Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




R.F.W. Bader


This thesis is concerned with the application of the theory of virial partitioning of a molecular system and its properties. In this theory the partitioning surfaces are defined in terms of the topographical features of the observable molecular charge distribution, ρ(r). Specifically, ρ(r) is partitioned by those closed surfaces through which the flux of ∇ρ(r) is everywhere zero, i.e.,

∇ρ(r) n(r) = 0 ∀ṟ ε S (ṟ) (A.1)

where n(ṟ) is the vector normal to the surface S(ṟ) at the point ṟ. Equation (A.1) has been derived as a boundary condition through the application of the variational principle in the definition of a quantum subspace. The virial partitioning of a molecular system is obtained by constructing for the system all surfaces which satisfy equation (A.1). This set of surfaces divides a molecule into a set of chemically identifiable atomic-like fragments. Each fragment so defined possess a unique set of quantum properties; the hypervirial and virial theorems are obeyed and all properties of the fragment· including its total energy are rigorously defined. Any property of the total molecular system may be equated to a sum of contributions from the spatially defined fragments. The calculated properties of the fragments, as demonstrated in this thesis, coincide with expectations based on experimental chemistry.

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Chemistry Commons