Pathway to Polyradicals: A Planar and Fully π-Conjugated Organic Tetraradical(oid).

In this work, we provide a general strategy to stabilize the ground state of polyradical(oid)s and make higher spin states thermally accessible. As a proof of concept, we propose to merge two planar fully π-conjugated diradical(oid)s to obtain a planar and cross-conjugated tetraradical(oid). Using multireference quantum chemistry methods, we show that the designed tetraradical(oid) is stabilized by aromaticity and delozalization in the π-system and has six thermally accessible spin states within 1.72 kcal/mol. Analysis of the electronic structure of these six states of the tetraradical(oid) shows that its frontier π-system consists of two weakly interacting subsystems: aromatic cycles and four unpaired electrons. Conjugation between unpaired electrons, which favors closed-shell structures, is mitigated by delocalization and the aromaticity of the bridging groups, leading to the synergistic cross-coupling between two diradical(oid) subunits to stabilize the tetraradical(oid) electronic structure.

An algorithm to find the optimal oriented external electrostatic field for annihilating a reaction barrier in a polarizable molecular system.

The use of oriented external electric fields (OEEFs) to promote and control chemical reactivity has motivated many theoretical and computational studies in the last decade to model the action of OEEFs on a molecular system and its effects on chemical processes. Given a reaction, a central goal in this research area is to predict the optimal OEEF (oOEEF) required to annihilate the reaction energy barrier with the smallest possible field strength. Here, we present a model rooted in catastrophe and optimum control theories that allows us to find the oOEEF for a given reaction valley in the potential energy surface (PES). In this model, the effective (or perturbed) PES of a polarizable molecular system is constructed by adding to the original, non-perturbed, PES a term accounting for the interaction of the OEEF with the intrinsic electric dipole and polarizability of the molecular system, so called the polarizable molecular electric dipole (PMED) model. We demonstrate that the oOEEF can be established by locating a point in the original PES with unique topological properties: the optimal barrier breakdown or bond-breaking point (oBBP). The essential feature of the oBBP structure is the fact that this point maintains its topological properties for all the applied OEEFs, also for the unperturbed PES, thus becoming much more relevant than the commonly used minima and transition state structures. The PMED model proposed here has been implemented in an open access package and is shown to successfully predict the oOEEF for two processes: an isomerization reaction of a cumulene derivative and the Huisgen cycloaddition reaction.

How does thickness affect magnetic coupling in Ti-based MXenes.

The magnetic nature of Ti2C, Ti3C2, and Ti4C3 MXenes is determined from periodic calculations within density functional theory and using the generalized gradient approximation based PBE functional, the PBE0 and HSE06 hybrids, and the on-site Hubbard corrected PBE+U one, in all cases using a very tight numerical setup. The results show that all functionals consistently predict a magnetic ground state for all MXenes, with spin densities mainly located at the Ti surface atoms. The analysis of solutions corresponding to different spin orderings consistently show that all functionals predict an antiferromagnetic conducting ground state with the two ferromagnetic outer (surface) Ti layers being antiferromagnetically coupled. A physically meaningful spin model is proposed, consistent with the analysis of the chemical bond, with closed shell, diamagnetic, Ti2+ like ions in inner layers and surface paramagnetic Ti+ like centers with one unpaired electron per magnetic center. From a Heisenberg spin model, the relevant isotropic magnetic coupling constants are extracted from an appropriate mapping of total energy differences per formula unit to the expected energy values of the spin Hamiltonian. While the numerical values of the magnetic coupling constants largely depend on the used functional, the nearest neighbor intralayer coupling is found to be always ferromagnetic, and constitutes the dominant interaction, although two other non-negligible interlayer antiferromagnetic terms are involved, implying that the spin description cannot be reduced to NN interaction only. The influence of the MXene thickness is noticeable for the dominant ferromagnetic interaction, increasing its value with the MXene width. However, the interlayer interactions are essentially due to the covalency effects observed in all metallic solutions which, as expected, decay with distance. Within the PBE+U approach, a U value of 5 eV is found to closely simulate the results from hybrid functionals for Ti2C and less accurately for Ti3C2 and Ti4C3.

Controlling the Diradical Character of Thiele Like Compounds.

Organic diradicals play an important role in many fields of chemistry, biochemistry, and materials science. In this work, by means of high-level theoretical calculations, we have investigated the effect of representative chemical substituents in p-quinodimethane (pQDM) and Thiele's hydrocarbons with respect to the singlet-triplet energy gap, a feature characterizing their diradical character. We show how the nature of the substituents has a very important effect in controlling the singlet-triplet energy gap so that several compounds show diradical features in their ground electronic state. Importantly, steric effects appear to play the most determinant role for pQDM analogues, with minor effects of the substituents in the central ring. For Thiele like compounds, we found that electron-withdrawing groups in the central ring favor the quinoidal form with a low or almost null diradical character, whereas electron-donating group substituents favor the aromatic-diradical form if the electron donation does not exceed 6-π electrons. In this case, if there is an excess of electron donation, the diradical character is reduced. The electronic spectrum of these compounds is also calculated, and we predict that the most intense bands occur in the visible region, although in some cases characteristic electronic transition in the near-IR region may appear.

Buckletronics: how compression-induced buckling affects the mechanical and electronic properties of sp2-based two-dimensional materials.

We explore the mechanical and electronic response of sp2-based two-dimensional materials under in-plane compression employing first principles density functional theory-based calculations. Taking two carbon-based graphynes (α-graphyne and γ-graphyne) as example systems, we show that the structures of both two-dimensional materials are susceptible to out-of-plane buckling, which emerges for modest in-plane biaxial compression (1.5-2%). Out-of-plane buckling is found to be more energetically stable than in-plane scaling/distortion and significantly lowers the in-plane stiffness of both graphenes. The buckling also gives rise to in-plane auxetic behaviour in both two-dimensional materials. Under compression, the induced in-plane distortions and out-of-plane buckling also lead to modulations of the electronic band gap. Our work highlights the possibility of using in-plane compression to induce out-of-plane buckling in, otherwise planar, sp2-based two-dimensional materials (e.g. graphynes, graphdiynes). We suggest that controllable compression-induced buckling in planar two-dimensional materials (as opposed to two-dimensional materials, which are buckled due to sp3 hybridization) could provide a route to a new 'buckletronics' approach for tuning the mechanical and electronic properties of sp2-based systems. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Theoretical Analysis of Magnetic Coupling in the Ti2C Bare MXene.

The nature of the electronic ground state of the Ti2C MXene is unambiguously determined by making use of density functional theory-based calculations including hybrid functionals together with a stringent computational setup providing numerically converged results up to 1 meV. All the explored density functionals (i.e., PBE, PBE0, and HSE06) consistently predict that the Ti2C MXene has a magnetic ground state corresponding to antiferromagnetic (AFM)-coupled ferromagnetic (FM) layers. A spin model, with one unpaired electron per Ti center, consistent with the nature of the chemical bond emerging from the calculations, is presented in which the relevant magnetic coupling constants are extracted from total energy differences of the involved magnetic solutions using an appropriate mapping approach. The use of different density functionals enables us to define a realistic range for the magnitude of each of the magnetic coupling constants. The intralayer FM interaction is the dominant term, but the other two AFM interlayer couplings are noticeable and cannot be neglected. Thus, the spin model cannot be reduced to include nearest-neighbor interactions only. The Néel temperature is roughly estimated to be in the 220 ± 30 K, suggesting that this material can be used in practical applications in spintronics and related fields.

Emergent Spin Frustration in Neutral Mixed-Valence 2D Conjugated Polymers: A Potential Quantum Materials Platform.

Two-dimensional conjugated polymers (2DCPs)─organic 2D materials composed of arrays of carbon sp2 centers connected by π-conjugated linkers─are attracting increasing attention due to their potential applications in device technologies. This interest stems from the ability of 2DCPs to host a range of correlated electronic and magnetic states (e.g., Mott insulators). Substitution of all carbon sp2 centers in 2DCPs by nitrogen or boron results in diamagnetic insulating states. Partial substitution of C sp2 centers by B or N atoms has not yet been considered for extended 2DCPs but has been extensively studied in the analogous neutral mixed-valence molecular systems. Here, we employ accurate first-principles calculations to predict the electronic and magnetic properties of a new class of hexagonally connected neutral mixed-valence 2DCPs in which every other C sp2 nodal center is substituted by either a N or B atom. We show that these neutral mixed-valence 2DCPs significantly energetically favor a state with emergent superexchange-mediated antiferromagnetic (AFM) interactions between C-based spin-1/2 centers on a triangular sublattice. These AFM interactions are surprisingly strong and comparable to those in the parent compounds of cuprate superconductors. The rigid and covalently linked symmetric triangular AFM lattice in these materials thus provides a highly promising and robust basis for 2D spin frustration. As such, extended mixed-valence 2DCPs are a highly attractive platform for the future bottom-up realization of a new class of all-organic quantum materials, which could host exotic correlated electronic states (e.g., unusual magnetic ordering, quantum spin liquids).

Highly Adiabatic Time-Optimal Quantum Driving at Low Energy Cost.

Time-efficient control schemes for manipulating quantum systems are of great importance in quantum technologies, where environmental forces rapidly degrade the quality of pure states over time. In this Letter, we formulate an approach to time-optimal control that circumvents the boundary-value problem that plagues the quantum brachistochrone equation at the expense of relaxing the form of the control Hamiltonian. In this setting, a coupled system of equations, one for the control Hamiltonian and another one for the duration of the protocol, realizes an ansatz-free approach to quantum control theory. We show how driven systems, in the form of a Landau-Zener type Hamiltonian, can be efficiently maneuvered to speed up a given state transformation in a highly adiabatic manner and with a low energy cost.

Electronic structure and magnetic coupling in selenium substituted pyridine-bridged bisdithiazolyl multifunctional molecular materials.

Bisdithiazolyl radicals have furnished in recent years multiple examples of molecular materials with promising conductive and magnetic properties. The electronic band structure and magnetic ordering in four different isostructural pyridine-bridged bisdithiazolyl and Selenium substituted compounds have been studied by means of hybrid DFT based methods as implemented in the CRYSTAL code. The full rationalization of the properties of these multifunctional magnetic molecular materials requires a careful description of their complex open-shell electronic structure. The results describe the systems as narrow band (0.2-0.3 eV dispersion) open-shell semiconductors with a gap of 1.15-1.40 eV between the valence and conducting bands. The bands defining the insulating gap are dominated by orbital contributions arising from the heteroatoms sitting in the outer rings. A low energy closed-shell metallic solution is found at 0.25-0.35 eV above the magnetic solutions thus suggesting a complex mechanism for electric conduction with band and hopping contributions. The observed trend of the conductivity is in line with the variation of the insulating gap but more rigorous modelling is required to take into account the details of the band structure of the systems. For all the systems the spin density is well localised on the molecular units and is independent of the magnetic solution. Thus the system can be described as an ensemble of well-defined S = 1/2 magnetic centres using a two-body Heisenberg-Dirac-van Vleck spin Hamiltonian. The lowest energy electronic solutions are in line with the observed magnetic behaviour at low temperature. The set of competing magnetic exchange interactions that emerges from using a suitable mapping to consistently describe the low energy magnetic solutions explains the variety of magnetic responses (absence of long-range magnetic order, antiferromagnetism or ferromagnetism) of the four studied compounds at low temperatures.

Controlling Chemical Reactivity with Optimally Oriented Electric Fields: A Generalization of the Newton Trajectory Method.

The use of oriented external electric fields (OEEF) as a tool to accelerate chemical reactions has recently attracted much interest. A new model to calculate the optimal OEEF of the least intensity to induce a barrierless chemical reaction path is presented. A suitable ansatz is provided by defining an effective potential energy surface (PES), which considers the unperturbed or original PES of the molecular reactive system and the action of a constant OEEF on the overall dipole moment of system. Based on a generalization of the Newton Trajectories (NT) method, it is demonstrated that the optimal OEEF can be determined upon locating a special point of the potential energy surface (PES), the so-called "optimal bond-breaking point" (optimal BBP), for which two different algorithms are proposed. At this point, the gradient of the original or unperturbed PES is an eigenvector of zero eigenvalue of the Hessian matrix of the effective PES. A thorough discussion of the geometrical aspects of the optimal BBP and the optimal OEEF is provided using a two-dimensional model, and numerical calculations of the optimal OEEF for a SN2 reaction and the 1,3-dipolar retrocycloaddition of isoxazole to fulminic acid plus acetylene reaction serve as a proof of concept. The knowledge of the orientation of optimal OEEF provides a practical way to reduce the effective barrier of a given chemical process.

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.

Quantum equilibration of the double-proton transfer in a model system porphine.

There is a renewed interest in the derivation of statistical mechanics from the dynamics of closed quantum systems. A central part of this program is to understand how closed quantum systems, i.e., in the absence of a thermal bath, initialized far-from-equilibrium can share a dynamics that is typical to the relaxation towards thermal equilibrium. Equilibration dynamics has been traditionally studied with a focus on the so-called quenches of large-scale many-body systems. We consider here the equilibration of a two-dimensional molecular model system describing the double proton transfer reaction in porphine. Using numerical simulations, we show that equilibration indeed takes place very rapidly (∼200 fs) for initial states induced by pump-dump laser pulse control with energies well above the synchronous barrier. The resulting equilibration state is characterized by a strong delocalization of the probability density of the protons that can be explained, mechanistically, as the result of (i) an initial state consisting of a large superposition of vibrational states, and (ii) the presence of a very effective dephasing mechanism.

Interplay between the Gentlest Ascent Dynamics Method and Conjugate Directions to Locate Transition States.

An algorithm to locate transition states on a potential energy surface (PES) is proposed and described. The technique is based on the GAD method where the gradient of the PES is projected into a given direction and also perpendicular to it. In the proposed method, named GAD-CD, the projection is not only applied to the gradient but also to the Hessian matrix. Then, the resulting Hessian matrix is block diagonal. The direction is updated according to the GAD method. Furthermore, to ensure stability and to avoid a high computational cost, a trust region technique is incorporated and the Hessian matrix is updated at each iteration. The performance of the algorithm in comparison with the standard ascent dynamics is discussed for a simple two dimensional model PES. Its efficiency for describing the reaction mechanisms involving small and medium size molecular systems is demonstrated for five molecular systems of interest.

Post-B3LYP Functionals Do Not Improve the Description of Magnetic Coupling in Cu(II) Dinuclear Complexes.

The accuracy of post-B3LYP functionals is analyzed using an open-shell database of Cu(II) dinuclear complexes with well-defined experimental values of the magnetic coupling constants. This database provides a sound open-shell training set to be used to improve the fitting schemes in defining new functionals or when reparametrizing the existing ones. For a large set of representative hybrid exchange-correlation functionals, it is shown that the overall description of moderate-to-strong antiferromagnetic interactions is significantly more accurate than the description of ferromagnetic or weakly antiferromagnetic interactions. In the case of global hybrids, the most reliable ones have 25-40% Fock exchange with SOGGA and PBE0 being the most reliable and M06 the exception. For range-corrected hybrids, the long-range corrected CAM-B3LYP and ωB97XD provide acceptable results, and M11 is comparable but more erratic. It is concluded that the reliability of the calculated values is system- and range-dependent, and this fact introduces a serious warning on the blind use of a single functional to predict magnetic coupling constants. Hence, to extract acceptable magnetostructural correlations, a "standardization" of the method to be used is advised to choose the optimal functional.

A 2D rhomboidal system of manganese(ii) [Mn(3-MeC6H4COO)2(H2O)2]n with spin canting: rationalization of the magnetic exchange.

The crystal structure of Mn(ii) carboxylate with 3-methylbenzoate as a bridging ligand [Mn(3-MeC6H4COO)2(H2O)2]n shows a rhomboidal layer, where each pair of neighbor Mn(ii) ions are bridged through only one carboxylate group with a syn-anti conformation. The magnetic exchange between neighbor ions is weakly antiferromagnetic (J = -0.52 cm-1, g = 2.04), and at low temperature the system shows spin canting with TB = 3.8 K. Computational studies, based on periodic calculations of the energies of the significant spin states on the magnetic cell and some higher supercells, corroborate the weak AF interaction between the adjacent Mn(ii) ions and preclude the negligible effect of frustration caused by very weak interactions between the non-adjacent ions in the magnetic response of the system. The results provide compelling evidence that the observed spin canting is due to the local coordination geometry of the manganese ions leading to two antiferromagnetically coupled subnets with different axial vectors.

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.

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

Through-bond interacting organic polyradicals, rendered by customizable capacities of the state-of-the-art synthetic routes, are ideal systems to investigate spin topologies. Relying on Rajca and co-workers' synthetic efforts, hereby we investigate the role of borders in the stability of the high-spin ground state in a series of realistic linear and ring-like arylmethyl polyradical derivatives. We show that, compared to their linear counterpart, the absence of borders in a ring-like arrangement of arylmethyl radicals imposes a larger number of spin-alternation rule violations, which strongly stabilizes the high-spin ground state. In addition, the structural flexibility of the investigated compounds translates into the existence of various structural energy minima for which the ferromagnetic ground state is always maintained. In view of the present results we propose these rings as possible candidates for the development of enhanced high spin single molecule toroics.

Experimental and Computational Evidence of the Biradical Structure and Reactivity of Titanium(IV) Enolates.

Quantum chemical calculations have unveiled the unexpected biradical character of titanium(IV) enolates from N-acyl oxazolidinones and thiazolidinethiones. The electronic structure of these species therefore involves a valence tautomerism consisting of an equilibrium between a closed shell (formally Ti(IV) enolates) and an open shell, biradical, singlet (formally Ti(III) enolates) electronic states, whose origin is to be basically found in changes of the Ti-O distance. Spectroscopic studies of the intermediate species lend support to such a model, which also turns out to be crucial for a better understanding of the overall reactivity of titanium(IV) enolates. In this context, a thorough computational analysis of the radical addition of titanium(IV) enolates from N-acyl oxazolidinones to TEMPO has permitted us to suggest an entire mechanism, which accounts for the experimental details and the diastereoselectivity of the process. All together, this evidence highlights the relevance of biradical intermediates from titanium(IV) enolates and may be a useful contribution to the foundations of a more insightful comprehension of the structure and reactivity of titanium(IV) enolates.

Redox-Induced Gating of the Exchange Interactions in a Single Organic Diradical.

Embedding a magnetic electroactive molecule in a three-terminal junction allows for the fast and local electric field control of magnetic properties desirable in spintronic devices and quantum gates. Here, we provide an example of this control through the reversible and stable charging of a single all-organic neutral diradical molecule. By means of inelastic electron tunnel spectroscopy we show that the added electron occupies a molecular orbital distinct from those containing the two radical electrons, forming a spin system with three antiferromagnetically coupled spins. Changing the redox state of the molecule therefore switches on and off a parallel exchange path between the two radical spins through the added electron. This electrically controlled gating of the intramolecular magnetic interactions constitutes an essential ingredient of a single-molecule [Formula: see text] quantum gate.

Design of multi-functional 2D open-shell organic networks with mechanically controllable properties.

Triarylmethyls (TAMs) are prominent highly attractive open shell organic molecular building blocks for materials science, having been used in breakthrough syntheses of organic magnetic polymers and metal organic frameworks. With their radical π-conjugated nature and a proven capacity to possess high stability via suitable chemical design, TAMs display a variety of desirable characteristics which can be exploited for a wide range of applications. Due to their particular molecular and electronic structure, the spin localization in TAMs almost entirely depends on the dihedral angles of their three aryl rings with respect to the central methyl carbon atom plane, which opens up the possibility of controlling their fundamental properties by twisting the three aryl rings. Aryl ring twist angles can be tuned to a single value by specific chemical functionalisation but controlling them by external means in organic materials or devices represents a challenging task which has not yet been experimentally achieved. Herein, through rational chemical design we propose two 2D covalent organic frameworks (2D-COFs) based on specific TAM building blocks. By employing ab initio computational modeling we demonstrate that it is possible to externally manipulate the aryl ring twist angles in these 2D-linked TAM frameworks by external mechanical means. Furthermore, we show this structural manipulation allows for finely tuning the most important characteristics of these materials such as spin localization, optical electronic transitions and magnetic interactions. Due to the enormous technological potential offered by this new class of material and the fact that our work is guided by real advances in organic materials synthesis, we believe that our predictions will inspire the experimental realization of radical-2D-COFs with externally controllable characteristics.