,\ \vartheta,\ \varphi\) are the spherical coordinates. Considering Equation (1) the system of coupled integro-differential equations for MO \(n\gamma\) has the form:  
\[\frac{d^{2}P_{l}^{n\gamma}(r)}{dr^{2}}=\sum_{l^{\prime}}\Omega_{l,l^{\prime}} ^{n\gamma}(r)P_{l^{\prime}}^{n\gamma}(r)+2X_{l}^{n\gamma}(r), \tag{2}\]  
where \(\Omega_{l,l^{\prime}}^{n\gamma}(r)\) is the local potential, describing the electron interaction of MO \(n\gamma\) with the nuclei of the molecular system and the direct Coulomb interaction with the electrons of other MO; \(X_{l}^{n\gamma}(r)\) is the nonlocal potential, describing the exchange Coulomb interaction of MO electrons \(n\gamma\) with electrons of other MO. Local potential \(\Omega_{l,l^{\prime}}^{n\gamma}(r)\) has the following form:  
\[\Omega_{l,l^{\prime}}^{n\gamma}(r)=\left[\frac{l(l+1)}{r^{2}}-\frac{2Z_{0}}{r}- \varepsilon_{n\gamma}\right]\delta_{l,l^{\prime}}+2W_{l,l^{\prime}}^{n\gamma}( r)+2V_{l,l^{\prime}}^{n\gamma}(r), \tag{3}\]  
where \(Z_{0}\) is the charge of molecular nucleus, located at the chosen origin of coordinates, \(W_{l,l^{\prime}}^{n\gamma}(r)\) is the potential of crystal field, describing the electron interaction of MO \(n\gamma\) with the nuclei of molecular system; \(V_{l,l^{\prime}}^{n\gamma}(r)\) is the potential of the direct Coulomb interaction of MO \(n\gamma\) electrons with the electrons of other MO; and \(\varepsilon_{n\gamma}\) is the single-electron energy \(n\gamma\) of MO. The expression for the potential of crystal field in Equation (3) has the form:  
\[W_{l,l^{\prime}}^{n\gamma}(r)=\sum_{\mu}\lambda_{\mu}^{n\gamma}\alpha_{l,l^{ \prime}}^{n\gamma\mu}(r), \tag{4}\]  
\[\omega_{l,l^{\prime}}^{n\gamma\mu}(r)=-\sum_{\alpha=1}^{N_{L}}Z_{\alpha}\sum _{k=|l-l^{\prime}|}^{l+l^{\prime},\alpha k=2}C_{l_{l}\;l^{\prime}\mu}^{k}C_{0 }^{k*}(\theta_{\alpha},\varphi_{\alpha})\left(\frac{r_{\alpha<}^{k}}{r_{ \alpha>}^{k+1}}\right), \tag{5}\]  
where \(\lambda_{\mu}^{n\gamma}\) is the number of \(n\gamma\) electrons of MO with \(\mu\), the projections of angular momentum to the quantization axis \(OZ\) (molecule axis); \(N_{L}\) is the number of ligands in the molecule; \(Z_{\alpha}\) is the charge of the \(\alpha\)-th ligand; \(C_{l}^{l}=\sqrt{4\pi/2l+1}Y_{lm}(\theta,\varphi)\) is the spherical harmonic; \(r_{\alpha>}=\max(r,R_{\alpha})\)\(w_{\alpha<}=\min(r,R_{\alpha}),\ R_{\alpha},\ \theta_{\alpha}\) are the coordinates of the \(\alpha\)-th ligand; and \(C_{l_{l}\;l^{\prime}\mu}^{k}\) is the matrix element of the spherical harmonic, the calculation methods of which are presented in [28].