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What make atoms to form co-valent bond?

If atoms are truely neutral(electrically) there should be no electrostic attraction between them, because there is no electric field out side the atom(All electric fields starting from the positive nucleus of the atom ends in the equal negative charge of electrons, which are inside the atom). Then what make them to form co-valent bond? To be precise, I want to know what kinds of physics lie behind this process.

Thanx in advance.
 
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If atoms are truely neutral(electrically) there should be no electrostic attraction between them, because there is no electric field out side the atom(All electric fields starting from the positive nucleus of the atom ends in the equal negative charge of electrons, which are inside the atom). Then what make them to form co-valent bond? To be precise, I want to know what kinds of physics lie behind this process.

Thanx in advance.
Covalent chemical bonds are formed when two atoms start sharing a pair of valence electrons, governed by an ordinary Coulombic potential. In the case of ionic bonds, electrons are TRANSFERRED from one atom to another. Such bonds lead to stable molecules if they share electrons in such a way as to create a noble gas configuration for each atom.

For example : Hydrogen gas (the H atom) forms the simplest covalent bond in the diatomic hydrogen molecule.

marlon

edit : here is the full QM picture which proofs that superposition (ie the bonding and anti bonding state) actually occurs in nature
 
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