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)

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

Assessment of atomic charge models for gas-phase computations on polypeptides

The concept of the atomic charge is extensively used to model the electrostatic properties of proteins. Atomic charges are not only the basis for the electrostatic energy term in biomolecular force fields but are also derived from quantum mechanical computations on protein fragments to get more insight into their electronic structure. Unfortunately there are many atomic charge schemes which lead to significantly different results, and it is not trivial to determine which scheme is most suitable for biomolecular studies. Therefore, we present an extensive methodological benchmark using a selection of atomic charge schemes [Mulliken, natural, restrained electrostatic potential, Hirshfeld-I, electronegativity equalization method (EEM), and split-charge equilibration (SQE)] applied to two sets of penta-alanine conformers. Our analysis clearly shows that Hirshfeld-I charges offer the best compromise between transferability (robustness with respect to conformational changes) and the ability to reproduce electrostatic properties of the penta-alanine. The benchmark also considers two charge equilibration models (EEM and SQE), which both clearly fail to describe the locally charged moieties in the zwitterionic form of penta-alanine. This issue is analyzed in detail because charge equilibration models are computationally much more attractive than the Hirshfeld-I scheme. Based on the latter analysis, a straightforward extension of the SQE model is proposed, SQE+Q0, that is suitable to describe biological systems bearing many locally charged functional groups

Reactivity of three-membered heterocyclic rings with respect to sodium methoxide

Aziridines can be ‘activated’ or ‘non-activated’, depending on whether their N-substituent is an electron-withdrawing group or an electron-donating group, respectively. Activated aziridines are much more susceptible to ring opening than non-activated aziridines and epoxides are even more reactive. The difference in reactivity between activated 2-(bromomethyl)-1-tosylaziridines, non-activated 1-benzyl-2-(bromomethyl)aziridines and epibromohydrins with respect to sodium methoxide was comparatively analysed by means of DFT calculations, such as BMK, MPW1K and MPWB95 [1]. Nucleophilic substitution reactions are known to be influenced by the solvent environment. Therefore, the gas-phase results were extended towards a discrete solvent approach. The solvent effect was taken into account by inspecting the convergence behaviour of the energy of solvation in terms of a systematically increasing number of solvent molecules. To model each of the reactive profiles of the various substrates, a supermolecule model was used with five explicit methanol molecules. Solvation has significantly changed the landscape of the energy profiles, which nicely shows the necessity of taking into account explicit solvation molecules to obtain the correct reaction profiles. The barriers for direct displacement of bromide by methoxide in methanol are comparable for all three heterocyclic species under study. However, ring opening is only feasible for the epoxide and the activated aziridine and not for the non-activated aziridine

Reformulating the Woodward-Hoffmann Rules in a Conceptual Density Functional Theory Context: the Case of Sigmatropic Reactions

In this contribution, we have investigated the performance of the initial hardness response, a reactivity index from conceptual DFT, in the prediction of the allowed or forbidden character of a series of sigmatropic hydrogen shifts, which are traditionally explained using the famous Woodward-Hoffmann rules for pericyclic reactions. Previously, it was observed that this quantity can be linked to the activation hardness of a chemical reaction and, in this case, thus to the aromaticity of the transition state in these kinds of reactions. It is shown, both by considering approximate reaction coordinates and intrinsic reaction coordinates that the allowed mode of the sigmatropic rearrangement corresponds to the largest value of the initial hardness response, in agreement with earlier work on cycloadditions and electrocyclizations

Accurate interaction energies at DFT level by means of an efficient dispersion correction

This paper presents an approach for obtaining accurate interaction energies at the DFT level for systems where dispersion interactions are important. This approach combines Becke and Johnson's [J. Chem. Phys. 127, 154108 (2007)] method for the evaluation of dispersion energy corrections and a Hirshfeld method for partitioning of molecular polarizability tensors into atomic contributions. Due to the availability of atomic polarizability tensors, the method is extended to incorporate anisotropic contributions, which prove to be important for complexes of lower symmetry. The method is validated for a set of eighteen complexes, for which interaction energies were obtained with the B3LYP, PBE and TPSS functionals combined with the aug-cc-pVTZ basis set and compared with the values obtained at CCSD(T) level extrapolated to a complete basis set limit. It is shown that very good quality interaction energies can be obtained by the proposed method for each of the examined functionals, the overall performance of the TPSS functional being the best, which with a slope of 1.00 in the linear regression equation and a constant term of only 0.1 kcal/mol allows to obtain accurate interaction energies without any need of a damping function for complexes close to their exact equilibrium geometry

Influence of the π–π interaction on the hydrogen bonding capacity of stacked DNA/RNA bases

The interplay between aromatic stacking and hydrogen bonding in nucleobases has been investigated via high-level quantum chemical calculations. The experimentally observed stacking arrangement between consecutive bases in DNA and RNA/DNA double helices is shown to enhance their hydrogen bonding ability as opposed to gas phase optimized complexes. This phenomenon results from more repulsive electrostatic interactions as is demonstrated in a model system of cytosine stacked offset-parallel with substituted benzenes. Therefore, the H-bonding capacity of the N3 and O2 atoms of cytosine increases linearly with the electrostatic repulsion between the stacked rings. The local hardness, a density functional theory-based reactivity descriptor, appears to be a key index associated with the molecular electrostatic potential (MEP) minima around H-bond accepting atoms, and is inversely proportional to the electrostatic interaction between stacked molecules. Finally, the MEP minima on surfaces around the bases in experimental structures of DNA and RNA–DNA double helices show that their hydrogen bonding capacity increases when taking more neighboring (intra-strand) stacking partners into account

New Insights and Horizons from the Linear Response Function in Conceptual DFT

An overview is given of our recent work on the linear response function (LRF) χrr′ and its congener, the softness kernel srr′, the second functional derivatives of the energy E and the grand potential Ω with respect to the external potential at constant N and μ, respectively. In a first section on new insights into the LRF in the context of conceptual DFT, the mathematical and physical properties of these kernels are scrutinized through the concavity of the E=ENv and Ω=Ωμv functionals in vr resulting, for example, in the negative semidefiniteness of χ. As an example of the analogy between the CDFT functionals and thermodynamic state functions, the analogy between the stability conditions of the macroscopic Gibbs free energy function and the concavity conditions for Ω is established, yielding a relationship between the global and local softness and the softness kernel. The role of LRF and especially the softness kernel in Kohn’s nearsightedness of electronic matter (NEM) principle is highlighted. The first numerical results on the softness kernel for molecules are reported and scrutinized for their nearsightedness, reconciling the physicists’ NEM view and the chemists’ transferability paradigm. The extension of LRF in the context of spin polarized conceptual DFT is presented. Finally, two sections are devoted to ‘new horizons’ for the LRF. The role of LRF in (evaluating) alchemical derivatives is stressed, the latter playing a promising role in exploring the chemical compound space. Examples for the transmutation of N2 and the CC→BN substitution pattern in 2D and 3D carbocyclic systems illustrate the computational efficiency of the use of alchemical derivatives in exploring nearest neighbours in the chemical compound space. As a second perspective, the role of LRF in evaluating and interpreting molecular conductivity is described. Returning to its forerunner, Coulson’s atom-atom polarizability, it is shown how in conjugated π systems (and within certain approximations) a remarkable integral-integrand relationship between the atom-atom polarizability and the transmission probability between the atoms/contacts exists, leading to similar trends in both properties. A simple selection rule for transmission probability in alternating hydrocarbons is derived based on the sign of the atom-atom polarizability

Relativistic effects on the Fukui function

The extent of relativistic effects on the Fukui function, which describes local reactivity trends within conceptual density functional theory (DFT), and frontier orbital densities has been analysed on the basis of three benchmark molecules containing the heavy elements: Au, Pb, and Bi. Various approximate relativistic approaches have been tested and compared with the four-component fully relativistic reference. Scalar relativistic effects, as described by the scalar zeroth-order regular approximation methodology and effective core potential calculations, already provide a large part of the relativistic corrections. Inclusion of spin-orbit coupling effects improves the results, especially for the heavy p-block compounds. We thus expect that future conceptual DFT-based reactivity studies on heavy-element molecules can rely on one of the approximate relativistic methodologie