Virial partitioning of polyatomic systems

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Abstract
Based on the recent demonstration of the existence of the quantum-mechanical virial theorem for a spatially defined fragment of a molecular system, we give here the method and consequences of its application to the partitioning of polyatomic systems. The theorem yields a rigorous method for the spatial partitioning of the total energy of a system. Using the techniques of second-quantization, it is demonstrated that the total hamiltonian of a system may be partitioned into a sum of terms, each of which yields the local energy of a particular well-defined region of space when averaged over the wavefunction of the system. The fragment virial theorem defines the theoretical conditions which must be obeyed for the transferability of fragment properties between systems. It also defines the nature of the fragments which may exhibit transferable properties and these correspond to atomic-like fragments, thereby suggesting that the fundamental basis for additivity is the result of the transferability of atomic-like fragments rather than of ‘bond’ contributions.