Hirshfeld analysis of molecular densities: subsystem probabilities and charge sensitivities
The Hirshfeld (“stockholder”) partitioning of molecular one-electron densities (or probabilities) is generalized to many-electron distributions using the minimum entropy deficiency principle of the Information Theory, and the ensemble interpretation of this division scheme is given. A distinction is made between changes of the ground-state density (“horizontal” displacements) and alternative divisions of the fixed molecular density (“vertical” displacements) and the relevant equilibrium criteria are discussed. Within the density functional theory the subsystem densities are interpreted as the ground-state densities for the effective external potentials of such molecular fragments. The charge sensitivities for the global equilibrium (mutually open subsystems) and constrained equilibria (mutually closed subsystems) are briefly summarized and the derivative properties of the quadratic Taylor expansion of the system energy in terms of the stockholder subsystem densities are examined. In the subsystem resolution the additive and nonadditive components of the hardness and softness kernels are identified and the relation between the linear response and softness kernels of molecular fragments is derived.