# Orbitals

The first example defines a basis. Note that this example does not produce output.

- Orbitals.Quanty
-- Although Quanty is a many body code, -- the basis set is defined by one particle -- orbitals with spin or sites. These are the -- "boxes" that either can contain an -- electron or not. -- These Fermionic modes (lets call them -- spin-orbitals) can either be the Wannier -- functions in a solid, molecular orbitals for a -- molecule or atomic wave-functions for an atom. -- We obtain these orbitals with the use of either -- DFT or Hartree Fock. -- A minimal definition of the basis set is given -- by the total number of Fermionic modes -- (site, spin, orbital, ...) and Bosonic modes -- (phonon modes, ...). -- Note that the current version needs NB=0. NF = 6; NB = 0; -- The elements of the basis are labeled by a -- number. In the case here (NF=6) there are -- six spin-orbitals with the imaginative name -- 0,1,2,3,4, and 5. -- In order to create Operators on this basis we -- can relate these spin-orbitals to shells -- in this case we could for example create a -- p-shell. The spin-orbitals then should be -- related to states with ml=-1, ml=0, or ml=1 and -- ms=-1/2 or ms=+1/2 -- This we can realize by grouping them. Several -- standard operators that only have a meaning -- for a given angular momentum shell will -- recognize this format. -- For a p-shell we could define IndexDn={0,2,4}; IndexUp={1,3,5}; -- the code knows that a 3 fold degenerate shell -- has l=1 and ml=-1, 0 and 1 are assigned to -- them automatically -- That's all for basis sets. We do not define the -- number of electrons at this point. Note that the -- code is written to deal with systems where one -- has 10^100 of possible determinants. The only -- reason one can do this is by never writing down -- those determinants.