Question

What is a sigma bond? How does the overlap of two 1/2 filled 1s orbitals produce a sigma bond?

Answer 1

A `sigma` bond could be achieved through the effective head-on overlap of two `s` atomic orbitals. Other `sigma` bonds can also be made when an `ns` and `np_z` of the same `n` orbital overlap, where the overlap is also head-on.

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EFFECTIVE ORBITAL OVERLAP BALANCES ATTRACTIVE-REPULSIVE INTERACTIONS

`"H"_2` is a common example for `1s` orbital overlap.

While making a chemical bond, there is a balance between the nuclear(A,B) repulsion energy and the nucleus(A/B)-electrons(B/A) attraction.

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When that is just right, i.e. the potential energy is minimized, the orbitals have overlapped effectively.

ORBITAL OVERLAP CAN BE IN-PHASE OR OUT-OF-PHASE

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When two `1s` orbitals overlap constructively (i.e. in-phase), they increase the electron density in between the two atomic orbitals and generate a `sigma` bonding molecular orbital**.

The electron density is the probability distribution for finding electrons in a certain region of space. The higher the density in a spot, the easier it is to find the electron in that spot.

In addition, when one of the `1s` atomic orbitals is out-of-phase with the other, they overlap destructively, creating a nodal plane in between the two atomic orbitals and generating a `sigma^"*"` antibonding molecular orbital**. No electrons are expected to exist precisely on the nodal plane.