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. Since the SOMOs are here of different symmetry, the wave function is free from ionic valence-bond component, and spin decontamination of the unrestricted DFT solutions and wave function calculations at the CASSCF-plus-second-order-perturbation level confirm the expected pure diradical character of such molecules. In contrast to disjoint diradicals, the SOMOs of present systems have large amplitudes on neighbor atoms, and we propose to name them entangled pure diradicals, further providing some prescription rules for their design. Additional calculations point out the qualitative contrast between these molecules and the related diradicaloids.

Phenalenyl Radical: Smallest Polycyclic Odd Alternant Hydrocarbon Present in the Graphene Sheet

Phenalenyl, a zigzag-edged odd alternant hydrocarbon unit can be found in the graphene nanosheet. Hückel molecular orbital calculations indicate the presence of a nonbonding molecular orbital (NBMO), which originates from the linear combination of atomic orbitals (LCAO) arising from 13 carbon atoms of the phenalenyl molecule. Three redox states (cationic, neutral radical, and anionic) of the phenalenyl-based molecules were attributed to the presence of this NBMO. The cationic state can undergo two consecutive reductions to result in neutral radical and anionic states, stepwise, respectively. The phenalenyl-based radicals were found as crucial building blocks and attracted the attention of various research fields such as organic synthesis, material science, computation, and device physics. From 2012 onward, a strategy was devised using the cationic state of phenalenyl-based molecules and in situ generated phenalenyl radicals, which created a new domain of catalysis. The in situ generated phenalenyl radicals were utilized for the single electron transfer (SET) process resulting in redox catalysis. This emerging range of applications rejuvenates the more than six decades-old phenalenyl chemistry. This review captures such developments ranging from fundamental understanding to multidirectional applications of phenalenyl-based radicals.

Conformational control over π-conjugated electron pairing in 1D organic polymers

During the past decades π-conjugated bi-radicals have attracted increasing attention, due to the existence of two close-in-energy resonant electronic configurations with very distinct characteristics: the open-shell bi-radical and the closed-shell quinoidal. The chemical design of the bi-radical structure has been shown to be very effective to shift the balance towards one, or the other, electronic distribution. Some reports have experimentally studied the analogous 1D oligomers and polymers, however, only the open-shell multi-radical configuration has been detected, and it is yet not very clear which structural and chemical parameters are relevant in such extended systems. In this work, via first principles quantum chemical simulations, we study a series of π-conjugated 1D polymers based on triarylmethyl radicals with different chemical functionalization. We find that dihedral angles of the aryl rings connecting the radical centres are the key conformational parameter determining the electronic balance. This provides a simple recipe to use chemical functionalization of aryl rings as a tool to shift the system towards either the electron paired or unpaired configurations. Additionally, we find such conformational control is also effective under the effect of thermal fluctuations, which highlights its potential technological applicability.

Multi- and single-reference methods for the analysis of multi-state peroxidation of enolates

In spite of being spin-forbidden, some enzymes are capable of catalyzing the incorporation of O₂(Σg-3) to organic substrates without needing any cofactor. It has been established that the process followed by these enzymes starts with the deprotonation of the substrate forming an enolate. In a second stage, the peroxidation of the enolate formation occurs, a process in which the system changes its spin multiplicity from a triplet state to a singlet state. In this article, we study the addition of O₂ to enolates using state-of-the-art multi-reference and single-reference methods. Our results confirm that intersystem crossing is promoted by stabilization of the singlet state along the reaction path. When multi-reference methods are used, large active spaces are required, and in this situation, semistochastic heat-bath configuration interaction emerges as a powerful method to study these multi-configurational systems and is in good agreement with PNO-LCCSD(T) when the system is well-represented by a single-configuration.

Controlling pairing of π-conjugated electrons in 2D covalent organic radical frameworks via in-plane strain

Controlling the electronic states of molecules is a fundamental challenge for future sub-nanoscale device technologies. π-conjugated bi-radicals are very attractive systems in this respect as they possess two energetically close, but optically and magnetically distinct, electronic states: the open-shell antiferromagnetic/paramagnetic and the closed-shell quinoidal diamagnetic states. While it has been shown that it is possible to statically induce one electronic ground state or the other by chemical design, the external dynamical control of these states in a rapid and reproducible manner still awaits experimental realization. Here, via quantum chemical calculations, we demonstrate that in-plane uniaxial strain of 2D covalently linked arrays of radical units leads to smooth and reversible conformational changes at the molecular scale that, in turn, induce robust transitions between the two kinds of electronic distributions. Our results pave a general route towards the external control, and thus technological exploitation, of molecular-scale electronic states in organic 2D materials.

Controlling the electronic states of molecules is a fundamental challenge for future sub-nanoscale device technologies but the external dynamical control of these states still awaits experimental realization. Here, via quantum chemical calculations, the authors demonstrate that in-plane uniaxial strain of 2D covalently linked arrays of radical units induces controlled pairing of π-conjugated electrons in a reversible way.

The effect of spin polarization on the electron transport of molecular wires with diradical character

Some of the most promising materials for application in molecular electronics and spintronics are based on diradical chains. Herein, the proposed relation between increasing conductance with length and diradical character is revisited using ab initio methods that account for the static electron correlation effects. Electron transmission was previously obtained from restricted single determinant wavefuntions or tight-binding approximations, which are unable to account for static correlation. Broken Symmetry Unrestricted Kohn-Sham Density Functional Theory (BS-UKS-DFT) in combination with electron transport analysis based on electron deformation orbitals (EDOs) reflects an exponential decay of the electrical conductance with length. Also, other important effects such as quantum interference are correctly accounted for, leading to a decrease of the conductance as the diradical character increases. As a proof-of-concept, the electrical conductance obtained from BS-UKS-DFT and CASSCF(2,2) wavefunctions were compared in diradical graphene strips in the frame of the pseudo-π approach, obtaining very similar results.

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) as a Simple yet Accurate Method for Diradicals and Diradicaloids

Due to their multiconfigurational nature featuring strong electron correlation, accurate description of diradicals and diradicaloids is a challenge for quantum chemical methods. The recently developed mixed-reference spin-flip (MRSF)-TDDFT method is capable of describing the multiconfigurational electronic states of these systems while avoiding the spin-contamination pitfalls of SF-TDDFT. Here, we apply MRSF-TDDFT to study the adiabatic singlet-triplet (ST) gaps in a series of well-known diradicals and diradicaloids. On average, MRSF displays a very high prediction accuracy of the adiabatic ST gaps with the mean absolute error (MAE) amounting to 0.14 eV. In addition, MRSF is capable of accurately describing the effect of the Jahn-Teller distortion occurring in the trimethylenemethane diradical, the violation of the Hund rule in a series of the didehydrotoluene diradicals, and the potential energy surfaces of the didehydrobenzene (benzyne) diradicals. A convenient criterion for distinguishing diradicals and diradicaloids is suggested on the basis of the easily obtainable quantities. In all of these cases, which are difficult for the conventional methods of density functional theory (DFT), MRSF shows results consistent with the experiment and the high-level ab initio computations. Hence, the present study documents the reliability and accuracy of MRSF and lays out the guidelines for its application to strongly correlated molecular systems.

Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces

Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way and, therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.

Exchange Rules for Diradical π-Conjugated Hydrocarbons

A variety of planar π-conjugated hydrocarbons such as heptauthrene, Clar's goblet and, recently synthesized, triangulene have two electrons occupying two degenerate molecular orbitals. The resulting spin of the interacting ground state is often correctly anticipated as S = 1, extending the application of Hund's rules to these systems, but this is not correct in some instances. Here we provide a set of rules to correctly predict the existence of zero mode states as well as the spin multiplicity of both the ground state and the low-lying excited states, together with their open- or closed-shell nature. This is accomplished using a combination of analytical arguments and configuration interaction calculations with a Hubbard model, both backed by quantum chemistry methods with a larger Gaussian basis set. Our results go beyond the well established Lieb's theorem and Ovchinnikov's rule, as we address the multiplicity and the open-/closed-shell nature of both ground and excited states.

Structural diradical character

A reliable first-principles description of singlet diradical character is essential for predicting nonlinear optical and magnetic properties of molecules. As diradical and closed-shell electronic structures differ in their distribution of single, double, triple, and aromatic bonds, modeling electronic diradical character requires accurate bond-length patterns, in addition to accurate absolute bond lengths. We therefore introduce structural diradical character, which we suggest as an additional measure for comparing first-principles calculations with experimental data. We employ this measure to identify suitable exchange-correlation functionals for predicting the bond length patterns and electronic diradical character of a biscobaltocene with the potential for photoswitchable nonlinear optical activity. Out of four popular approximate exchange-correlation functionals with different exact-exchange admixtures (BP86, TPSS, B3LYP, TPSSh), the two hybrid functionals TPSSh and B3LYP perform best for diradical bond length patterns, with TPSSh being best for the organometallic validation systems and B3LYP for the organic ones (for which the D3 dispersion correction was included). Still, none of the functionals is suitable for correctly describing relative bond lengths across the range of molecules studied, so that none can be recommended for predictive studies of (potential) diradicals without reservation. © 2018 Wiley Periodicals, Inc.

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. Various structurally-close neutral alternatives such as oxiranones or carbene-acid forms are also considered. In the linear polyenic chain family, there is stark contrast between 4N + 1 and 4N - 1 lengths, with ensuing substantial consequences for stabilities and structures. Amino substitutions can favor mesoionic arrangements through their cation-stabilizing π-donor properties, further supported by possible strong intramolecular hydrogen bonds, but they can also contribute to weaken their kinetic stability through the existence of stable neutral imino alternatives. All in all, mesoionics including tropylium, phenalene, or 4N + 1 odd polyene frames as cationic parts could be reasonable targets.

Electronic properties of the coronene series from thermally-assisted-occupation density functional theory

To fully utilize the great potential of graphene in electronics, a comprehensive understanding of the electronic properties of finite-size graphene flakes is essential. While the coronene series with n fused benzene rings at each side (designated as n-coronenes) are possible structures for opening a band gap in graphene, their electronic properties are not yet fully understood. Nevertheless, because of their radical character, it remains very difficult to reliably predict the electronic properties of the larger n-coronenes with conventional computational approaches. In order to circumvent this, the various electronic properties of n-coronenes (n = 2-11) are investigated using thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys., 2012, 136, 154104], a very efficient electronic structure method for studying nanoscale systems with strong static correlation effects. The ground states of the larger n-coronenes are shown to be polyradical singlets, where the active orbitals are mainly localized at the zigzag edges.

Investigating the importance of edge-structure in the loss of H/H2 of PAH cations: the case of dibenzopyrene isomers

We present a detailed study of the main dehydrogenation processes of two dibenzopyrene cation (C₂₄H₁₄⁺) isomers, namely dibenzo(a,e)pyrene (AE⁺) and dibenzo(a,l)pyrene (AL⁺). First, action spectroscopy under VUV photons was performed using synchrotron radiation in the 8-20 eV range. We observed lower dissociation thresholds for the non-planar molecule (AL⁺) than for the planar one (AE⁺) for the main dissociation pathways: H and 2H/H₂ loss. In order to rationalize the experimental results, dissociation paths were investigated by means of density functional theory calculations. In the case of H loss, which is the dominant channel at the lowest energies, the observed difference between the two isomers can be explained by the presence in AL⁺ of two C-H bonds with considerably lower adiabatic dissociation energies. In both isomers the 2H/H₂ loss channels are observed only at about 1 eV higher than H loss. We suggest that this is due to the propensity of bay H atoms to easily form H₂. In addition, in the case of AL⁺, we cannot exclude a competition between 2H and H₂ channels. In particular, the formation of a stable dissociation product with a five-membered ring could account for the low energy sequential loss of 2 hydrogens. This work shows the potential role of non-compact PAHs containing bay regions in the production of H₂ in space.

Existence of multi-radical and closed-shell semiconducting states in post-graphene organic Dirac materials

Post-graphene organic Dirac (PGOD) materials are ordered two-dimensional networks of triply bonded sp 2 carbon nodes spaced by π-conjugated linkers. PGOD materials are natural chemical extensions of graphene that promise to have an enhanced range of properties and applications. Experimentally realised molecules based on two PGOD nodes exhibit a bi-stable closed-shell/multi-radical character that can be understood through competing Lewis resonance forms. Here, following the same rationale, we predict that similar states should be accessible in PGOD materials, which we confirm using accurate density functional theory calculations. Although for graphene the semimetallic state is always dominant, for PGOD materials this state becomes marginally meta-stable relative to open-shell multi-radical and/or closed-shell states that are stabilised through symmetry breaking, in line with analogous molecular systems. These latter states are semiconducting, increasing the potential use of PGOD materials as highly tuneable platforms for future organic nano-electronics and spintronics.

Spreading out spin density in polyphenalenyl radicals

Properly-designed monoradicals built from polycondensed phenalene units can enforce flattening of spin distributions.

A new architecture for high spin organics based on Baird's rule of 4n electron triplet aromatics

This work reports triplet aromatic high spin ground states of cyclopentadienyl cation polyads as alternative to high spin polyradicals or polycarbenes.

Calix[n]arene-based polyradicals: enhancing ferromagnetism by avoiding edge effects

The absence of edges in circular structures derived from 1,3-arylmethyl polyradical results in realistic molecules showing largely stabilized high-spin ground states.

Role of Kekulé and Non-Kekulé Structures in the Radical Character of Alternant Polycyclic Aromatic Hydrocarbons: A TAO-DFT Study

We investigate the role of Kekulé and non-Kekulé structures in the radical character of alternant polycyclic aromatic hydrocarbons (PAHs) using thermally-assisted-occupation density functional theory (TAO-DFT), an efficient electronic structure method for the study of large ground-state systems with strong static correlation effects. Our results reveal that the studies of Kekulé and non-Kekulé structures qualitatively describe the radical character of alternant PAHs, which could be useful when electronic structure calculations are infeasible due to the expensive computational cost. In addition, our results support previous findings on the increase in radical character with increasing system size. For alternant PAHs with the same number of aromatic rings, the geometrical arrangements of aromatic rings are responsible for their radical character.

Redox-Active Tetraruthenium Macrocycles Built from 1,4-Divinylphenylene-Bridged Diruthenium Complexes

Metallamacrocylic tetraruthenium complexes were generated by treatment of 1,4-divinylphenylene-bridged diruthenium complexes with functionalized 1,3-benzene dicarboxylic acids and characterized by HR ESI-MS and multinuclear NMR spectroscopy. Every divinylphenylene diruthenium subunit is oxidized in two consecutive one-electron steps with half-wave potential splittings in the range of 250 to 330 mV. Additional, smaller redox-splittings between the +/2+ and 0/+ and the 3+/4+ and 2+/3+ redox processes, corresponding to the first and the second oxidations of every divinylphenylene diruthenium entity, are due to electrostatic effects. The lack of electronic coupling through bond or through space is explained by the nodal properties of the relevant molecular orbitals and the lateral side-by-side arrangement of the divinylphenylene linkers. The polyelectrochromic behavior of the divinylphenylene diruthenium precursors is retained and even amplified in these metallamacrocyclic structures. EPR studies down to T=4 K indicate that the dications 1-H(2+) and 1-OBu(2+) are paramagnetic. The dications and the tetracation of macrocycle 3-H display intense (dications) or weak (3-H(4+) ) EPR signals. Quantum chemical calculations indicate that the four most stable conformers of the macrocycles are largely devoid of strain. Bond parameters, energies as well as charge and spin density distributions of model macrocycle 5-H(Me) were calculated for the different charge and spin states.

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.

Electronic Structures of Anti-Ferromagnetic Tetraradicals: Ab Initio and Semi-Empirical Studies

The energy relationships and electronic structures of the lowest-lying spin states in several anti-ferromagnetic tetraradical model systems are studied with high-level ab initio and semi-empirical methods. The Full-CI method (FCI), the complete active space second-order perturbation theory (CASPT2), and the n-electron valence state perturbation theory (NEVPT2) are employed to obtain reference results. By comparing the energy relationships predicted from the Heisenberg and Hubbard models with ab initio benchmarks, the accuracy of the widely used Heisenberg model for anti-ferromagnetic spin-coupling in low-spin polyradicals is cautiously tested in this work. It is found that the strength of electron correlation (|U/t|) concerning anti-ferromagnetically coupled radical centers could range widely from strong to moderate correlation regimes and could become another degree of freedom besides the spin multiplicity. Accordingly, the Heisenberg-type model works well in the regime of strong correlation, which reproduces well the energy relationships along with the wave functions of all the spin states. In moderately spin-correlated tetraradicals, the results of the prototype Heisenberg model deviate severely from those of multi-reference electron correlation ab initio methods, while the extended Heisenberg model, containing four-body terms, can introduce reasonable corrections and maintains its accuracy in this condition. In the weak correlation regime, both the prototype Heisenberg model and its extended forms containing higher-order correction terms will encounter difficulties. Meanwhile, the Hubbard model shows balanced accuracy from strong to weak correlation cases and can reproduce qualitatively correct electronic structures, which makes it more suitable for the study of anti-ferromagnetic coupling in polyradical systems.

Spin decontamination of broken-symmetry density functional theory calculations: deeper insight and new formulations

This work proposes rigorous and physically based spin decontamination factors for broken-symmetry treatments of diradicals.