Dear Andrii, you should calculate the energy of a system containing N carbon atoms with one vacancy (W) and the energy of a system containing N carbon atoms without vacancy (Wi). The energy of a vacancy formation is W - Wi. During vacancy formation one carbon atom does not leave a nanotube, but goes to the butt end of it. YK

Hi Andrii,

To calculate exactly the energy difference between two states in DFT calculations you need to ensure that two states have same number of matter ( more exactly same number of electrons.) In the case described by Yuri this is guaranteed, because you only move one carbon atom far from the vacancy place to end of the nanotube. However in this case you need to wory about interaction of the carbon atom and vacancy, which is probably very small in the case of carbon nanotube.

In the case you decide to calculate the energy of isolated carbon, use the same setup file as in the case of the supercell containing N and system containing N-1 carbon atoms. This will guarantee that you have same cutoff energy, k-point mesh etc.. so your energies can be compared properly.

Thank you all for the valuable advise and for the reference. I think, I found the sourse of such the unexpected results. I modeled the system with a formed vacancy as such, where all of the dangling bonds on carbon atoms are saturated with hydrogen atoms. At the same time in reallity two of them might create a bond between themselves (forming a pentagon) and only one bond remains free.

If this is so, I wonder why nature chooses formation of a covalent bond between carbon atoms over saturating them with hydrogen from the outside if this is more advantageous from the energetic point of view?

Well, a carbon nanotube has different chemical bonding structure than that seen in most organic molecules. Also, did you determine the energy as that from a complete reaction (e.g. including breaking of H-H bonds to form the C-H bonds)?

Dear all,

In fact there is no reaction as so considered, but energy of different systems were calculated separately, namely:

1.Energy of SWCNT_ideal

2.Energy of carbon atom

3. Energy of hydrogen atom

4. Energy of SWCNT_with_vacancy_with_hydrogen_atoms_attached_where_free_bondings_remained

delta Energy then was calculated as (1-2) - (4-3)

All the systems were treated within the same level of approximation, with regards to exchange-correlation potential and basis functions

Victor, how did you make a suggestion (or did you calculate that) that Delta_Potential_Energy and Delta_Free_energy have positive values as written by you above?

Well, this thread is getting very difficult to follow because the fabric seems to changing over time (initial conditions of the nanotube, methods, etc.) Andrii, you can begin to answer your question, "why nature chooses formation of a covalent bond between carbon atoms over saturating them with hydrogen..." by considering benzene and what chemists call aromaticity. Organic chemists have a saying, "from structure comes function". To begin to account for the emergent properties of aromatics compared to polyenes (e.g. substitution products rather than addition products, also your reversal of sign in reaction energies) physical chemists devised isodesmic reaction energies (which account for structure) rather than relying on the chemical physicists' approach of reaction energies of fragments.

The formation of a vacancy is always endothermic process because vacancy formation means the removal of particles from a particular area. Therefore it is always endothermic process. Your result is not understandable. Because as we know that energy is always required to separate particles from each other. When the created vacancy is filled by foreign particles either through chemical forces or physical forces, energy will be produced.

I can agree with the last reply in a part when you say "Energy is needed to brake the bindings" and when you say "Energy is produced, when vacancy is filled". Can you think of a situtation when the difference of former and later is negative, in other words we gain some energy after all?

I agree with Dipayan