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Spin-polarized density functional theory (SP-DFT) allows both the analysis of charge-transfer (e.g., electrophilic and nucleophilic reactivity) and of spin-polarization processes (e.g., photophysical changes arising from electron transitions). In analogy with the dual descriptor introduced by Morell et al. [J. Phys. Chem. A 109, 205 (2005)], we introduce new dual descriptors intended to simultaneously give information of the molecular regions where the spin-polarization process linking states of different multiplicity will drive electron density and spin density changes. The electronic charge and spin rearrangement in the spin forbidden radiative transitions S0→T(n,π*) and S0→T(π,π*) in formaldehyde and ethylene, respectively, have been used as benchmark examples illustrating the usefulness of the new spin-polarization dual descriptors. These quantities indicate those regions where spin-orbit coupling effects are at work in such processes. Additionally, the qualitative relationship between the topology of the spin-polarization dual descriptors and the vertical singlet triplet energy gap in simple substituted carbene series has been also discussed. It is shown that the electron density and spin density rearrangements arise in agreement with spectroscopic experimental evidence and other theoretical results on the selected target systems. [ABSTRACT FROM AUTHOR]

A hardness based similarity index for studying the quantum similarity for atoms is analyzed. The investigation of hardness and Fukui functions of atoms leads to the construction of a quantum similarity measure, which can be interpreted as a quantified comparison of chemical reactivity of atoms. Evaluation of the new measure reveals periodic tendencies throughout Mendeleev’s table. Moreover on the diagonal the global hardness was recovered. Considering a corresponding quantum similarity index reveals that renormalization of the measure can mask periodic patterns. The hardness was calculated for atoms with nuclear charge 3≤=Z≤=103, using the best single configuration electron density functions available. Different hardness kernels were used and the importance of the different contributions to the kernel was investigated. The atomic self-similarities constructed in this way show a fair correlation with experimental atomic polarizability [ABSTRACT FROM AUTHOR]

The central role of the shape function σ(r_) from the density functional theory (DFT), the ratio of the electron density ρ(r_) and the number of electrons N of the system (density per particle), is investigated. Moreover, its relationship with DFT based reactivity indices is established. In the first part, it is shown that an estimate for the chemical hardness can be obtained from the long range behavior of the shape function and its derivative with respect to the number of electrons at a fixed external potential. Next, the energy of the system is minimized with the constraint that the shape function should integrate to unity; the associated Lagrange multiplier is shown to be related to the electronic chemical potential μ of the system. Finally, the importance of the shape function for both molecular structure, reactivity, and similarity is outlined. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Abstract: Numerical calculations on the gradient and Laplacian forms of the position space Fisher information measure are reported using the 1-normalised Dirac–Fock densities (shape function), , for atoms H–Lr. It is shown that the difference in effective electrostatic potentials, corresponding to the gradient and the Laplacian form of Fishers'' information, is completely defined by the shape function (the density per particle) at the nucleus, . The influence of relativistic effects on the Fisher information is recovered for the first time. [Copyright &y& Elsevier]

Quantum molecular similarity (QMS), for which the first measures were introduced by Carbó in the early 1980s, has been shown to be an important concept when comparing properties and reactivity of different, albeit mostly related, molecules. In this article we investigate how various subfields of Density Functional Theory (DFT) contribute in their own way to the evaluation and the understanding of QMS, reflecting the combined interest of our group in both domains in recent years. The contribution of computational DFT is easy to pinpoint, as DFT can now be used in the evaluation of electron densities of ever-increasing quality. When establishing a link between the fundamental(s) of DFT and QMS the role of the shape function turns out to be predominant and an extension of Mezey's Holographic Electron Density Theorem for p(r) to the shape function σ(r) is presented. On this basis, similarity in shape is the fundamental issue to be looked at, both globally and locally. As an application, global and local similarity measures were evaluated using the Hirshfeld partitioning technique for the two enantiomers of CHFClBr, giving numerical evidence for the Holographic Electron Density Theorem. As an application of conceptual DFT, similarity indices constructed via DFT based local reactivity descriptors (e.g., local softness) are used to probe the ‘similarity of reactivity’ of a series of peptide isosteres. The use of the autocorrelation function for condensed indices turns out to be a valuable technique to circumvent the orientation-translation dependence of similarity indices. [ABSTRACT FROM AUTHOR]

Abstract: The three-parameter two-electron correlated analytic wavefunction of Chandrasekhar, parametrized using three physically meaningful conditions on the electron density, is assessed using several information theory measures, the Fisher information, Shannon entropy, and statistical complexity, and compared to the results for the same measures using hydrogenic and Hartree–Fock (HF) orbitals. [Copyright &y& Elsevier]

Abstract: Using the Dawson–March transformation, the Dirac density matrix γ(r, r′) can be written in terms of the density amplitude and a phase θ(r), where ρ(r)≡ γ(r, r) is the ground-state electron density. Here, for systems such as LiH or , it is shown how the force −∂V(r)/∂r corresponding to the one-body potential V(r) can be written, given the ground-state density ρ(r) from a high-level ab initio calculation or a diffraction experiment. The Hartree–Fock ground-state densities for LiH and are utilized to calculate approximate phase angles θ(r). Finally, for the force −∂V(r)/∂r corresponding to V(r) is calculated. [Copyright &y& Elsevier]

Abstract: The Shannon entropy of the ratio of electron density and the number of electrons, shape function entropy, is reported for the atoms He–Ac within the non-relativistic exchange-only optimized effective potential model. The derivative of the shape function entropy with electron number at constant external potential is related to an integral containing the difference between the average Fukui function and the shape function weighted by the logarithm of electron density. The trends in the shape function entropy, its spin analogue and the corresponding derivatives with electron number reveal interesting periodic behaviour. [Copyright &y& Elsevier]

Abstract: In this Letter Quantum Similarity for Atoms (H–Xe) is investigated using electron densities and shape functions, looking for patterns of periodicity as in Mendeleev’s Table. An LS-dependent restricted Hartree–Fock method is used to obtain the wave functions from which the electron densities are calculated. Utilizing the quantum similarity proposed by Carbó a nearest neighbour dominated similarity is retrieved, masking periodicity. Introduction of the information discrimination concept with reference to the noble gas atom of the previous row is found to reveal periodicity, with improved results when densities are replaced by shape functions throughout. This confirms recent literature on the fundamental role of the shape function as carrier of information. [Copyright &y& Elsevier]