  We present the first hardware implementation of electrostatic interaction
energies using a trapped-ion quantum computer. As test system for our
computation, we focus on the reduction of $\mathrm{NO}$ to
$\mathrm{N}_2\mathrm{O}$ catalyzed by a nitric oxide reductase (NOR). The
quantum computer is used to generate an approximate ground state within the NOR
active space. To efficiently measure the necessary one-particle density
matrices, we incorporate fermionic basis rotations into the quantum circuit
without extending the circuit length, laying the groundwork for further
efficient measurement routines using factorizations. Measurements in the
computational basis are then used as inputs for computing the electrostatic
interaction energies on a classical computer. Our experimental results strongly
agree with classical noise-less simulations of the same circuits, finding
electrostatic interaction energies within chemical accuracy despite hardware
noise. This work shows that algorithms tailored to specific observables of
interest, such as interaction energies, may require significantly fewer quantum
resources than individual ground state energies would in the straightforward
supermolecular approach.
