One-electron Delocalization Research Articles

4f/5d Hybridization Induced Single-Electron Delocalization in an Azide-Bridged Dicerium Complex.

Dilanthanide complexes with one-electron delocalization are important targets for understanding the specific 4f/5d-bonding feature in lanthanide chemistry. Here, we report an isolable azide-bridged dicerium complex 3 [{(TrapenTMS)Ce}2(μ-N3)]• [Trapen = tris (2-aminobenzyl)amine; TMS = SiMe3], which is synthesized by the reaction of tripodal ligand-supported (TrapenTMS)CeIVCl complex 2 with NaN3. The structure and bonding nature of 3 are fully characterized by X-ray crystal diffraction analysis, electron paramagnetic resonance (EPR), magnetic measurement, cyclic voltammetry, X-ray absorption spectroscopy, and quantum-theoretical studies. Complex 3 presents a trans-bent central Ce-N3-Ce unit with a single electron of two mixed-valent Ce atoms. The unique low-temperature (2 K) anisotropic EPR signals [g = 1.135, 2.003, and 3.034] of 3 indicate that its spin density is distributed on the central Ce-N3-Ce unit with marked electron delocalization. Quantum chemical analyses show strong 4f/5d orbital mixing in the singly occupied molecular orbital of 3, which allows for the unpaired electron to extend throughout the cerium-azide-cerium unit via a multicentered one-electron (Ce-N3-Ce) interaction. This work extends the family of mixed-valent dilanthanide complexes and provides a paradigm for understanding the bonding motif of ligand-bridged dilanthanide complexes.

Invariant description of the behavior of electrons in donor–acceptor molecules

The sharing of electrons in the donor–acceptor complexes BH 3NH 3, BCl 3NH 3, AlH 3NH 3, AlCl 3NH 3, and GaCl 3NH 3 is investigated by the one-electron delocalization indices. Three prevailing aspects of the analysis are: (1) the nature of the compounds based upon the average number of electrons in atomic basins, (2) the quantitative extent of electron delocalization based upon the basin–basin indices, and (3) the sharing of electrons between the groups constituting the molecules. Because the analysis is rooted in the first-order density matrix, no reference to orbitals has been invoked. This study provides new insight into the electronic basis of the DA interactions.

Increased-Valence Structures for Qualitative Valence-Bond Representations of Electronic Structure for Electron-Rich Molecules

Whereas familiar Lewis-type valence-bond structures for singlet-spin systems involve electron-pair bonds and lone-pairs of electrons, increased-valence structures involve one-electron bonds and fractional electron-pair bonds. An increased-valence structure may be easily derived from a familiar Lewis structure via one-electron delocalizations of lone-pair electrons into two-centre bonding molecular orbitals. The increased-valence structure is equivalent to resonance between several Lewis structures, including the familiar Lewis structure from which it was derived, and therefore it is more stable than the latter structure. Some of the properties of increased-valence structures, and their associated Pauling three-electron bonds as diatomic components of these structures, are discussed, with specific reference to N2O and the FeIIO2 linkages of oxyhaemoglobin. Applications to numerous other systems that involve 4-electron 3-centre, 6-electron 4-centre, and 6-electron 5-centre bonding units are presented. Brief consideration is also given to a speculative Bohr approach to electronic structure.

Increased-Valence Structures for Qualitative Valence-Bond Representations of Electronic Structure for Electron-Rich Molecules

Whereas familiar Lewis-type valence-bond structures for singlet-spin systems involve electron-pair bonds and lone-pairs of electrons, increased-valence structures involve one-electron bonds and fractional electron-pair bonds. An increased-valence structure may be easily derived from a familiar Lewis structure via one-electron delocalizations of lone-pair electrons into two-centre bonding molecular orbitals. The increased-valence structure is equivalent to resonance between several Lewis structures, including the familiar Lewis structure from which it was derived, and therefore it is more stable than the latter structure. Some of the properties of increased-valence structures, and their associated Pauling three-electron bonds as diatomic components of these structures, are discussed, with specific reference to N2O and the FeIIO2 linkages of oxyhaemoglobin. Applications to numerous other systems that involve 4-electron 3-centre, 6-electron 4-centre, and 6-electron 5-centre bonding units are presented. Brief consideration is also given to a speculative Bohr approach to electronic structure.

Four-Electron Three-Center Bonding: One-Electron and Concerted Two-Electron Delocalizations into Bonding and Antibonding Molecular Orbitals

For a four-electron three-center bonding unit that arises from the interaction between an atomic electron donor Y and a diatomic electron acceptor A:B, it is deduced that some concerted delocalization of the two lone-pair electrons of Y into the antibonding molecular orbital of A:B is equivalent to the concerted delocalization of these electrons into a Y−A bonding molecular orbital. For neutral intermolecular electron donors and acceptors that involve a four-electron three-center bonding unit, second-order perturbation theory is used to deduce a condition for which concerted delocalization of the two Y electrons into the Y−A bonding molecular orbital may generate a higher energy than does a one-electron delocalization into this molecular orbital. The theory is illustrated via the results of STO-6G valence-bond studies for the hydrogen-bonding interactions that arise for an idealized HF dimer.

Statistics of energy spectra of a strongly disordered system of interacting electrons

The statistics of many-particle energy levels of a finite two-dimensional system of interacting electrons is studied numerically. It is shown that the statistics of these levels undergoes a Poisson-to-Wigner crossover as the strength of the disorder is decreased. This crossover occurs at a similar strength of disorder to the one-electron delocalization crossover in a finite two-dimensional system and develops almost simultaneously at all energies. We interpret this crossover in terms of delocalization in the space of occupation numbers of strongly bound and compact electron-hole pairs (excitons).

Increased-valence structures and some valence bond representations for reaction mechanisms

The paper presents a summary and extension of some of the recently published work on increased-valence theory. For four-electron three-centre bonding units, increased-valence structures 2 and 4 may be derived from the Lewis structures 1 and 3 by means of the one-electron delocalizations that are indicated in the latter structures. ▪ The three bonding electrons in each of the structures 2 and 4 occupy non-orthogonal two-centre bonding molecular orbitals, and the A atom contributes only one atomic orbital to the bonding scheme. It is demonstrated that the A-atom valence is able to exceed unity in each of these structures when the valence is calculated according to a Wiberg-type procedure. Increased-valence structures are used to illustrate how electronic reorganization may proceed for radical transfer, thermal decomposition and cycloaddition reactions that involve the 1,3-dipolar molecule N 2O, and gas-phase S N2 reactions. A relationship is established between increased-valence and approximate molecular orbital descriptions of hydrogen bonding.

Increased-valence structures and hypervalent molecules

Hypervalent molecules may involve the use of increased-valence structures to provide valence bond descriptions of their electronic structure. For electron-rich molecules with four electrons distributed among three overlapping (nuclear-centered) atomic orbitals, the increased-valence structures are Y(BOND)A·B and Y·A——B. Each structure involves a fractional electron-pair bond and a one-electron bond. It is deduced that the Armstrong-Perkins-Stewart valence of the A atom is able to exceed unity in each of these structures when the three bonding electrons occupy nonorthogonal localized molecular orbitals. It is also shown that increased valence for the A atom does not occur when the four electrons occupy localized molecular orbitals to give the valence-bond structure Y—A—B with three overlapping atomic orbitals, and the same number of orbital variational parameters as occurs in the wave functions for either of the increased-valence structures. The results of ab initio valence bond calculations with minimal basis sets are reported for H−3l, CH−5, HF−2, F−3, CIF3, and FF3, and the resulting wave functions for resonance between six canonical Lewis structures are related to those for resonance between the two increased-valence structures. The use of the latter structures to indicate how electronic reorganization proceeds via one-electron delocalizations for SN2 reactions is redescribed, and an elementary argument is presented to deduce that this class of reactions cannot involve the delocalization of a pair of electrons in concert from the nucleophile. Increased-valence wave functions are used to deduce an expression for the avoided crossing for the transition state of the identity SN2 reaction. © 1996 John Wiley & Sons, Inc.

Examples of valence bond representations for the decompositions of N 3NO and N 3NO 2

Valence bond representations are provided for the decompositions of N 3NO and N 3NO 2. Standard Lewis and increased-valence structures are used for this purpose. The electronic reorganizations that are associated with the use of these two types of structures involve electron-pair delocalizations and one-electron delocalizations, respectively, which afford polar and non-polar representations for the decompositions.

Valence bond representations for S N2 reactions: one-electron delocalizations and electron-pair delocalizations

A comparison is made between the one-electron delocalization representation ▪ and the electron-pair delocalization representation ▪ for the generalized S N2 reaction N − + RX → NR + X −. It is concluded that although the one-electron delocalization representation is less familiar, its wavefunction is easier to manipulate.

Aspects of hypercoordination and one-electron delocalizations via increased-valence structures

Consideration is given to increased-valence descriptions of bonding for four-electron three-centre and three-electron three-centre bonding units, with special attention given to hypercoordinated AH 5 − and AH 5 systems with D 3h symmetry. Increased-valence structures of types I–IV ▪ accommodate the nearest-neighbour bonding electrons in localized molecular orbitals (MOs). When the A-atom orbital in I and II includes some s as well as pa character in the formation of the one-electron bonds, it is shown that each of these structures is equivalent to resonance between one of the Lewis structures V or VI and four structures in which an electron is transferred ▪ from the H − of the Lewis structure into one of the four A-H antibonding σ MOs that are vacant in this structure. Using increased-valence structures which are similar to I–IV, master equations are provided for S N2 and radical substitution reactions via one-electron delocalizations or shifts, as in ▪ for the latter type of reaction. The associated state correlation diagrams and valence bond (VB) representations for these reactions are compared with those provided by Shaik and Press. Valence bond representations are also provided for (a) electron conduction in an n-type semi-conductor and the YBa 2Cu 3O 7 superconductor, and (b) hydrogen bonding in the N 20 + HF complex.

ChemInform Abstract: Chemical Bonding Across the Periodic Table

Interdisciplinary barriers separating the “organic”, “inorganic” and “solid state” subdisciplines of chemistry exist because there is no conceptual apparatus which clearly delineates how the rules of bonding depend on the identity of the atoms comprising a molecule and how they change as we move from the domain to another. We present a theory which is based on a fusion of MO and VB concepts which enables one to do the following: Dissect a molecule into fragments, apportion the valence electrons in the fragment orbitals, and then make “bonds” connecting the fragments. In this way two key elements of the bonding problem become transparent: (a) The interplay between fragment excitation (investment) and “bond” making (return) in engendering net stabilization (profit) of the system. (b) The mechanism of bond-making. Nonmetals bind primarily by spin-pairing plus one-electron delocalization due to overlap while metals bind mainly by two-electron delocalization in which overlap is assisted by an overlap-independent mechamism of bonding.

Valence bond representations for S N2 reactions

Valence bond representations for gas-phase S N2 reactions are developed, with one-electron de-localizations used to help convert the reactants into the products. Particular attention is given to the increased-valence representation, ▪ in which an electron is transferred either from an atomic orbital of the nucleophile N − into an NR bonding molecular orbital, or from an RX bonding molecular orbital into an atomic orbital of the leaving group X. It is shown that if each bonding electron occupies a separate spatial molecular orbital in the increased-valence structures ( ·N·R: X) − and ( N: R··X) −, then resonance between these structures corresponds to th wavefunction of lowest energy at each stage along the reaction coordinate. Relationships that exist between the increased-valence formulation, and that proposed by Shaik and Pross, are described.