A decomposition of an N‐particle operator as a sum of N + 1 components is defined such that, in the case of a model system employing a finite one‐particle basis set, the decomposition is invariant under unitary transformations of the basis set. Applied to a two‐particle Hamiltonian, this decomposition gives rise to the distinction between the independent‐particle energy and the coupling energy defined in previous papers. Applied to the reduced density operator for a quantum state, the decomposition corresponds to partitioning the density into irreducible components. This partitioning is illustrated by graphs of electron density for the water molecule.
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Coleman et al. (1980) studied this question.