Theoretical Study on the Relationship between Diradical Character and Second Hyperpolarizabilities of Four‐Membered‐Ring Diradicals Involving Heavy Main‐Group Elements

By using spin‐unrestricted density functional theory methods, the relationship between the diradical character y and the second hyperpolarizability γ (the third‐order nonlinear optical (NLO) properties at the molecular scale) for four‐membered‐ring diradical compounds, that is, cyclobutane‐1,3‐diyl, Niecke‐type diradicals, and Bertrand‐type diradicals, were investigated by focusing on the substitution effects of heavy main‐group elements as well as of donor/acceptor groups on the y and γ values. It has been found that i) γ is enhanced in the intermediate y region for these four‐membered‐ring diradicals, ii) Niecke‐type diradicals with intermediate y values, which are realized by tuning the combination of the main‐group elements involved, exhibit larger γ values than Bertrand‐type diradicals, and iii) the y value and thus γ value can be controlled by modifying the both‐end donor/acceptor substituents attached to carbon atoms in Nicke‐type C₂P₂ diradicals. These results demonstrate that four‐membered‐ring diradicals involving heavy main‐group elements exhibit high controllability of the y and γ, which indicates the potential applications of four‐membered‐ring diradicals as a building block of highly efficient open‐shell NLO materials.     

meta‐ and para‐Phenylenediamine‐Fused Porphyrin Dimers: Synthesis and Magnetic Interactions of Their Dication Diradicals

meta‐ and para‐Phenylenediamine‐fused nickel(II) porphyrin dimers were synthesized by S_NAr reaction of meso,β,β‐trichloro nickel(II) porphyrin with meta‐ and para‐phenylenediamines and subsequent Pd‐catalyzed intramolecular C?H arylation. Their tetrachlorinated dication diradicals are very stable, allowing SQUID magnetometry and revealing clear open‐shell characters for both meta and para isomers with ferro‐ and anti‐ferromagnetic interactions, respectively. The nitrogen analogue of Thiele's hydrocarbon usually displays predominant closed‐shell nature but its hidden diradical characters increase either in a twisted conformation or upon insertion of an additional phenylene spacer. The observed distinct diradical nature of the para‐congener indicates that diradical properties can be enhanced also by efficient spin delocalization.     

Stable Expanded Porphycene‐Based Diradicaloid and Tetraradicaloid

The synthesis of a bithiophene‐bridged 34π conjugated aromatic expanded porphycene 1 and a cyclopentabithiophene bridged 32π conjugated anti‐aromatic expanded porphycene 2 by a McMurry coupling strategy is presented. Magnetic measurements and theoretical calculations reveal that both 1 and 2 exhibit an open‐shell singlet ground state with significant radical character (y₀=0.63 for 1 ; y₀=0.68, y₁=0.18 for 2 ; y₀: diradical character, y₁: tetraradical character) and a small singlet–triplet energy gap (ΔE_S‐T=?3.25 kcal mol^?1 for 1 and ΔE_S‐T=?0.92 kcal mol^?1 for 2 ). Despite the open‐shell radical character, both compounds display exceptional stability under ambient air and light conditions owing to effective delocalization of unpaired electrons in the extended cyclic π‐conjugation pathway.     

Gold‐Catalyzed Oxa‐Povarov Reactions for the Synthesis of Highly Substituted Dihydrobenzopyrans from Diaryloxymethylarenes and Olefins

Oxa‐Povarov reactions involving readily available diaryloxymethylarenes and aryl‐substituted alkenes are reported. Their [4+2] cycloadditions were efficiently catalyzed by IPrAuSbF₆ (IPr=1,3‐bis(diisopropylphenyl)imidazol‐2‐ylidene) with high diastereoselectivity. Product analysis revealed that the reactions likely proceed by a stepwise ionic mechanism, because both E‐ and Z‐configured β‐methylstyrene gave the same cycloadducts in the same proportions.     

A Stable Trimethylenemethane Triplet Diradical Based on a Trimeric Porphyrin Fused π‐System

Trimethylenemethane (TMM) diradical is the simplest non‐Kekulé non‐disjoint molecule with the triplet ground state (ΔE_ST=+16.1 kcal mol^?1) and is extremely reactive. It is a challenge to design and synthesize a stable TMM diradical with key properties, such as actual aliphatic TMM diradical centers and the triplet ground state with a large positive ΔE_ST value, since such species provide detailed information on the electronic structure of TMM diradical. Herein we report a TMM derivative, in which the TMM segment is fused with three Ni^II meso‐triarylporphyrins, that satisfies the above criteria. The diradical shows delocalized spin density on the propeller‐like porphyrin π‐network and the triplet ground state owing to the strong ferromagnetic interaction. Despite the apparent TMM structure, the diradical can be handled under ambient conditions and can be stored for months in the solid state, thus allowing its X‐ray diffraction structural analysis.     

Concerted vs stepwise mechanism in 1,3-dipolar cycloaddition of nitrone to ethene, cyclobutadiene, and benzocyclobutadiene. A computational study

The problem of competition between concerted and stepwise diradical mechanisms in 1,3-dipolar cycloadditions was addressed by studying the reaction between nitrone and ethene with DFT (R(U)B3LYP/6-31G) and post HF methods. According to calculations this reaction should take place via the concerted cycloaddition path. The stepwise process is a viable but not competitive alternative. The R(U)B3LYP/6-31G study was extended to the reaction of the same 1, 3-dipole with cyclobutadiene and benzocyclobutadiene. The very reactive antiaromatic cyclobutadiene has an electronic structure that is particularly disposed to promote stepwise diradical pathways. Calculations suggest that its reaction with nitrone represents a borderline case in which the stepwise process can compete with the concerted one on similar footing. Attenuation of the antiaromatic character of the dipolarophile, i.e., on passing from cyclobutadiene to benzocyclobutadiene, causes the concerted 1,3-dipolar cycloaddition to become once again prevalent over the two-step path. Thus, our results suggest that, in 1,3-dipolar cycloadditions that involve normal dipolarophiles, the concerted path (Huisgen's mechanism) should clearly overwhelm its stepwise diradical (Firestone's mechanism) counterpart.     

Bulky Substituent Effect on Reactivity of Localized Singlet Cyclopentane‐1,3‐diyls with π‐Single Bonding (C‐π‐C) Character

Thorough investigation of key intermediates, such as long‐lived singlet diradicals, is essential to understand the homolytic bond cleavage reactions. In this study, we evaluate the effect of bulky substituents at the meta‐position of the phenyl ring on the bond formation process in singlet 2,2‐diethoxy‐1,3‐diarylcyclopentane‐1,3‐diyls. The bulky groups have significant influence on the diradical lifetime, as such, when the triisopropylphenyl group was used, the lifetime was 45 times longer than that of the parent diradical in benzene at 293 K.     

Crystalline Diradical Dianions of Pyrene‐Fused Azaacenes

Although diradicals and azaacenes have been greatly attractive in fundamental chemistry and functional materials, the isolable diradical dianions of azaacenes are still unknown. Herein, we describe the first isolation of pyrene‐fused azaacene diradical dianion salts [(18‐c‐6)K(THF)₂]⁺[(18‐c‐6)K]⁺? 1 ^2?.. and [(18‐c‐6)K(THF)]²⁺? 2 ^2?.. by reduction of the neutral pyrene‐fused azaacene derivatives 1 and 2 with excess potassium graphite in THF in the presence of 18‐crown‐6. Their electronic structures were investigated by various experiments, in conjunction with theoretical calculations. It was found that both dianions are open‐shell singlets in the ground state and their triplet states are thermally readily accessible owing to the small singlet–triplet energy gap. This work provides the first examples of crystalline diradical dianions of azaacenes with considerable diradical character.     

The Mesomeric Effect of Thiazolium on non‐Kekulé Diradicals in Pichia stipitis Transketolase

It is theoretically plausible that thiazolium mesomerizes to congeners other than carbene in a low effective dielectric binding site; especially given the energetics and uneven electronegativity of carbene groups. However, such a phenomenon has never been reported. Nine crystal structures of transketolase obtained from Pichia stipitis (TKps) are reported with subatomic resolution, where thiazolium displays an extraordinary ring‐bending effect. The bent thiazolium congeners correlate with non‐Kekulé diradicals because there is no gain or loss of electrons. In conjunction with biophysical and biochemical analyses, it is concluded that ring bending is a result of tautomerization of thiazolium with its non‐ Kekulé diradicals, exclusively in the binding site of TKps. The chemophysical properties of these thiazolium mesomers may account for the great variety of reactivities carried out by thiamine–diphosphate‐containing (ThDP) enzymes. The stability of ThDP in living systems can be regulated by the levels of substrates, and hydration and dehydration, as well as diradical‐mediated oxidative degradation.     

反式-1,4,5,8-四硝基-1,4,5,8-四氮杂萘烷异构体热解机理与稳定性的理论研究

运用密度泛函理论和半经验分子轨道方法,对一系列高能杂环硝胺—反式-1,4,5,8-四硝基-1,4,5,8-四氮杂萘烷异构体的热解机理和稳定性进行了系统地计算研究。在B3LYP/6-31G**和PM3水平上,分别计算了标题物的化学键离解能(BDE)和热解反应活化能(Ea),并根据BDE和Ea数值考察了硝胺取代基对化合物稳定性和热解机理的影响;同时,还详细考察了BDE与Ea、化学键重叠布居数、前线轨道能级以及能隙之间的相关性。结果表明,由BDE、Ea和静态电子结构参数推断的标题物热稳定性和热解机理的结论基本是一致的,N-NO2键均裂是标题物的热解引发步骤,间位取代异构体较对位取代异构体稳定,而邻位取代的异构体稳定性最差。     

A high-spin diradical dianion and its bridged chemically switchable single-molecule magnet

Triplet diradicals have attracted tremendous attention due to their promising application in organic spintronics, organic magnets and spin filters. However, very few examples of triplet diradicals with singlet–triplet energy gaps (ΔE_ST) over 0.59 kcal mol⁻¹ (298 K) have been reported to date. In this work, we first proved that the dianion of 2,7-di-tert-butyl-pyrene-4,5,9,10-tetraone (2,7-tBu₂-PTO) was a triplet ground state diradical in the magnesium complex 1 with a singlet–triplet energy gap ΔE_ST = 0.94 kcal mol⁻¹ (473 K). This is a rare example of stable diradicals with singlet–triplet energy gaps exceeding the thermal energy at room temperature (298 K). Moreover, the iron analog 2 containing the 2,7-tBu₂-PTO diradical dianion was isolated, which was the first single-molecule magnet bridged by a diradical dianion. When 2 was doubly reduced to the dianion salt 2K2, single-molecule magnetism was switched off, highlighting the importance of diradicals in single-molecule magnetism.

We report a triplet diradical dianion in magnesium complex with ΔE_ST = 0.94 kcal mol⁻¹ (473 K). Its iron analog is the first single-molecule magnet bridged by a diradical dianion, and the SMM property is switched off through two-electron reduction.     

Ab initio study of reactions of hydroxyl radicals with chloro‐ and fluoro‐substituted methanes

Ab initio calculations at the unrestricted Hartree–Fock (UHF) level have been performed to investigate the hydrogen abstraction reactions of ^? OH radicals with methane and nine halogen‐substituted methanes (F, Cl). Geometry optimization and vibrational frequency calculations have been performed on all reactants, adducts, products, and transition states at the UHF/6‐31G* level. Single‐point energy calculations at the MP2/6‐31++G* level using the UHF/6‐31G* optimized geometries have also been carried out on all species. Pre‐ and postreaction adducts have been detected on the UHF/6‐31G* potential energy surfaces of the studied reactions. Energy barriers, ΔE^?, reaction energies, ΔE_r, reaction enthalpies, ΔH_r, and activation energies, E_a, have been determined for all reactions and corrected for zero‐point energy effects. Both E_a and ΔH_r come into reasonable agreement with the experiment when correlation energy is taken into account and when more polarized and diffuse basis sets are used. The E_a values, estimated at the PMP2/6‐31++G* level, are found to be in good agreement with the experimental ones and correctly reproduce the experimentally observed trends in fluorine and chlorine substitution effects. A linear correlation between E_a and ΔH_r is obtained, suggesting the presence of an Evans–Polanyi type of relationship. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 426–440, 2001     

Stepwise Versus Concerted Mechanisms in General‐Base Catalysis by Serine Proteases

General‐base catalysis in serine proteases still poses mechanistic challenges despite decades of research. Whether proton transfer from the catalytic Ser to His and nucleophilic attack on the substrate are concerted or stepwise is still under debate, even for the classical Asp‐His‐Ser catalytic triad. To address these key catalytic steps, the transformation of the Michaelis complex to tetrahedral complex in the covalent inhibition of two prototype serine proteases was studied: chymotrypsin (with the catalytic triad) inhibition by a peptidyl trifluoromethane and GlpG rhomboid (with Ser‐His dyad) inhibition by an isocoumarin derivative. The sampled MD trajectories of averaged pK_a values of catalytic residues were QM calculated by the MD‐QM/SCRF(VS) method on molecular clusters simulating the active site. Differences between concerted and stepwise mechanisms are controlled by the dynamically changing pK_a values of the catalytic residues as a function of their progressively reduced water exposure, caused by the incoming ligand.     

Reaction of Paramagnetic Synthon,Lithiated 4,4,5,5‐Tetramethyl‐4,5‐dihydro‐1H‐imidazol‐1‐oxyl 3‐oxide,with Cyclic Aldonitrones of the Imidazole Series

It was shown that dipole‐stabilized paramagnetic carbanion lithiated 4,4,5,5‐tetramethyl‐4,5‐dihydro‐1H‐imidazol‐1‐oxyl 3‐oxide can be attached in a nucleophilic manner to either isolated or conjugated aldonitrones of the 2,5‐dihydroimidazole 3‐oxide and 2H‐imidazole 1‐oxide series to afford adducts the subsequent oxidation of which leads to polyfunctional mono‐ and diradicals. According to XRD, at least two polymorphic modifications can be formed during crystallization of the resulting paramagnetic compounds, and for each of them, geometric parameters of the molecules are similar. An EPR spectrum of the diradical in frozen toluene has a complicated lineshape, which can be fairly well reproduced by using X‐ray diffraction structural analysis and the following set of parameters: D=14.9 mT, E=1.7 mT; tensor a(¹⁴N)=[0.260 0.260 1.625] mT, two equivalent tensors for the nitronyl nitroxide moiety a(¹⁴N)=[0.198 0.198 0.700] mT, and g≈2.007. According to our DFT and ab initio calculations, the intramolecular exchange in the diradical is very weak and most likely ferromagnetic.     

Stable Oxindolyl‐Based Analogues of Chichibabin's and Müller's Hydrocarbons

Chichibabin's and Müller's hydrocarbons are classical open‐shell singlet diradicaloids but they are highly reactive. Herein we report the successful synthesis of their respective stable analogues, OxR‐2 and OxR‐3 , based on the newly developed oxindolyl radical. X‐ray crystallographic analysis on OxR‐2 reveals a planar quinoidal backbone similar to Chichibabin's hydrocarbon, in accordance with its small diradical character (y₀=11.1 %) and large singlet–triplet gap (ΔE_S‐T=−10.8 kcal mol⁻¹). Variable‐temperature NMR studies on OxR‐2 disclose a slow cis/trans isomerization process in solution through a diradical transition state, with a moderate energy barrier (ΔG^≠_298K=15–16 kcal mol⁻¹). OxR‐3 exhibits a much larger diradical character (y₀=80.6 %) and a smaller singlet–triplet gap (ΔE_S‐T=−3.5 kcal mol⁻¹), and thus can be easily populated to paramagnetic triplet diradical. Our studies provide a new type of stable carbon‐centered monoradical and diradicaloid.     

Distance Dependence of Bidirectional Concerted Proton–Electron Transfer in Phenol‐Ru(2,2′‐bipyridine)32+ Dyads

Proton‐coupled electron transfer (PCET) was investigated in three covalent donor–bridge–acceptor molecules with different bridge lengths. Upon photoexcitation of their Ru(bpy)₃²⁺ (bpy=2,2′‐bipyridine) photosensitizer in acetonitrile, intramolecular long‐range electron transfer from a phenolic unit to Ru(bpy)₃²⁺ occurs in concert with release of the phenolic proton to pyrrolidine base. The kinetics of this bidirectional concerted proton–electron transfer (CPET) reaction were studied as a function of phenol–Ru(bpy)₃²⁺ distance by increasing the number of bridging p‐xylene units. A distance decay constant (β) of 0.67±0.23 Å^?1 was determined. The distance dependence of the rates for CPET is thus not significantly steeper than that for ordinary (i.e., not proton coupled) electron transfer across the same bridges, despite the concerted motion of oppositely charged particles into different directions. Long‐range bidirectional CPET is an important reaction in many proteins and plays a key role in photosynthesis; our results are relevant in the context of photoinduced separation of protons and electrons as a means of light‐to‐chemical energy conversion. This is the first determination of β for a bidirectional CPET reaction.     

1,6‐Anhydro‐2,3‐di‐O‐benzyl‐5C‐[(R)‐ethoxycarbonyl(hydroxy)methyl]‐β‐l‐altrofuranose

The crystal structure of the title compound, C₂₄H₂₈O₈, has been determined. The conformation of the furan­ose ring can be described as 58% ideal envelope ^OE conformer and 42% ideal twisted ^OT₁ conformer. The 1,3‐dioxane ring adopts a chair conformation with the anhydro‐O atom pointing upwards. Both phenyl rings are quasi‐perpendicular to the mean plane of the furan­ose ring. The hydrogen bonding is intermolecular and consists of infinite chains parallel to the a axis.     

On the Enantioselectivity of Transition Metal‐Catalyzed 1,3‐Cycloadditions of 2‐Diazocyclohexane‐1,3‐diones

The formal 1,3‐cycloaddition of 2‐diazocyclohexane‐1,3‐diones 1a –1 d to acyclic and cyclic enol ethers in the presence of Rh^II‐catalysts to afford dihydrofurans has been investigated. Reaction with a cis/trans mixture of 1‐ethoxyprop‐1‐ene ( 13a ) yielded the dihydrofuran 14a with a cis/trans ratio of 85 : 15, while that with (Z)‐1‐ethoxy‐3,3,3‐trifluoroprop‐1‐ene ( 13b ) gave the cis‐product 14b exclusively. The stereochemical outcome of the reaction is consistent with a concerted rather than stepwise mechanism for cycloaddition. The asymmetric cycloaddition of 2‐diazocyclohexane‐1,3‐dione ( 1a ) or 2‐diazodimedone (=2‐diazo‐5,5‐dimethylcyclohexane‐1,3‐dione; 1b ) to furan and dihydrofuran was investigated with a representative selection of chiral, nonracemic Rh^II catalysts, but no significant enantioselectivity was observed, and the reported enantioselective cycloadditions of these diazo compounds could not be reproduced. The absence of enantioselectivity in the cycloadditions of 2‐diazocyclohexane‐1,3‐diones is tentatively explained in terms of the Hammond postulate. The transition state for the cycloaddition occurs early on the reaction coordinate owing to the high reactivity of the intermediate metallocarbene. An early transition state is associated with low selectivity. In contrast, the transition state for transfer of stabilized metallocarbenes occurs later, and the reactions exhibit higher selectivity.     

Exploring the Border between Concerted and Two‐Step Pathways of 1,3‐Dipolar Cycloadditions of Organic Azides to Cyclic Ketene N,X‐Acetals. – Synthesis and 15N‐NMR Spectra of Zwitterions and Spirocyclic Cycloadducts

Cyclic ketene N,X‐acetals 1 are electron‐rich dipolarophiles that undergo 1,3‐dipolar cycloaddition reactions with organic azides 2 ranging from alkyl to strongly electron‐deficient azides, e.g., picryl azide ( 2L ; R¹=2,4,6‐(NO₂)₃C₆H₂) and sulfonyl azides 2M – O (R¹=XSO₂; cf. Scheme 1). Reactions of the latter with the most‐nucleophilic ketene N,N‐acetals 1A provided the first examples for two‐step HOMO(dipolarophile)–LUMO(1,3‐dipole)‐controlled 1,3‐dipolar cycloadditions via intermediate zwitterions 3 . To set the stage for an exploration of the frontier between concerted and two‐step 1,3‐dipolar cycloadditions of this type, we first describe the scope and limitations of concerted cycloadditions of 2 to 1 and delineate a number of zwitterions 3 . Alkyl azides 2A – C add exclusively to ketene N,N‐acetals that are derived from 1H‐tetrazole (see 1A ) and 1H‐imidazole (see 1B , C ), while almost all aryl azides yield cycloadducts 4 with the ketene N,X‐acetals (X=NR, O, S) employed, except for the case of extreme steric hindrance of the 1,3‐dipole (see 2E ; R¹=2,4,6‐(^tBu)₃C₆H₂). The most electron‐deficient paradigm, 2L , affords zwitterions 16D , E in the reactions with 1A , while ketene N,O‐ and N,S‐acetals furnish products of unstable intermediate cycloadducts. By tuning the electronic and steric demands of aryl azides to those of ketene N,N‐acetals 1A , we discovered new borderlines between concerted and two‐step 1,3‐dipolar cycloadditions that involve similar pairs of dipoles and dipolarophiles: 4‐Nitrophenyl azide ( 2G ) and the 2,2‐dimethylpropylidene dipolarophile 1A (R, R=H, ^tBu) gave a cycloadduct 13 H , while 2‐nitrophenyl azide ( 2 H ) and the same dipolarophile afforded a zwitterion 16A . Isopropylidene dipolarophile 1A (R=Me) reacted with both 2G and 2 H to afford cycloadducts 13G , J ) but furnished a zwitterion 16B with 2,4‐dinitrophenyl azide ( 2I) . Likewise, 1A (R=Me) reacted with the isomeric encumbered nitrophenyl azides 2J and 2K to yield a cycloadduct 13L and a zwitterion 16C , respectively. These examples suggest that, in principle, a host of such borderlines exist which can be crossed by means of small structural variations of the reactants. Eventually, we use ¹⁵N‐NMR spectroscopy for the first time to characterize spirocyclic cycloadducts 10 – 14 and 17 (Table 6), and zwitterions 16 (Table 7).     

Concerted vs stepwise mechanisms in dehydro-Diels-Alder reactions

The Diels-Alder reaction is not limited to 1,3-dienes. Many cycloadditions of enynes and a smaller number of examples with 1,3-diynes have been reported. These "dehydro"-Diels-Alder cycloadditions are one class of dehydropericyclic reactions which have long been used to generate strained cyclic allenes and other novel structures. CCSD(T)//M05-2X computational results are reported for the cycloadditions of vinylacetylene and butadiyne with ethylene and acetylene. Both concerted and stepwise diradical routes have been explored for each reaction, with location of relevant stationary points. Relative to 1,3-dienes, replacement of one double bond by a triple bond adds 6-6.5 kcal/mol to the activation barrier; a second triple bond adds 4.3-4.5 kcal/mol to the barrier. Product strain decreases the predicted exothermicity. In every case, a concerted reaction is favored energetically. The difference between concerted and stepwise reactions is 5.2-6.6 kcal/mol for enynes but diminishes to 0.5-2 kcal/mol for diynes. Experimental studies on intramolecular diyne + ene cycloadditions show two distinct reaction pathways, providing evidence for competing concerted and stepwise mechanisms. Diyne + yne cycloadditions connect with arynes and ethynyl-1,3-cyclobutadiene. This potential energy surface appears to be flat, with only a minute advantage for a concerted process; many diyne cycloadditions or aryne cycloreversions will proceed by a stepwise mechanism.