definition of a closed cluster can be given as a cluster, where each atom is linked to the same number of neighbor atoms as in the corresponding crystal.

Building of a Hamiltonian matrix and solution of secular equations {#sec:Ham}
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The basic idea underlying the CC approach is the same as in the usual molecular orbital approach (MO) [@Heilbronner]. In particular, this is the representation of the wave function of the cluster $\Psi (\underline{r})$ as a linear combination of the wave functions of the atoms $$\label{eq:1}
\Psi (\textbf{r}) = \sum\limits_{n=1}^{N} c_n \varphi  (\bold{r} - {\bold a_n}).$$

Functions $\varphi$ in graphene are $\ket{p_z}$ - orbitals of carbon atoms, with axis z being perpendicular to the layer. We designate wave functions along and opposed this axis as “+” and “-”.

The standard procedure of obtaining secular equations leads to a system of linear equations which help to find the coefficients $c_n$ in $$\label{eq:2}
\sum\limits_{n=1}^{N} M_{mn} c_n =  0 , \qquad  m= 1,2,\ldots , N ,$$

where $$\label{eq:3}
M_{mn} = \varepsilon \delta_{mn} + (1-\delta_{mn}) \eta_{mn},$$

$\delta_{mn} = \begin{cases} 1, m=n \\   0, m \neq n, \end{cases}$

$\eta_{mn} = \begin{cases} 1, \textnormal{if atom m is bound with atom n}  \\  0, \textnormal{if atom m 