How hydrogen molecule is formed? [closed]

How two hydrogen atoms come close to form a bond ? Textbooks refer to a potential energy diagram but what i cant understand is what is this potential energy if the atoms are neutral . How they come close and how when they come close they stay in an specific distance (bond length) ? From classical physics in order to not accelarate NET FORCE must be equal 0 ? is the same with hydrogen bonding and bonding in general ? also if potential energy decreases then kinetic must increase, but where does that kinetic energy goes when a molecules is formed ?

• Hydrogen bonds are not formed when two hydrogens attract: they are formed when certain hydrogens attract atoms in other molecules such as oxygen. Water being the archetypal example. – matt_black Dec 28 '18 at 15:38
• Well the atoms are not exactly neutral. There is a charge seperation between the proton and the electron in a H atom. So both repulsive and attractive forces exist. At a certain point, there is an equilibrium – Harshit Joshi Dec 28 '18 at 20:16

From a one-electron quantum mechanical view ($$\ce{H_2^+}$$), the system is described by Schrodinger's equation $$\hat{H}\psi = E\psi$$, where $$\psi$$ is the wavefunction for the electron, $$E$$ is the energy of the electron, and $$\hat{H}$$ is an operator that relates the two. The Hamiltonian operator has two parts: $$\hat{H}\psi = \hat{T}\psi + \hat{V}\psi = E\psi$$. These two parts are attributed to kinetic energy $$\hat{T} \propto \frac{d^2}{dx^2} + \frac{d^2}{dy^2} + \frac{d^2}{dz^2}$$, and potential energy $$\hat{V}$$ described by Coulomb potential. In order to be well behaved, the curvature increases as the electron wavefunction is closer to the nucleus, and since the kinetic energy is proportional to curvature, the kinetic energy is higher. The Coulomb potential is smaller when closer to the nucleus. So the equilibrium wave-function is a balance between these two potentials.
This treatment is more complicated when you add a second electron since the potential energy also includes the repulsion between the two electrons. But the concept is the same and the resulting hydrogen molecule is the configuration of nuclei and electrons that minimizes total energy based on the opposing influences of $$\hat{T}$$ and $$\hat{V}$$.