Möbius and Hückel Cyclacenes with Dewar and Ladenburg Defects

Cyclacene nanobelts have not been synthesized in over 60 years and remain one of the last unsynthesized building blocks of carbon nanotubes. Recent work has predicted that Hückel-cyclacenes containing Dewar benzenoid ring isomers are the most stable isomeric forms for several of the smaller sizes of cyclacene belts. Here, we give a more complete picture of the isomers that are possible within these nanobelt systems by simulating embedded Ladenburg (prismane) benzenoid rings in Hückel-[n]cyclacenes (n = 5-14) and embedded Dewar benzenoid rings in twisted Möbius-[n]cyclacenes (n = 9-14). The Möbius-[9]cyclacene isomer containing one Dewar benzenoid defect and the Hückel-[5]cyclacene isomer containing two maximally spaced Ladenburg benzenoid defects are found to be more stable than their conventional Kekulé benzenoid ring counterparts. The isomers that contain Dewar and Ladenburg benzenoid rings have larger electronic singlet-triplet energy gaps and lower polyradical character when compared with the conventional isomers.

Electronic Properties of Möbius Cyclacenes Studied by Thermally-Assisted-Occupation Density Functional Theory

It has been extremely difficult for traditional theoretical methods to adequately predict the properties of systems possessing radical character (i.e., multi-reference systems), especially for multi-reference systems at the nanoscale. To circumvent this, we employ thermally-assisted-occupation density functional theory (TAO-DFT) to predict the electronic properties of Möbius cyclacenes, with the number of fused benzene rings (n) ranging from 8 to 100. In addition, to investigate the significance of Möbius topology, we also compare these properties with the respective properties of cyclacenes and acenes, containing the same number of fused benzene rings. From our TAO-DFT results, Möbius cyclacenes, cyclacenes, and acenes have singlet ground states for all the cases examined. However, unlike acenes, the electronic properties of Möbius cyclacenes and cyclacenes display clear oscillation patterns when n is small (e.g., n ≤ 10 for Möbius cyclacenes and n ≤ 23 for cyclacenes), and converge to the respective properties of acenes when n greatly exceeds 30. The polyradical character of the ground states of Möbius cyclacenes should increase with the molecular size, intimately correlated with the localization of active orbitals at the edges of molecules.

Theoretical study of substituent effects on electride characteristics and the nonlinear optical properties of Li@calix[4]pyrrole

A relationship between the electride characteristics and the NLO properties is found: the more delocalization the excess electron of the electride experiences, the larger the β₀ value is.

Remarkable nonlinear optical response of excess electron compounds: theoretically designed alkali-doped aziridine M–(C2NH5)n

Newly theoretically designed alkali-doped aziridine M–(C₂NH₅)₄ shows a remarkable NLO response and its first hyperpolarizability is 10 to 100 times larger than those of M@Calix[4]pyrrole.

Introducing the triangular BN nanodot or its cooperation with the edge-modification via the electron-donating/withdrawing group to achieve the large first hyperpolarizability in a carbon nanotube system

Doping the triangular BN nanodomain or its cooperation with the edge-modification can significantly improve the NLO properties of CNT systems.

Role of a singlet diradical character in carbon nanomaterials: a novel hot spot for efficient nonlinear optical materials

Carbon atoms have the potential to produce a variety of fascinating all-carbon structures with amazing electronic and mechanical properties. Over the last few decades, several efforts have been made using experimental and computational techniques to functionalize graphene, carbon nanotubes and fullerenes for potential use in modern hi-tech electronic, medicinal, optical and nonlinear optical (NLO) applications. Since photons replaced electrons as a carrier of information, the field of NLO material design has drawn immense interest in contemporary materials science. There have been several reports of bridging the gap between the exciting fields of carbon nanomaterials and NLO materials by functionalizing carbon nanomaterials for potential NLO applications. In contrast to previous reports of the design of third-order NLO materials using conventional closed-shell materials, a novel strategy using open-shell diradical molecular systems has recently been proposed. Quantum chemically, diradical character is explained in terms of the instability of the chemical bonds in open-shell molecular systems. Interestingly, several carbon nanomaterials, which naturally possess open-shell singlet configurations, have recently gained momentum in the design of these classes of open-shell NLO materials with excellent NLO properties, stability and diversity. The present review establishes a systematic sequence of different studies (spanning over two decades of intense research efforts), starting from the simplest theoretical two-site diradical model, continuing to its experimental and theoretical realization in actual chemical systems, and finally applying the abovementioned model/rule to novel carbon nanomaterials to tune their NLO properties, particularly their second hyperpolarizability (γ). In the present report, we highlight several recent efforts to functionalize carbon nanomaterials by exploiting their open-shell diradical character to achieve efficient third-order NLO properties. Several issues and opportunities are discussed, including the inherited disadvantages of both experimental (the high reactivity and short life of diradical compounds) and quantum (need for multi-reference methodology) techniques when dealing with carbon nanomaterials. A comparative analysis of several quantum chemical investigations, along with contemporary experimental results, will be performed to emphasize the core issues and opportunities related to carbon nanomaterials with singlet open-shell diradical character. Thus, the present review will highlight carbon nanomaterials with diradical/biradical character for their prospective applications in the NLO field.

The inner-induced effects of YCN in C76 on the structures and nonlinear optical properties

Very recently, an unprecedented novel monometallic cluster of fullerenes entrapping a yttrium cyanide (YCN) cluster inside a popular C82 cage YCN@Cs(6)-C82 was synthesized and characterized. Inspired by this investigation, four non-IPR YCN@C1(17459)-C76, YCN@C2v(19138)-C76, YCN@C2(17646)-C76, and YCN@C1(17894)-C76 (1, 2, 3, and 4) containing a pair of adjacent pentagons are designed to explore the encapsulated molecular effect on their interaction energies and nonlinear optical properties. The interaction energy (E int) values of 1, 2, 3, and 4 are -481.35 (1), -477.91 (2), -482.04 (3), -482.69 (4) kcal mol(-1), respectively, which shows that the E int value of 4 is the largest. Furthermore, the electron-transfer is mainly from the YCN to C76 cage. When YCN is encapsulated into C76 cage, we can find that the α0 values of the four molecules are very close, ranging from 6.50 × 10(2) to 6.65 × 10(2) au. Significantly, the first hyperpolarizabilities are in relation to the encapsulated molecular: 1.63 × 10(3) (1) > 8.03 × 10(2) (2) > 7.76 × 10(2) (4) > 4.86 × 10(2) au (3), the results show that the βtot value of 1 is the largest. Besides this, the encapsulation of the YCN to C76 cage brings some distinctive changes in its UV-vis spectra along with its other electronic properties that might be used by the experimentalists to develop the potential nonlinear optical nanomaterials based on endohedral metallofullerenes.

Influence of material stretchability on the equilibrium shape of a Möbius band

We use a two-dimensional discrete, lattice-based model to show that Möbius bands made with stretchable materials are less likely to crease or tear. This stems from a delocalization of twisting strain that occurs if stretching is allowed. The associated low-energy configurations provide strategic target shapes for the guided assembly of nanometer and micron scale Möbius bands. To predict macroscopic band shapes for a given material, we establish a connection between stretchability and relevant continuum moduli, leading to insight regarding the practical feasibility of synthesizing Möbius bands from materials with continuum parameters that can be measured experimentally or estimated by upscale averaging.

The effect of heterocyclic π bridges on second order nonlinear optical properties of compounds formed between ferrocenyl and corannulenyl

Among D–π–A type compounds, when imidazole acts as a π bridge (endo/exo-3), the β_tot values are almost 2 times as large as when the phenyl acts as a π bridge (endo/exo-2).

Constructing a mixed π-conjugated bridge to effectively enhance the nonlinear optical response in the Möbius cyclacene-based systems

Using density functional theory computations, employing the concept of a mixed π-conjugated bridge can effectively improve the first hyperpolarizability (β0) of Möbius cyclacene (MC)-based systems with a D-π-A framework. This mixed π-conjugated bridge is constructed by applying a -(CH=CH)x-NH2 or -(CH=CH)x-NO2 chain to modify [8]MC, which can lead to a considerable β0 value (e.g. [8]MC-(CH=CH)12-NO2 (9.87 × 10(5) au) with only a certain chain length), much larger than the sole [8]MC (261 au) and the corresponding NH2/NO2-modified polyethylene chain with the same π-conjugated length. It is revealed that the substituent sites and the chain length can play a crucial role in improving β0 values of these MC-chain systems, where the β0 value can monotonically increase with increasing -(CH=CH)x- length, and the substituent electron-withdrawing -(CH=CH)x-NO2 chain is superior to the parallel electron-donating -(CH=CH)x-NH2. These appealing findings can provide valuable insights into the design of novel NLO materials based on MC.

The effect of ring sizes and alkali metal cations on interaction energy, charge transfer and nonlinear optical properties of crown ether derivatives

A series of the crown ethers are designed to explore the effect of ring sizes and the nature of alkali metal cations doping on the interaction energy, charge transfer and nonlinear optical property.

The V-shaped polar molecules encapsulated into Cs (10528)-C72: stability and nonlinear optical response

Recently, a new sulfide cluster fullerene, Sc2S@Cs (10528)-C72 containing two pairs of fused pentagons has been isolated and characterized (Chen et al., J. Am. Chem. Soc., 2012, 134, 7851). Inspired by this investigation, we propose a question: what properties will be influenced by the interaction between the encapsulated V-shaped polar molecule and C72? To answer this question, four encapsulated metallic fullerenes (EMFs) M2N@C72 (M = Sc or Y, N = S or O) along with pristine Cs-C72 (10528) were investigated by quantum chemistry methods. The results show that the Egap (3.01-3.14 eV) of M2N@C72 are significantly greater than that of pristine Cs-C72 (10528) (2.34 eV). This indicates that the stabilities of these EMFs increase by encapsulating the V-shaped polar molecule into the fullerene. Furthermore, the natural bond orbital (NBO) charge analysis indicates electron transfer from M2N to C72 cage, which plays a crucial role in enhancing first hyperpolarizability (βtot). The βtot follows the order of 1174 au (Y2O@C72) ≈ 1179 au (Sc2O@C72) > 886 au (Y2S@C72) ≈ 864 au (Sc2S@C72) > 355 au (C72). This indicates that the βtot of M2N@C72 is more remarkable than that of pristine Cs-C72 (10528) due to the induction effect of the encapsulated molecule. Compared with sulfide cluster fullerenes (Y2S@C72 and Sc2S@C72), oxide cluster fullerenes (Sc2O@C72 and Y2O@C72) show much larger βtot due to the small ionic radius and the large electronegativity of oxygen. In contrast, the metal element (scandium and yttrium) has a slight influence on the βtot. Thus, oxide cluster fullerenes are candidates to become promising nonlinear optical materials with higher performance.

Design and synthesis of the first triply twisted Möbius annulene

As long as 50 years ago theoretical calculations predicted that Möbius annulenes with only one π surface and one edge would exhibit peculiar electronic properties and violate the Hückel rules. Numerous synthetic attempts notwithstanding, the first singly twisted Möbius annulene was not prepared until 2003. Here we present a general, rational strategy to synthesize triply or even more highly twisted cyclic π systems. We apply this strategy to the preparation of a triply twisted [24]dehydroannulene, the structure of which was confirmed by X-ray analysis. Our strategy is based on the topological transformation of 'twist' into 'writhe'. The advantage is twofold: the product exhibits a lower degree of strain and precursors can be designed that inherently include the writhe, which, after cyclization, ends up in the Möbius product. With our strategy, triply twisted systems are easier to prepare than their singly twisted counterparts.