Orbitals are just solutions to the relevant wavefunction equation. They look like that because they are 3D repeating functions (analogous to 1D periodic functions like sin(x)) called "spherical harmonics". More nodes arise from higher energy orbitals, just like more nodes on a vibrating string means its vibrational frequency is higher, thus it has more energy. The wavefunction of an atom is then the linear combination of all the atomic orbitals.
>>11879957nothing degenerate about DFT... it's fundamentally the same as wavefunction theory, just a different representation. The problem is no one knows the exact functional that relates the electron density to the electron energy, so we have to use approximate functionals. There is no systematic way to improve these approximations, so you can't just use more complicated functionals and guarantee more accurate results.
Ab initio techniques like MP and CC and CI use no approximations but are very expensive. Increasing "complexity" (e.g., including singles and doubles in CCSD, and then including perturbative triples in CCSD(T)) will guarantee more accurate solutions to the wavefunciton.
Canonical formulations of CCSD(T) are too expensive to run on computer hardware, as it scales by N^7. There are linear-scaling semi-canonical approximations (DLPNO-CCSD(T)) to it that use the fact that correlation is a short-range phenomenon, and then use a local orbital approach to improve the results with about 99% the accuracy of normal CCSD(T). These kinds of calculations have been performed on proteins with regular computer hardware.
If someone were to figure out the exact functional one day, then all WFT treatments would be pointless as DFT is far more efficient, easier to implement, requires almost no knowledge about the electronics of the system, and trivially gives you the electron density of the system (which can be used later for chemical interpretation).
