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The electron density changes from reactants towards the transition state of a chemical reaction is expressed as a linear combination of the state-specific dual descriptors (SSDD) of the corresponding reactant complexes. Consequently, the SSDD can be expected to bear important resemblance to the so-called natural orbitals for chemical valence (NOCV), introduced as the orbitals that diagonalize the deformation density matrix of interacting molecules. This agreement is shown for three case studies: the complexation of a Lewis acid with a Lewis base, a SN2 nucleophilic substitution reaction and a Diels-Alder cycloaddition reaction. As such, the SSDD computed for reactant complexes are shown to provide important information about charge transfer interactions during a chemical reaction.

Halogen bonds between the trifluoromethyl halides CF(3)Cl, CF(3)Br and CF(3)I, and dimethyl ether, dimethyl sulfide, trimethylamine and trimethyl phosphine were investigated using Pearson's hard and soft acids and bases (HSAB) concept with conceptual DFT reactivity indices, the Ziegler-Rauk-type energy-decomposition analysis, the natural orbital for chemical valence (NOCV) framework and the non-covalent interaction (NCI) index. It is found that the relative importance of electrostatic and orbital (charge transfer) interactions varies as a function of both the donor and acceptor molecules. Hard and soft interactions were distinguished and characterised by atomic charges, electrophilicity and local softness indices. Dual-descriptor plots indicate an orbital σ hole on the halogen similar to the electrostatic σ hole manifested in the molecular electrostatic potential. The predicted high halogen-bond-acceptor affinity of N-heterocyclic carbenes was evidenced in the highest complexation energy for the hitherto unknown CF(3) I·NHC complex. The dominant NOCV orbital represents an electron-density deformation according to a n→σ*-type interaction. The characteristic signal found in the reduced density gradient versus electron-density diagram corresponds to the non-covalent interaction between contact atoms in the NCI plots, which is the manifestation of halogen bonding within the NCI theory. The unexpected C-X bond strengthening observed in several cases was rationalised within the molecular orbital framework., (Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Branched alkane hydrocarbons are thermodynamically more stable than straight-chain linear alkanes. This thermodynamic stability is also manifest in alkane bond separation energies. To understand the physical differences between branched and linear alkanes, we have utilized a novel density functional theory (DFT) definition of steric energy based on the Weizäcker kinetic energy. Using the M06-2X functional, the total DFT energy was partitioned into a steric energy term (E(s)[ρ]), an electrostatic energy term (E(e)[ρ]), and a fermionic quantum energy term (E(q)[ρ]). This analysis revealed that branched alkanes have less (destabilizing) DFT steric energy than linear alkanes. The lower steric energy of branched alkanes is mitigated by an equal and opposite quantum energy term that contains the Pauli component of the kinetic energy and exchange-correlation energy. Because the steric and quantum energy terms cancel, this leaves the electrostatic energy term that favors alkane branching. Electrostatic effects, combined with correlation energy, explains why branched alkanes are more stable than linear alkanes.

Heme is a key cofactor of hemoproteins in which porphyrin is often found to be preferentially metalated by the iron cation. In our previous work [Feng, X. T.; Yu, J. G.; Lei, M.; Fang, W. H.; Liu, S. B. J. Phys. Chem. B 2009, 113, 13381], conceptual density functional theory (CDFT) descriptors have been applied to understand the metal-binding specificity of porphyrin. We found that the iron-porphyrin complex significantly differs in many aspects from porphyrin complexes with other metal cations except Ru, for which similar behaviors for the reactivity descriptors were discovered. In this study, we employ the spin-polarized version of CDFT to investigate the reactivity for a series of (pyridine)(n)-M(ll)-porphyrin complexes-where M = Mg, Ca, Cr, Mn, Co, Ni, Cu, Zn, Ru, and Cd, and n = 0, 1, and 2-to further appreciate the metal-binding specificity of porphyrin. Both global and local descriptors were examined within this framework. We found that, within the spin resolution, not only chemical reactivity descriptors from CDFT of the iron complex are markedly different from that of other metal complexes, but we also discovered substantial differences in reactivity descriptors between Fe and Ru complexes. These results confirm that spin properties play a highly important role in physiological functions of hemoproteins. Quantitative reactivity relationships have been revealed between global and local spin-polarized reactivity descriptors. These results contribute to our better understanding of the metal binding specificity and reactivity for heme-containing enzymes and other metalloproteins alike.

Spatial confinement of atoms and molecules influences electronic structures, energy spectra, and chemical reactivity. A simple potential barrier approach involving a single parameter is used to study confinement in both atoms and molecules, focusing on the reactivity of the systems through the HOMO-LUMO gap, which is linked to the global chemical hardness. Both atoms and molecules are shown to respond with an increase in hardness when confined. The results suggest that previous observations of a HOMO-LUMO gap decrease for guest molecules in zeolites cannot be assigned exclusively to electron confinement.

A simple method was recently proposed [D. J. Tozer and F. De Proft, J. Chem. Phys., 2007, 127, 034108] for performing explicit density functional theory (DFT) calculations on temporary anions. The excess electron in the anion is bound by a potential wall, the position of which is determined by a single parameter lambda, chosen to reproduce an approximate, theoretical negative electron affinity in the corresponding neutral. In the present study, the system-dependence of lambda and the sensitivity of the negative affinities to this parameter are investigated for 34 organic molecules. The results demonstrate that the system-dependent lambda values can be replaced by a global, average value, with minimal effect on the affinities. It follows that the orbitals, electron density, and other properties of a temporary anion can be determined from a single DFT calculation on that anion, using a large, diffuse basis set. As an illustration, singly occupied molecular orbitals and spin densities are determined for the anions of guanine and adenine nucleobases. Despite the use of a diffuse basis set, the method yields quantities that are localised in the molecular framework, associated with vertical electron affinities of -1.2 eV and -0.8 eV, respectively.

Molecular quantum similarity is evaluated for enantiomers in the case of molecules showing conformational flexibility, using our earlier proposed Boltzmann weighted similarity index. The conformers of the enantiomers of the amino acids alanine, asparagine, cysteine, leucine, serine, and valine were examined. Next to studying global indices, the evaluation of local similarity is carried out using our earlier proposed local similarity index based on the Hirshfeld partitioning, to further illustrate Mezey's holographic electron density theorem in chiral systems and to quantify dissimilarity of enantiomers.

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]

A novel quantum similarity measure (QSM) is constructed based on concepts from information theory. In an application of QSM to atoms, the new QSM and its corresponding quantum similarity index (QSI) are evaluated throughout the periodic table, using the atomic electron densities and shape functions calculated in the Hartree-Fock approximation. The periodicity of Mendeleev’s table is regained for the first time through the evaluation of a QSM. Evaluation of the information theory based QSI demonstrates, however, that the patterns of periodicity are lost due to the renormalization of the QSM, yielding chemically less appealing results for the QSI. A comparison of the information content of a given atom on top of a group with the information content of the elements in the subsequent rows reveals another periodicity pattern. Relativistic effects on the electronic density functions of atoms are investigated. Their importance is quantified in a QSI study by comparing for each atom, the density functions evaluated in the Hartree-Fock and Dirac-Fock approximations. The smooth decreasing of the relevant QSI along the periodic table illustrates in a quantitative way the increase of relativistic corrections with the nuclear charge. [ABSTRACT FROM AUTHOR]

Abstract: a [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: 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]