Topological partitioning

The properties of the topologically defined atoms and their temporal changes are identified within a general formulation of subspace quantum mechanics. It is shown that the quantum mechanical partitioning of a system into subsystems coincides with the topological partitioning both are defined by the set of zero flux surfaces in Vp(r). Consequently the total energy and any other property of a molecular system are partitioned into additive atomic contributions. 

Electrostatic Distributed multipoles e.g., DMA, CAMM, Topologically partitioned electric properties Polyatomics, up to polypeptides... 

Topologically partitioned dispersion energies Small polyatomics, up to urea... 

G. Jansen, C. Hattig, B. A. Hess, and J. G. Angyan, Mol. Phys., 88,69 (1996). Intermolecular Interaction Energies by Topologically Partitioned Electric Properties. 1. Electrostatic and Induction Energies in One-Center and Multicenter Multipole Expansions. 

B. Silvi, How topological partitions of the electron distribution reveal delocalization, Phys. Chem. Chem. Phys. 6, 256-260 (2004). 

Bader has shown that the topological partitioning of the molecules into atomic basins coincides with the requirements of formulating quantum mechanics for open systems [93], and in this way all the so-called theorems of quantum mechanics can be derived for an open system [94], Furthermore, the zero-flux condition, Eq. 1, turns out to be the necessary constraint for the application of Schwinger s principle of stationary action [95] to a part of a quantum system [93], The successful application of QTAIM to numerous chemical problems has thus deep physical roots since it is a theory which expands and generalises quantum mechanics themselves to include open and total systems, both treated on equal formal footing. 

Figure 2.5 gives a three-dimensional view of the topological partitioning of the pilot molecule. The vertical solid lines appearing in Figs. 2.3 and 2.4 now show... 

A. Otero-de-la-Roza, V. Luana, Topological partition of the elastic constants of crystals. J. Phys. Chem. A 115(45), 12953-12961 (2011)... 

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