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

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

Arabidopsis thaliana dehydroascorbate reductase 2 : conformational flexibility during catalysis

Dehydroascorbate reductase (DHAR) catalyzes the glutathione (GSH)-dependent reduction of dehydroascorbate and plays a direct role in regenerating ascorbic acid, an essential plant antioxidant vital for defense against oxidative stress. DHAR enzymes bear close structural homology to the glutathione transferase (GST) superfamily of enzymes and contain the same active site motif, but most GSTs do not exhibit DHAR activity. The presence of a cysteine at the active site is essential for the catalytic functioning of DHAR, as mutation of this cysteine abolishes the activity. Here we present the crystal structure of DHAR2 from Arabidopsis thaliana with GSH bound to the catalytic cysteine. This structure reveals localized conformational differences around the active site which distinguishes the GSH-bound DHAR2 structure from that of DHAR1. We also unraveled the enzymatic step in which DHAR releases oxidized glutathione (GSSG). To consolidate our structural and kinetic findings, we investigated potential conformational flexibility in DHAR2 by normal mode analysis and found that subdomain mobility could be linked to GSH binding or GSSG release

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

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

Extending conceptual DFT to include external variables: the influence of magnetic fields

An extension of conceptual DFT to include the influence of an external magnetic field is proposed in the context of a program set up to cope with the ever increasing variability of reaction conditions and concomitant reactivity. The two simplest global reactivity descriptors, the electronic chemical potential (μ) and the hardness (η), are considered for the main group atoms H-Kr using current density-functional theory. The magnetic field strength, |B|, is varied between 0.0 and 1.0 B0 = ħe−1a0−2 ≈ 2.3505 × 105 T, encompassing the Coulomb and intermediate regimes. The carbon atom is studied as an exemplar system to gain insight into the behaviour of the neutral, cationic and anionic species under these conditions. Their electronic configurations change with increasing |B|, leading to a piecewise behaviour of the ionization energy (I) and electron affinity (A) values as a function of |B|. This results in complex behaviour of properties such as the electronegativity χ = −1/2(I + A) = −μ and hardness η = 1/2(I − A). This raises an interesting question: to what extent are atomic properties periodic in the presence of a magnetic field? In the Coulomb regime, close to |B| = 0, we find the familiar periodicity of the atomic properties, and make the connections to response functions central to conceptual DFT. However, as the field increases in the intermediate regime configurational changes of the atomic species lead to discontinuous changes in their properties; fundamentally changing their behaviour, which is illustrated by constructing a periodic table of χ and η values at |B| = 0.5 B0. These values tend to increase for groups 1-2 and decrease for groups 16-18, leading to a narrower range overall and suggesting substantial changes in the chemistry of the main group elements. Changes within each group are also examined as a function of |B|. These are more complex to interpret due to the larger number of configurations accessible to heavier elements at high field. This is illustrated for group 17 where Cl and Br have qualitatively different configurations to their lighter cogener at |B| = 0.5 B0. The insight into periodic trends in strong magnetic fields may provide a crucial starting point for predicting chemical reactivity under these exotic conditions

Molecular charge distributions in strong magnetic fields: a conceptual and current DFT study

The effect of strong magnetic fields on the charge distribution of the hydrogen halides, H2O and NH3 is studied in the context of recent extensions of conceptual density functional theory to include additional variables such as external magnetic fields. From conceptual DFT studies on atoms in strong magnetic fields, changes in electronegativity and hardness suggest a reversal in polarity for all three diatomic molecules under these conditions. This is confirmed by current DFT calculations on these molecules in the presence of strong magnetic fields parallel and perpendicular to the internuclear axis; in the former case the electric dipole moment only undergoes small changes whereas in the latter case it changes significantly and also reverses in direction, doing so at lower field strength if the geometry is relaxed. The absence of a dipole moment induced perpendicular to the bond when a magnetic field is applied in this direction is understood by consideration of time reversal symmetry. Similar results are obtained for H2O and NH3; this may be an important point to consider in future studies focused on the unresolved question on the behaviour of hydrogen bonding in applied magnetic fields

Национально-психологические особенности иностранных учащихся начального этапа обучения

In recent years, a considerable interest has grown in the design of molecular nanowires with an increasing conductance with length. The development of such nanowires is highly desirable because they could play an important role in future molecular-scale circuitry. Whereas the first experimental observation of this nonclassical behavior still has to be realized, a growing number of candidate wires have been proposed theoretically. In this Letter, we point out that all the wires with an anti-Ohmic increasing conductance with length proposed so far share a common characteristic: their diradical character increases with length. The conceptual connection between diradical character and conductance enables a systematic design of such anti-Ohmic wires and explains the difficulty in their syntheses. A strategy is proposed to balance the stability and conductance so that this nonclassical phenomenon can be observed