A Recipe for Geometry Optimization of Diradicalar Singlet States from Broken-Symmetry Calculations

A General Concept for the Electronic and Steric Modification of 1-Metallacyclobuta-2,3-dienes: A Case Study of Group 4 Metallocene Complexes

The synthesis of group 4 metal 1-metallacyclobuta-2,3-dienes as organometallic analogues of elusive 1,2-cyclobutadiene has so far been limited to SiMe3 substituted examples. We present the synthesis of two Ph substituted dilithiated ligand precursors for the preparation of four new 1-metallacyclobuta-2,3-dienes [rac-(ebthi)M] (M=Ti, Zr; ebthi=1,2-ethylene-1,10-bis(η5-tetrahydroindenyl)). The organolithium compounds [Li2(RC3Ph)] (1 b: R=Ph, 1 c: R=SiMe3) as well as the metallacycles of the general formula [rac-(ebthi)M(R1C3R2)] (2 b: M=Ti, R1=R2=Ph, 2 c: M=Ti, R1=Ph, R2=SiMe3; 3 b: M=Zr, R1=R2=Ph; 3 c: M=Zr, R1=Ph, R2=SiMe3) were fully characterised. Single crystal X-ray diffraction and quantum chemical bond analysis of the Ti and Zr complexes reveal ligand influence on the biradicaloid character of the titanocene complexes. X-band EPR spectroscopy of structurally similar Ti complexes [rac-(ebthi)Ti(Me3SiC3SiMe3)] (2 a), 2 b, and 2 c was carried out to evaluate the accessibility of an EPR active triplet state. Cyclic voltammetry shows that introduction of Ph groups renders the complexes easier to reduce. 13C CPMAS NMR analysis provides insights into the cause of the low field shift of the resonances of metal-bonded carbon atoms and provides evidence of the absence of the β-C-Ti interaction.

Rational Design of a Phosphorus-Centered Disbiradical

Phosphorus-centered disbiradicals, in which the radical sites exist as individual spin doublets with weak spin-spin interaction have not been known so far. Starting from monoradicals of the type [⋅P(μ-NTer)2 P-R], we have now succeeded in linking two such monoradical phosphorus centers by appropriate choice of a linker. To this end, biradical [⋅P(μ-NTer)2 P⋅] (1) was treated with 1,6-dibromohexane, affording the brominated species {Br[P(μ-NTer)]2 }2 C6 H12 (3). Subsequent reduction with KC8 led to the formation of the disbiradical {⋅[P(μ-NTer)]2 }2 C6 H12 (4) featuring a large distance between the radical phosphorus sites in the solid state and formally the highest biradical character observed in a P-centered biradical so far, approaching 100 %. EPR spectroscopy revealed a three-line signal in solution with a considerably larger exchange interaction than would be expected from the molecular structure of the single crystal. Quantum chemical calculations revealed a highly dynamic conformational space; thus, the two radical sites can approach each other with a much smaller distance in solution. Further reduction of 4 resulted in the formation of a potassium salt featuring the first structurally characterized P-centered distonic radical anion (5- ). Moreover, 4 could be used in small molecule activation.

Heteroatom-Based Diradical(oid)s

Heteroatom-centered diradical(oid)s have been in the focus of molecular main group chemistry for nearly 30 years. During this time, the diradical concept has evolved and the focus has shifted to the rational design of diradical(oid)s for specific applications. This review article begins with some important theoretical considerations of the diradical and tetraradical concept. Based on these theoretical considerations, the design of diradical(oid)s in terms of ligand choice, steric, symmetry, electronic situation, element choice, and reactivity is highlighted with examples. In particular, heteroatom-centered diradical reactions are discussed and compared with closed-shell reactions such as pericyclic additions. The comparison between closed-shell reactivity, which proceeds in a concerted manner, and open-shell reactivity, which proceeds in a stepwise fashion, along with considerations of diradical(oid) design, provides a rational understanding of this interesting and unusual class of compounds. The application of diradical(oid)s, for example in small molecule activation or as molecular switches, is also highlighted. The final part of this review begins with application-related details of the spectroscopy of diradical(oid)s, followed by an update of the heteroatom-centered diradical(oid)s and tetraradical(oid)s published in the last 10 years since 2013.

Electronic structure analysis of electrochemical CO2 reduction by iron-porphyrins reveals basic requirements to design catalysts bearing non-innocent ligands

Electrocatalytic CO2 reduction is a possible solution to the increasing CO2 concentration in the earth atmosphere, because it enables storage of energy while using the harmful CO2 feedstock as starting...

Acene-Linked Zethrenes and Bisphenalenyls: A DFT Search for Organic Tetraradicals

Polycyclic aromatic hydrocarbons are of special interest due to their promising nonlinear optical and magnetic properties. A series of acene-linked zethrenes and bisphenalenyls comprising from five to nine benzene rings in the linker group have been computationally studied by the DFT UB3LYP/6-311++G(d,p) quantum-chemical modeling of their electronic structure, possible spin states, and exchange interactions. The zethrenes with octacene and nonacene linkers as well as bisphenalenyls comprising heptacene, octacene, and nonacene linker groups have been revealed to possess tetraradicaloid nature, which makes them promising building blocks for organic optoelectronic and spintronic devices. The results obtained open a way of constructing tetraradicaloid organic molecules characterized by the presence of two types of paramagnetic centers.

Photoisomerization of a phosphorus-based biradicaloid: ultrafast dynamics through a conical intersection

As previously reported, photoisomerization of the open-shell singlet biradicaloid [TerNP]₂CNDmp (2) yields its closed-shell housane-type isomer (3). In the present study, pump-probe spectroscopy was applied to investigate the excited-state dynamics of the photoisomerization, indicating ultrafast de-excitation of the S₁ state through a conical intersection, in agreement with computational predictions. The structural and electronic changes during the isomerization process are discussed to gain an understanding of the reaction pathway and the transformation of the biradicaloid to a closed-shell species.

Unconventional singlet fission materials

Singlet fission (SF) is a photophysical downconversion pathway, in which a singlet excitation transforms into two triplet excited states. As such, it constitutes an exciton multiplication generation process, which is currently at the focal point for future integration into solar energy conversion devices. Beyond this, various other exciting applications were proposed, including quantum cryptography or organic light emitting diodes. Also, the mechanistic understanding evolved rapidly during the last year. Unfortunately, the number of suitable SF-chromophores is still limited. This is per se problematic, considering the wide range of envisaged applicability. With that in mind, we emphasize uncommon SF-scaffolds and outline requirements as well as strategies to expand the chromophore pool of SF-materials.

Spin-symmetrised structures and vibrational frequencies of iron-sulfur clusters

Calculations of relaxed geometries of multi-centre transition metal compounds are routinely carried out using Broken Symmetry Density Functional Theory. The resulting low-spin open shell electronic state is described by one single Slater determinant and is affected by spin contamination. To alleviate this symmetry breaking, the Extended Broken Symmetry (EBS) approach can be applied to complexes with an arbitrary number of local high-spin metal ions. The actual symmetry is therefore reconstructed through minimization of an effective Hamiltonian leading to a relaxed geometry consistent with the magnetic couplings. In the present work we extend the approach already introduced by [Chu et al., J. Chem. Theory Comput., 2017, 13, 4675] to the calculation of vibrational frequencies. As prototypes we have considered the iron-sulfur clusters Fe₂S₂Cl₄^2- and Fe₄S₄Cl₄. We have compared the results obtained for different spin states (high spin, broken symmetry and extended broken symmetry) and by using different DFT functionals (B3LYP, OPBE, BP, M06 and B2PLYP) and a post-HF method (SCS-MP2). The data have shown that for specific vibrational modes the EBS technique produces shifts up to 40 cm^-1 with respect to the routinely used Broken Symmetry approach, indicating that the use of a consistent spin-symmetrised state is a crucial ingredient for an accurate description of vibrational properties, as certified by the comparison with the experimental data for the Fe₂S₂Cl₄^2- cluster.

Understanding the Role of Solvents and Spin-Orbit Coupling in an Oxygen-Assisted SN 2-Type Oxidative Transmetalation Reaction

The aerial oxidation of Pd^II to Pd^IV has emerged as an integral component of sustainable catalytic C-H functionalization processes. However, a proper understanding of the factors that control the viability of this oxidative process remains elusive. An investigation of the intricate mechanism of the transmetalation reaction of the aerial oxidative transformation of [(Me₃ tacn)Pd^II Me₂ ] (Me₃ tacn=N,N',N''-trimethyl-1,4,7-triazacyclononane) to [(Me₃ tacn)Pd^IV Me₃ ]⁺ has been conducted by using DFT, along with multireference methods, such as second-order n-electron valence-state perturbation theory (NEVPT2) with complete active space self-consistent field theory (CASSCF). The present endeavor predicts that the thermodynamics and kinetics of the oxygen activation step are primarily dictated by the polarity of the solvents, which determine the amount of charge transfer to the oxygen molecule from the Pd^II center. Additionally, it is observed that the presence of a protic solvent has a significant effect on the spin-orbit coupling term at the minimum energy crossing point of the triplet and singlet surfaces. Moreover, it is shown that the intermetal ligand-transfer phenomenon is an important instance of an oxygen-assisted S_N 2 reaction.

Assessing the Calculation of Exchange Coupling Constants and Spin Crossover Gaps Using the Approximate Projection Model To Improve Density Functional Calculations

This work evaluates the quality of exchange coupling constant and spin crossover gap calculations using density functional theory corrected by the approximate projection model. Results show that improvements using the approximate projection model range from modest to significant. This study demonstrates that, at least for the class of systems examined here, spin projection generally improves the quality of density functional theory calculations of J-coupling constants and spin crossover gaps. Furthermore, it is shown that spin projection can be important for both geometry optimization and energy evaluations. The approximate projection model provides an affordable and practical approach for effectively correcting spin-contamination errors in such calculations.

Biradical rotamer states tune electron J coupling and MAS dynamic nuclear polarization enhancement

Cross Effect (CE) Dynamic Nuclear Polarization (DNP) relies on the dipolar (D) and exchange (J) coupling interaction between two electron spins. Until recently only the electron spin D coupling was explicitly included in quantifying the DNP mechanism. Recent literature discusses the potential role of J coupling in DNP, but does not provide an account of the distribution and source of electron spin J coupling of commonly used biradicals in DNP. In this study, we quantified the distribution of electron spin J coupling in AMUPol and TOTAPol biradicals using a combination of continuous wave (CW) X-band electron paramagnetic resonance (EPR) lineshape analysis in a series of solvents and at variable temperatures in solution - a state to be vitrified for DNP. We found that both radicals show a temperature dependent distribution of J couplings, and the source of this distribution to be conformational dynamics. To qualify this conformational dependence of J coupling in both molecules we carry out Broken Symmetry DFT calculations which show that the biradical rotamer distribution can account for a large distribution of J couplings, with the magnitude of J coupling directly depending on the relative orientation of the electron spin pair. We demonstrate that the electron spin J couplings in both AMUPol and TOTAPol span a much wider distribution than suggested in the literature. We affirm the importance of electron spin J coupling for DNP with density matrix simulations of DNP in Liouville space and under magic angle spinning, showcasing that a rotamer with high J coupling and optimum relative g-tensor orientation can significantly boost the DNP performance compared to random orientations of the electron spin pair. We conclude that moderate electron spin J coupling above a threshold value can facilitate DNP enhancements.

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.

Carbene derived diradicaloids - building blocks for singlet fission?

Organic singlet diradicaloids promise application in non-linear optics, electronic devices and singlet fission. The stabilization of carbon allotropes/cumulenes (C1, C2, C4) by carbenes has been equally an area of high activity. Combining these fields, we showed recently that carbene scaffolds allow as well for the design of diradicaloids. Herein, we report a comprehensive computational investigation (CASSCF/NEVPT2; fractional occupation DFT) on the electronic properties of carbene-bridge-carbene type diradicaloids. We delineate how to adjust the properties of these ensembles through the choice of carbene and bridge and show that already a short C2 bridge results in remarkable diradicaloid character. The choice of the carbene separately tunes the energies of the S1 and T1 excited states, whereas the bridge adjusts the overall energy level of the excited states. Accordingly, we develop guidelines on how to tailor the electronic properties of these molecules. Of particular note, fractional occupation DFT is an excellent tool to predict singlet-triplet gaps.

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.

Computational Modeling of Cobalt-Based Water Oxidation: Current Status and Future Challenges

A lot of effort is nowadays put into the development of novel water oxidation catalysts. In this context, mechanistic studies are crucial in order to elucidate the reaction mechanisms governing this complex process, new design paradigms and strategies how to improve the stability and efficiency of those catalysts. This review is focused on recent theoretical mechanistic studies in the field of homogeneous cobalt-based water oxidation catalysts. In the first part, computational methodologies and protocols are summarized and evaluated on the basis of their applicability toward real catalytic or smaller model systems, whereby special emphasis is laid on the choice of an appropriate model system. In the second part, an overview of mechanistic studies is presented, from which conceptual guidelines are drawn on how to approach novel studies of catalysts and how to further develop the field of computational modeling of water oxidation reactions.

How to tame a palladium terminal oxo

The isolation of terminal oxo complexes of the late transition metals promises new avenues in oxidation catalysis like the selective and catalytic hydroxylation of unreactive CH bonds, the activation of water, or the upgrading of olefins. While terminal oxo ligands are ubiquitous for early transition metals, well-characterized examples with group 10 metals remain hitherto elusive. In search for palladium terminal oxo complexes, the relative stability/reactivity of such compounds are evaluated computationally (CASSCF/NEVPT2; DFT). The calculations investigate only well-known ligand systems with established synthetic procedures and relevance for coordination chemistry and homogeneous catalysis. They delineate and quantify, which electronic properties of ancillary ligands are crucial for taming otherwise highly reactive terminal oxo intermediates. Notably, carbene ligands with both strong σ-donor and strong π-acceptor properties are best suited for the stabilization of palladium(ii) terminal oxo complexes, whereas ligands with a weaker ligand field lead to highly reactive complexes. Strongly donating ligands are an excellent choice for high-valent palladium(iv) terminal oxo compounds. Low coordinate palladium(ii) as well as high-valent palladium(iv) complexes are best suited for the activation of strong bonds.

Design of a Binuclear Ni(II) Complex with Large Ising-type Anisotropy and Weak Anti-Ferromagnetic Coupling

The preparation of a binuclear Ni(II) complex with a pentacoordinate environment using a cryptand organic ligand and the imidazolate bridge is reported. The coordination sphere is close to trigonal bipyramidal (tbp) for one Ni(II) and to square pyramidal (spy) for the other. The use of the imidazolate bridge that undergoes π-π stacking with two benzene rings of the chelating ligand induces steric hindrance that stabilizes the pentacoordinate environment. Magnetic measurements together with theoretical studies of the spin states energy levels allow fitting the data and reveal a large Ising-type anisotropy and a weak anti-ferromagnetic exchange coupling between the metal ions. The magnitude and the nature of the magnetic anisotropy and the difference in anisotropy between the two metal ions are rationalized using wave-function-based calculations. We show that a slight distortion of the coordination sphere of Ni(II) from spy to tbp leads to an Ising-type anisotropy. Broken-symmetry density functional calculations rationalize the weak anti-ferromagnetic exchange coupling through the imidazolate bridge.

Optical response of the Cu2 S2 diamond core in Cu2II(NGuaS)2 Cl2

Density functional theory (DFT) and time-dependent DFT calculations are presented for the dicopper thiolate complex Cu2 (NGuaS)2 Cl2 [NGuaS=2-(1,1,3,3-tetramethylguanidino) benzenethiolate] with a special focus on the bonding mechanism of the Cu2 S2 Cl2 core and the spectroscopic response. This complex is relevant for the understanding of dicopper redox centers, for example, the CuA center. Its UV/Vis absorption is theoretically studied and found to be similar to other structural CuA models. The spectrum can be roughly divided in the known regions of metal d-d absorptions and metal to ligand charge transfer regions. Nevertheless the chloride ions play an important role as electron donors, with the thiolate groups as electron acceptors. The bonding mechanism is dissected by means of charge decomposition analysis which reveals the large covalency of the Cu2 S2 diamond core mediated between Cu dz2 and S-S π and π* orbitals forming Cu-S σ bonds. Measured resonant Raman spectra are shown for 360- and 720-nm excitation wavelength and interpreted using the calculated vibrational eigenmodes and frequencies. The calculations help to rationalize the varying resonant behavior at different optical excitations. Especially the phenylene rings are only resonant for 720 nm. © 2016 Wiley Periodicals, Inc.

Approximate Spin-Projected Density-Based Romberg Differentiation Procedure to Evaluate the Second-Hyperpolarizability of p-Quinodimethane and Twisted Ethylene and Their Diradical Character Dependence

The evaluation of the static second hyperpolarizability (γ) of diradical species is a challenging task due to the use of spin-unrestricted methods, which may suffer from spin contamination. Here, we present the methodological aspect of a density-based differentiation procedure to evaluate static polarizability and hyperpolarizabilities. The finite-field calculations are done on the spin-projected electron density to remove the spin contamination, and the automatized Romberg's differentiation procedure is used to improve the numerical accuracy in the finite-field method. This implementation is tested in the present report for the challenging case of the evaluation of the second hyperpolarizability of the singlet ground state of p-quinodimethane (PQM) for the equilibrium geometry as well as for a stretched geometry where the diradical character of PQM is increased, and for twisted ethylene models where the diradical character changes with the dihedral angle. The application of the approximate spin-projected (ASP) scheme leads to a major improvement of the density functional theory calculations. In particular, for PQM models, BHandHLYP functional reproduces the UCCSD(T) values when the diradical character is below 0.5. The visualization of the γ-densities shows that (i) when increasing the diradical character, the amount of γ-density increases on the -CH2(•) extremities, and (ii) the ASP scheme decreases the amount of "p-like" γ-density for diradical character below 0.4, and increases it for larger diradical character. For twisted ethylene model, we show that the UCCSD(T) reference values can be reproduced by the ASP-UB3LYP method for y < 0.4 and by the ASP-UBHandHLYP method for y > 0.6. To best reproduce the UCCSD(T) reference calculations, the amount of exact exchange in hybrid functionals needs to be tuned along the range of diradical characters.

Oxidation of Electron Donor-Substituted Verdazyls: Building Blocks for Molecular Switches

Species that can undergo changes in electronic configuration as a result of an external stimulus such as pH or solvent polarity can play an important role in sensors, conducting polymers, and molecular switches. One way to achieve such structures is to couple two redox-active fragments, where the redox activity of one of them is strongly dependent upon environment. We report on two new verdazyls, one subsituted with a di-tert-butyl phenol group and the other with a dimethylaminophenyl group, that have the potential for such behavior upon oxidation. Oxidation of both verdazyls with copper(II) triflate in acetonitrile gives diamagnetic verdazylium ions characterized by NMR and UV-vis spectroscopies. Deprotonation of the phenol-verdazylium results in electron transfer and a switch from a singlet state to a paramagnetic triplet diradical identified by electron spin resonance. The dimethylaminoverdazylium 9 has a diamagnetic ground state, in line with predictions from simple empirical methods and supported by density functional theory calculations. These results indicate that verdazyls may complement nitroxides as spin carriers in the design of organic molecular electronics.

Fine-Tuning of Magnetic Properties in Nickel(II) Trinuclear EMACs via Modifications of Equatorial Ligands

The relationship between equatorial ligands structures and magnetic response of [Ni3]6+ extended metal atom chain core has been investigated. The distances between metal ions in Ni metal strings are largely predefined by framework provided through equatorial ligands. The equatorial ligands thus have primary influence on the magnitude of magnetic coupling between terminal high spin centers. Since the σ channel has greatest contribution to J, the variations in Ni–Ni bond lengths have immediate and strong effect on magnetic properties. The secondary, yet important role is played by ligand field strength and nucleophilicity. It has been shown that energy difference between singly occupied σ-type MOs composed of d(z2) of terminal ions and doubly occupied σ-type MO evolved from d(z2) of the central ion in antiferromagnetic state solution is inversely proportional to magnitude of J. Hence, the alignment between energies of d(z2) orbitals on HS and LS centers directly affected by ligand field strength governs the magnetic response. Moreover, the greater basicity of lone pairs coordinating terminal metal atoms correlates with the larger absolute value of magnetic coupling constant.

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.

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 strategy based on the physical analysis of the leading interactions is followed in order to energetically favor a high-spin ground state. It is shown that the most promising compounds involve bridges that have both a large gap between the highest occupied and the lowest unoccupied molecular orbitals and small coefficients on the atoms to which the magnetic units are connected. While the followed strategy enables one to conceive organic compounds exhibiting a double exchange phenomenon, it is shown that the electronic mechanism ruling the spectrum of such organic double exchange compounds is different from that of their inorganic homologues. A new method to reconstruct the spectrum of low energy from various spin unrestricted DFT solutions is proposed and applied. Finally monodimensional and bidimensional periodic lattices based on the most promising organic architecture are suggested.