A Chemically Meaningful Measure of Electron Localization

Electron localization and delocalization are commonly invoked in the day-to-day rationalization of chemistry. This work addresses the challenges of quantifying this elusive concept in a chemically useful manner. A general principle, requiring the simultaneous quantification of (1) a limited physical volume (classical criterion) and (2) same-spin loneliness (quantum criterion), is introduced. It is demonstrated how, by beginning with the Electron Localization Function (ELF) scalar field, one can choose to discard all points in space where the same-spin loneliness is lower than a certain value. Such a partitioning approach ensures that both criteria for quantifying localization (1 and 2) are simultaneously met. The most chemically instructive results arise when the dividing boundary condition is set by the local behavior of a homogeneous electron gas. The High Electron Localization domain Population (HELP) is introduced and applied for quantifying the localization of individual domains within molecules, as well as a measure of total electron localization in atoms and molecules. Several striking agreements with chemical intuition, experimental measurable quantities, and quantum chemical constructs are demonstrated along with understandable differences. Studies of diatomic molecules agree with current ideas on chemical bonding. The size-dependence and magnitude of localization in linear hydrocarbons is studied and compared to cyclic systems, such as benzene. The proposed methodology offers a straightforward measure for direct and quantitative comparisons between atoms, molecules, and extended condensed matter

Toward an Experimental Quantum Chemistry: Exploring a New Energy Partitioning

Following the work of L. C. Allen, this work begins by relating the central chemical concept of electronegativity with the average binding energy of electrons in a system. The average electron binding energy, χ̅, is in principle accessible from experiment, through photoelectron and X-ray spectroscopy. It can also be estimated theoretically. χ̅ has a rigorous and understandable connection to the total energy. That connection defines a new kind of energy decomposition scheme. The changing total energy in a reaction has three primary contributions to it: the average electron binding energy, the nuclear–nuclear repulsion, and multielectron interactions. This partitioning allows one to gain insight into the predominant factors behind a particular energetic preference. We can conclude whether an energy change in a transformation is favored or resisted by collective changes to the binding energy of electrons, the movement of nuclei, or multielectron interactions. For example, in the classical formation of H₂ from atoms, orbital interactions dominate nearly canceling nuclear–nuclear repulsion and two-electron interactions. While in electron attachment to an H atom, the multielectron interactions drive the reaction. Looking at the balance of average electron binding energy, multielectron, and nuclear–nuclear contributions one can judge when more traditional electronegativity arguments can be justifiably invoked in the rationalization of a particular chemical event

Unprecedented Conformational Variability in Main Group Inorganic Chemistry: the Tetraazidoarsenite and -Antimonite Salts A⁺[M(N₃)₄]⁻ (A = NMe₄, PPh₄, (Ph₃P)₂N; M = As, Sb), Five Similar Salts, Five Different Anion Structures

A unique example for conformational variability in inorganic main group chemistry has been discovered. The arrangement of the azido ligands in the pseudotrigonal bipyramidal [As­(N₃)₄]⁻ and [Sb­(N₃)₄]⁻ anions theoretically can give rise to seven different conformers which have identical MN₄ skeletons but different azido ligand arrangements and very similar energies. We have now synthesized and structurally characterized five of these conformers by subtle variations in the nature of the counterion. Whereas conformational variability is common in organic chemistry, it is rare in inorganic main group chemistry and is usually limited to two. To our best knowledge, the experimental observation of five distinct single conformers for the same type of anion is unprecedented. Theoretical calculations at the M06-2X/cc-pwCVTZ-PP level for all seven possible basic conformers show that (1) the energy differences between the five experimentally observed conformers are about 1 kcal/mol or less, and (2) the free monomeric anions are the energetically favored species in the gas phase and also for [As­(N₃)₄]⁻ in the solid state, whereas for [Sb­(N₃)₄]⁻ associated anions are energetically favored in the solid state and possibly in solutions. Raman spectroscopy shows that in the azide antisymmetric stretching region, the solid-state spectra are distinct for the different conformers, and permits their identification. The spectra of solutions are solvent dependent and differ from those of the solids indicating the presence of rapidly exchanging equilibria of different conformers. The only compound for which a solid with a single well-ordered conformer could not be isolated was [N­(CH₃)₄]­[As­(N₃)₄] which formed a viscous, room-temperature ionic liquid. Its Raman spectrum was identical to that of its CH₃CN solution indicating the presence of an equilibrium of multiple conformers

Ternary Gold Hydrides: Routes to Stable and Potentially Superconducting Compounds

In a search for gold hydrides, an initial discouraging result of no theoretical stability in any binary AuH_<i>n</i> at <i>P</i> < 300 GPa was overcome by introducing alkali atoms as reductants. A set of AAuH₂ compounds, A = Li, Na, K, Rb, and Cs, is examined; of these, certain K, Rb, and Cs compounds are predicted to be thermodynamically stable. All contain AuH₂^– molecular units and are semiconducting at <i>P</i> = 1 atm, and some form metallic and superconducting symmetrically bonded AuHAu sheets under compression. To induce metallicity by bringing the Au atoms closer together under ambient conditions, we examined alkaline earth ion substitution for two A, i.e., materials of composition AE­(AuH₂)₂. For AE = Ba and Sr, the materials are already marginally metallic at <i>P</i> = 1 atm and the combination of high and low phonon frequencies and good electron–phonon coupling leads to reasonably high calculated superconducting transition temperatures for these materials

A Density Functional Theory for the Average Electron Energy

A formally exact density functional theory (DFT) determination of the average electron energy is presented. Our theory, which is based on a different accounting of energy functional terms, partially solves one well-known downside of conventional Kohn–Sham (KS) DFT: that electronic energies have but tenuous connections to physical quantities. Calculated average electron energies are close to experimental ionization potentials (IPs) in one-electron systems, demonstrating a surprisingly small effect of self-interaction and other exchange-correlation errors in established DFT methods. Remarkable agreement with ab initio quantum mechanical calculations of multielectron systems is demonstrated using several flavors of DFT, and we argue for the use of the average electron energy as a design criterion for density functional approximations

A Density Functional Theory for the Average Electron Energy

A formally exact density functional theory (DFT) determination of the average electron energy is presented. Our theory, which is based on a different accounting of energy functional terms, partially solves one well-known downside of conventional Kohn–Sham (KS) DFT: that electronic energies have but tenuous connections to physical quantities. Calculated average electron energies are close to experimental ionization potentials (IPs) in one-electron systems, demonstrating a surprisingly small effect of self-interaction and other exchange-correlation errors in established DFT methods. Remarkable agreement with ab initio quantum mechanical calculations of multielectron systems is demonstrated using several flavors of DFT, and we argue for the use of the average electron energy as a design criterion for density functional approximations

Regioselective Acetylation of Diols and Polyols by Acetate Catalysis: Mechanism and Application

We propose a principle for H-bonding activation in acylation of hydroxyl groups, where the acylation is activated by the formation of hydrogen bonds between hydroxyl groups and anions. With the guidance of this principle, we demonstrate a method for the selective acylation of carbohydrates. By this method, diols and polyols are regioselectively acetylated in high yields under mild conditions using catalytic amounts of acetate. In comparison to other methods involving reagents such as organotin, organoboron, organosilicon, organobase, and metal salts, this method is more environmentally friendly, convenient, and efficient and is also associated with higher regioselectivity. We have performed a thorough quantum chemical study to decipher the mechanism, which suggests that acetate first forms a dual H-bond complex with a diol, which enables subsequent monoacylation by acetic anhydride under mild conditions. The regioselectivity appears to originate from the inherent structure of the diols and polyols and their specific interactions with the coordinating acetate catalyst

H‑Bonding Activation in Highly Regioselective Acetylation of Diols

H-bonding activation in the regioselective acetylation of vicinal and 1,3-diols is presented. Herein, the acetylation of the hydroxyl group with acetic anhydride can be activated by the formation of H-bonds between the hydroxyl group and anions. The reaction exhibits high regioselectivity when a catalytic amount of tetrabutylammonium acetate is employed. Mechanistic studies indicated that acetate anion forms dual H-bonding complexes with the diol, which facilitates the subsequent regioselective monoacetylation

Syntheses of Diphenylaminodiazidophosphane and Diphenylaminofluoroazidophosphane

Diphenylaminodiazidophosphane (C₆H₅)₂NP­(N₃)₂ was synthesized from the corresponding dihalides (C₆H₅)₂NPX₂ (X = F, Cl) and (CH₃)₃SiN₃, and was characterized by vibrational and multinuclear NMR spectroscopy. The intermediate compound (C₆H₅)₂NPF­(N₃) was also observed by NMR spectroscopy in solution. Some physical properties and reactions of all these compounds are discussed

Binary Group 15 Polyazides. Structural Characterization of [Bi(N₃)₄]⁻, [Bi(N₃)₅]^2–, [bipy·Bi(N₃)₅]^2–, [Bi(N₃)₆]^3–, bipy·As(N₃)₃, bipy·Sb(N₃)₃, and [(bipy)₂·Bi(N₃)₃]₂ and on the Lone Pair Activation of Valence Electrons

The binary group 15 polyazides As(N₃)₃, Sb(N₃)₃, and Bi(N₃)₃ were stabilized by either anion or donor−acceptor adduct formation. Crystal structures are reported for [Bi(N₃)₄]^–, [Bi(N₃)₅]^2–, [bipy·Bi(N₃)₅]^2–, [Bi(N₃)₆]^3–, bipy·As(N₃)₃, bipy·Sb(N₃)₃, and [(bipy)₂·Bi(N₃)₃]₂. The lone valence electron pair on the central atom of these pnictogen(+III) compounds can be either sterically active or inactive. The [Bi(N₃)₅]^2– anion possesses a sterically active lone pair and a monomeric pseudo-octahedral structure with a coordination number of 6, whereas its 2,2′-bipyridine adduct exhibits a pseudo-monocapped trigonal prismatic structure with CN 7 and a sterically inactive lone pair. Because of the high oxidizing power of Bi(+V), reactions aimed at Bi(N₃)₅ and [Bi(N₃)₆]^– resulted in the reduction to bismuth(+III) compounds by [N₃]^–. The powder X-ray diffraction pattern of Bi(N₃)₃ was recorded at 298 K and is distinct from that calculated for Sb(N₃)₃ from its single-crystal data at 223 K. The [(bipy)₂·Bi(N₃)₃]₂ adduct is dimeric and derived from two BiN₈ square antiprisms sharing an edge consisting of two μ^1,1-bridging N₃ ligands and with bismuth having CN 8 and a sterically inactive lone pair. The novel bipy·As(N₃)₃ and bipy·Sb(N₃)₃ adducts are monomeric and isostructural and contain a sterically active lone pair on their central atom and a CN of 6. A systematic quantum chemical analysis of the structures of these polyazides suggests that the M06-2X density functional is well suited for the prediction of the steric activity of lone pairs in main-group chemistry. Furthermore, it was found that the solid-state structures can strongly differ from those of the free gas-phase species or those in solutions and that lone pairs that are sterically inactive in a chemical surrounding can become activated in the free isolated species