# openfermion.chem.make_reduced_hamiltonian

Construct the reduced Hamiltonian.

This Hamiltonian is equivalent to the electronic structure Hamiltonian but contains only two-body terms. To do this, the operator now depends on the number of particles being simulated. We use the RDM sum rule to lift the 1-body terms to the two-body space.

#### Derivation:

use the fact that i^l = (1/(n -1)) sum{jk}\delta{jk}i^ j^ k l i^l = (-1/(n -1)) sum{jk}\delta{jk}j^ i^ k l i^l = (-1/(n -1)) sum{jk}\delta{jk}i^ j^ l k i^l = (1/(n -1)) sum{jk}\delta{jk}j^ i^ l k

Rewrite each one-body term as an even weighting of all four 2-RDM elements with delta functions. Then rearrange terms so that each ijkl term gets a sum of permuted one-body terms multiplied by delta function. One should notice that this results in the same formula if one was to apply the wedge product!

molecular_hamiltonian operator to write reduced hamiltonian for
n_electrons number of electrons in the system

InteractionOperator with a zero one-body component.