Question

During elementary school chemistry, when they teach about the covalent bond, they say that both atoms need the electron but they can't lose or gain them so they share it.

And for instance they show us the Lewis dot structure to clarify how do they share an electron.
If we move further into the question about how electrons actually get shared among two atoms, then we learn about orbitals, overlapping, sigma bond, pi bond etc.
But the actual question remains unsatisfied...
They say that the orbitals of two atoms overlap each other and that the electron will move there, but how?
How can the same electron that is shared in a covalent bond orbit nucleons of both atoms simultaneously? How is it actually shared between atoms? And what will be the path of its trajectory around two atoms?
A good analogue to the puzzle of how an electron in a molecule (say in the H_2^+cation) can be shared between two nuclei is a circumbinary planet. This gravitational equivalent involves a planet orbiting a binary star system. The planet moves along a trajectory about the center of mass of the two stars. Kinetic energy keeps the various bodies from crashing into each other, while centripetal force due to the mutual gravitational attraction keeps them in orbit. It should be possible to construct an even closer analogue involving electrostatic charges, a set of charged spheres, say, where two are positively charged and the third negatively.
While a classical analogue misses important details regarding the delocalized distribution of an electron in a molecule, something that requires quantum mechanics, it explains how it is possible for one particle to move in the basin of two attractors. One important difference with the gravitational example is that in that case all of the bodies attract, whereas in the molecule the electron functions as a sort of glue that keeps the nuclei, which otherwise repel, from flying away from each other.

Answer 1

In a covalent bond, electrons are shared between atoms through overlapping atomic orbitals, forming a molecular orbital encompassing both nuclei. These electrons are described by a probability cloud rather than a fixed path, and their distribution may be uneven if there's a difference in electronegativity between the atoms.

Step-by-step explanation:

To understand how electrons are shared in a covalent bond and can orbit the nuclei of both atoms simultaneously, we must delve into quantum mechanics and valence bond theory.

In a covalent bond, the atomic orbitals of the bonding atoms overlap, allowing unpaired electrons to be shared and occupy a new orbital space that encompasses both nuclei.

This shared pair of electrons enables the bond, and though the electron does not have a fixed path like a planet around the sun, quantum mechanics allows for a probability distribution where the electron is likely to be found between the atoms.

For example, in the hydrogen molecule (H2), the two 1s atomic orbitals from each hydrogen atom overlap to allow two electrons to pair up and exist in the space between the two nuclei.

The shared electrons are attracted to both nuclei, stabilizing the molecule. The electrons do not have a defined trajectory as classical physics would suggest; instead, their positions are described by a probability cloud within the molecular orbital.

It is also important to consider that electrons are not always shared equally due to differences in electronegativity. The electron distribution will be skewed towards the atom with higher electronegativity, hence defining the polarity of the bond.