is not bound with atom n,} \end{cases}  $

$$\varepsilon = \frac{E-E_0} {\gamma_0}$$

with

$E$ - energy of an electron

$E_0$ - energy of an electron in the $\ket{2p_z}$ state in an isolated carbon atom. We use $E_0=0$

and

$-\gamma_0$ - the transfer integral between neighbor atoms with wave functions with the same sign, $\gamma_0 > 0$.

The problem of calculating the corresponding values of energy $\varepsilon$ (in $\gamma_0$ units) is then reduced to solving the secular equation $$\label{eq:4}
\det {M_{mn} = 0}.$$

Now we consider some examples of applications of the approach. We begin with the simplest closed cluster $N=6$, which is shown in Fig.\[Fig1b\]. The secular equation (4) has the form (empty matrix cells standing here and further for zeroes):\
$$\label{eq:5}
 D_{6} =    \left|   
 \begin{array}  {rrrrrr} 
\varepsilon & 1 & & 1 & & 1  \\
1 & \varepsilon & 1 & & 1 &  \\
& 1 & \varepsilon & 1 & & 1 \\
1 & & 1 & \varepsilon & 1 &  \\
& 1 & & 1 & \varepsilon & 1 \\
1 & & 1 & & 1 & \varepsilon  \\
\end{array}
\right| = 0.$$

Calculating the determinant leads to the following equation for 