## 2 Materials and Methods
### The Inclusion of Higher Spherical Harmonics in SC Expansion of MO  
To accurately describe the electron density in the vicinity of the molecular system nuclei and solve the problem of slow convergence of the functional series (1), MO \(n\gamma\) for calculating the system of coupled differential equations has the following form:  
\[\Phi_{n\gamma\mu}(r,\vartheta,\varphi)=\mathrm{A}_{n\gamma\mu}\left[\frac{1}{r} \sum_{l=l_{mn}}^{l_{0}}P_{l}^{n\gamma}(r)\Upsilon_{l}^{\mu}(\vartheta,\varphi) +\sum_{n^{\prime}\gamma L}\Lambda_{\mu}^{n^{\prime}\gamma L}\psi_{\mu l_{0}}^{ n^{\prime}\gamma L}(r)\right], \tag{11}\]  
where \(\mathrm{A}_{n\gamma\mu}\) is the normalization factor; \(\Lambda_{\mu\alpha}^{n\gamma L}\) is the contribution coefficients of the wave function \(\psi_{\mu l_{0}}^{n^{\prime}\gamma L}(r)\) with the main quantum number \(n\) and symmetry \(\gamma\) of the \(L\)-th ligand of the molecular system in the form:  
\[\Psi_{\mu l_{0}}^{n\gamma L}(r)=\frac{1}{r}\sum_{l>l_{0}}P_{l}^{n\gamma L}(r)Y _{l}^{\mu}(\vartheta,\ \varphi) \tag{12}\]  
The functions \(\psi_{\mu l_{0}}^{n\gamma L}(r)\) are the wave functions of the electron shells of atoms entering the molecular system as ligands (atoms are not at the origin) expanded in a series of spherical harmonics. In this case, the partial harmonics of MO in Equation (11) with the values of the orbital angular momentum \(l>l_{0}\) are obtained by solving the system of Equation (2). The terms of the expansion Equation (11) with orbital angular momenta \(l>l_{0}\) are obtained on the basis of the linear combination \(\psi_{\mu l_{0}}^{n^{\prime}\gamma L}(r)\) with the contribution coefficients \(\Lambda_{\mu\alpha}^{n\gamma L}\). Such a representation of MO is due to the fact that the shape of the partial spherical harmonics with large values of the orbital angular momentum is determined to within a coefficient by the ligand potential of the molecular system. The choice of the value of \(l_{0}\) in Equation (11) is a result of a numerical experiment and depends on the nature of the molecular system and the number of partial harmonics involved in the formation of the chemical bond of the compound. To determine the contribution coefficients \(\Lambda_{\mu\alpha}^{n\gamma L}\) in Equation (11) the partial harmonics are linked in using the equation:  
\[P_{l_{0}}^{n\gamma}(r)=\sum_{n^{\prime}\gamma L}\Lambda_{\mu\alpha}^{n^{\prime }\gamma L}p_{l_{0}}^{n^{\prime}\gamma L}(r). \tag{13}\]  
That is, radial part of the \(l_{0}\)-th partial harmonic of the \(n\gamma\) molecular orbital is represented as a superposition of radial partial harmonics of ligand functions with weighting coefficients \(\Lambda_{\mu\alpha}^{n\gamma L}\). Equation (13) allows compiling a system of algebraic equations for determining the contribution coefficients \(\Lambda_{\mu\alpha}^{n\gamma L}\) of ligand functions with \(\gamma\) symmetry in the form of:  
\[\sum_{n^{\prime}\gamma L}\langle P_{l_{0}}^{j\gamma L}\Big{|}p_{l_{0}}^{n^{ \prime}\gamma L}\rangle\Lambda_{\mu\alpha}^{n^{\prime}\gamma L}=\langle P_{l_{ 0}}^{j\gamma L}\Big{|}p_{l_{0}}^{n\gamma}\rangle, \tag{14}\]  
Thus, the determined MO is normalized to unity. The Expansion of the Wave Functions of the Electron Shells of an Atom in a Series of Spherical Harmonics  
The procedure of obtaining the ligand functions \(\psi_{\mu l_{0}}^{n\gamma L}(r)\) used in Section 2.2 is based on the recalculation of the wave functions of the electron shells of atoms \(P_{nl}^{A}(r)\), entering the molecular system in a new unified system of coordinates.