Features of the $E_{2g}$ phonon mode in $MgB_{2}$

A model estimate of the energy eigenvalues of the $E_{2g}$ phonon mode of the ion vibrations in the plane of boron atoms is obtained. It is shown that the anharmonic contribution to the energy of $E_{2g}$ monotonously increases with the increase in $z=A_4/A_2^2$, where $A_4$ is the fourth-order anharmonic coefficient and $A_2$ is the harmonic constant. The results agree with the estimate in the Hartree-Fock approach. However, the discrepancy between these results and Raman spectroscopy data indicates the necessity to account for the influence of the electron-phonon interaction on the energy of $E_{2g}$ in more detail.