Towards an exact orbital-free single-particle kinetic energy density for the inhomogeneous electron liquid in the Be atom

Holas and March (Phys. Rev. A51, 2040 (1995)) wrote the gradient of the one-body potential V(r) in terms of low-order derivatives of the idempotent Dirac density matrix built from a single Slater determinant of Kohn-Sham orbitals. Here, this is first combined with the study of Dawson and March (J. Chem. Phys. 81, 5850 (1984)) to express the single-particle kinetic energy density of the Be atom ground-state in terms of both the electron density n(r) and potential V(r). While this is the more compact formulation, we then, by removing V(r), demonstrate that the ratio t(r)/n(r) depends, though non-locally, only on the single variable n'(r)/n(r), no high-order gradients entering for the spherical Be atom.Comment: Submitted to Journal of Mathematical Chemistr

Investigation of the chirality of enantiomers through information theory

In this work [1] we probed the Kullback-Leibler information entropy as a chirality measure, as an extension of previous studies on molecular quantum similarity evaluated for different enantiomers (enantiomers possessing two asymmetric centra in [2], with a single asymmetric carbon atom in [3] and with a chiral axis in [4]). The entropy was calculated using the shape functions of the R and S enantiomers considering one as reference for the other, resulting in an information theory based expression useful for quantifying chirality. It was evaluated for 5 chiral halomethanes possessing one asymmetric carbon atom with H, F, Cl, Br and I as substituents. To demonstrate the general applicability, a study of two halogen-substituted ethanes possessing two asymmetric carbon atoms has been included as well. Avnir’s Continuous Chirality Measure (CCM) [5] has been computed and confronted with the information deficiency. By these means we quantified the dissimilarity of enantiomers and illustrated Mezey’s Holographic Electron Density Theorem in chiral systems [6]. A comparison is made with the optical rotation and with the Carbó similarity index. As an alternative chirality index, we recently also calculated the information deficiency in a way which is consistent with experiments as VCD spectroscopy and optical rotation measurements. The entropy calculates the difference in information between the shape function of one enantiomer and a normalized shape function of the racemate. Comparing the latter index with the optical rotation reveals a similar trend. [1] S. Janssens, A. Borgoo, C. Van Alsenoy, P. Geerlings, J. Phys. Chem. A, 112, 10560 (2008). [2] S. Janssens, C. Van Alsenoy, P. Geerlings, J. Phys. Chem. A, 111, 3143 (2007). [3] G. Boon, C. Van Alsenoy, F. De Proft, P. Bultinck, P. Geerlings, J. Phys. Chem. A, 110, 5114 (2006). [4] S. Janssens, G. Boon, P. Geerlings, J. Phys. Chem. A, 110, 9267 (2006). [5] H. Zabrodsky, D. Avnir, J. Am. Chem. Soc., 117, 462 (1995). [6] P.G. Mezey, Mol. Phys., 96, 169 (1999)

Google’s Advisory Council Hearings: Things to Remember and Things to Forget

The last hearing of the Google Advisory Council on the Right to be Forgotten took place in Brussels on Tuesday. Brendan Van Alsenoy and Jef Ausloos of the Interdisciplinary Centre for Law and ICT at KU Leuven look back at the series of hearings and highlight some of the most important (and less important) points

Why EU authorities are taking a closer look at Facebook’s privacy practices

On 13 May 2015, the Belgian Privacy Commission issued a recommendation as part of an ongoing investigation into Facebook’s privacy practices. Brendan Van Alsenoy and Valerie Verdoodt describe why Facebook is facing increased regulatory scrutiny and summarize the highlights of the recent recommendation

Quantum similarity of isosteres coordinate versus momentum space and influence of alignment

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Alternative Kullback-Leibler information entropy for enantiomers

In our series of studies on quantifying chirality, a new chirality measure is proposed in this work based on the Kullback-Leibler information entropy. The index computes the extra information that the shape function of one enantiomer carries over a normalized shape function of the racemate, while in our previous studies the shape functions of the R and S enantiomers were used considering one as reference for the other. Besides being mathematically more elegant (symmetric, positive definite, zero in the case of a nonchiral system), this new index bears a more direct relation with chirality oriented experimental measurements such as circular dichroism (CD) and optical rotation measurements, where the racemate is frequently used as a reference, The five chiral halomethanes holding one asymmetric carbon atom and H, F, Cl, Br, and I as substituents have been analyzed. A comparison with our calculated optical rotation and with Avnir's Continuous Chirality Measure (CCM) is computed. The results show that with this index the emphasis lies on the differences between the noncoinciding substituents

Mapping indefinites: towards a Neo-Aristotelian map

The semantic map that Haspelmath (1997) offered for indefinite pronouns is highly valuable, but it is problematic and too simple about the relation between the meaning of the indefinite pronoun itself, its context, and the resulting meaning-in-context. As a representation of the meaning-in-context, it is claimed that one should go back to the Square of Oppositions, more particularly, to a three layered ‘Neo-Aristotelian’ representation of this square

An Overview of Self-Consistent Field Calculations Within Finite Basis Sets

A uniform derivation of the self-consistent field equations in a finite basis set is presented. Both restricted and unrestricted Hartree–Fock (HF) theory as well as various density functional approximations are considered. The unitary invariance of the HF and density functional models is discussed, paving the way for the use of localized molecular orbitals. The self-consistent field equations are derived in a non-orthogonal basis set, and their solution is discussed also in the presence of linear dependencies in the basis. It is argued why iterative diagonalization of the Kohn–Sham–Fock matrix leads to the minimization of the total energy. Alternative methods for the solution of the self-consistent field equations via direct minimization as well as stability analysis are briefly discussed. Explicit expressions are given for the contributions to the Kohn–Sham–Fock matrix up to meta-GGA functionals. Range-separated hybrids and non-local correlation functionals are summarily reviewed