If antibonding orbitals are formed from destructive interference then why the probability is not zero everywhere

#1

if antibonding orbitals are formed from destructive interference then why the probability is not zero everywhere

#2

That would have been possible if the atomic orbitals were lying on the same point. However, that's not the case, the orbitals are separated by some distance, so there will be many points where the probability will be decreased, and not zero.

#3

the bonding case, the two 1s orbitals interfere constructively, leading to an increase in density in the region between the two atoms. On the other hand, the antibonding case has destructive interference. The two orbitals however exactly cancel themselves along only one plane-the one equidistant from both atoms, where the atomic orbital (AO) amplitudes are equal from symmetry and so perfectly cancel. At all other points, one of the AO amplitudes is larger in magnitude than the other one, leading to a residual amplitude being left behind even after subtraction from destructive interference, which allows an electron to persist there. Consequently anti-bonding orbitals lower electron density between the two nuclei, leading to an increase in kinetic energy (which is a quantum mechanical effect-just keep in mind that kinetic energy density is proportional to the square of the slope of the orbital and so the more steep transition in the anti-bonding orbital (ABO) as can be seen in the center figure on bottom row) causing it to have higher energy.

In summary, there are certainly regions of space where complete destructive interference leads to zero probability-those are called nodes and are present in all molecular orbitals besides the absolute lowest energy one. However the destructive interference is not complete at most points in space due to one orbital having a larger amplitude than the other, leading to regions with reduced densities in some places (and conversely regions with higher density in other places since the whole density must integrate to one) . ABOs typically reduce density between the bonding atoms, pushing density to the fringes-leading to an increase in kinetic energy, and causing them to be higher up in energy than the corresponding bonding orbitals.

#4

That is so because during anti bonding molecular orbital , the orbitals may lie in different planes due to which some electron density remains as a result the probability is not zero