 Orbital overlap

The orbital overlap of normalized real atomic orbitals is their inner product $S=\int {\varphi }_A{\varphi }_B$. It is a dimensionless measure of their common amplitude, not an Electron count. For the Gaussian function toy, increasing $a$ from $1$ to $2$ reduces $S$ from $e^{-1}\approx 0.367879$ to $e^{-4}\approx 0.018316$. As $S$ tends to zero, both LCAO normalization denominators tend to $\sqrt{2}$.

Orbital overlap refers to the phenomenon that occurs when atomic orbitals from two adjacent atoms come close enough to each other that their electron clouds can interact. This overlap is crucial for the formation of chemical bonds, such as covalent bonds, in which electrons are shared between atoms. In covalent bonding, the greater the overlap of the atomic orbitals, the stronger the bond that is formed.