Open-shell Singlet Ground State Research Articles

Fate of the open-shell singlet ground state in the experimentally accessible acenes: A quantum Monte Carlo study.

By means of the Jastrow correlated antisymmetrized geminal power (JAGP) wave function and quantum Monte Carlo (QMC) methods, we study the ground state properties of the oligoacene series, up to the nonacene. The JAGP is the accurate variational realization of the resonating-valence-bond (RVB) ansatz proposed by Pauling and Wheland to describe aromatic compounds. We show that the long-ranged RVB correlations built in the acenes' ground state are detrimental for the occurrence of open-shell diradical or polyradical instabilities, previously found by lower-level theories. We substantiate our outcome by a direct comparison with another wave function, tailored to be an open-shell singlet (OSS) for long-enough acenes. By comparing on the same footing the RVB and OSS wave functions, both optimized at a variational QMC level and further projected by the lattice regularized diffusion Monte Carlo method, we prove that the RVB wave function has always a lower variational energy and better nodes than the OSS, for all molecular species considered in this work. The entangled multi-reference RVB state acts against the electron edge localization implied by the OSS wave function and weakens the diradical tendency for higher oligoacenes. These properties are reflected by several descriptors, including wave function parameters, bond length alternation, aromatic indices, and spin-spin correlation functions. In this context, we propose a new aromatic index estimator suitable for geminal wave functions. For the largest acenes taken into account, the long-range decay of the charge-charge correlation functions is compatible with a quasi-metallic behavior.

Studies on the Bridge Dependence of Bis(triarylamine) Diradical Dications: Long-Range π-Conjugation and π-π Coupling Systems.

Three bis(triarylamine) dications bridged with 2,2'-bithienyl group (12+), biphenyl group (22+) and [2,2]paracyclophane (32+) have been successfully isolated. The electronic structures of 12+ - 32+ show bridge dependence. Magnetic studies and DFT calculations show that dications 12+ - 32+ possess an open-shell singlet ground state with a thermally excited triplet state. Dication 32+ has rather small singlet-triplet energy gap and could basically be regarded as a nearly pure diradical. Diradical dications 12+ - 32+ represent rare examples of diradicaloids with intramolecular long-range π-conjugation or π-π coupling interaction.

Group 10 Bis(iminosemiquinone) Complexes: Measurement of Singlet-Triplet Gaps and Analysis of the Effects of Metal and Geometry on Electronic Structure.

Bis(iminosemiquinone) complexes of divalent group 10 metals have been described as having open-shell singlet ground states characteristic of very strong coupling between the two ligand radicals. By using the nonlinear temperature dependence of the chemical shifts of the 1H NMR spectra, the singlet-triplet gaps in seven of these compounds have been measured, with the nickel compounds having gaps of about 2400 cm-1 and the palladium compounds about 1800 cm-1. Bis(iminosemiquinone)platinum complexes have singlet-triplet gaps too large to measure by this technique (over 2800 cm-1, estimated to be about 3000 cm-1), though bis(3,5-di- tert-butylbenzosemiquinonato)platinum(II) has a measurable singlet-triplet gap of 1850 cm-1. In combination with near-IR absorption data of the neutral, cationic, and anionic bis(iminosemiquinone) complexes, a simplified two-electron, two-orbital bonding model describing these compounds can be fully parametrized based on experimental data. The identity of the central metal principally affects the difference in energy between metal-ligand π nonbonding and metal-ligand π antibonding orbitals, with the strength of the bonding interactions increasing in the order Pd < Ni < Pt. Twisting the ligands out of planarity (by using a 2,2'-biphenylenediyl linker) has a marked effect on the optical spectra of the compounds but not on their singlet-triplet gaps; this indicates that the effect is not due to changes in bonding interactions but rather due to a decrease in the magnitude of the quantum mechanical exchange interactions in the twisted compared to the flat compounds.

Stable Nitrogen-Centered Bis(imino)rylene Diradicaloids.

The synthesis of stable open-shell singlet diradicaloids is critical for their practical material application. So far, most reported examples are based on carbon-centered radicals, which are intrinsically reactive, and there are very few examples of stable nitrogen-centered diradicaloids. In this full paper, a series of soluble and stable bis(imino)rylenes up to octarylene were synthesized on the basis of newly developed dibromorylene intermediates. It was found that from hexarylene onward, these quinoidal rylenes showed open-shell singlet ground states and could be thermally populated to paramagnetic triplet aminyl diradicals. They are stable due to efficient spin delocalization onto the rylene backbone as well as kinetic blocking of the aminyl sites by the bulky and electron-deficient 2,4,6-trichlorophenyl groups. They exhibited very different electronic structures, diradical character, excited-state dynamics, one-photon absorption, two-photon absorption, and electrochemical properties from their respective aromatic rylene counterparts. These bis(imino)rylenes represent a rare class of stable, neutral, nitrogen-centered aminyl diradicaloids.

Experimental Observation of Thermally Excited Triplet States of Heavier Group 15 Element Centered Diradical Dianions.

One-electron reductions of Mes*As=Fl* (1; Fl*=2,7-di-tert-butylfluorenylidene, Mes*=2,4,6-tBu3 C6 H2 ) and diarsaalkenes [1,2-b]-IF(=AsMes*)2 (2; IF=indenofluorene) with potassium led to the isolation of the arsenic-centered radical anion salts 1K and 2K, respectively. The diradical dianion salts 2K2 and 3K2 were afforded by the reduction of 2 and 2,8-tBu2 -[2,1-b]-IF(=AsMes*)2 (3) with an excess amount of KC8 . The radicals have been investigated by single-crystal X-ray crystallography, EPR, and UV/Vis absorption spectroscopy, along with theoretical calculations. The calculations revealed that 2K2 and 3K2 feature open-shell singlet ground states with singlet-triplet energy gaps of 2.1 and 1.0 kcal mol-1 , respectively. They are readily thermally excited to triplet states as demonstrated by EPR spectroscopy. The obtained diradicals represent the first examples of heavier Group 15 element centered diradicals with experimentally observable triplet states.

Electronic Structure of Cobalt-Corrole-Pyridine Complexes: Noninnocent Five-Coordinate Co(II) Corrole-Radical States.

Two sets of complexes of Co-triarylcorrole-bispyridine complexes, Co[TpXPC](py)2 and Co[Br8TpXPC](py)2 have been synthesized, where TpXPC refers to a meso-tris(para-X-phenyl)corrole ligand with X = CF3, H, Me, and OMe and Br8TpXPC to the corresponding β-octabrominated ligand. The axial pyridines in these complexes were found to be labile and, in dilute solutions in dichloromethane, the complexes dissociate almost completely to the five-coordinate monopyridine complexes. Upon addition of a small quantity of pyridine, the complexes revert back to the six-coordinate forms. These transformations are accompanied by dramatic changes in color and optical spectra. 1H NMR spectroscopy and X-ray crystallography have confirmed that the bispyridine complexes are authentic low-spin Co(III) species. Strong substituent effects on the Soret maxima and broken-symmetry DFT calculations, however, indicate a CoII-corrole•2- formulation for the five-coordinate Co[TpXPC](py) series. The calculations implicate a Co(dz2)-corrole("a2u") orbital interaction as responsible for the metal-ligand antiferromagnetic coupling that leads to the open-shell singlet ground state of these species. Furthermore, the calculations predict two low-energy S = 1 intermediate-spin Co(III) states, a scenario that we have been able to experimentally corroborate with temperature-dependent EPR studies. Our findings add to the growing body of evidence for noninnocent electronic structures among first-row transition metal corrole derivatives.

Isolable Borane-Based Diradical and Triradical Fused by a Diamagnetic Transition Metal Ion.

Complex Fe(bpyB)3 (1, bpyB = 5,5'-bis(dimesitylboranyl)-2,2'-bipyridine) and its reduced species [(18-c-6)K(THF)2]·[Fe(bpyB)3] (2) were synthesized. Their solid state and electronic structures were investigated by single crystal X-ray crystallography, electron paramagnetic resonance and UV-vis spectroscopy, and SQUID measurements. In 1 two bpyB radical anions are fused by a diamagnetic FeII ion, whereas in 2 all three bpyB ligands are in the radical state. Complex 1 possesses an open-shell singlet ground state with a singlet-triplet gap of 0.18 kcal mol-1 and 2 features an open-shell doublet ground state with a doublet-quartet gap of 1.4 kcal mol-1, as determined by SQUID measurements. The unpaired-electrons in 1 and 2 mainly delocalize over the boron atoms and the bipyrdine moieties with negligible spin density at the iron center. Complex 2 represents the first isolable example of boron-based triradicals.

Tuning the Spin Coupling Interactions in the Nitroxide-Based Bisphenol-Like Diradicals.

The intramolecular spin coupling interactions of bisphenol-like trinary-bridged diradicals [nitroxide-(para/meta)phenylene-X-phenylene(para/meta)-nitroxide, X=C=CH2 , O, BH, NH and SO2 ] were explored with an emphasis on the tuning role of the X coupler at the (U)B3LYP/6-311++G(d,p) level. Our results indicate that all designed trinary-bridged diradicals featuring a V-type structure with a bending angle of 104-130° and torsional angles of two phenylene rings being 20-90° exhibit different diradical character and magnetism, depending on the structures and properties of the X bridges. More interestingly, although meta/para-phenylene supports a ferromagnetic (FM)/antiferromagnetic (AFM) coupling, their combinations by using X as a trinary bridge can mediate spin coupling, but the coupling magnitude strongly depends on X. In general, a para/para or meta/meta combination with X leads to an open-shell singlet ground state and thus AFM, but the meta/meta combination considerably decreases the spin coupling interaction. In contrast, a para/meta combination with X produces a triplet ground state and FM. Their combination with a single-electron conjugation end coupler (C=CH2 ) leads to an inverse coupling regularity. All results can be reasonably explained by the spin alternation rule, molecular structures, and properties. In particular, detailed spin coupling mechanisms are suggested to involve cooperative through-space and through-bond pathways with different levels of cooperativity. This is rationalized with the X-induced bending of the diradicals not only modifying the through-bond (extended π conjugation) pathway but also provididng a through-space (face-to-face vs. side-to-side π-π interaction) possibility for spin coupling, in conjunction with twisting of the phenylene rings. Different contributions of the through-space and through-bond couplings are quantitatively distinguished and depend on the structure and property of the X coupler. Clearly, this work reports interesting aspects of the trinary bridged diradicals and also provides important information for the design of molecules for functional magnetic materials and tuning their magnetic properties.

Toward Benzobis(thiadiazole)-based Diradicaloids.

We theoretically predicted that acetylene-bridged benzo[1,2-c;4,5-c']bis[1,2,5]thiadiazole (BBT) oligomers would show a quick increase of diradical character with the extension of chain length. To validate the hypothesis, six stable BBT-based diradicaloids were synthesized and fully characterized by X-ray crystallographic analysis and various spectroscopic measurements. Three of them showed prominent paramagnetic activity at elevated temperatures due to thermal population from the open-shell singlet ground state to triplet excited state. It was also found that substitution by electron-donating triphenylamine groups at the termini promoted the diradical character and reduced the singlet-triplet energy gap, and at the same time, resulted in intense near-infrared absorption.

Bis(boryl anion)-Substituted Pyrenes: Syntheses, Characterizations, and Crystal Structures

The two new diboranes 1 and 2 connected by a pyrene moiety at the 1,6- and 1,3-positions, respectively, were synthesized, and their two-electron-reduction reactions were investigated. The doubly reduced species 1••2– is silent in electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) spectroscopic measurements, suggesting a quasi-quinoidal structure with a diradical character of 1••2–, which has a singlet–triplet gap of 6.6 kcal mol–1 as determined by theoretical calculations. In contrast, the reduction product 2••2– is EPR active and theoretical calculations indicate that 2••2– has an open-shell singlet ground state with a singlet–triplet energy gap of 4.9 kcal mol–1.

Cyclopenta Ring Fused Bisanthene and Its Charged Species with Open-Shell Singlet Diradical Character and Global Aromaticity/ Anti-Aromaticity.

Cyclopenta ring fused bisanthene and its charged species were synthesized. The neutral compound has an open-shell singlet ground state and displays global anti-aromaticity. The dication also exhibits singlet diradical character but has a unique [10]annulene-within-[18]annulene global aromatic structure. The dianion is closed-shell singlet in the ground state and shows global aromaticity with 22 π electrons delocalized on the periphery. These findings prrovide new insight into the design and properties of global aromatic/anti-aromatic systems based on π-conjugated polycyclic hydrocarbons.

Remarkable Magnetic Coupling Interactions in Multi-Beryllium-Expanded Small Graphene-like Molecules with Well-Defined Polyradical Characters

Multi-beryllium-expanded small graphene-like molecules including oligoacenes (mBe-nA) and graphene patches (mBe-GP) are computationally designed through introducing two or three Be atoms into the specific benzenoid rings of the graphene-like molecules, leading to replacement of some C–C bonds by the C–Be–C linkages with elongated C···C distances of about 3.3 Å in them. As a result, the elongation of the C···C bonds and insertion of more Be atoms make the two radical moieties in each molecule relatively separated and their interaction relatively weak. Both density functional theory and CASSCF calculations indicate that all these multi-Be-expanded graphene-like molecules exhibit well-defined polyradical characters: an open-shell singlet diradical for all mBe-nA and an open-shell singlet diradical or quintet tetraradical for mBe-GP depending on the Be-insertion patterns of the patches. The main findings in this work are that (i) a switching from the parent graphene-like closed-shell molecules (e.g., linear oligoacenes and graphene patches) to the open-shell singlet (diradical) or quintet (tetraradical) ground states can be realized by introducing Be as linkers into the graphene-like molecules; (ii) more importantly, the spin-coupling interactions of such mBe-nA and mBe-GP are remarkably large; and (iii) in these Be-modified molecules the Be–C bonds exhibit considerable covalent character and the Be···Be distances are 2.67–2.84 Å, implying weak Be(s2)···Be(s2) metallophilic interaction. This work would open a new perspective for the rational design of perfect and stable singlet diradicals or polyradicals with large spin-coupling constants on the basis of small closed-shell graphene-like molecules by multimetal incorporation and also encourage experimentalists to pursue and realize these interesting structures with enhanced magnetic properties in the future.

Toward Stable Superbenzoquinone Diradicaloids.

Superbenzoquinone (SBQ) is a quinone derived from a classic polycyclic aromatic hydrocarbon (PAH), hexa-peri-hexabenzocoronene (so-called "superbenzene"), and is a challenging synthetic target. Herein we report the successful synthesis and characterization of its derivatives. We reveal that the high reactivity of SBQ is due to its intrinsic open-shell diradical character. Thus, two kinetically blocked SBQs, SBQ-Me and SBQ-Ph, were prepared by different synthetic strategies. 4-tert-Butylphenyl-substituted SBQ-Ph demonstrated good stability and could be isolated in crystalline form. Both compounds have an open-shell singlet ground state and show thermally populated paramagnetic activity. Our studies provide effective strategies toward stable quinone-based diradicaloids.

Higher Order π-Conjugated Polycyclic Hydrocarbons with Open-Shell Singlet Ground State: Nonazethrene versus Nonacene.

Higher order acenes (i.e., acenes longer than pentacene) and extended zethrenes (i.e., zethrenes longer than zethrene) are theoretically predicted to have an open-shell singlet ground state, and the radical character is supposed to increase with extension of molecular size. The increasing radical character makes the synthesis of long zethrenes and acenes very challenging, and so far, the longest reported zethrene and acene derivatives are octazethrene and nonacene, respectively. In addition, there is a lack of fundamental understanding of the differences between these two closely related open-shell singlet systems. In this work, we report the first synthesis of a challenging nonazethrene derivative, HR-NZ, and its full structural and physical characterizations including variable temperature NMR, ESR, SQUID, UV-vis-NIR absorption and electrochemical measurements. Compound HR-NZ has an open-shell singlet ground state with a moderate diradical character (y0 = 0.48 based on UCAM-B3LYP calculation) and a small singlet-triplet gap (ΔES-T = -5.2 kcal/mol based on SQUID data), thus showing magnetic activity at room temperature. It also shows amphoteric redox behavior, with a small electrochemical energy gap (1.33 eV). Its electronic structure and physical properties are compared with those of Anthony's nonacene derivative JA-NA and other zethrene derivatives. A more general comparison between higher order acenes and extended zethrenes was also conducted on the basis of ab initio electronic structure calculations, and it was found that zethrenes and acenes have very different spatial localization of the unpaired electrons. As a result, a faster decrease of singlet-triplet energy gap and a faster increase of radical character with increase of the number of benzenoid rings were observed in zethrene series. Our studies reveal that spatial localization of the frontier molecular orbitals play a very important role on the nature of radical character as well as the excitation energy.

Fully Fused Quinoidal/Aromatic Carbazole Macrocycles with Poly-radical Characters.

While the chemistry of open-shell singlet diradicaloids has been successfully developed in recent years, the synthesis of π-conjugated systems with poly-radical characters (i.e., beyond diradical) in the singlet ground state has been mostly unsuccessful. In this study, we report the synthesis and isolation of two fully fused macrocycles containing four (4MC) and six (6MC) alternatingly arranged quinoidal/aromatic carbazole units. Ab initio electronic structure calculations and various experimental measurements indicate that both 4MC and 6MC have an open-shell singlet ground state with moderate tetraradical and hexaradical characters, respectively. Both compounds can be thermally populated to high-spin excited states, resulting in weak magnetization at room temperature. Our study represents the first demonstration of singlet π-conjugated molecules with poly-radical characters and also gives some insights into molecular magnetism in neutral π-conjugated polycyclic heteroarenes.

Assigning the Cerium Oxidation State for CH2CeF2 and OCeF2 Based on Multireference Wave Function Analysis.

The geometric and electronic structure of the recently experimentally studied molecules ZCeF2 (Z = CH2, O) was investigated by density functional theory (DFT) and wave function-based ab initio methods. Special attention was paid to the Ce-Z metal-ligand bonding, especially to the nature of the interaction between the Ce 4f and the Z 2p orbitals and the possible multiconfigurational character arising from it, as well as to the assignment of an oxidation state of Ce reflecting the electronic structure. Complete active space self-consistent field (CASSCF) calculations were performed, followed by orbital rotations in the active orbital space. The methylene compound CH2CeF2 has an open-shell singlet ground state, which is characterized by a two-configurational wave function in the basis of the strongly mixed natural CASSCF orbitals. The system can also be described in a very compact way by the dominant Ce 4f(1) C 2p(1) configuration, if nearly pure Ce 4f and C 2p orbitals are used. In the basis of these localized orbitals, the molecule is almost monoconfigurational and should be best described as a Ce(III) system. The singlet ground state of the oxygen OCeF2 complex is of closed-shell character when a monoconfigurational wave function with very strongly mixed Ce 4f and O 2p CASSCF natural orbitals is used for the description. The transformation to orbitals localized on the cerium and oxygen atoms leads to a multiconfigurational wave function and reveals characteristics of a mixed valent Ce(IV)/Ce(III) compound. Additionally, the interactions of the localized active orbitals were analyzed by evaluating the expectation values of the charge fluctuation operator and the local spin operator. The Ce 4f and C 2p orbital interaction of the CH2CeF2 compound is weakly covalent and resembles the interaction of the H 1s orbitals in a stretched hydrogen dimer. In contrast, the interaction of the localized active orbitals for OCeF2 shows ionic character. Calculated vibrational Ce-C and Ce-O stretching frequencies at the DFT, CASSCF, second-order Rayleigh-Schrödinger perturbation theory (RS2C), multireference configuration interaction (MRCI), as well as single, doubles, and perturbative triples coupled cluster (CCSD(T)) level are reported and compared to experimental infrared absorption data in a Ne and Ar matrix.

Isolable Diphosphorus-Centered Radical Anion and Diradical Dianion.

Two salts containing diphosphorus-centered radical anion 1(•-) and diradical dianion 1(2-••) were obtained by one- and two-electron reductions of an indenofluorene-bridging diphosphaalkene (1) with K and KC8, respectively. The salts have been characterized by electron paramagnetic resonance (EPR) spectroscopy, UV-vis absorption spectroscopy, and single-crystal X-ray diffraction analysis. EPR spectroscopy and theoretical calculations reveal that the spin density of the radicals mainly resides on the phosphorus atoms, and 1(2-••) has an open-shell singlet ground state. 1(•-) and 1(2-••) represent the first isolable and structurally characterized diphosphorus-centered radical anion and dianion.

Octazethrene and Its Isomer with Different Diradical Characters and Chemical Reactivity: The Role of the Bridge Structure.

The fundamental relationship between structure and diradical character is important for the development of open-shell diradicaloid-based materials. In this work, we synthesized two structural isomers bearing a 2,6-naphthoquinodimethane or a 1,5-naphthoquinodimethane bridge and demonstrated that their diradical characters and chemical reactivity are quite different. The mesityl-or pentafluorophenyl-substituted octazethrene derivatives OZ-M/OZ-F and their isomer OZI-M (with mesityl substituents) were synthesized via an intramolecular Friedel-Crafts alkylation followed by oxidative dehydrogenation strategy from the key building blocks 4 and 11. Our detailed experimental and theoretical studies showed that both isomers have an open-shell singlet ground state with a remarkable diradical character (y0 = 0.35 and 0.34 for OZ-M and OZ-F, and y0 = 0.58 for OZI-M). Compounds OZ-M and OZ-F have good stability in an ambient environment, while OZI-M has high reactivity and can be easily oxidized to a dioxo product 15, which can be correlated to their different diradical characters. Additionally, we investigated the physical properties of OZ-M, OZ-F, and 15.

Evaluation of modern DFT functionals and G3n-RAD composite methods in the modelization of organic singlet diradicals.

The evaluation of four high-level composite methods based on the modification of Gaussian-3 (G3) theory for radicals and 18 exchange-correlation density functionals, including modern long-range and dispersion-corrected functionals, in the modelization of singlet diradicals has been performed in this work. Structural parameters and properties such as singlet-triplet gaps, electron affinities, ionization potentials, dipole moments, enthalpies of formation, and bond dissociation energies have been calculated in a set of six well-characterized singlet diradicals, and benchmarked against experimental data and wavefunction-based CASSCF/CASPT2 calculations. The complexity of the open-shell singlet ground state is revealed in the difficulties to properly represent the diradical character reported by some DFT functionals, specially those that do not comprise a certain amount of Hartree-Fock exchange in their formulation. We find that STGs, EAs, dipole moments, and thermochemical properties are, in general, satisfactorily calculated, while for IPs larger deviations with respect to the experiments are found in all cases. The best overall performance is accounted for by hybrid functionals, including some of the long-range corrected functionals, but also pure functionals, comprising the kinetic energy density in their formulation, are found to be competent. Composite methods perform satisfactorily, especially G3(MP2)-RAD and G3X(MP2)-RAD, which calculate singlet-triplet gaps and electron affinities more accurately. On the other hand, G3-RAD and G3X-RAD provide better ionization potentials. This study emphasizes that the use of recently developed functionals, within the broken symmetry approximation, is an appropriate tool for the simulation of organic singlet diradicals, with similar accuracy compared to more expensive composite methods. Nevertheless, suitable selection of the methodology is still crucial for the accomplishment of accurate results.

Multi-reference character and Ce 4f orbital contributions in terminal multiple Ce[sbnd]Z bonds of Cp2CeZ (Z = CH2, CH−, NH, O, F+) complexes

The geometric and electronic structures of bis(cyclopentadienyl)cerium compounds of the type Cp2CeZ (Z=CH2, CH−, NH, O, F+) are analyzed paying special attention to the terminal metal–ligand multiple bonding in the CeZ units. Complete active space self-consistent field calculations were performed, followed by unitary transformations in the active orbital space in order to monitor the weights of the leading configurations, as well as the Ce and Z character of the orbitals. It is shown that all compounds, except the closed-shell Ce(IV) complex Cp2CeF+, have an open-shell singlet ground state and the 4f orbitals are important for their electronic structure. In case of Z=CH2, CH− the singlet ground state consists to more than 90% of the Cefπ1Zpπ1 configuration when using nearly pure cerium 4f and carbon 2p orbitals of the Z group, implying Ce(III) systems. In contrast, the systems containing Z=NH, O revealed a more mixed Ce(III)/Ce(IV) ground state wavefunction. The interactions of the active orbitals were characterized by calculating the expectation values of the charge fluctuation operator and the local spin operator. The results are evaluated by comparison with the values achieved by stretching the covalent bond of a H2 molecule. The CH2 and the CH− complexes show, besides a CeZ σ bond, a quite weak covalent Ce fZ p orbital interaction in π symmetry, while the other two complexes (Z=NH, O) exhibit a stronger covalent interaction with a noticeable ionic character because of the higher electronegativities of nitrogen and oxygen.