A variational coupled cluster theory for closed shells using a propagator modification procedure

A general partial summation method for including arbitrary classes of diagrams to all orders in the coupled cluster based size consistent energy functional for closed shell states is developed. Since the various reduced density matrices which appear in the energy functional are essentially the time-independent analogues of the corresponding many body Green functions, it is possible to derive Dyson-like equations for these quantities. By expanding the associated proper self energy parts in terms of the T-amplitudes, one can carry out partial summations in the reduced density matrices and thus in energy. At a higher level, higher order terms in a proper self energy can also be generated by renormalizing the internal propagators in it, and considering only the irreducible self-energy terms.     

Comparison of low-order multireference many-body perturbation theories

Tests have been made to benchmark and assess the relative accuracies of low-order multireference perturbation theories as compared to coupled cluster (CC) and full configuration interaction (FCI) methods. Test calculations include the ground and some excited states of the Be, H(2), BeH(2), CH(2), and SiH(2) systems. Comparisons with FCI and CC calculations show that in most cases the effective valence shell Hamiltonian (H(v)) method is more accurate than other low-order multireference perturbation theories, although none of the perturbative methods is as accurate as the CC approximations. We also briefly discuss some of the basic differences among the multireference perturbation theories considered in this work.     

Eigenvalues of large even annulenes in terms ofK 3,S 4 andS 5

Squares of the adjacency matrices of bipartite cycles (C_v) can be block-factored into matrices which correspond to vertex-weighted complete graphs forv = 6, vertex-weighted strongly regular graphs forv = 8 and 10, and vertex-weighted metrically regular graphs forv > 10. Using this fact and some properties of strongly and metrically regular graphs, it is shown that eigenvalues of large bipartite C _v graphs (i.e. large even annulenes) can be expressed by the general formula ± (2 ± (2 ± (... ± (2 +r _p)) ...), wherev = 2 ⁿ ×p,n is the number of surd () signs required andp = 3, 4 and 5. Here,r ₃,r ₄, andr ₅, are the eigenvalues of the complete graphK ₃ and the strongly regular graphsS ₄ andS ₅ respectively. The procedure does not require construction of characteristic polynomials for the determination of eigenvalues, and brings out a common topological origin for the two-fold degeneracies observed in the eigenvalue spectra of all even cycles and many odd cycles.     

Redox reactions of disulfiram: a pulse-radiolysis study

Redox reactions of disulfiram (DSF) were studied in aqueous solutions using the pulse-radiolysis technique. Reactions of DSF with one-electron oxidants Br₂ ^- and N₃, generated pulse radiolytically in aqueous solution at pH 7, yielded a transient (_max = 480 nm) which exhibited the characteristics of a disulphide cation radical and decayed by second-order kinetics. Reactions of DSF with halogenated peroxyl radicals CCl₃O₂, CHCl₂O₂, CH₂ClO₂ and CBr₃O₂ led to the formation of an adduct absorbing at 580 nm. The reduction potential was estimated to be 1.24 ± 0.06 V vs. NHE.     

Two (E)‐2‐arylidene‐1,4‐di‐p‐tosyl‐1,2,3,4‐tetrahydroquinoxaline compounds: supramolecular frameworks built with C—H...O and C—H...π(arene) hydrogen bonds and π–π stacking interactions

The pyrazine ring in two N‐substituted quinoxaline derivatives, namely (E)‐2‐(2‐methoxybenzylidene)‐1,4‐di‐p‐tosyl‐1,2,3,4‐tetrahydroquinoxaline, C₃₀H₂₈N₂S₂O₅, (II), and (E)‐methyl 2‐[(1,4‐di‐p‐tosyl‐1,2,3,4‐tetrahydroquinoxalin‐2‐ylidene)methyl]benzoate, C₃₁H₂₈N₂S₂O₆, (III), assumes a half‐chair conformation and is shielded by the terminal tosyl groups. In the molecular packing of the compounds, intermolecular C—H...O hydrogen bonds between centrosymmetrically related molecules generate dimeric rings, viz. R₂²(22) in (II) and R₂²(26) in (III), which are further connected through C—H...π(arene) hydrogen bonds and π–π stacking interactions into novel supramolecular frameworks.     

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.     

Reversible fluorescence sensing of Zn2+ based on pyridine-constrained bis(triazole-linked hydroxyquinoline) sensor

Zinc ion (Zn²⁺) is an important and a most useful biological trace nutrient responsible for the activity of several enzymes. Zn²⁺ concentrations in the environment as well as in the human body increase beyond permissible limits as a consequence of its mining and widespread industrial applications. Such excess Zn²⁺ concentrations are toxic to humans and many aquatic organisms. The magnetic inertness and spin paired electronic configuration of Zn²⁺ makes it hard to detect by common analytical techniques. Therefore, fluorometric detection using chemosensor is the most effective tool for the environmental and biological detection of Zn²⁺. We have developed a novel pyridine-constrained bis(triazole-linked hydroxyquinoline) ligand as a reversible fluorescent chemosensor for Zn²⁺. The symmetrical ligand is highly selective for Zn²⁺ and fluoresces brightly upon complexation compared with other metal ions based on chelation-enhanced fluorescence mechanism. Interestingly, free ligand can be regenerated by treating the ligand–Zn²⁺ complex with aqueous ammonia.     

A simple and effective technique to locate quasi-degeneracy in a symmetric double well potential

Perturbation theory based model can be used to locate the quasi-degeneracy in an arbitrary double well potential. This method, extensively explain the effect of the coupling term on pair of states called quasi-degenerate. This model helps us to calculate the energy of the pair of quasi-degenerate states using appreciably small basis. Dispersion equation corresponding to the split energy levels are presented in a very explicit form. Numerical calculation shows that the proposed method can give extremely accurate results for symmetric double-well potentials.     

MYMIV-AC2, a Geminiviral RNAi Suppressor Protein, Has Potential to Increase the Transgene Expression

Gene silencing is one of the limiting factors for transgene expression in plants. But the plant viruses have learnt to suppress gene silencing by encoding the protein(s), called RNA silencing suppressor(s) (RSS). Hence, these proteins could be used to overcome the limitation for transgene expression. The RNAi suppressors, namely HC-Pro and P19, have been shown to enhance the transgene expression but other RSS proteins have not been screened for similar role. Moreover, none of RSSs from the DNA viruses are known for enhancing the expression of transgenes. The Mungbean Yellow Mosaic India Virus (MYMIV) belonging to the genus Begomovirus within the family of Geminiviridae encodes an RSS called the AC2 protein. Here, we used AC2 to elevate the expression of the transgenes. Upon introduction of MYMIV-AC2 in the silenced GFP transgenic tobacco lines, by either genetic hybridisation or transgenesis, the GFP expression was enhanced several fold in F1 and T0 lines. The GFP-siRNA levels were much reduced in F1 and T0 lines compared with those of the initial parental silenced lines. The enhanced GFP expression was also observed at the cellular level. This approach was also successful in enhancing the expression of another transgene, namely topoisomeraseII.     

Observation of field induced anomalous quantum criticality in Ce0.6Y0.4NiGe2 compound

We report the results of our investigation of magnetization and heat capacity on a series of compounds Ce${}_{1?x}$Y_xNiGe₂ ($x=0.1,0.2\text{ and }0.4$) under the influence of external magnetic field. Our studies of the thermodynamic quantity $?\mathrm{d}M/\mathrm{d}T$ on these compounds indicate that magnetic frustration persists in Ce_0.9Y_0.1NiGe₂, as also reported for the parent compound CeNiGe₂. The weak signature of this frustration is also noted in Ce_0.8Y_0.2NiGe₂, whereas, it is suppressed in Ce_0.6Y_0.4NiGe₂. Heat capacity studies on Ce_0.9Y_0.1NiGe₂ and Ce_0.8Y_0.2NiGe₂ indicate the presence of a new magnetic anomaly at high field which indicates that quantum criticality is absent in these compounds. However, for Ce_0.6Y_0.4NiGe₂ such an anomaly is not noted. For this later compound, the magnetic field (H) and temperature (T) dependence of heat capacity and magnetization obey $H/T$ scaling above critical fields. However, the obtained scaling critical parameter (δ) is 1.6, which is away from mean field value of 3. This deviation suggests the presence of unusual fluctuations and anomalous quantum criticality in these compounds. This unusual fluctuation may arise from disorderness induced by Y-substitution.