The purpose of Psi2 is to visualize molecular orbitals in chemical bonding. We do so by using an approximation to the solution of the Schrodenger equation for an electron in the presence of the two (we assume fixed) nuclei. This approximation is to represent the MO (molecular orbital) as a weighted sum of the AO (atomic orbitals) of the two nuclei that the electrons are bonding together. We can explicitly calculate these wavefunctions, and thus the square of their magnitude, which is proportional to the probability of the electron occupying that location. We can solve for a level set of this function, (of three-dimensional position) for each (theta, tao) ordered pair, getting the radius (or noting a lack thereof) for the level set. These points are determined via nested for loops, allowing for triangle strips to render the surface.
This is a picture of a pi bond as computed by Psi2. 
This is a picture of a sigma bond as computed by Psi2 
Further discussion of the technical background behind the project can be found here.
The checklist of completed portions of the project can be found here.