Superconducting first‐order pairing: Finite‐temperature simulations

A recently developed first‐order mechanism for superconducting pairing has been extended from T = 0 K to finite temperatures. On the basis of quantum statistical considerations, we have suggested a direct pairing interaction that does not necessarily involve second‐order elements, such as the electron–phonon coupling or specific magnetic interactions submitted by spin fluctuations. The driving force for the (energy‐driven) first‐order pairing is an attenuation of the destabilizing influence of the Pauli antisymmetry principle (PAP). Only the moves of unpaired fermions are controlled by the PAP, while the moves of superconducting Cooper pairs are not. The quantum statistics of Cooper pairs is of a mixed type, as it combines fermionic on‐site and bosonic intersite properties. The strong correlation between the strength of PAP constraints and system topology in combination with the electron number has been discussed for some larger clusters. Detailed finite‐temperature simulations on first‐order pairing have been performed for four‐center–four‐electron clusters with different topologies. A canonical ensemble statistics has been employed to derive the electronic energy, the electronic configuration entropy, and the free energy of paired and unpaired states in thermal equilibrium. The simulations show that pairing can be caused by either the electronic energy or the electronic configuration entropy. The coexistence of two different sets of quantum particles in paired states (i.e., the Cooper pairs and the unpaired electrons) can lead to an enhanced configuration entropy. In this context, we discuss the possibility of an entropy‐driven high‐temperature superconductor emerging from a low‐temperature unpaired state. The charge and spin degrees of freedom of the four‐center–four‐electron systems have been studied with the help of the charge and spin fluctuations. The spin fluctuations are helpful in judging the validity of pairing theories based on magnetic interactions. The charge fluctuations are a measure for the carrier delocalization in unpaired and paired states. The well‐known proximity between Jahn–Teller activity and superconductivity is analyzed in the zero‐temperature limit. It is demonstrated that both processes compete in their ability to reduce PAP constraints. All theoretical results have been derived within the framework of the simple Hubbard Hamiltonian. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Coexistence of ferromagnetism and superconductivity in YBCO nanoparticles

Nanoparticles of superconducting YBa(2)Cu(3)O(7-δ) were synthesized via a citrate pyrolysis technique. Room temperature ferromagnetism was revealed in the samples by a vibrating sample magnetometer. Electron spin resonance spectra at selected temperatures indicated that there is a transition from the normal to the superconducting state at temperatures below 100 K. The M-T curves with various applied magnetic fields showed that the superconducting transition temperatures are 92 K and 55 K for the air-annealed and the post-annealed samples, respectively. Compared to the air-annealed sample, the saturation magnetization of the sample by reheating the air-annealed one in argon atmosphere is enhanced but its superconductivity is weakened, which implies that the ferromagnetism maybe originates from the surface oxygen defects. By superconducting quantum interference device measurements, we further confirmed the ferromagnetic behavior at high temperatures and interesting upturns in field cooling magnetization curves within the superconducting region are found. We attributed the upturn phenomena to the coexistence of ferromagnetism and superconductivity at low temperatures. Room temperature ferromagnetism of superconducting YBa(2)Cu(3)O(7-δ) nanoparticles has been observed in some previous related studies, but the issue of the coexistence of ferromagnetism and superconductivity within the superconducting region is still unclear. In the present work, it will be addressed in detail. The cooperation phenomena found in the spin-singlet superconductors will help us to understand the nature of superconductivity and ferromagnetism in more depth.     

Superconductivity in a Copper(II)‐Based Coordination Polymer with Perfect Kagome Structure

A highly crystalline copper(II) benzenehexathiolate coordination polymer (Cu‐BHT) has been prepared. The two‐dimensional kagome structure has been confirmed by powder X‐ray diffraction, high‐resolution transmission electron microscopy, and high‐resolution scanning transmission electron microscopy. The as‐prepared sample exhibits bulk superconductivity at about 0.25 K, which is confirmed by the zero resistivity, AC magnetic susceptibility, and specific heat measurements. Another diamagnetic transition at about 3 K suggests that there is a second superconducting phase that may be associated with a single layer or few layers of Cu‐BHT. It is the first time that superconductivity has been observed in a coordination polymer.     

High‐temperature superconductivity and long‐range order in strongly correlated electronic systems

A selective review of the question of how repulsive electron correlations might give rise to off‐diagonal long‐range order (ODLRO) in high‐temperature superconductors is presented. The article makes detailed explanations of the relevance to superconductivity of reduced electronic density matrices and how these can be used to understand whether ODLRO might arise from Coulombic repulsions in strongly correlated electronic systems. Time‐reversed electron pairs on alternant Cuprate and the iron‐based pnictide and chalcogenide lattices may have a weak long‐range attractive tail and much stronger short‐range repulsive Coulomb interaction. The long‐range attractive tail may find its origin in one of the many suggested proposals for high‐T_c superconductivity and thus has an uncertain origin. A phenomenological Hamiltonian is invoked whose model parameters are obtained by fitting to experimental data. A detailed summary is given of the arguments that such interacting electrons can cooperate to produce a superconducting state in which time‐reversed pairs of electrons effectively avoid the repulsive hard‐core of the Coulomb interaction but reside on average in the attractive well of the long‐range potential. Thus, the pairing of electrons itself provides an enhanced screening mechanism. The alternant lattice structure is the key to achieving robust high‐temperature superconductivity with dx²‐y² or sign alternating s‐wave or s± condensate symmetries in cuprates and iron‐based compounds. Some attention is also given to the question first raised by Leggett as to where the Coulombic energy is saved in the superconducting transition in cuprates. A mean‐field‐type model in which the condensate density serves as an order parameter is discussed. Many of the observed trends in the thermal properties of cuprate superconductors are reproduced giving strong support for the proposed model for high‐temperature superconductivity in such strongly correlated electronic systems. © 2015 Wiley Periodicals, Inc.     

Triplet State Aromaticity: NICS Criterion,Hyperconjugation, and Charge Effects

Aromaticity, one of the most important concepts in organic chemistry, has attracted considerable interest from both experimentalists and theoreticians. It remains unclear which NICS index is best to evaluate the triplet‐state aromaticity. Here, we carry out thorough density functional theory (DFT) calculations to examine this issue. Our results indicate that among the various computationally available NICS indices, NICS(1)_zz is the best for the triplet state. The correlations can be improved from 0.840 to 0.938 when only neutral species are considered, demonstrating the significant effect of the charge on the triplet‐state aromaticity. In addition, calculations suggest that five‐membered cyclic species with “hyperconjugative” aromaticity (and antiaromaticity) in the S₀ state will become antiaromatic (and aromatic) in the T₁ state, indicating an important role of hyperconjugation. Finally, a moderate correlation (r²=0.708) is identified between the NICS(1)_zz values and spin distributions.     

Exploiting the Aromatic Chameleon Character of Fulvenes for Computational Design of Baird‐Aromatic Triplet Ground State Compounds

Due to the reversal in electron counts for aromaticity and antiaromaticity in the closed‐shell singlet state (normally ground state, S₀) and lowest ππ* triplet state (T₁ or T₀), as given by Hückel's and Baird's rules, respectively, fulvenes are influenced by their substituents in the opposite manner in the T₁ and S₀ states. This effect is caused by a reversal in the dipole moment when going from S₀ to T₁ as fulvenes adapt to the difference in electron counts for aromaticity in various states; they are aromatic chameleons. Thus, a substituent pattern that enhances (reduces) fulvene aromaticity in S₀ reduces (enhances) aromaticity in T₁, allowing for rationalizations of the triplet state energies (E_T) of substituted fulvenes. Through quantum chemical calculations, we now assess which substituents and which positions on the pentafulvene core are the most powerful for designing compounds with low or inverted E_T. As a means to increase the π‐electron withdrawing capacity of cyano groups, we found that protonation at the cyano N atoms of 6,6‐dicyanopentafulvenes can be a route to on‐demand formation of a fulvenium dication with a triplet ground state (T₀). The five‐membered ring of this species is markedly Baird‐aromatic, although less than the cyclopentadienyl cation known to have a Baird‐aromatic T₀ state.     

Facile Synthesis of Polycyclic Pentalenes with Enhanced Hückel Antiaromaticity

Pentalenes represent highly reactive Hückel antiaromatics with 8π electrons. Usually, pentalenes are stabilized by incorporation of two benzene rings in a fused fashion. In dibenzo[a ,e ]pentalenes, however, the high aromaticity of the fused benzene rings compromises the inherent antiaromaticity of the pentalene core. Herein, we disclose that this forfeited antiaromaticity can be restored by fusing four additional aromatic rings onto the peripheral positions of dibenzo[a,e]pentalenes. Such polycyclic pentalenes were prepared by successive transannular cyclizations via in situ‐generated tetrakisdehydro[16]annulenes. The thus obtained compounds showed intriguing properties, for example, characteristic absorptions in the visible‐to‐near‐infrared (NIR) region and low reduction potentials. These results hence afford a design principle to produce highly antiaromatic yet stable pentalenes. The antiaromaticity of the pentalene core can be widely tuned via the degree of aromaticity of the peripherally fused rings.     

Global Aromaticity and Antiaromaticity in Porphyrin Nanoring Anions

Doping, through oxidation or reduction, is often used to modify the properties of π‐conjugated oligomers. In most cases, the resulting charge distribution is difficult to determine. If the oligomer is cyclic and doping establishes global aromaticity or antiaromaticity, then it is certain that the charge is fully delocalized over the entire perimeter of the ring. Herein we show that reduction of a six‐porphyrin nanoring using decamethylcobaltocene results in global aromaticity (in the 6? state; [90 π]) and antiaromaticity (in the 4? state; [88 π]), consistent with the Hückel rules. Aromaticity is assigned by NMR spectroscopy and density‐functional theory calculations.     

Proton transfers in aromatic and antiaromatic systems. How aromatic or antiaromatic is the transition state? An ab initio study

An ab initio study of six carbon-to-carbon identity proton transfers is reported. They refer to the benzenium ion/benzene (C6H7(+)/C6H6), the 2,4-cyclopentadiene/cyclopentadienyl anion (C5H6/C5H5(-)), and the cyclobutenyl cation/cyclobutadiene (C4H5(+)/C4H4) systems and their respective noncyclic reference systems, that is, [structure: see text], [structure: see text] and [structure: see text]. For the aromatic C6H7(+)/C6H6 and C5H6/C5H5(-) systems, geometric parameters and aromaticity indices indicate that the transition states are highly aromatic. The proton-transfer barriers in these systems are quite low, which is consistent with a disproportionately high degree of transition-state aromaticity. For the antiaromatic C4H5(+)/C4H4 system, the geometric parameters and aromaticity indices indicate a rather small degree of antiaromaticity of the transition state. However, the proton-transfer barrier is higher than expected for a transition state with a low antiaromaticity. This implies that another factor contributes to the barrier; it is suggested that this factor is angle and torsional strain in the transition state. The question whether charge delocalization at the transition state might correlate with the development of aromaticity was also examined. No such correlation was found, that is, charge delocalization lags behind proton transfer as is commonly observed in nonaromatic systems involving pi-acceptor groups.     

Effect of transition state aromaticity and antiaromaticity on intrinsic barriers of proton transfers in aromatic and antiaromatic heterocyclic systems; an ab initio study

An ab initio study of two series of carbon-to-carbon proton transfer reactions is reported. The first series refers to the heterocyclic C(4)H(5)X(+)/C(4)H(4)X (X = CH(-), NH, S, O, PH, CH(2), AlH, BH) systems, and the second to the linear [Formula: see text] (X = CH(-), NH, S, PH, O, CH(2), AlH, BH) reference systems . The major objective of this study was to examine to what degree the aromaticity of C(4)H(4)X (X = CH(-), NH, S, O, PH) and the antiaromaticity of C(4)H(4)X (X = AlH, BH) is expressed at the transition state of the proton transfer and how this affects the respective intrinsic barriers. From the differences in the barriers between a given cyclic system and the corresponding linear reference system , ΔΔH(++) = ΔH(++)(cyclic) - ΔH(++)(linear), it was inferred that in the cyclic systems both aromaticity and antiaromaticity lower ΔH(++)(cyclic). This conclusion was based on the assumption that the factors not associated with aromaticity or antiaromaticity such as resonance, inductive and polarizability effects in the protonated species, and charge delocalization occurring along the reaction coordinate affect ΔH(++) for the cyclic and linear systems in a similar way and hence offset each other in ΔΔH(++). The extent by which ΔH(++)(cyclic) is lowered in the aromatic systems correlates quite well with the degree of aromaticity of C(4)H(4)X as measured by aromatic stabilization energies as well as the NICS(1) values of the respective C(4)H(4)X. According to the rules of the principle of nonperfect synchronization (PNS), these results imply a disproportionately large degree of aromaticity at the transition state for the aromatic systems and a disproportionately small degree of transition state antiaromaticity for the antiaromatic systems. These conclusions are consistent with the changes in the NICS(1) values along the reaction coordinate. Other points discussed in the paper include the complex interplay of resonance, inductive, and polarizability effects, along with aromaticity and antiaromaticity on the proton affinities of C(4)H(4)X.     

Aromaticity Reversal in the Lowest Excited Triplet State of Archetypical Möbius Heteroannulenic Systems

The aromaticity reversal in the lowest triplet state (T₁) of a comparable set of Hückel/Möbius aromatic metalated expanded porphyrins was explored by optical spectroscopy and quantum calculations. In the absorption spectra, the T₁ states of the Möbius aromatic species showed broad, weak, and ill‐defined spectral features with small extinction coefficients, which is in line with typical antiaromatic expanded porphyrins. In combination with quantum calculations, these results indicate that the Möbius aromatic nature of the S₀ state is reversed to Möbius antiaromaticity in the T₁ state. This is the first experimental observation of aromaticity reversal in the T₁ state of Möbius aromatic molecules.     

BaxC60 fullerides: π Electronic peculiarities of the C60 molecule and their consequences for the solid state

The electronic structure of Ba_xC₆₀ fullerides was studied theoretically under special consideration of π electronic effects in the C₆₀ molecule. Band structure data were derived by an intermediate neglect of differential overlap (INDO) crystal orbital (CO) approach. Different electronic configuration were evaluated in the Ba-doped C₆₀ fullerides. Ba_xC₆₀ solids with x=0, 3, 4, 6 are insulators. For a Ba₅C₆₀ model extrapolated from the crystal structure of Ba₆C₆₀, a finite band gap is also predicted. For a Ca₅C₆₀-like structure of Ba₅C₆₀, a quasi-degeneracy between a metallic configuration and an insulating Mott-like state was found. With an increasing Ba-to-C₆₀ charge transfer (CT), sizable changes in the π system of C₆₀ occur. In the neural molecule and for not too high an electron count, the π electrons form more or less electronically isolated hexagon–hexagon (6–6) “double” bonds with only minor hexagon–pentagon (6–5) “double-bond” admixtures. In the vicinity of C₆₀¹²⁻, the 6–6 bonds have lost most of their double-bond character while it is enhanced for the 6–5 bonds. In highly charged anions, the π electron system of the soccer ball approaches a configuration with 12 decoupled 6π electron pentagons. For electron numbers between C₆₀ and C₆₀¹²⁻, the net π bonding is not weakened. The INDO CO results of the Ba_xC₆₀ solids are supplemented by INDO MO and ab initio (3-21 G* split-valence basis) calculations of molecular C₆₀ and some highly charged anions. Ab initio geometry optimizations show that the bond alternation of C₆₀ with short 6–6 and long 6–5 bonds is inverted in C¹²⁻₆₀. The high acceptor capability of C₆₀ is explained microscopically on the basis of quantum statistical arguments. In the π electron configurations of C₆₀ and C₆₀¹²⁻, the influence of the Pauli antisymmetry principle (PAP) is minimized. The quantum statistics of (π) electron ensembles with a deactivated PAP is of the so-called hard-core bosonic (hcb) type. In these ensembles, the on-site interaction is fermionic while the intersite interaction is bosonic. Energetic consequences of the quantum statistical peculiarities of π systems are explained with the aid of simple model systems; we selected annulenes and polyenes. Computational tools in this step are Green's function quantum Monte Carlo (GF QMC) and full configuration interaction (CI) calculations for the π electrons of the model systems. These many-body techniques were combined with a Pariser–Parr–Pople (PPP) Hamiltonian. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 333–373, 1997     

Effect on ring current of the Kekulé vibration in aromatic and antiaromatic rings

Derivative current-density maps are used to follow the changes in ring-current (and hence, on the magnetic criterion, the changes in aromaticity) with the Kekulé vibrations of the prototypical aromatic, antiaromatic, and nonaromatic systems of benzene, cyclooctatetraene (COT), and borazine. Maps are computed at the ipsocentric CHF/6-31G**//RHF/6-31G** level. The first-derivative map for benzene shows a growing-in of localized bond currents, and the second-derivative map shows a pure, paratropic "antiring-current", leading to the conclusion that vibrational motion along the Kekulé mode will reduce the net aromaticity of benzene, on average. For planar-constrained D(4h) COT, the Kekulé mode (positive for reduction of bond-length alternation) increases paratropicity at both first and second order, indicating an average increase in antiaromaticity with zero-point motion along this mode. On the ring-current criterion, breathing expansions of benzene and D(4h) COT reduce aromaticity and increase antiaromaticity, respectively.     

Cyclobis(7,8‐(para‐quinodimethane)‐4,4′‐triphenylamine) and Its Cationic Species Showing Annulene‐Like Global (Anti)Aromaticity

π‐Conjugated macrocycles containing all‐benzenoid rings usually show local aromaticity, but reported herein is the macrocycle CBQT , containing alternating para‐quinodimethane and triphenylamine units displaying annulene‐like anti‐aromaticity at low temperatures as a result of structural rigidity and participation of the bridging nitrogen atoms in π‐conjugation. It was easily synthesized by intermolecular Friedel–Crafts alkylation followed by oxidative dehydrogenation. X‐ray crystallographic structures of CBQT , as well as those of its dication, trication, and tetracation were obtained. The dication and tetracation exhibited global aromaticity and antiaromaticity, respectively, as confirmed by NMR measurements and theoretical calculations. Both the dication and tetracation possess open‐shell singlet ground states, with a small singlet–triplet gap.     

Hexaphyrin–Cyclodextrin Hybrids: A Nest for Switchable Aromaticity,Asymmetric Confinement,and Isomorphic Fluxionality

Conformational control over the highly flexible π‐conjugated system of expanded porphyrins is a key step toward the fundamental understanding of aromaticity and for the development of molecular electronics. We have synthesized unprecedented hexaphyrin–cyclodextrin (HCD) capped hybrids in which the hexaphyrin part is constrained in a planar rectangular conformation in either a 26 or a 28 π‐electron oxidation state ( [26] / [28]HCD ). These structures display strong aromaticity and antiaromaticity, respectively, exhibit markedly different chiroptical properties, and are interconvertible upon the addition of DDQ or NaBH(OAc)₃, thus affording a rare switchable aromatic–antiaromatic system with a free‐base expanded porphyrin. Conformational analysis revealed discrimination of the two coordination sites of the hexaphyrin, one of which was coupled to a confined asymmetric environment, and fluxional behavior consisting of apparent rotation of the hexaphyrin cap through a shape‐shifting mechanism.     

Thiophene-Fused 1,4-Diazapentalene: A Stable C=N-Containing π-Conjugated System with Restored Antiaromaticity

A thiophene-fused 1,4-diazapentalene (TAP) was rationally designed and synthesized as a C=N-containing 4n π-electron system that exhibits restored antiaromaticity impaired by the doping with C=N bonds. X-ray crystallographic analysis and quantum chemical calculations revealed that the annulation of thiophene rings with the 1,4-diazapentalene moiety resulted in a much higher antiaromaticity than the pristine 1,4-diazapentalene. These effects can be ascribed to the reduced bond alternation of the eight-membered-ring periphery caused by stabilization of the less-stable bond-shifted resonance structure upon increasing the degree of substitution of imine moieties. Consequently, TAP underwent facile hydrogenation even under mild conditions because of its pronounced antiaromaticity and the high aromaticity of the corresponding hydrogenated product H₂-TAP. In addition, the electrophilic C=N moieties in TAP led to the formation of a dense π-stacked structure. These results highlight the effect of partial replacement of C=C bonds with C=N bonds in antiaromatic π-electron systems.     

Ring Size Determines the Conformation,Global Aromaticity and Photophysical Properties of Macrocyclic Oligofurans

In π-conjugated macrocycles, there is a trade-off between the global and local expression of effects such as aromaticity, with the outcome of the trade-off determined by the geometry and aromaticity of the constituent units. Compared with other aromatic rings, the aromatic character of furan is relatively small, and therefore global effects in macrocyclic furans are expected to be more pronounced. Following our introduction of macrocyclic oligofuran, we present the first synthesis of a series of π-conjugated bifuran macrocycles of various ring sizes, from trimer to hexamer, and characterize them using both computational and experimental methods. The properties of macrocyclic oligofurans change considerably with size: The smaller trimer is rigid, weakly emissive and planar as revealed by its single crystal structure, and displays global antiaromaticity. In contrast, the larger pentamer and hexamer are flexible, emissive, have non-planar structures, and exhibit local aromaticity. The results are supported by NICS and ACID calculations that indicate the global antiaromaticity of planar furan macrocycles, and by transient absorption measurements showing sharp absorption band for the trimer and only the internal conversion decay pathway.     

Hexaphyrin–Cyclodextrin Hybrids: A Nest for Switchable Aromaticity,Asymmetric Confinement,and Isomorphic Fluxionality

Conformational control over the highly flexible π‐conjugated system of expanded porphyrins is a key step toward the fundamental understanding of aromaticity and for the development of molecular electronics. We have synthesized unprecedented hexaphyrin–cyclodextrin (HCD) capped hybrids in which the hexaphyrin part is constrained in a planar rectangular conformation in either a 26 or a 28 π‐electron oxidation state ( [26] / [28]HCD ). These structures display strong aromaticity and antiaromaticity, respectively, exhibit markedly different chiroptical properties, and are interconvertible upon the addition of DDQ or NaBH(OAc)₃, thus affording a rare switchable aromatic–antiaromatic system with a free‐base expanded porphyrin. Conformational analysis revealed discrimination of the two coordination sites of the hexaphyrin, one of which was coupled to a confined asymmetric environment, and fluxional behavior consisting of apparent rotation of the hexaphyrin cap through a shape‐shifting mechanism.