In Search of Entangled Singlet Pure Diradicals.

Recent work has documented conjugate polycyclic hydrocarbons presenting unusual properties: accepting full on-bond electron pairing, they could be considered as closed-shell architectures, but their ground-state wave function is actually a pure diradical singlet, free of any ionic component, in contrast to diradicaloids. These so-called molecules also differ from disjoint diradicals, which do not accept on-bond electron pairing, in that their singly occupied molecular orbitals (SOMOs) are spatially entangled rather than disjoint. The present work first extends the study to a broad series of architectures exhibiting the same properties, namely: they present two degenerate SOMOs in the topological Hückel Hamiltonian, and their pure diradical wave functions lead to symmetry-keeping geometries.

Mapping the Slow Stabilization of End States with Length along a Laterally Extended Graphene Nanoribbon.

With a lateral bisnaphtho-extended chemical structure, finite 7-13 carbon atom wide armchair graphene nanoribbons (7-13-aGNRs) were on-surface synthesized. For all lengths up to = 7 monomer units, low-temperature ultrahigh vacuum scanning tunneling spectroscopy and spatial d/d maps were recorded at each captured tunneling resonance. The degeneracy of the two central electronic end states (ESs) occurs in a slowly decaying regime with converging toward zero for = 6 long 7-13-aGNR (12 bonded anthracenes), while it is = 2 (4 bonded anthracenes) for seven carbon atoms wide armchair GNRs (7-aGNRs).

On Entangled Singlet Pure Diradicals.

This work addresses a class of conjugated hydrocarbons that are expected to be singlet diradicals according to the topological Hückel Hamiltonian while possibly satisfying full on-bond electron pairing. These systems possess two degenerate singly occupied molecular orbitals (SOMOs), but aromaticity brought by properly positioned six-membered rings does prevent Jahn-Teller distortions. Density functional theory (DFT) calculations performed on two emblematic examples confirm the strong bond-length alternation in the closed-shell solutions and the clear spatial symmetry in the open-shell spin-unrestricted determinants, the latter solution always being found to have significantly lower energy.

Difficulty of the evaluation of the barrier height of an open-shell transition state between closed shell minima: The case of small C rings.

C cyclacenes exhibit strong bond-alternation in their equilibrium geometry. In the two equivalent geometries, the system keeps an essentially closed-shell character. The two energy minima are separated by a transition state suppressing the bond-alternation, where the wave function is strongly diradical.

Consistent spin decontamination of broken-symmetry calculations of diradicals.

Broken-symmetry calculations of diradicals exploit the mean-field energies of determinants that are not eigenfunctions of the Ŝ operator, the mean value of which is close to 1 for the m = 0 solution. This spin contamination must be corrected. Two different contributions affect ⟨Ŝ⟩, namely, the mixing between neutral and ionic valence bond components, the so-called kinetic exchange, which decreases ⟨Ŝ⟩, and the spin polarization of the supposedly closed shell orbitals, which increases ⟨Ŝ⟩.

Improved evaluation of spin-polarization energy contributions using broken-symmetry calculations.

Spin-polarization effects may play an important role in free radicals and in the magnetic coupling between radical centers. Starting from restricted open-shell calculations, i.e.

Spin polarization as an electronic cooperative effect.

Taking as an example the simple CH radical, this work demonstrates the cooperative character of the spin-polarization phenomenon of the closed-shell core in free radicals. Spin polarization of CH σ bonds is not additive here, as spin polarization of one bond enhances that of the next bond. This cooperativity is demonstrated by a series of configuration interaction calculations converging to the full valence limit and is rationalized by analytic developments.

Dodecacene Generated on Surface: Reopening of the Energy Gap.

The acene series represents a model system to investigate the intriguing electronic properties of extended π-electron structures in the one-dimensional limit, which are important for applications in electronics and spintronics and for the fundamental understanding of electronic transport. Here, we present the on-surface generation of the longest acene obtained so far: dodecacene. Scanning tunneling spectroscopy gives access to the energy position and spatial distribution of its electronic states on the Au(111) surface.

Oxidative addition of carbon dioxide into mesoionics.

This work examines the prospect of making stable mesoionic compounds of the type mesomeric betaine R+-CO2- from direct oxidative additions of carbon dioxide to suitably-delocalized singlet carbene moieties, with bold objectives of carbon sequestration and overall energy storage. A set of possible candidates for such mesoionic compounds is theoretically explored through DFT calculations, inspecting coupling paths, thermodynamic and kinetic stabilities, and geometric and electronic structural features. Among others, the addressed cationic parts include aromatic rings in their broader sense, phenalene systems, and odd linear polyenic chains.

Qualitative Views on the Polyradical Character of Long Acenes.

Spin-symmetry breaking appears in the DFT treatment of polyacenes, beyond a certain length, the critical length depending on the exchange-correlation potential. This phenomenon may be attributed to an instability with respect to HOMO-LUMO mixing, which suggests a diradical character of long acenes. However, the increase of the S operator with acene length questions this simple view.

Electronic Resonances and Gap Stabilization of Higher Acenes on a Gold Surface.

On-surface synthesis provides a powerful method for the generation of long acene molecules, making possible the detailed investigation of the electronic properties of single higher acenes on a surface. By means of scanning tunneling microscopy and spectroscopy combined with theoretical considerations, we discuss the polyradical character of the ground state of higher acenes as a function of the number of linearly fused benzene rings. We present energy and spatial mapping of the tunneling resonances of hexacene, heptacene, and decacene, and discuss the role of molecular orbitals in the observed tunneling conductance maps.

Predicting the Open-Shell Character of Polycyclic Hydrocarbons in Terms of Clar Sextets.

Rather unexpected spin-symmetry breakings of mean-field single determinants occur in singlet ground states of many families of alternating conjugated hydrocarbons which accept a full on-bond electron pairing. These symmetry breakings may be seen as an indication of the existence of unpaired electrons. Although qualitative, the concept of disjoint electronic sextets proposed by Clar (hereafter called CS) is at least a heuristic tool for predicting various features of fused polybenzenic hydrocarbons.

Spreading out spin density in polyphenalenyl radicals.

As suggested by simple topological arguments, monoradical arrangements of properly-oriented polycondensed phenalenyl units can produce highly-delocalized spin distributions. This work examines under which geometrical conditions and to which extent these flat distributions take place. UDFT calculations performed on various instances gathering up to 19 such fused phenalene units confirm the spin-density spreading over entire conjugated skeletons.

Can a Topological Approach Predict Spin-Symmetry Breaking in Conjugated Hydrocarbons?

The closed-shell mean-field single determinants of large alternant hydrocarbons are frequently unstable with respect to a possible spin-symmetry breaking which produces different orbitals for the α and β electrons, either in Hartree-Fock or in Kohn-Sham DFT calculations. The present work shows that one may easily predict whether such a symmetry breaking will take place from the elementary topological Hückel Hamiltonian which introduces a simple hopping integral t. The demonstration makes use of the simplest representation of the bielectronic repulsion, namely, the Hubbard bielectronic operator, reduced to an on-site repulsion U, and takes benefit of the mirror theorem.

Communication: Proper use of broken-symmetry calculations in antiferromagnetic polyradicals.

The present comment formulates some recommendations regarding the use of broken-symmetry Unrestricted Density Functional Theory (UDFT) solutions in those polyradical architectures predicted to be of ground-state singlet character according to Ovchinnikov's rule. It proposes a procedure to identify the number of open shells, to reach the relevant Ms = 0 solution, and to estimate the low-energy spectrum of the states which keeps this number of open shells.

Towards Magnetic Carbo-meric Molecular Materials.

Numerous studies have underlined the putative diradical character of π-conjugated molecules that can be described by closed-shell Lewis structures, for instance, p-dimethylene p-n phenylenes, or long polyacenes. In the latter compounds, the only way to save the aromaticity of the six-membered rings is to give up the Lewis electron pairing in the singlet biradical ground state. The present work considers the possibility of doing the same by using the basic C2 units of carbo-meric architectures.

Kekulé versus Lewis: when aromaticity prevents electron pairing and imposes polyradical character.

Some conjugated alternant hydrocarbons, of singlet ground state according to Ovchinnikov's rule, may exhibit strong polyradical character, despite admitting complete pairing of electrons in bond orbitals between adjacent atoms. Typical organizations of this kind are encountered in polycyclic frames supporting two or more extracyclic methylene groups. Lewis bond pairing would require quinonization of six-membered rings, whereas safeguarding aromaticity proves sufficient to impose ground-state open-shell character, that is, the existence of unpaired electrons, providing the number of benzene rings to be quinonized is larger than two.

When a single hole aligns several spins: double exchange in organic systems.

The double exchange is a well-known and technically important phenomenon in solid state physics. Ionizing a system composed of two antiferromagnetically coupled high-spin units, the ground state of which is a singlet state, may actually produce a high-spin ground state. This work illustrates the possible occurrence of such a phenomenon in organic chemistry.

In Search of Organic Compounds Presenting a Double Exchange Phenomenon.

The objective of this paper is to design a consistent series of organic molecules that may present a double exchange mechanism and study their low energy spectrum using spin unrestricted Density Functional Theory. For this purpose, organic tetra-methylene methane units having an S = 1 spin ground state and diamagnetic organic bridges are taken as building blocks for constructing molecules having two or more magnetic units. When biunit systems are ionized, the ground state of the resulting molecular ions may be either a quartet, if the spectrum is ruled by a double exchange mechanism, or a doublet, if it obeys the logic of a monoelectronic picture.

A recipe for geometry optimization of diradicalar singlet states from broken-symmetry calculations.

The equilibrium geometries of the singlet and triplet states of diradicals may be somewhat different, which may have an influence on their magnetic properties. The single-determinantal methods, such as Hartree-Fock or Kohn-Sham density functional theory, in general rely on broken-symmetry solutions to approach the singlet-state energy and geometry. An approximate spin decontamination is rather easy for the energy of this state but is rarely performed for its geometry optimization.

The -BF-NH- link as a peptide-bond surrogate.

A new peptidomimetic is proposed, resulting from substitution of the C═O carbonyl group by a B-F bond at the amide linkage. The effects of such chemical alteration are theoretically investigated through comparative calculations on dimethyl-fluoro-aminoborane H(3)C-BF-NH-CH(3) and N-methylacetamide H(3)C-CO-NH-CH(3), the simplest model of a peptide linkage. While little difference is found regarding size, electronic structure, and plaque rigidity, substantial distinctions are, however, observed between the polarities and association energies of the two compounds, with a B-F···H-N hydrogen bond estimated to be about one-third as strong as the natural C═O···H-N one.

Designing magnetic organic lattices from high-spin polycyclic units.

This work addresses the conception of purely organic magnetic materials by properly bridging high-spin polycyclic hydrocarbons A and B, through covalent ligands L. The strategy varies two degrees of freedom that govern the magnetic character of the A-L--B sequence, namely, the bridge response to spin polarization and the relative signs of spin density on carbon atoms to which the bridge is attached. Topological prescriptions based on Ovchinnikov's rule are proposed to predict ground-state spin multiplicities of various A-L-B sets.

Theoretical design of high-spin polycyclic hydrocarbons.

High-spin organic structures can be obtained from fused polycyclic hydrocarbons, by converting selected peripheral HC(sp(2)) sites into H(2)C(sp(3)) ones, guided by Ovchinnikov's rule. Theoretical investigation is performed on a few examples of such systems, involving three to twelve fused rings, and maintaining threefold symmetry. Unrestricted DFT (UDFT) calculations, including geometry optimizations, confirm the high-spin multiplicity of the ground state.