We are studying the optical spectra of impurity centers in the case when the optical transition takes place between nondegenerate and two-fold degenerate electronic E-states characterized by a strong vibronic coupling. In the latter state the adiabatic surface has a shape of a deformed Mexican hat with three flat minima on the trough of the “hat.” We have found that in this case the usual T7-dependence of the homogeneous width of the zero-phonon line at low temperatures is replaced by a dependence close to the T3-one. Besides, the usual T4-dependent redshift of the line is replaced by the T2-dependent shift. Depending on the flatness of the adiabatic surface, the latter shift may be to the red or to the blue. The theory is applied to the zero-phonon line 637 nm of the nitrogen-containing N-V center in a diamond. In this system the temperature dependence of the ZPL results from the common action of the Jahn–Teller effect and the pseudo-Jahn–Teller effect in the excited E-state: the pseudo-Jahn–Teller effect “helps” to get the system close to the dynamical instability due to the enlargement of the Jahn–Teller distortion.

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Hybrid materials built from conjoined structures of graphene nanoribbons (GNRs) and carbon nanotubes (CNTs) have important properties for novel applications. In this communication we have performed a numerical study of these structures and have found two types: (i) CNT and GNR structures formed by van der Waals forces with a distance close to 0.35 nm and (ii) CNT and GNR structures interconnected by short (0.17 nm) and strong chemical bonds. It appears that the latter bonds essentially perturb conjoined carbon C6 rings. The reason for the perturbation is the pseudo-Jahn–Teller effect.

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Chemically bound states of benzene molecules with graphene are studied both analytically and numerically. The states are formed by switching off intrabonds of π-electrons in C6 rings to interbonds. A number of different undistorted and distorted structures are established both with aligned and with transversal mutual orientation of benzene and graphene. The vibronic interactions causing distortions of bound states are found, by using a combination of analytical and numerical considerations. This allows one to determine all electronic transitions of π-electrons without explicit numerical calculations of excited states, to find the conical intersections of potentials, and to show that the mechanism of distortions is the pseudo-Jahn-Teller effect. It is found that the aligned distorted benzene molecule placed between two graphene sheets makes a chemical bond with both of them, which may be used for fastening of graphene sheets together.

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