Theoretical and numerical analysis on multispectral bioluminescence tomography

Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions.     

A fourth‐order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations

A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd.     

Unlabeled Fluoroimmunoassay with a Europium Chelate

Unlabeled fluoroimmunoassay with a europium chelate is described. The recommended method is simple because the complicated labeling process is omitted. The recovery of some samples ranges from 91 to 111%. The relative standard deviation of the method is less than 10%. The detection limit is about 10⁻¹⁰mol liter⁻¹antigen.     

Ligand-promoted palladium-catalyzed β-methylene C–H arylation of primary aldehydes

The transient directing group (TDG) strategy allowed long awaited access to the direct β-C(sp³)–H functionalization of unmasked aliphatic aldehydes via palladium catalysis. However, the current techniques are restricted to terminal methyl functionalization, limiting their structural scopes and applicability. Herein, we report the development of a direct Pd-catalyzed methylene β-C–H arylation of linear unmasked aldehydes by using 3-amino-3-methylbutanoic acid as a TDG and 2-pyridone as an external ligand. Density functional theory calculations provided insights into the reaction mechanism and shed light on the roles of the external and transient directing ligands in the catalytic transformation.

Aliphatic aldehydes are among the most common structural units in organic and medicinal chemistry research. Direct C–H functionalization has enabled efficient and site-selective derivatization of aliphatic aldehydes.

Simple aliphatic functional groups enrich the skeletal backbones of many natural products, pharmaceuticals, and other industrial materials, influencing the utility and applications of these substances and dictating their reactivity and synthetic modification pathways. Aliphatic aldehydes are some of the most ubiquitous structural units in organic materials.¹ Their relevance in nature and industry alike, combined with their reactivity and synthetic versatility, attracted much attention from the synthetic organic and medicinal chemistry communities over the years (Fig. 1).² Efficient means to the functionalization of these molecules have always been highly sought after.Open in a separate windowFig. 1Select aliphatic aldehyde-containing medicines and biologically active molecules.Traditionally, scientists have utilized the high reactivity of the aldehyde moiety in derivatizing a variety of functional groups by the means of red-ox and nucleophilic addition reactions. The resourceful moiety was also notoriously used to install functional groups at the α-position via condensation and substitution pathways.³ Although β-functionalization is just as robust, it has generally been more restrictive as it often requires the use of α,β-unsaturated aldehydes.^4,5 Hence, transition metal catalysis emerged as a powerful tool to access β-functionalization in saturated aldehydes.⁶ Most original examples of metal-catalyzed β-C–H functionalization of aliphatic aldehydes required the masking of aldehydes into better metal coordinating units since free unmasked aldehydes could not form stable intermediates with metals like palladium on their own.⁷ Although the masking of the aldehyde moiety into an oxime, for example, enabled the formation of stable 5-membered palladacycles, affording β-functionalized products, this system requires the installation of the directing group prior to the functionalization, as well as the subsequent unmasking upon the reaction completion, compromising the step economy and atom efficiency of the overall process.⁸ Besides, some masking and unmasking protocols might not be compatible with select substrates, especially ones rich in functional groups. As a result, the development of a one-step direct approach to the β-C–H functionalization of free aliphatic aldehydes was a demanding target for synthetic chemists.α-Amino acids have been demonstrated as effective transient directing groups (TDGs) in the remote functionalization of o-alkyl benzaldehydes and aliphatic ketones by the Yu group in 2016.⁹ Shortly after, our group disclosed the first report on the direct β-C–H arylation of aliphatic aldehydes using 3-aminopropanoic acid or 3-amino-3-methylbutanoic acid as a TDG.¹⁰ The TDG was found to play a similar role to that of the oxime directing group by binding to the substrate via reversible imine formation, upon which, it assists in the assembly of a stable palladacycle, effectively functionalizing the β-position.¹¹ Since the binding of the TDG is reversible and temporary, it is automatically removed upon functionalization, yielding an efficient and step-economic transformation. This work was succeeded by many other reports that expanded the reaction and the TDG scopes.^12–14 However, this system suffers from a significant restriction that demanded resolution; only substitution of methyl C–H bonds of linear aldehydes was made possible via this approach (Scheme 1a–e). The steric limitations caused by incorporating additional groups at the β-carbon proved to compromise the formation of the palladacycle intermediate, rendering the subsequent functionalization a difficult task.¹²Open in a separate windowScheme 1Pd-catalyzed β-C–H bond functionalization of aliphatic aldehydes enabled by transient directing groups.Encouraged by the recent surge in use of 2-pyridone ligands to stabilize palladacycle intermediates,^15,16 we have successfully developed the first example of TDG-enabled Pd-catalyzed methylene β-C–H arylation in primary aldehydes via the assistance of 2-pyridones as external ligands (Scheme 1f). The incorporation of 2-pyridones proved to lower the activation energy of the C–H bond cleavage, promoting the formation of the intermediate palladacycles even in the presence of relatively bulky β-substituents.¹⁷ This key advancement significantly broadens the structural scopes and applications of this process and promises future asymmetric possibilities, perhaps via the use of a chiral TDG or external ligand or both. Notably, a closely related work from Yu''s group was published at almost the same time.¹⁸We commenced our investigation of the reaction parameters by employing n-pentanal (1a) as an unbiased linear aldehyde and 4-iodoanisole (2a) in the presence of catalytic Pd(OAc)₂ and stoichiometric AgTFA, alongside 3-amino-3-methylbutanoic acid (TDG1) and 3-(trifluoromethyl)-5-nitropyridin-2-ol (L1) at 100 °C (ii) sources proved Pd(OAc)₂ to be the optimal catalyst, while Pd(TFA)₂, PdCl₂ and PdBr₂ provided only moderate yields (entries 10–12). Notably, a significantly lower yield was observed in the absence of the 2-pyridone ligand, and no desired product was isolated altogether in the absence of the TDG (entries 13 and 14). The incorporation of 15 mol% Pd catalyst was deemed necessary after only 55% yield of 3a was obtained when 10 mol% loading of Pd(OAc)₂ was instead used (entry 15).Optimization of reaction conditions^a

Entry	Pd source	L (mol%)	TDG1 (mol%)	Solvent (v/v, mL)	Yield (%)
1	Pd(OAc)2	L1 (30)	TDG1 (40)	HFIP	30
2	Pd(OAc)2	L1 (30)	TDG1 (40)	AcOH	<5
3	Pd(OAc)2	L1 (30)	TDG1 (40)	HFIP/AcOH (1 : 1)	28
4	Pd(OAc)2	L1 (30)	TDG1 (40)	HFIP/AcOH (9 : 1)	47
5	Pd(OAc)2	L1 (30)	TDG1 (40)	HFIP/AcOH (1 : 9)	<5
6	Pd(OAc)2	L1 (30)	TDG1 (60)	HFIP/AcOH (9 : 1)	50
7	Pd(OAc)2	L1 (30)	TDG1 (80)	HFIP/AcOH (9 : 1)	25
8	Pd(OAc)2	L1 (60)	TDG1 (60)	HFIP/AcOH (9 : 1)	70(68)b
9	Pd(OAc)2	L1 (75)	TDG1 (60)	HFIP/AcOH (9 : 1)	51
10	Pd(TFA)2	L1 (60)	TDG1 (60)	HFIP/AcOH (9 : 1)	60
11	PdCl2	L1 (60)	TDG1 (60)	HFIP/AcOH (9 : 1)	52
12	PdBr2	L1 (60)	TDG1 (60)	HFIP/AcOH (9 : 1)	54
13	Pd(OAc)2	—	TDG1 (60)	HFIP/AcOH (9 : 1)	9
14	Pd(OAc)2	L1 (60)	—	HFIP/AcOH (9 : 1)	0
15c	Pd(OAc)2	L1 (60)	TDG1 (60)	HFIP/AcOH (9 : 1)	55

Open in a separate window^aReaction conditions: 1a (0.2 mmol), 2a (0.4 mmol), Pd source (15 mol%), AgTFA (0.3 mmol), L1, TDG1, solvent (2.0 mL), 100 °C, 12 h. Yields are based on 1a, determined by ¹H-NMR using dibromomethane as an internal standard.^bIsolated yield.^cPd(OAc)₂ (10 mol%).To advance our optimization of the reaction conditions, a variety of 2-pyridones and TDGs were tested (Scheme 2). Originally, pyridine-2(1H)-one (L2) was examined as the external ligand, but it only yielded the product (3a) in 7% NMR yield. Similarly, other mono- and di-substituted 2-pyridone ligands (L3–L10) also produced low yields, fixating L1 as the optimal external ligand. Next, various α- and β-amino acids (TDG1–10) were evaluated, yet TDG1 persisted as the optimal transient directing group. These amino acid screening results also suggest that a [5,6]-bicyclic palladium species is likely the key intermediate in this protocol since only β-amino acids were found to provide appreciable yields, whereas α-amino acids failed to yield more than trace amounts of the product. The supremacy of TDG1 when compared to other β-amino acids is presumably due to the Thorpe–Ingold effect that perhaps helps facilitate the C–H bond cleavage and stabilize the [5,6]-bicyclic intermediate further.Open in a separate windowScheme 2Optimization of 2-pyridone ligands and transient directing groups.With the optimized reaction conditions in hand, substrate scope study of primary aliphatic aldehydes was subsequently carried out (Scheme 3). A variety of linear primary aliphatic aldehydes bearing different chain lengths provided the corresponding products 3a–e in good yields. Notably, relatively sterically hindered methylene C–H bonds were also functionalized effectively (3f and 3g). Additionally, 4-phenylbutanal gave rise to the desired product 3h in a highly site-selective manner, suggesting that functionalization of the methylene β-C–H bond is predominantly favored over the more labile benzylic C–H bond. It is noteworthy that the amide group was also well-tolerated and the desired product 3j was isolated in 60% yield. As expected, with n-propanal as the substrate, β-mono- (3k1) and β,β-disubstituted products (3k2) were isolated in 22% and 21% yields respectively. However, in the absence of the key external 2-pyridone ligand, β-monosubstituted product (3k1) was obtained exclusively, albeit with a low yield, indicating preference for functionalizing the β-C(sp³)–H bond of the methyl group over the benzylic methylene group.Open in a separate windowScheme 3Scope of primary aliphatic aldehydes. Reaction conditions: 1 (0.2 mmol), 2a (0.4 mmol), Pd(OAc)₂ (15 mol%), AgTFA (0.3 mmol), L1 (60 mol%), TDG1 (60 mol%), HFIP (1.8 mL), HOAc (0.2 mL), 100 °C, 12 h. Isolated yields. ^aL1 (60 mol%) was absent and yields are given in parentheses.Next, substrate scope study on aryl iodides was surveyed (Scheme 4). Iodobenzenes bearing either an electron-donating or electron-withdrawing group at the para-, meta-, or ortho-position were all found compatible with our catalytic system (3l–3ah). Surprisingly, ortho-methyl- and fluoro-substituted aryl iodides afforded the products in only trace amounts. However, aryl iodide with ortho-methoxy group provided the desired product 3ac in a moderate yield. Notably, a distinctive electronic effect pattern was not observed in the process. It should be mentioned that arylated products bearing halogen, ester, and cyano groups could be readily converted to other molecules, which significantly improves the synthetic applicability of the process. Delightfully, aryl iodide-containing natural products like ketoprofen, fenchol and menthol were proven compatible, supplying the corresponding products in moderate yields. Unfortunately, (hetero)aryl iodides including 2-iodopyridine, 3-iodopyridine, 4-iodopyridine and 4-iodo-2-chloropyridine failed to produce the corresponding products. Although our protocol provides a novel and direct pathway to construct β-arylated primary aliphatic aldehydes, the yields of most examples are modest. The leading reasons for this compromise are the following: (1) aliphatic aldehydes are easily decomposed or oxidized to acids; (2) some of the prepared β-arylated aldehyde products may be further transformed into the corresponding α,β-unsaturated aldehydes.Open in a separate windowScheme 4Scope of aryl iodides. Reaction conditions: 1a (0.2 mmol), 2 (0.4 mmol), Pd(OAc)₂ (15 mol%), AgTFA (0.3 mmol), L1 (60 mol%), TDG1 (60 mol%), HFIP (1.8 mL), HOAc (0.2 mL), 100 °C, 12 h. Isolated yields.Density functional theory (DFT) calculations were performed to help investigate the reaction mechanism and to elucidate the role of the ligand in improving the reactivity (Fig. 2). The condensation of the aliphatic aldehyde 1a with the TDG to form imine-1a was found thermodynamically neutral (ΔG° = −0.1 kcal mol⁻¹). As a result, it was permissible to use imine-1a directly in the calculations. According to the calculations results, the precatalyst [Pd(OAc)₂]₃, a trimeric complex, initially experiences dissociation and ligand metathesis with imine-1a to generate the Pd(ii) intermediate IM1, which is thermodynamically favorable by 21.9 kcal mol⁻¹. Consequently, the deprotonated imine-1a couples to the bidentate ligand to form the stable six-membered chelate complex IM1. Therefore, IM1 is indeed the catalyst resting state and serves as the zero point to the energy profile. We have identified two competitive pathways for the Pd(ii)-catalyzed C–H activation starting from IM1, one of which incorporates L1 and another which does not. On the one hand, an acetate ligand substitutes one imine-1a chelator in IM1 to facilitate the subsequent C–H activation leading to IM2, which undergoes C(sp³)–H activation through concerted metalation-deprotonation (CMD) viaTS1 (ΔG^‡ = 37.4 kcal mol⁻¹). However, this kinetic barrier is thought to be too high to account for the catalytic activity at 100 °C. On the other hand, the chelate imine-1a could be replaced by two N-coordinated ligands (L1) leading to the Pd(ii) complex IM3. This process is endergonic by 6.4 kcal mol⁻¹. To allow the ensuing C–H activation, IM3 dissociates one ligand (L1) producing the active species IM4, which undergoes TS2 to cleave the β-C(sp³)–H bond and form the [5,6]-bicyclic Pd(ii) intermediate IM5. Although this step features an energy barrier of 31.2 kcal mol⁻¹, it is thought to be feasible under the experimental conditions (100 °C). Possessing similar coordination ability to that of pyridine, the ligand (L1) effectively stabilizes the Pd(ii) center in the C–H activation process, indicating that this step most likely involves a manageable kinetic barrier. This result explicates the origin of the ligand-enabled reactivity (TS2vs.TS1). Additionally, we considered the γ-C(sp³)–H activation pathway viaTS2′ which was found to have a barrier of 35.5 kcal mol⁻¹. The higher energy barrier of TS2′ compared to that of TS2 is attributed to its larger ring strain in the [6,6]-bicyclic Pd(ii) transition state, which reveals the motive for the site-selectivity. Reverting back to the supposed pathway, upon the formation of the bicyclic intermediate IM5, it undergoes ligand/substrate replacement to afford intermediate IM6, at which the Ar–I coordinates to the Pd(ii) center to enable oxidative addition viaTS3 (ΔG^‡ = 27.4 kcal mol⁻¹) leading to the five-coordinate Pd(iv) complex IM7. Undergoing direct C–C reductive elimination in IM7 would entail a barrier of 29.6 kcal mol⁻¹ (TS4). Alternatively, iodine abstraction by the silver(i) salt in IM7 is thermodynamically favorable and irreversible, yielding the Pd(iv) intermediate IM8 coordinated to a TFA ligand. Subsequently, C–C reductive coupling viaTS5 generates the Pd(ii) complex IM9 and concludes the arylation process. This step was found both kinetically facile (6.1 kcal mol⁻¹) and thermodynamically favorable (30.7 kcal mol⁻¹). Finally, IM9 reacts with imine-1avia metathesis to regenerate the palladium catalyst IM1 and release imine-3a in a highly exergonic step (21.0 kcal mol⁻¹). Ultimately, imine-3a undergoes hydrolysis to yield the aldehyde product 3a and to release the TDG.Open in a separate windowFig. 2Free energy profiles for the ligand-promoted Pd(ii)-catalyzed site-selective C–H activation and C–C bond formation, alongside the optimized structures of the C–H activation transition states TS1 and TS2 (selected bond distances are labelled in Å). Energies are relative to the complex IM1 and are mass-balanced.     

Visible Light-Driven Alkyne-Grafted Ethylene-Bridged Azobenzene Chromophores for Photothermal Utilization

Molecular photoswitches are considered to be important candidates in the field of solar energy storage due to their sensitive and reversible bidirectional optical response. Nevertheless, it is still a daunting challenge to design a molecular photoswitch to improve the low solar spectrum utilization and quantum yields while achieving charging and discharging of heat without solvent assistance. Herein, a series of visible-light-driven ethylene-bridged azobenzene (b-Azo) chromophores with different alkyne substituents which can undergo isomerization reactions promoted in both directions by visible light are reported. Their visible light responsiveness improves their solar spectrum utilization while also having high quantum yields. In addition, as the compounds are liquids, there is no need to dissolve the compounds in order to exploit this switching. The photoisomerization of b-Azo can be adjusted by alkyne-related substituents, and hexyne-substituted b-Azo is able to store and release photothermal energy with a high density of 106.1 J·g⁻¹, and can achieve a temperature increase of 1.8 °C at a low temperature of −1 °C.     

平面、斜坡、动静摩擦力演示仪的制作

平面、斜坡、动静摩擦力演示仪的制作。     

一种电流引线的热力学计算方法

从超导磁体气冷电流引线的热平衡方程出发,对电流引线进行分段,提出了一种较为精确计算电流引线长横比及由电流引线末端流入低温容器热量的计算方法;电流引线中氦气流阻是设计电流引线时一个很重要的参数,由于电流引线片形状很复杂,计算其中氦气流阻比较好的方法是采用CFD软件Fluent。氦气模型单元数很庞大,因此对氦气模型进行了简化和分段,相邻两段模型间采用流量和压力边界条件进行耦合。     

DFT Investigations of Aun Nano-Clusters Supported on TiO2 Nanotubes: Structures and Electronic Properties

TiO₂ nanotubes (TiO₂NTs) are beneficial for photogenerated electron separation in photocatalysis. In order to improve the utilization rate of TiO₂NTs in the visible light region, an effective method is to use Au_n cluster deposition-modified TiO₂NTs. It is of great significance to investigate the mechanism of Au_n clusters supported on TiO₂NTs to strengthen its visible-light response. In this work, the structures, electronic properties, Mulliken atomic charge, density of states, band structure, and deformation density of Au_n (n = 1, 8, 13) clusters supported on TiO₂NTs were investigated by DMOL3. Based on published research results, the most stable adsorption configurations of Au_n (n = 1, 8, 13) clusters supported with TiO₂NTs were obtained. The adsorption energy increased as the number of Au adatoms increased linearly. The Au_n clusters supported on TiO₂NTs carry a negative charge. The band gaps of the three most stable structures of each adsorption system decreased compared to TiO₂NTs; the valence top and the conduction bottom of the Fermi level come mainly from the contribution of 5d and 6s-Au. The electronic properties of the 5d and 6s impurity orbitals cause valence widening and band gap narrowing.