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

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.

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.

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

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.