Using the general-purpose reactivity indicator: challenging examples.

We elucidate the regioselectivity of nucleophilic attack on substituted benzenesulfonates, quinolines, and pyridines using a general-purpose reactivity indicator (GPRI) for electrophiles. We observe that the GPRI is most accurate when the incoming nucleophile resembles a point charge. We further observe that the GPRI often chooses reactive "dead ends" as the most reactive sites as well as sterically hindered reactive sites. This means that care must be taken to remove sites that are inherently unreactive. Generally, among sites where reactions actually occur, the GPRI identifies the sites in the molecule that lead to the kinetically favored product(s). Furthermore, the GPRI can discern which sites react with hard reagents and which sites react with soft reagents. Because it is currently impossible to use the mathematical framework of conceptual DFT to identify sterically inaccessible sites and reactive dead ends, the GPRI is primarily useful as an interpretative, not a predictive, tool.

On the intrinsic reactivity index for electrophilicity/nucleophilicity responses.

We present a critical discussion related to the recent definition of the intrinsic reactivity index, IRI, (Tetrahedron Lett. 2013, 54, 339-342; Tetrahedron 2013, 69, 4247-4258) formulated to describe both, electrophilicity (charge acceptance) and nucleophilicity (charge donation) reactivities. We here stress that such an IRI model, based on the quantity µ/η, should be properly related to theoretical approximations associated to the change in the global electronic energy of a given chemical system under interaction with a suitable electron bath (Gazquez JL et al. J Phys Chem A 2007, 111, 1966-1970). Further, the limitations of the IRI model are presented by emphasizing that the intrinsic relative scales of electrophilicity and nucleophilicity within a second-order perturbation approach must account for the further stabilization of the two interacting species (Chamorro E et al. J Phys Chem A 2013, 117, 2636-2643).

Efficient evaluation of analytic Fukui functions.

An efficient method for the analytic evaluation of Fukui functions is proposed. Working equations are derived and numerical results are used to validate the method on medium size set of molecules. In addition to the obvious advantages of analytic differentiation, the proposed method is efficient enough to be considered a practical alternative to the finite difference formulation used routinely. The reliability of the approximations used here is demonstrated and discussed. Problems found in other methods for prediction of electrophilic centers are corrected automatically when using the new method.

New insights in the photochromic spiro-dihydroindolizine/betaine-system.

We have revisited the photochromic spiro-dihydroindolizine/betaine (DHI/B) system applying state-of-the-art density functional theory (DFT) calculations in combination with stationary and time-resolved absorption measurements. DHI/B-systems are becoming increasingly important as potential molecular machines, molecular switches, and photoswitchable electron-acceptors. The knowledge of the exact mechanisms of ring opening and closure, as well as of the geometries of DHI and betaine can provide critical information that will enable the design of better molecular machines and optical switches. The first surprising result concerns the electronic structure of the betaines, which is quite different than commonly assumed. The photochemical ring opening of DHI's to betaines is a conrotatory 1,5 electrocyclic reaction, whereas the thermal ring-closing occurs in the disrotatory mode. According to our results, the electrocyclic back reaction of the betaines to the DHI is NOT rate determining, as previously thought, but instead the kinetics are dictated by the cis-trans-isomerization of the betaine.

Tautomeric forms of azolide anions: vertical electron detachment energies and Dyson orbitals.

Several decouplings of the electron propagator, including the relatively new P3+ approximation for the self-energy, have been used to calculate vertical electron detachment energies of tautomeric forms of closed-shell, pentagonal, aromatic anions in which ring carbons without bonds to hydrogens appear. This study extends previous work in which the most stable forms of anionic, five-member rings with one to five nitrogens were considered. Whereas the lowest electron detachment energies sometimes are assigned by Koopmans's theorem results to pi orbital vacancies, electron propagator calculations always obtain sigma orbital vacancies for the ground states of the doublet radicals. Higher electron detachment energies that correspond to excited doublets with pi vacancies also are presented. The predicted transition energies are in good agreement with low-intensity peaks in recent anion photoelectron spectra that have been assigned to less stable, tautomeric forms of these anions.

Removing electrons can increase the electron density: a computational study of negative Fukui functions.

Ab initio and density-functional theory calculations for a family of substituted acetylenes show that removing electrons from these molecules causes the electron density along the C-C bond to increase. This result contradicts the predictions of simple frontier molecular orbital theory, but it is easily explained using the nucleophilic Fukui function-provided that one is willing to allow for the Fukui function to be negative. Negative Fukui functions emerge as key indicators of redox-induced electron rearrangements, where oxidation of an entire molecule (acetylene) leads to reduction of a specific region of the molecule (along the bond axis, between the carbon atoms). Remarkably, further oxidization of these substituted acetylenes (one can remove as many as four electrons!) causes the electron density along the C-C bond to increase even more. This work provides substantial evidence that the molecular Fukui function is sometimes negative and reveals that this is due to orbital relaxation.

OH(3) (-) and O(2)H(5) (-) double Rydberg anions: predictions and comparisons with NH(4) (-) and N(2)H(7) (-).

A low barrier in the reaction pathway between the double Rydberg isomer of OH(3) (-) and a hydride-water complex indicates that the former species is more difficult to isolate and characterize through anion photoelectron spectroscopy than the well known double Rydberg anion (DRA), tetrahedral NH(4) (-). Electron propagator calculations of vertical electron detachment energies (VEDEs) and isosurface plots of the electron localization function disclose that the transition state's electronic structure more closely resembles that of the DRA than that of the hydride-water complex. Possible stabilization of the OH(3) (-) DRA through hydrogen bonding or ion-dipole interactions is examined through calculations on O(2)H(5) (-) species. Three O(2)H(5) (-) minima with H(-)(H(2)O)(2), hydrogen-bridged, and DRA-molecule structures resemble previously discovered N(2)H(7) (-) species and have well separated VEDEs that may be observable in anion photoelectron spectra.

Further links between the maximum hardness principle and the hard/soft acid/base principle: insights from hard/soft exchange reactions.

Ayers, Parr, and Pearson recently showed that insight into the hard/soft acid/base (HSAB) principle could be obtained by analyzing the energy of reactions in hard/soft exchange reactions, i.e., reactions in which a soft acid replaces a hard acid or a soft base replaces a hard base [J. Chem. Phys., 2006, 124, 194107]. We show, in accord with the maximum hardness principle, that the hardness increases for favorable hard/soft exchange reactions and decreases when the HSAB principle indicates that hard/soft exchange reactions are unfavorable. This extends the previous work of the authors, which treated only the "double hard/soft exchange" reaction [P. K. Chattaraj and P. W. Ayers, J. Chem. Phys., 2005, 123, 086101]. We also discuss two different approaches to computing the hardness of molecules from the hardness of the composing fragments, and explain how the results differ. In the present context, it seems that the arithmetic mean of fragment softnesses is the preferable definition.

Conceptual Density-Functional Theory for General Chemical Reactions, Including Those That Are Neither Charge- nor Frontier-Orbital-Controlled. 1. Theory and Derivation of a General-Purpose Reactivity Indicator.

A new general-purpose reactivity indicator is derived. Unlike existing indicators, this indicator can describe the reactivity of molecules that lie between the electrostatic (or charge) control and electron-transfer (or frontier-orbital) control paradigms. Depending on the parameters in the indicator, it describes electrostatic control (where the electrostatic potential is the appropriate indicator), electron-transfer control (where the Fukui function's potential is the appropriate indicator), and intermediate cases (where linear combinations of the electrostatic potential and the Fukui function's potential are appropriate indicators). Our analysis gives some insight into the origins of the local hard/soft-acid/base principle. The "minimum Fukui function" rule for hard reagents also emerges naturally from our analysis: if (1) a reaction is strongly electrostatically controlled and (2) there are two sites that are equally favorable from an electrostatic standpoint, then the most reactive of the electrostatically equivalent sites is the site with the smallest Fukui function. An analogous electrostatic potential rule for soft reagents is also introduced: if (1) a reaction is strongly electron-transfer-controlled and (2) there are two sites where the Fukui function's potential are equivalent, then the most reactive of the Fukui-equivalent sites will be the one with greatest electrostatic potential (for electrophilic attack on a nucleophile) or smallest electrostatic potential (for nucleophilic attack on an electrophile).

Conceptual Density-Functional Theory for General Chemical Reactions, Including Those That Are Neither Charge- nor Frontier-Orbital-Controlled. 2. Application to Molecules Where Frontier Molecular Orbital Theory Fails.

This paper examines cases where frontier molecular orbital theory is known to fail, specifically electrophilic aromatic substitution reactions on isoquinoline and borazarophenanthrenes. While we are able to explain the experimental regioselectivity preferences for isoquinoline without too much difficulty, describing the regioselectivity of the borazarophenanthrenes is much more challenging. This is attributed to the fact that these molecules lie between the electrostatic (or charge) control and electron-transfer (or frontier-orbital) control paradigms. These molecules can, however, be described using the general-purpose reactivity indicator introduced in the first paper of this series. The variation of the general-purpose reactivity indicator with respect to the parameters is readily summed up using what we term "reactivity transition tables", which provide a compact summary of which products form under different reaction conditions. For the otherwise problematic molecules considered here, the new reactivity indicator performs better than either the Fukui function or the electrostatic potential alone.

Electronic structure analysis and electron detachment energies of polynitrogen pentagonal aromatic anions.

Various decouplings of the electron propagator have been employed to provide theoretical comparison to experimental electron detachment energies for the pyrrolide, imidazolide, and pyrazolide anions. Predictions for isoelectronic anions in which CH groups are replaced by N atoms also are reported. The ab initio electron propagator results agree closely with experimental values, and the associated Dyson orbitals provide a detailed catalog of bonding changes as the number and positions of N atoms vary within the set of pentagonal aromatic anions.

Ground and excited states of the Rydberg radical H3O: electron propagator and quantum defect analysis.

Vertical excitation energies of the Rydberg radical H(3)O are inferred from ab initio electron propagator calculations on the electron affinities of H(3)O(+). The adiabatic ionization energy of H(3)O is evaluated with coupled-cluster calculations. These predictions provide optimal parameters for the molecular-adapted quantum defect orbital method, which is used to determine oscillator strengths. Given that the experimental spectrum of H(3)O does not seem to be available, comparisons with previous calculations are discussed. A simple model Hamiltonian, suitable for the study of bound states with arbitrarily high energies is generated by these means.