[Borek]

But in the chlorine molecule, each atoms should have an octet structure?

Yep, but some electrons are shared - and they are parts of BOTH octets at the same time.

Look at the H₂ molecule - each atom gives 1 electron, but both have 2

[deutdeut]

Then, since the number of electrons in the octet structure of the atom increases, like chlorine atom, from 7 to 8,  isn't it is charged?

[Borek]

Then, since the number of electrons in the octet structure of the atom increases, like chlorine atom, from 7 to 8,  isn't it is charged?

No, some electrons are shared.

Imagine two flats with one bedrrom each. You live in one flat, someone else lives in the second. Each of you has its own bedroom. Now you decide to make a door in the wall to combine both flats into one. What you have inow is a single flat with bedrooms - you share the flat, you have two shared bedrooms, the other person has the same two shared bedrooms as well. Does it mean you have two, other person has two, and you have together four bedrooms, or does it mean there are still two bedrooms only? Same happens to the electrons.

[Yggdrasil]

Think of it this way.  The two electrons in the covalent bond are in the space between the two chlorine atoms and are free to move from the possession of one chlorine to the other chlorine.  So, sometimes both electrons will be localized near one chlorine, and sometimes both electrons will be localized near the other chlorine.  However, on average, each chlorine will possess one electron of the two in the bond, so the average charge on each chlorine is zero.

[deutdeut]

I know that the chlorine molecule has a total 34 protons and electrons, and the net charge is zero. But if I just looks at only one chlorine atom in the molecule, then the charge on the chlorine atom should be 17protons - 18 electrons and the result will be 1-. The net charge of the molecule calculated in this way will be 2-, how can it be so weird?

[constant thinker]

I'm sorry but I also don't understand your logic.

There simply is no charge on either chlorine atoms in this case. In the molecule there is 34 protons and 34 electrons. 2 of those electrons are shared equally (the difference in electronegativity between them is 0) and in a localized region. Neither atom truly gains an electron, they only share. Cl^- isn't the same as Cl₂, nor is Cl^- a part of Cl₂. Borek has a good analogy.

[deutdeut]

But the chlorine "atom" in the molecule has 8 valence electrons, why does it still be called as an atom, as it has an extra electron from the other species?

[enahs]

But the chlorine "atom" in the molecule has 8 valence electrons, why does it still be called as an atom, as it has an extra electron from the other species?

It is not called a chlorine atom then. It is a molecule.
http://web1.caryacademy.org/chemistry/rushin/StudentProjects/ElementWebSites/chlorine/structure.htm

The Cl atom does not exist in nature by its self as Cl, it is one of the 8 diatomic elements.
http://en.wikipedia.org/wiki/Diatomic

When anybody says "chlorine" they are referring to Cl₂.

[Yggdrasil]

Maybe the best way to approach the problem is through molecular orbital theory.  When people talk about the octet rule, it's a convenient lie.  Its a convenient way to understand why molecules are stable.  But what really happens is that the atomic orbitals of each chlorine combine to give a set of molecular orbitals and for Cl₂ the molecular orbitals have a stable electron configuration.  For simplicity, lets take the molecular orbital structure of F₂ (see attached picture).  In F₂ (the middle column) you see 18 electrons split among 9 molecular orbitals.  Because of symmetry arguments and energetics/electronegativity arguments, the electron density from these molecular orbitals is split evenly between the fluorine nuclei.  So, on average, the electron density surrounding each fluorine nucleus is equivalent to 9 electrons, which balances out the charge of the 9 protons in each nucleus.

Charges and partial charges in covalent bonds come when the electron density is not evenly distributed.  For example, in C=O, the atomic orbitals of carbon are a higher energy than the atomic orbitals of oxygen.  Therefore, the electron density of the bonding orbitals of C=O resides nearer to the oxygen while the electron density of the antibonding orbitals resides nearer to the carbon.  Since more of the electrons are in bonding orbitals, the oxygen has a slight negative charge and the carbon has a slight positive charge.

[Borek]

I know that the chlorine molecule has a total 34 protons and electrons, and the net charge is zero. But if I just looks at only one chlorine atom in the molecule, then the charge on the chlorine atom should be 17protons - 18 electrons and the result will be 1-. The net charge of the molecule calculated in this way will be 2-, how can it be so weird?

You were already told that your assumptions are wrong, but instead of trying to understand it you repeat the same allegation again and again.