# Atomic coulomb repulsion

Note: parts of the functionality of this function will be available in the release of October 2019

NewOperator(“AtomicU”,indices,RadialWavefunctions1,RadialWavefunctions2,options) calculates the full Coulomb interaction operator between all given atomic orbitals.

## Input

• indices : indices of atomic orbitals belonging to the radial wave-functions
• RadialWavefunctions1 : table of InterpolatingFunction objects
• RadialWavefunctions2 : optional - table of InterpolatingFunction objects - if given, the function calculates relativistic Slater integrals where RadialWavefunctions1 are the large parts and RadialWavefunctions2 the small ones
• options : possible Options are {“conserve”, bool} and {“1P-Operator”, bool}
• “conserve” : if true only occupation conserving Slater integrals are calculated
• “1P-Operator” : only if “conserve” is true and additional arguments are given, transforms interaction to 1-particle operator (see example)

## Example

The example below shows how to create the full Coulomb interaction between multiple atomic orbitals with relativistic wave-functions. It is recommended to use CreateAtomicIndicesList(orbitallabels,kappas_true) for index creation, since it automatically calculates the quantum numbers kappa and stores them in the field ind.kappas which needs to be set when calling NewOperator(“AtomicU”,…) with relativistic wave-functions.

### Input

Example.Quanty
orbitallabels = {"1s1/2","2s1/2","2p1/2","2p3/2"}
ind, NF = CreateAtomicIndicesList(orbitallabels,{{"Kappas",true}})

U = NewOperator("AtomicU",NF,ind,G,F) -- creates full Coulomb interaction

-- now occupation of the s-orbitals shall be conserved

function Take(list,n1,n2)
local result={}
if n2== nil then
if n1 > 0 then
for i = 1, n1 do
result[i]=list[i]
end
else
for i=1,-n1 do
result[i]=list[#list+n1+i]
end
end
else
for i = n1, n2 do
result[i+1-n1] = list[i]
end
end
return result
end

n0 = 3
n1 = 4

indConserved = Take(ind,1,n0-1)
indConserved.kappas = Take(ind.kappas,1,n0-1)
GConserved = Take(G,1,n0-1)
FConserved = Take(F,1,n0-1)

indNonCnsrvd = Take(ind,n0,n1)
indNonCnsrvd.kappas = Take(ind.kappas,n0,n1)
GNonCnsrvd = Take(G,n0,n1)
FNonCnsrvd = Take(F,n0,n1)

U0 = NewOperator("AU",NF,indConserved,GConserved,FConserved,{{"conserve",true}}) -- Coulomb interaction between conserved orbitals only

U1 = NewOperator("AU",NF,ind,G,F,indConserved.kappas,indNonCnsrvd.kappas,{{"conserve",true},{"1P-Operator",true}}) -- Coulomb interaction between conserved orbitals and others transformed to a one-particle operator given that the conserved orbitals are always completely filled.

U2 = NewOperator("AU",NF,indNonCnsrvd,GNonCnsrvd,FNonCnsrvd) -- Coulomb interaction between non-conserved orbitals

Uconserved = U0 + U1 + U2