Mechanism and rate constants of the CH2 + CH2CO reactions in triplet and singlet states: A theoretical study

Ab initio and density functional CCSD(T)-F12/cc-pVQZ-f12//B2PLYPD3/6-311G** calculations have been performed to unravel the reaction mechanism of triplet and singlet methylene CH₂ with ketene CH₂CO. The computed potential energy diagrams and molecular properties have been then utilized in Rice–Ramsperger–Kassel–Marcus-Master Equation (RRKM-ME) calculations of the reaction rate constants and product branching ratios combined with the use of nonadiabatic transition state theory for spin-forbidden triplet-singlet isomerization. The results indicate that the most important channels of the reaction of ketene with triplet methylene lead to the formation of the HCCO + CH₃ and C₂H₄ + CO products, where the former channel is preferable at higher temperatures from 1000 K and above. In the C₂H₄ + CO product pair, the ethylene molecule can be formed either adiabatically in the triplet electronic state or via triplet-singlet intersystem crossing in the singlet electronic state occurring in the vicinity of the CH₂COCH₂ intermediate or along the pathway of CO elimination from the initial CH₂CH₂CO complex. The predominant products of the reaction of ketene with singlet methylene have been shown to be C₂H₄ + CO. The formation of these products mostly proceeds via a well-skipping mechanism but at high pressures may to some extent involve collisional stabilization of the CH₃CHCO and cyclic CH₂COCH₂ intermediates followed by their thermal unimolecular decomposition. The calculated rate constants at different pressures from 0.01 to 100 atm have been fitted by the modified Arrhenius expressions in the temperature range of 300–3000 K, which are proposed for kinetic modeling of ketene reactions in combustion. © 2018 Wiley Periodicals, Inc.     

Theoretical study of lanthanide-based in vivo luminescent probes for detecting hydrogen peroxide

The 4f-4f emissions from lanthanide trication (Ln³⁺) complexes are widely used in bioimaging probes. The emission intensity from Ln³⁺ depends on the surroundings, and thus, the design of appropriate photo-antenna ligands is indispensable. In this study, we focus on two probes for detecting hydrogen peroxide, for which emission intensities from Tb³⁺ are enhanced chemo-selectively by the H₂O₂-mediated oxidation of ligands. To understand the mechanism, the Gibbs free energy profiles of the ground and excited states related to emission and quenching are computed by combining our approximation—called the energy shift method—and density functional theory. The different emission intensities are mainly attributed to different activation barriers for excitation energy transfer from the ligand-centered triplet (T1) to the Tb³⁺-centered excited state. Additionally, quenching from T1 to the ground state via intersystem crossing was inhibited by intramolecular hydrogen bonds only in the highly emissive Tb³⁺ complexes. © 2018 Wiley Periodicals, Inc.     

Spin–Orbit Charge-Transfer Intersystem Crossing (ISC) in Compact Electron Donor–Acceptor Dyads: ISC Mechanism and Application as Novel and Potent Photodynamic Therapy Reagents

Spin–orbit charge-transfer intersystem crossing (SOCT-ISC) is useful for the preparation of heavy atom-free triplet photosensitisers (PSs). Herein, a series of perylene-Bodipy compact electron donor/acceptor dyads showing efficient SOCT-ISC is prepared. The photophysical properties of the dyads were studied with steady-state and time-resolved spectroscopies. Efficient triplet state formation (quantum yield Φ_T=60 %) was observed, with a triplet state lifetime (τ_T=436 μs) much longer than that accessed with the conventional heavy atom effect (τ_T=62 μs). The SOCT-ISC mechanism was unambiguously confirmed by direct excitation of the charge transfer (CT) absorption band by using nanosecond transient absorption spectroscopy and time-resolved electron paramagnetic resonance (TREPR) spectroscopy. The factors affecting the SOCT-ISC efficiency include the geometry, the potential energy surface of the torsion, the spin density for the atoms of the linker, solvent polarity, and the energy matching of the ¹CT/³LE states. Remarkably, these heavy atom-free triplet PSs were demonstrated as a new type of efficient photodynamic therapy (PDT) reagents (phototoxicity, EC₅₀=75 nm ), with a negligible dark toxicity (EC₅₀=78.1 μm ) compared with the conventional heavy atom PSs (dark toxicity, EC₅₀=6.0 μm, light toxicity, EC₅₀=4.0 nm ). This study provides in-depth understanding of the SOCT-ISC, unveils the design principles of triplet PSs based on SOCT-ISC, and underlines their application as a new generation of potent PDT reagents.     

Tuning the Triplet Excited State of Bis(dipyrrin) Zinc(II) Complexes: Symmetry Breaking Charge Transfer Architecture with Exceptionally Long Lived Triplet State for Upconversion

Zinc(II) bis(dipyrrin) complexes, which feature intense visible absorption and efficient symmetry breaking charge transfer (SBCT) are outstanding candidates for photovoltaics but their short lived triplet states limit applications in several areas. Herein we demonstrate that triplet excited state dynamics of bis(dipyrrin) complexes can be efficiently tuned by attaching electron donating aryl moieties at the 5,5′-position of the complexes. For the first time, a long lived triplet excited state (τ_T=296 μs) along with efficient ISC ability (Φ_Δ=71 %) was observed for zinc(II) bis(dipyrrin) complexes, formed via SBCT. The results revealed that molecular geometry and energy gap between the charge transfer (CT) state and triplet energy levels strongly control the triplet excited state properties of the complexes. An efficient triplet–triplet annihilation upconversion system was devised for the first time using a SBCT architecture as triplet photosensitizer, reaching a high upconversion quantum yield of 6.2 %. Our findings provide a blueprint for the development of triplet photosensitizers based on earth abundant metal complexes with long lived triplet state for revolutionary photochemical applications.     

Using block designs in crossing number bounds

The crossing number $\mathrm{\text{CR}}\left(G\right)$ of a graph $G=\left(V,E\right)$ is the smallest number of edge crossings over all drawings of $G$ in the plane. For any $k\ge 1$, the $k$‐planar crossing number of $G,{\mathrm{\text{CR}}}_k\left(G\right)$, is defined as the minimum of $\text{CR}\left(G_1\right)+\text{CR}\left(G_2\right)+?+\text{CR}\left(G_k\right)$ over all graphs $G_1,G_2,\dots ,G_k$ with ${\cup }_{i=1}^k{G}_i=G$. Pach et al [Comput. Geom.: Theory Appl. 68 (2018), pp. 2–6] showed that for every $k\ge 1$, we have ${\text{CR}}_k\left(G\right)\le (2/k^2?1/k^3)\text{CR}\left(G\right)$ and that this bound does not remain true if we replace the constant $2/k^2?1/k^3$ by any number smaller than $1/k^2$. We improve the upper bound to $(1/k^2)\left(1+o\left(1\right)\right)$ as $k\to \infty$. For the class of bipartite graphs, we show that the best constant is exactly $1/k^2$ for every $k$. The results extend to the rectilinear variant of the $k$‐planar crossing number.     

On the Pseudolinear Crossing Number

A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing number of a graph G is the minimum number of pairwise crossings of edges in a pseudolinear drawing of G. We establish several facts on the pseudolinear crossing number, including its computational complexity and its relationship to the usual crossing number and to the rectilinear crossing number. This investigation was motivated by open questions and issues raised by Marcus Schaefer in his comprehensive survey of the many variants of the crossing number of a graph.     

六阶图Q与星图S_n的积图交叉数

目前关于积图的交叉数的研究已经推广到六阶图与星图的积图.研究得到了一个特殊六阶图Q与n个孤立点nK_1的联图交叉数,然后通过收缩的方法,得到了Q与星图S_n的积图交叉数.     

多共振热激活延迟荧光过程的理论研究

本工作借助第一性原理和动力学演化,系统地研究了四个叔丁基-咔唑及吩噻嗪取代的硼-氮化合物(BCz-BN、2PTZ-BN、Cz-PTZ-BN和2Cz-PTZ-BN)的多共振热激活延迟荧光的高效发光机制.结果表明上述分子T₁与T₂间的内转换速率远大于其它辐射与非辐射速率,同时T₂到S₁的反向系间窜越速率也高于T₁到S₁的反向系间窜越速率,因此其多共振热激活延迟荧光过程应遵循T₁→T₂→S₁→S₀的路径.进一步动力学演化表明,T₁与T₂之间的内转换主要发生在演化初期,随着时间的推移,能量逐渐由T₂向S₁转移,并最终在S₁完成荧光发射.上述研究揭示了多共振延迟荧光的微观本质,为未来设计及合成新的多共振热激活延迟荧光分子提供了理论依据.