[molpro-user] definition of quad

[Taube, Andrew]

Hi,
I have a question about the definition of the external field operator QUAD. What exactly is the operator that is being added to the Hamiltonian? Given an input
quad, fxx, fyy, fzz, fxy, fxz, fyz
is the perturbation to the Hamiltonian (H=H0+V) one of the following using i to indicate electron labels, a,b to indicate x,y,z Cartesian coordinates, f_{ab} = f_{ba} (being very pedantic, I know)
V = - 1/3 sum_i sum_a sum_b 1/2 * (3 r_{ia} r_{ib} - |r|^2 delta_{ab}) f_{ab}
Or 
V = - sum_i sum_a sum_b 1/2 * (3 r_{ia} r_{ib} - |r|^2 delta_{ab}) f_{ab}
Or
V = - 1/3 sum_i sum_a sum_b 1/2 * (3 r_{ia} r_{ib} - |r|^2 delta_{ab}) (f_{ab}+f_{aa}delta_{ab})

Or something else? 

Thank you,
Andrew
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Andrew Taube
D. E. Shaw Research
email: Andrew.TaubeXX_AT_XXDEShawResearch.com