To calculate the binding energy per Si atom substitutionally doped in a (5,5) armchair single-walled carbon nanotube (SWCNT), you can use the following formula:

E_binding = (E_SiCNT - E_CNT - n * E_Si) / n

where:

• E_binding is the binding energy per Si atom
• E_SiCNT is the total energy of the Si-doped carbon nanotube
• E_CNT is the total energy of the pristine (undoped) carbon nanotube
• n is the number of Si atoms doped (1, 2, 3, or 4 in your case)
• E_Si is the energy of an isolated Si atom in a similar reference state

To calculate these energies, you can use computational methods such as density functional theory (DFT) or molecular dynamics (MD) simulations, depending on your system size and the level of accuracy you need. Make sure you use the same computational method and level of theory for all the energy calculations to ensure consistency.

There is no computerize equation technic exist for nature.

Simply one dimension flat static equation or any number that do not recognize temperature & pressure simultaneously, cannot describe three dimension of atom that, it is changing constantly with Temp/pressure.

Atoms are not mechanic.

https://www.academia.edu/44088541/Hydrogens_Journey_in_the_Quantum_Universe

Thank you so much Javad.