The orbital of a single atom have a simple closed formula.
H2 is harder, you must determine the distance, make some aproximations and solve the problem that is like the eigenvalues of a matrix, and there is no closed form
With more atoms/electrons the matrix gets exponentialy bigger. Without too many aproximations, probably water is the biggest one you can solve.
If you want something bigger like most molecules in biology, you must do more aproximations. If you want to go down the rabit hole, try googling DFT.
