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documentation:tutorials:introduction_to_quanty:orbitals [2016/10/07 20:13] – created Maurits W. Haverkortdocumentation:tutorials:introduction_to_quanty:orbitals [2016/10/10 09:41] (current) – external edit 127.0.0.1
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 +{{indexmenu_n>1}}
 +====== Orbitals ======
  
 +###
 +The first example defines a basis. Note that this example does not produce output.
 +###
 +
 +###
 +<code Quanty 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.
 +</code>
 +###
 +
 +===== Table of contents =====
 +{{indexmenu>.#1|msort}}

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