= 2\gamma$. The presence of this gap in bilayer graphene is a fact discussed in many papers [@Castro][@Seyller]. In the model which we are using, the energy gap is caused by the interaction between the layers and disappears if we set $\gamma_1$=0.

Wave functions {#sec:Wave functions}
==============

Within our considered model the cluster wave functions are determined by the totality of coefficients $c_n$, according to . To obtain the latters one must solve the system of equations under defined energy values $\varepsilon$. For $\varepsilon = 3$ and $\varepsilon = -3$ the result is obvious and shown in Tab.\[table2\]. Let us now consider the cases $\varepsilon = \pm $1 and $\varepsilon$ = 0 in more detail. Latter is most interesting, since at this point the valence band meets the conduction band.

As an example, let us consider the cluster $N=12$, which is shown in Fig.\[Fig2b\], but with a different atoms numbering (Fig.\[Fig5\]).

![Cluster $N=12$ for calculation of graphene wave functions.[]{data-label="Fig5"}](./Fig5){width="6cm"}

To determine the coefficients $c_1, c_2, \ldots, c_{12}$ in we must solve a system of twelve linear equations. For cluster in Fig.\[Fig5\] it has the form

$$\begin{cases}

(1) \qquad \varepsilon c_1 + c_2 + c_6 + c_7 = 0 \\
(2) 