The recently developed concept of a correlation entropy, S, as a quantitative measure of the correlation strength present in a correlated quantum many-body state is applied to the ground states of the He isoelectronic series He(Z) with varying nuclear charge Z and of the Hooke’s law model HLM(ω) with varying oscillator frequency ω. S is constructed from the natural orbital occupation numbers. It vanishes for weak correlation (large coupling constants Z or ω), and increases monotonically with decreasing Z or ω (strengthening correlation). A reduced correlation energy per particle Δecorr and a dimensionless ratio ε=|Ecorr/E| are introduced which vanish asymptotically in the weak correlation limit in contrast to Ecorr and ecorr=Ecorr/N. These two intensive quantities, Δecorr and ε, are compared with s=S/N. For both model systems, dΔecorr/ds⩾0 and dε/ds⩾0 (which modifies Collins’ conjecture that |Ecorr|∼S).

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Collins's conjecture ͓Z. Naturforsch. 48A, 68 ͑1993͔͒ that the correlation energy of a system is proportional to the Jaynes entropy ͓in Papers on Probability, Statistics and Statistical Physics, edited by R. Rosencrantz ͑Reidel, Dordrecht, 1983͔͒ is investigated for small molecular systems. Numerical evidence supporting the conjecture is obtained by computing entropies from highly correlated configuration-interaction wave functions at various correlation levels, using sequences of increasingly larger basis sets. Further evidence is also obtained by examination of results obtained from a variety of correlation methods utilizing a fixed basis set.

Hirshfeld-I charges were implemented in the Crystal code, for periodic calculations with localized atomic basis sets. Some particular features of the present periodic implementation are detailed and discussed by means of selected illustrating examples. In these examples, the Hirshfeld-I charges are somewhere between the Bader and the Mulliken values and closer to the former. The implementation exploits heavily symmetry aspects and is shown to scale linearly with the unit cell dimension.Keywords Hirshfeld Iterative · Periodic calculations · Ab Initio · LCAO To A. Vela for his high human and scientific qualities.

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