Stability conditions for density functional reactivity theory: an interpretation of the total local hardness

The second-order Taylor series expansions commonly used in the density functional chemical reactivity theory are used to define local stability conditions for electronic states. Systems which satisfy these conditions are stable to infinitesimal perturbations due to approaching chemical reagents. The basic formalism considered here supersedes previous variational approaches to chemical reactivity theory like the electrophilicity, potentialphilicity, and chargephilicity. The total local hardness emerges naturally in this analysis, and can be clearly interpreted. When the total local hardness is small, the system is relatively insensitive to perturbations. Furthermore, minus the total local hardness is an energetically favorable perturbation of the external potential.     

Geometric interpretation of density displacements and charge sensitivities

The “geometric” interpretation of the electronic density displacements in the Hilbert space is given and the associated projection-operator partitioning of the hardness and softness operators (kernels) is developed. The eigenvectors |?〉= |α〉 of the hardness operator define the complete (identity) projector P =Σ_α| α〉〈α | = 1 for general density displacements, including thecharge-transfer (CT) component, while the eigenvectors |i〉= |i〉 of the linear response operator determine thepolarizational P-projector, P_p = Σ_i |i〉〈i| . Their difference thus defines the complementary CT-projector: P_CT = 1-P_P. The complete vector space for density displacements can be also spanned by supplementing the P-modes with the homogeneous CT-mode. These subspaces separate the integral (normalization) and local aspects of density shifts in molecular systems.     

Hydrogen bonding in Schiff bases--NMR, structural and experimental charge density studies

A series of sixteen Schiff bases (derivatives of salicylaldehydes and aryl amines) was studied to reveal the influence of substituents and the length of the linker on the properties of the H-bonding formed. In theory, two groups of compounds, derivatives of 2-(2-hydroxybenzylidenoamine)phenol) and 2-hydroxy-N-(2-hydroxybenzylideno)benzylamine, can form different types of H-bonds using one or two hydroxyl groups present in the molecules. Two other groups of compounds, derivatives of 4-(2-hydroxybenzylidenoamine)phenol and N-(2-hydroxybenzyideno)benzylamine, can form only one type of H-bond. It was confirmed by (15)N and (13)C NMR experiments, that in all cases only traditional, H-bonded six-membered chelate rings were formed. The positions of the hydrogen atom in the rings depend on the substituent and phase. Generally, the OH H-bond form dominates in solution, with exception of the nitro derivatives, where the NH tautomer is present. In the solid state the tautomeric equilibrium is strongly shifted to the NH form. Only for the 5-Br derivative of one compound was the reverse relationship found. According to the results of experimental charge density investigations, two intramolecular H-bonds in the 5-methoxy derivative of 2-hydroxy-N-(2'-hydroxybenzylideno)benzylamine) differ significantly in terms of charge density properties. The intra- and intermolecular H-bonds formed by the deprotonated oxygen atom from 2-OH group are strong, with significant charge density concentration at the bond critical point and a straight, well-defined bond path, whereas the second intramolecular H-bond formed by the oxygen atom from the 2'-OH group is quite weak, with ca. five times smaller charge density concentration than in the previous case and a bent bond path. In terms of energy densities, the latter H-bond appears to be a non-bonding interaction, with total energy density being slightly positive. In terms of source contributions to the density at the H-bond critical point from the atoms involved, the intermolecular, linear H-bond is very strong and charge-assisted in the source function classification, the N(1)-H(1N)···O(1) H-bond is medium-strength, while the third H-bond is extremely weak.     

Understanding the chemical reactivity of phenylhalocarbene systems: an analysis based on the spin-polarized density functional theory

Global and local indices based on the spin-polarized density functional theory (SP-DFT) have been used to rationalize the philicity power and spin polarization pattern of a family of singlet substituted phenylhalocarbenes, (pYPhXC, Y = –NO₂ , –CN, –CHO, –F, –H, –CH₃ , –OH, –OCH₃ , –NH₂ ; X = –F, –Cl, –Br). The local reactivity may be traced out by the simple condensed-to-atoms model for the SP-DFT Fukui functions, namely and . For the addition of some singlet phenylhalocarbenes on tetramethylethylene a linear correlation among the global and local electrophilicity index , and the observed rate constants were found. This result supports a mechanistic model where the carbene adds to the olefin in a single step that is controlled by the carbene electrophilicity. These results emphasize the usefulness of general SP-DFT philicities in the rationalization of chemical reactivity at initial stages of reactions that could involve both charge transfer and spin polarization processes.     

Use of13C chemical shift/charge density linear relationship for ranking chemical structures

A novel approach to molecular structure elucidation based on ranking chemical structures in agreement with the¹³C NMR chemical shift/charge density linear relationship is suggested. The structure having the lowest standard approximation error (SAE) is considered to be the correct one. Each ranked structure is additionally tested for the¹³C chemical shift equivalence corresponding to its constitutional symmetry (in terms of the charge densities).This paper is Part VI of the series Automatic assignment of¹³C NMR signals. For Part V see ref. [1].     

S=N versus S+-N-: an experimental and theoretical charge density study

To elucidate the bonding situation in the widely discussed hypervalent sulfur nitrogen species, the charge density distributions rho(r) and related properties of four representative compounds, methyl(diimido)sulfinic acid H(NtBu)(2)SMe (1), methylene-bis(triimido)sulfonic acid H(2)C[S(NtBu)(2) (NHtBu)](2) (2), sulfurdiimide S(NtBu)(2) (3), and sulfurtriimide S(NtBu)(3) (4), were determined experimentally by high-resolution low-temperature X-ray diffraction experiments (T = 100 K). This set of molecules represents an ideal frame of reference for the comparison of SN bonding modes, because they contain short formal S=N double bonds as well as long S-N single bonds, some of them influenced by inter- or intramolecular hydrogen bonds. For comparison, the gas-phase ab initio calculations of the four model compounds, H(NMe)(2)SMe, H(2)C[S(NMe)(2)(NHMe)](2), S(NMe)(2), and S(NMe)(3), were performed. The topological features were found to be not particularly sensitive with respect to different substituents R (R = H, Me, tBu). In this paper, it is documented that theory and experiment differ in the eigenvalues of the Hessian matrix because of systematically differing positions of the bond critical points but agree very well concerning the spatial Laplacian distribution and the distinct polarization of all investigated sulfur-nitrogen bonds. Both recommend the S(+)-N(-) formulation of sulfur nitrogen bonds in 1 and 2 since all nitrogen atoms are found to be sp(3) hybridized. The planar SNx (x = 2, 3) units in the diimide 3 and the triimide 4 reveal characteristics of m-center-n-electron systems. For none of the investigated S-N bonds, a classical double bond formulation can be supported. This is further substantiated by the NBO/NRT approach. Valence expansion to more than eight electrons at the sulfur atom can definitely be excluded to explain the bonding.     

Automatic assignment of 13C NMR spectra based on the chemical shift/charge density relationship

An approach for the automatic assignment of ¹³C spectra, based on the chemical shift/charge density relationship, is suggested. All permutations of spectral signals are computer-generated, and for every permutation a least squares adjustment is carried out. The permutation presenting the highest correlation coefficient, or the lowest Hamilton's agreement factor, is considered to be correct. The application is exemplified by the ¹³C chemical shifts of a series of aromatic compounds. It is shown that more reliable assignment is achieved if the considered permutations are restricted by taking intoaccount the signal multiplicity.     

Topological analysis and charge density studies of an alpha-diimine macrocyclic complex of cobalt(II)--a combined experimental and theoretical study

A combined experimental and theoretical study of the paramagnetic [Co(II)(C12H20N8)(H2O)2] x 2 ClO4 complex was made on the basis of the electron density distribution and topological analysis. Accurate single-crystal diffraction data were measured on a suitable crystal with Mo(K alpha) radiation at 125 K. The CoII ion is coordinated in a square bipyramidal fashion with four imino nitrogen atoms at the equatorial plane and two water molecules at the axial positions. The hydrogen-bonding interaction at 125 K between the coordinated water molecule and the ClO(4)(-) ion makes the space group different from that at 298 K. Parallel MO calculations were made at UHF and DFT/UB3LYP. The agreement between experiment and theory is reasonably good. The chemical bonding characterization is presented in terms of the topological properties associated with bond critical points and the natural bond orbital (NBO) analysis as well. The Co-N(imino) and Co-O(water) bonds are dative bonds, where the lone-pair electrons of N or O serve as a -donor; however, a certain covalent character is identified in the Co-N(imino) bond. A delocalized C-N, N-N pi-bond model is proposed. The d-orbital energies of Co in this complex are such that E(d(xz)) is approximately equal to E(d(yz)) is approximately equal to E(dx(2-y2)) < E(d(z2)) < E(d(xy)); notice that d(xy) and d(z2) are d(sigma) orbitals in this case. The Co(II) ion is in a low-spin d7 state with the singly occupied d(z2) orbital. The asphericity in electron density at Co and Cl nuclei is nicely demonstrated by the Laplacian of electron density. The envelope plot of the isovalue Laplacian surface around the nucleus gives the exact shape of such asphericity. The isovalue Laplacian surfaces of these two nuclei show significantly different VSCC character in both experimental and theoretical results.     

Electron (charge) density studies of cellulose models

Introductory material first describes electron density approaches and demonstrates visualization of electron lone pairs and bonding as concentrations of electron density. Then it focuses on the application of Bader’s Quantum Theory of Atoms-in-Molecules (AIM) to cellulose models. The purpose of the work is to identify the various interactions that stabilize cellulose structure. AIM analysis aids study of non-covalent interactions, especially those for which geometric criteria are not well established. The models were in the form of pairs of cellotriose molecules, methylated at the O1 and O4 ends. Based on the unit cell of cellulose Iβ, there were corner–corner, and center–center pairs that correspond to (200) sheets, and corner–center pairings that corresponded to (1–10) and (110) stacks. AIM analysis (or charge-density topology analysis) was applied before and after minimization in vacuum and in continuum solvation. Besides the conventional O–H···O hydrogen bonds, all of which were known from geometric criteria, C–H···O hydrogen bonds (some previously reported), and some O···O and H···H interactions were found. Non-covalent bonds in the (200) sheets were maintained in all calculations with the exception of a weak, bifurcated O6–H···O2′′ bond that was not found in the corner–corner pair model and did not survive minimization. Nor did the O6···O4 interactions on the reducing ends of the triosides. Pairs of molecules along the (110) plane had an equal number (12) of non-covalent bonds compared to the pairs along the (1–10) plane, but the AIM parameters indicated the bonds between the pairs in the (110) plane were weaker. Intra-molecular O–H···O hydrogen bonds survived in these minimized pairs, but the relative chain alignments usually did not.     

Use of the 13C-NMR chemical shift/charge density linear relationship for recognition and ranking of chemical structures

A novel scheme for computer-aided recognition of chemical structures based on the ¹³C-NMR chemical shift/charge density linear relationship is described. The spectral signals are uniquely assigned to the carbon atoms of each of the compared structures via an automatic assignment procedure. On the basis of this assignment, a factor reflecting the agreement between the spectrum and the molecular structure is defined. This factor has different values for different structures, similar values for similar structures, equal values for equivalent (isomorphic in the graph-theoretical sense) structures, and the lowest value for the structure best corresponding to the ¹³C-NMR spectrum. The potential of this approach for retrieval and ranking of chemical structures is discussed with examples.     

Iminonitroso ene reactions: experimental studies on reactivity, regioselectivity, and enantioselectivity

Ene reactions of iminonitroso agents with olefins were investigated in both solution and solid phase. Reactions afforded allyl hydroxylamine products in up to 99% yield and with high regioselectivity. A Cu(I)-mediated enantioselective nitroso ene reaction gave an ene product with up to 40% ee.     

Additivity rules using similarity models for chemical reactivity: calculation and interpretation of electrofugality and nucleofugality

A recently proposed, multi-parameter correlation: log k (25 degrees C)=s(f) (Ef + Nf), where Ef is electrofugality and Nf is nucleofugality, for the substituent and solvent effects on the rate constants for solvolyses of benzhydryl and substituted benzhydryl substrates, is re-evaluated. A new formula (Ef=log k (RCl/EtOH/25 degrees C) -1.87), where RCl/EtOH refers to ethanolysis of chlorides, reproduces published values of Ef satisfactorily, avoids multi-parameter optimisations and provides additional values of Ef. From the formula for Ef, it is shown that the term (sfxEf) is compatible with the Hammett-Brown (rho+sigma+) equation for substituent effects. However, the previously published values of N(f) do not accurately account for solvent and leaving group effects (e.g. nucleofuge Cl or X), even for benzhydryl solvolyses; alternatively, if the more exact, two-parameter term, (sfxNf) is used, calculated effects are less accurate. A new formula (Nf=6.14 + log k(BX/any solvent/25 degrees C)), where BX refers to solvolysis of the parent benzhydryl as electrofuge, defines improved Nf values for benzhydryl substrates. The new formulae for Ef and Nf are consistent with an assumption that sf=1.00(,) and so improved correlations for benzhydryl substrates can be obtained from the additive formula: log k(RX/any solvent/25 degrees C)=(Ef + Nf). Possible extensions of this approach are also discussed.     

Structure-property relationships in push-pull amino/cyanovinyl end-capped oligothiophenes: quantum chemical and experimental studies

A series of push-pull chromophores built around thiophene-based pi-conjugating spacers and bearing various types of amino donors and cyanovinyl acceptors have been analyzed by means of UV-vis-NIR, IR, and Raman spectroscopic measurements in the solid state as well as in solution. The intramolecular charge transfer (ICT) of these pi-conjugated systems has also been tested by analyzing the ability of the solute molecules to undergo shifts in their fluorescence emission maxima with increasing solvent polarity. These push-pull oligomers also display an attractive electrochemical behavior since they generate stable species both upon oxidation and reduction. Oxidation mainly involves changes in the electron-rich aminooligothienyl half-part of the molecule and leads to the formation of stable cations. On the other hand, reduction to radical anions and dianions is mainly cyanovinyl-centered but also affects the pi-conjugated electron relay. Density functional theory (DFT) calculations have been carried out to help the assignment of the most relevant electronic and vibrational features and to derive useful information about the molecular structure of these NLO-phores.     

Insight into the chemical bonding and electrostatic potential: A charge density study on a quinazoline derivative

2,3-Trimethylene-3,4-dihydroquinazoline shares the heterocyclic core with natural compounds and synthetic drugs. The hydrochloride of the compound forms excellent dihydrate crystals which have allowed us to collect high-resolution X-ray diffraction data and obtain the experimental charge density. The solid may be understood as built up from pairs of heterocyclic cations and chloride anions; a direct hydrogen bond links the halide to the formally cationic pyrimidine NH group. The hydrate water molecules interact with the anions, forming an infinite chain along the crystallographic a axis between the stacks of the heterocyclic cations. Based on the experimental charge density, a dipole moment of 16.1 Debye is calculated for a pair of the hydrogen-bonded quinazolinium cation and the chloride anion in the extended crystal structure.     

Variable temperature neutron diffraction and X-ray charge density studies of tetraacetylethane

Single crystal neutron diffraction data have been collected on a sample of enolized 3,4-diacetyl-2,5-hexanedione (tetraacetylethane, TAE) at five temperatures between 20 and 298 K to characterize the temperature-dependent behavior of the short, strong, intramolecular hydrogen bond. Upon decreasing the temperature from 298 K to 20 K, the O2-H1 distance decreases from 1.171(11) to 1.081(2) A and the O1...H1 distance increases from 1.327(10) to 1.416(6) A. The convergence of the C-O bond lengths from inequivalent distances at low temperature to identical values (1.285(4) A) at 298 K is consistent with a resonance-assisted hydrogen bond. However, a rigid bond analysis indicates that the structure at 298 K is disordered. The disorder vanishes at lower temperatures. Short intermolecular C-H...O contacts may be responsible for the ordering at low temperature. The intramolecular O...O distance (2.432 +/- 0.006 A) does not change with temperature. X-ray data at 20 K were measured to analyze the charge density and to gain additional insight into the nature of the strong hydrogen bond. Quantum mechanical calculations demonstrate that periodic boundary conditions provide significant enhancement over gas phase models in that superior agreement with the experimental structure is achieved when applying periodicity. One-dimensional potential energy calculations followed by quantum treatment of the proton reproduce the location of the proton nearer to the O2 site reasonably well, although they overestimate the O-H distance at low temperatures. The choice of the single-point energy calculation strategy for the proton potential is justified by the fact that the proton is preferably located nearer to O2 rather than being equally distant to O1 and O2 or evenly distributed (disordered) between them.     

Aqueous solutions that model the cytosol: studies on polarity, chemical reactivity and enzyme kinetics

Concentrated solutions of a series of organic compounds have been prepared and the effects of these solutes on the properties of the solvent system assessed as a function of their concentration and nature. Polarity, as measured by Reichardt's E(T)(30) probe, exhibits a linear variation with both solute and water concentration for simple solutes. Non-linear behaviour was also observed and is associated with preferential solvation or binding of the E(T)(30) probe molecule by the added solute. The observed trends in polarity are mirrored in the effects of these solutes on chemical reactivity and enzyme kinetics. Environmental effects on the kinetics of hydrolysis of 4-nitrophenyl dichloroacetate, the hydronium-ion catalysed hydrolysis of 2-(4-nitrophenoxy)-tetrahydropyran, the acyl transfer reaction between 4-nitrophenyl acetate and TRIS, the Diels-Alder reaction between 1,4-naphthoquinone and cyclopentadiene and the trypsin-catalysed hydrolysis of 4-nitrophenyl acetate are reported and discussed in terms of the properties of the solutes and the mechanistic requirements of these reactions. Linear correlations were observed between the logarithms of the rate constants for the acetal hydrolysis, acyl transfer and Diels-Alder reactions with water concentration. Since the latter varies linearly with E(T)(30), this indicates a linear free energy relationship between solution polarity and chemical reactivity.