Linear combinations of 1s atomic orbitals about nucleus "a" and nucleus "b" to approximate a molecular orbital about both nuclei.
What is shown below is a simulation of two hydrogen-like 1s atomic orbitals in one dimension. This is essentially an exact animation in one dimension of what appears in FIGURE 14.25. (Ignore the labels on the x- and y- axes.) One atomic orbital (call it 1sa) is located at "50" on the x-axis and the other (call it 1sb) starts at "58". The form of the 1s wave function (see text Table 12.1) is e-x where x is the displacement from each nucleus' location and where the atomic wave functions each peak. The total square of the wave function for an electron about both nuclei is calculated as (1sa + 1sb)2. This corresponds the the electron's density distribution in the approximate molecular orbital since it is the square of the wave function. Note the accumulation of density in the region between the nuclei as "b" is moved closer to "a" and constructive interference occurs, keeping the area under the density distribution constant (so that it always corresponds to 1.00 electrons). An electron occupying this molecular orbital at the final frame would be in a binding situation.
Now we do the same but take the other linear combination, (1sa - 1sb)2, corresponding to destructive interference as "b" is moved closer to "a", again keeping the area under the resulting density distribution unchanged. An electron in this molecular orbital would be in an antibonding situation. Note that density is removed between the nuclei because of destructive interference and accumulates on the outside regions of the one-dimensional system.