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Using the group theory and the method of invariants, it is shown how thevibronic potential can be written in a matrix form and the correspondingadiabatic potentials can be found. The molecule having $D_{3d}$ symmetry isconsidered herein as an example. The symmetries of normal vibrations active inJahn-Teller's effect were defined. $E-E$ vibronic interaction was considered toobtain vibronic potential energy in a matrix form and thus the adiabaticpotential. Significant differences are shown in the construction of a secularmatrix $D(\vec{k})$ for defining a dispersion law for charge carriers in thecrystals and the matrix of vibronic potential energy, which depends on thenormal coordinates of normal vibrations active in Jahn-Teller's effect.Dispersion law of charge carriers in the vicinity of $\Gamma$ point ofBrillouin zone of the crystal with $D_{3d}^2$ symmetry was considered as anexample.

condensed matter physics

Similarities and differences in the construction of dispersion laws for  charge carriers in semiconductor crystals and adiabatic potentials in  molecules