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60c73e14337d6ca46ae26282 | 36 | We have developed and implemented specific algorithms that handle all nuances of all nine of the Sequence Rules for tetrahedral centers and double bond stereochemistry, two of which are opensource Java applications (Centres and Jmol, which also has a JavaScript equivalent). All are freely available in binary format. We have developed a robust testing suite for algorithms that implement the CIP Sequence Rules. This suite covers a wide variety of possible issues that might arise in the course of any algorithm development. |
60c73e14337d6ca46ae26282 | 37 | In addition, in the process of this work, we have identified and addressed a number of issues with the eight Sequence Rules as presented Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names 2013 (1a, 1b, 2, 3, 4a, 4b, 4c, and 5) and propose simple solutions, including a new Rule 6. In particular, we provide a definitive method of implementing Kekulé averaging in Rules 1a, 1b, and 2. We propose a simple solution to working with isotope masses in Rule 2. We argue for the necessity for fully elaborated auxiliary descriptors prior to Rule |
62fbfe7e08a44bb1a2735acc | 0 | The soaring, large-scale production of single-use plastics creates huge amount of nondegradable waste that severely threats the environment. The inefficacy of existing approaches for plastic waste processing, such as recycling and incineration, leads to the demands for chemical routes that "upcycle" plastics into valuable chemicals. Besides environmental benefits, upcycling plastics also compensates for the oil consumption by their production through circular economy. |
62fbfe7e08a44bb1a2735acc | 1 | Polyolefins, including polypropylene (PP) and polyethylene (PE), are the most common types of plastics, making up > 50% of the annual production, and also the most difficult to convert because they are entirely made of inert C-C single bonds. As a result, the upcycling of polyolefins requires either high temperature in pyrolysis, which causes high energy consumption and low selectivity, or effective catalytic processes. |
62fbfe7e08a44bb1a2735acc | 2 | Two of the most promising routes for catalytic polyolefin upcycling are hydrogenolysis and hydrocracking. They require no additional feedstocks as metathesis or alkylation, and are less susceptible to deactivation than pyrolysis or Haag-Dessau cracking on monofunctional acidic catalysts. Besides, these two reactions have been crucial parts of the oil refining industry and thus extensively studied with small alkane substrates, with established operation infrastructure and fundamental understanding partially applicable to polyolefin substrates. Both hydrogenolysis and hydrocracking refer to C-C bond cleavage under H2 on supported metal catalysts, but the former cleaves C-C bonds on the metal, while the latter cleaves C-C bonds (and isomerizes substrates) on Brønsted acid sites after dehydrogenation on the metal, thus requiring metal-acid bifunctional catalysts. Despite initial success, the catalyst development for both routes is at a very preliminary stage. Meanwhile, polyolefins substrates often behave very differently from small alkanes, and fundamental understanding specific to them is lacking. For hydrogenolysis, most studies used catalysts with high noble metal (Ru or Pt) content, and the selectivity needs to be steered away from low-valued gas alkanes, especially CH4, to high-valued liquid alkanes. We have shown that disordered Ru clusters have better activity and selectivity in the reaction than rigid particles, but the structure-function relationship needs further understanding for the rational design of active sites. For hydrocracking, most studies used expensive, scarce Pt as the metal, and zeolites as the acidic support, the microporous structure of which creates difficulty for the diffusion of long-chain polymers and thus limits active site accessibility. Also, mechanistic understanding is very rare, which hinders tuning product distribution rationally. Furthermore, there are no studies of the two reactions occurring simultaneously, which is common on bifunctional catalysts with small alkanes. This type of studies do not only help understand the complex reaction network, also offer insights on how to choose between the processes and design catalyst functionality. |
62fbfe7e08a44bb1a2735acc | 3 | In this work, we investigated the hydrogenolysis and hydrocracking of PP, LDPE, and model alkanes that co-occur on a low-loading Ru/TiO2 catalyst. Ni/TiO2 was also studied for hydrocracking as a noble-metal-free catalyst. We show that the superior activity and selectivity of hydrocracking to hydrogenolysis make the bifunctional Ru/TiO2 more suitable than monofunctional Ru catalysts for PP conversion. Lower hydrogen pressure and more branched products increase the tendency for the reaction to occur through hydrocracking, which can also be effectively catalyzed by Ni/TiO2. The unexpected bifunctionality of Ru/TiO2 was attributed to auto-adsorbed carboxylates on TiO2. This work elucidates the co-existence of the two routes on a bifunctional catalyst, the relationship and comparisons between them, and how the mechanism of polyolefin upcycling is altered by reaction conditions and catalysts. Also, the results on the Brønsted acidity of TiO2 opens brand new opportunities in developing novel acid catalysts. |
62fbfe7e08a44bb1a2735acc | 4 | We previously discovered that decreasing Ru loading on CeO2 to a threshold triggers an increase in the disorder in the Ru structure, which coincides with drastic increases in the activity, selectivity, and isomerization ability in polyolefin hydrogenolysis. This discovery motivated us to examine how the support regulates the properties and thus performance of highly dispersed Ru species. Therefore, we impregnated low-loading Ru (0.07 Ru/nm 2 ) onto various supposedly nonacidic supports (see Table for BET surface area), and tested them in the hydrogenolysis of PP and LDPE (260 ℃, 30 bar H2). Results are summarized in Figure , with the best catalyst studied from previous works, Ru/CeO2, as a reference point. Surprisingly, an anatase TiO2 synthesized by a sol-gel method (referred to as "TiO2-A-SG", XRD see Figure ) clearly stands out with PP as the substrate (Figure ), showing by far the best per-Ru conversion rate (~350 gPP gRu -1 h - 1 , patterned bar, 3 times as high as Ru/CeO2), selectivity (< 5% CH4, green, ~80% liquid products, purple), and isomerization ability (> 60% isomers, orange). Nevertheless, its activity and selectivity with LDPE as the substrate is mediocre (Figure ), except for the high fraction of branched products (red). Meanwhile, among other supports, the performance of low-loading Ru is highly support-dependent with both PP and LDPE, and particularly, they surprisingly exhibit negligible activity on two supports, commercial anatase TiO2, ("TiO2-A-comm"), and carbon. This manuscript will only present detailed studies to understand the unique, intriguing performance of the TiO2-A-SG support. The strong support-dependence among other catalysts was hypothesized to be due to different morphology of highly dispersed Ru species, which we will report in a separated manuscript. ). |
62fbfe7e08a44bb1a2735acc | 5 | Figure shows the product distribution typical for PP hydrogenolysis over other Ru catalysts, with Ru/CeO2 as the example. It has abundant C2-3 besides CH4, and wide distribution among liquid products centered around C22, while both liquid products and solid residue have no color. In contrast, Figure shows that Ru/TiO2-A-SG generates abundant C4-5 with minimal C2-3, the liquid products have a much narrower distribution centered around C10, and both liquid products and solid residue are light yellow (Figures and Since the high isomerization level and the lack of C1-2 products are typical characteristics for alkane hydrocracking, we suspect that Ru/TiO2-A-SG converts PP mainly through hydrocracking, instead of hydrogenolysis. In hydrocracking, C-C bonds are cleaved on Brønsted acid sites (BAS), and the metal only needs to catalyze dehydrogenation/hydrogenation. Thus, to test the hypothesis, we impregnated Ni and Pt onto TiO2-A-SG (0.07 M/nm 2 ), both of which are inert for C-C bond cleavage, i.e., hydrogenolysis, under these conditions. Figure shows that both Ni and Pt convert PP on TiO2-A-SG more efficiently than Ru, yielding similar product distribution (Figures and): no CH4, much more C4-5 than C2-3, narrow liquid distribution around C10, and yellow-colored products (Figure ). In addition, the TiO2-A-SG support alone, without any metal, can convert ~5% PP (Figure ), also with similar product distribution (Figure ). These results confirm that M/TiO2-A-SG can convert PP through hydrocracking, in which C-C bond cleavage occur on TiO2-A-SG, while the metal facilitates (de)hydrogenation steps. The presence of the more selective hydrocracking pathway on Ru/TiO2-A-SG explains its unique performance in PP upcycling in Figure . Since the two pathways on M/TiO2-A-SG exhibit very different selectivity between C4-5 and C2-3, we use the ratio between C2-3 yields and C4 yield (referred to as "(C2 + C3) / C4", cyan in Figure , C5 hard to quantify due to the high vapor pressure) as a reaction pathway indicator, along with the CH4 selectivity. |
62fbfe7e08a44bb1a2735acc | 6 | The obvious question here is why TiO2-A-SG can catalyze C-C bond cleavage, as TiO2 is not expected to have BAS required for it. Therefore, we impregnated Ni onto various oxides (0.07 Ni/nm 2 if not specified), and tested them in PP upcycling under the same conditions to verify that the second pathway is hydrocracking. Table shows that Ni only converts PP and forms yellow solid residues on supports known for having BAS, i.e., Nb2O5 and SSZ-13 zeolite (entries 4-6), while other supports showing relatively good PP upcycling performance with Ru in Figure , i.e., CeO2, rutile TiO2, "TiO2-R" and fumed SiO2, do not convert PP with Ni (entries 1-3). These results further support that the superior performance of Ru/TiO2-A-SG in Figure is due to its unique bifunctionality that enables hydrocracking. Hydrocracking allows efficient PP conversion using non-noble metals with good (de)hydrogenation ability, such as Ni, another advantage over hydrogenolysis besides the desired selectivity. We note that TiO2-A-SG is a particularly effective acidic support for PP hydrocracking, showing higher activity than SSZ-13 with even 10 times Ni loading (entry 7 compared to 6). This could be due to the absence of micropores on TiO2-A-SG (Figure ) causing less diffusion limits of the long-chain polymers. C This sample uses a second batch of TiO2-A-SG synthesized following the same procedure. d Calcination was performed at 500 ℃ for 4 h before the reaction (~5 min air exposure in between). e Acetic acid exposure was performed using the procedure described previously after 3 weeks RT air exposure. Since TiO2 surfaces were known to auto-adsorb ppm-level formic/acetic acids in the air to form mixed carboxylate layers, we suspected that the unexpected BAS on TiO2-A-SG are associated with these chemisorbed layers. M/TiO2-A-SG were calcined at 400 ℃ for 4 h in the final step of the synthesis. This step would remove the carboxylic layers, which re-accumulate during the storage (Figure mid showing their presence after long-term storage by C 1s XPS). |
62fbfe7e08a44bb1a2735acc | 7 | Thus, we controlled the post-synthesis history of Ni/TiO2-A-SG to test the hypothesis. Table shows that the PP conversion on Ni/TiO2-A-SG increases with longer post-synthesis air exposure at room temperature (entries 8-9), and drops to ~0 after calcining the catalyst again before the reaction (entry 10). The results indicate that the BAS on TiO2-A-SG are formed by contacting air at room temperature, and removed by high-temperature calcination, aligning well with the behaviors of the carboxylate layers on TiO2 surfaces. We also exposed Ni/TiO2-A-SG to acetic acid vapor to saturate TiO2 surfaces with the layers, which increases the PP conversion (entry 11 compared to entry 9), further supporting the hypothesis. We note that after the acetic acid vapor exposure, the catalyst also carries a significant amount of physisorbed acetic acid (reflected by the significant mass increase and strong smell). The fact that the PP conversion increase caused by it is not significant (46% to 57%) indicates that the chemisorbed carboxylate layers are much more active in PP hydrocracking than physisorbed acetic acid. Calcining acetic-acid-saturated Ni/TiO2-A-SG still eliminates its hydrocracking activity, i.e., BAS on it, as we expected (entry 12). Overall, the control experiments strongly imply that the BAS on TiO2-A-SG originate from the carboxylates it adsorbs from the air. We will discuss the carboxylate layers and BAS in more details in the Discussions section. |
62fbfe7e08a44bb1a2735acc | 8 | For hydrogenolysis over monofunctional Ru catalysts, when PH2 increases, the CH4 selectivity always decreases because the cleavage of terminal C-C bonds involves more dehydrogenated transition states (TS) than that of internal C-C bonds, and the more facile product desorption suppresses sequential C-C bond cleavage that favors CH4 formation, while the (C2 + C3) / C4 value also decreases in all our studies (Figure ). Therefore, the increase in both values at high PH2 cannot be explained by regioselectivity shifts in hydrogenolysis. Instead, it reflects the transition from a low-PH2 regime, in which hydrocracking dominates, to a high-PH2 regime, in which the contribution from hydrogenolysis is significant. This is consistent with the changes in liquid product distribution, from a narrow distribution around C10-12 with yellow color at ≤ 30 bar (Figures 2b and S3f-g), to a wide double distribution around C10-12 and C18 with no color at ≥ 45 bar (Figures and). In the high-PH2 regime, the isomerization level remains at ~60%, which, along with the double liquid distribution, indicates that both pathways have significant contribution to the reaction. The shift in the prevailing pathway with PH2 suggests that the rate of hydrocracking is less sensitive to PH2 than that of hydrogenolysis. As a result, the bifunctional Ru/TiO2-A-SG converts PP much more effectively at low PH2 than most active monofunctional Ru catalysts (223 gPP gRu -1 h -1 at 5 bar, Figure , compared to ~30 gPP gRu -1 h -1 on Ru/CeO2 26 ). Interestingly, when PH2 increases from 15 to 45 bar, the PP conversion remains constant (Figure ) while the hydrogenolysis rate increases (reflected by higher C1 -C3 yields, Figures ), indicating that the rate of hydrocracking decreases as PH2 increases. In hydrocracking, alkanes are dehydrogenated on the metal, resulted alkenes are transported to BAS, isomerized and cracked through C + intermediates, and then transported back to the metal for hydrogenation (Scheme 1). Since TiO2-A-SG does not have shape selectivity effect from micropores (Figure ), the high C4-5 yields in Figures suggest severe secondary cracking before desorption. |
62fbfe7e08a44bb1a2735acc | 9 | Also, the formation of C3 from PP indicates appreciable C-C bond cleavage through type-B β-scissions. Both observations suggest that on Ru/TiO2-A-SG, the alkane dehydrogenation step is not equilibrated (see the Discussions section for detailed mechanistic explanations), which is not surprising with the low metal loading. In this situation, the consumption of dehydrogenated intermediates on Ru (in the purple box in Scheme 1) through hydrogenolysis, i.e., C-C bond cleavage, reduces the amount of them desorbing as alkenes. The faster hydrogenolysis at higher PH2 thus decreases free alkene concentrations in the system, suppressing hydrocracking. |
62fbfe7e08a44bb1a2735acc | 10 | The conclusion is further supported by Table , which shows that doubling Ru loading on TiO2-A-SG does not increase the PP conversion but makes the product distribution more resemble hydrogenolysis (Figures S3d and S3e compared to Figures and, respectively), i.e., higher Ru loading leads to slower hydrocracking. Since the alkane dehydrogenation step over Ru is not equilibrated, more Ru would increase hydrocracking rate if hydrogenolysis did not interfere with it. Thus, the lower hydrocracking rate reflects that it is suppressed by the faster hydrogenolysis on larger Ru particles. Scheme 1. Mechanistic scheme of the dual-pathway PP upcycling over M/TiO2-A-SG catalysts. |
62fbfe7e08a44bb1a2735acc | 11 | We have demonstrated the co-existence of hydrocracking and hydrogenolysis pathways in the PP conversion on bifunctional Ru/TiO2-A-SG, which brings the question of whether the dual-pathway scheme is applicable to other less branched substrates. Thus, we compared the reaction of four substrates with various branching levels (quantified by the fraction of 3 C in total C, n-C16H34, no 3 C; LDPE, ~ 2% 3 C, squalane, structure see Scheme 2a, 20% C, and PP, 33% all substrates, yielding no C1-2, minimal C3, and high fraction of isomers (Table and Figure ), indicating that hydrocracking is present with all substrates. Since hydrogenolysis is not catalyzed by Ni and its rate is more sensitive to PH2 than that of hydrocracking, we used two parameters: 1) |
62fbfe7e08a44bb1a2735acc | 12 | the ratio between the rate on Ni and Ru at 30 bar, and 2) the ratio between the rate on Ru at 5 bar and 30 bar, to gauge the relative importance of the two pathways. Table and Figure show that increasing substrate branching level leads to increases in both indicators, i.e., the relative importance of hydrocracking to hydrogenolysis. The conclusion is also supported by the lower (C2 + C3) / C4 value with more branched substrates under identical conditions on Ru (Table and Figure ). It is expected based on previous studies with small-alkanes, as 1) hydrocracking mainly proceeds through 3 C + intermediates (type-A β-scissions), and less branched substrates require more extensive isomerization prior to C-C bond cleavage, and 2) 3 C-x C bonds are less reactive than 2 C-2 C and 2 C-1 C bonds in hydrogenolysis due to their high steric hindrance limiting the ability to access the most stable TS. ), further emphasizing that hydrocracking is more favored with more branched substrates. The substrate-dependence of the two pathways explains why in Figure , the bifunctionality of Ru/TiO2-A-SG does not lead to superior performance in LDPE upcycling: the contribution of hydrocracking is minimal with LDPE, and Ru/TiO2-A-SG has mediocre activity/selectivity in hydrogenolysis (will be shown in detail in a separated manuscript). We note that Ru/TiO2-A-SG yields higher fraction of branched alkanes from LDPE than other Ru catalysts with similar CH4 selectivity, but the regioselectivity of hydrogenolysis predicts the two parameters to move in sync. This is because branched alkanes can also be produced on Ru/TiO2-A-SG by isomerization on BAS. The close examination of C10 products from squalane offers further mechanistic insights. |
62fbfe7e08a44bb1a2735acc | 13 | Table shows that on Ru/TiO2-A-SG at 30 bar, 75% of the C10 products are non-isomers (see discussions related to Figure for analysis details), indicating that hydrogenolysis is the main pathway under such conditions. Meanwhile, the absolute majority of non-isomerized products are dimethyloctanes, which are produced by cleaving only 2 C-2 C bonds (blue in Scheme 2b), rather than methylnonanes, the formation of which requires cleaving at least one 3 C-x C bonds (red in Scheme 2b). Considering that isomerization is insignificant, the observation indicate that in hydrogenolysis, the cleavage of 2 C-2 C is strongly favored over that of 3 C-x C bonds, aligning well with the literature of small-alkane hydrogenolysis. In comparison, on Ni/TiO2-A-SG or at 5 bar, significantly more isomers are produced, supporting that decreasing PH2 or replacing Ru with the hydrogenolysis-inactive Ni shift the reaction pathway towards hydrocracking. |
62fbfe7e08a44bb1a2735acc | 14 | Our results demonstrated the two pathways of polyolefin conversion on the bifunctional Ru/TiO2-A-SG: hydrocracking and hydrogenolysis. Compared to hydrogenolysis, hydrocracking has several advantages. First, it produces minimal low-valued C1-3 products (Figure ). C-C cleavage in hydrocracking is mainly achieved through two types of β-scissions: type-A, which starts and ends both with a 3 C + , and type-B, which starts or ends with one 2 C + (Scheme 3). C1-2 are absent because the 1 C + intermediates involved in their formation are too unstable. 10 C3 yield is low because only type-B β-scissions at the chain ends can produce C3 (Scheme 3), which are much slower than type-A β-scissions. Besides, at the chain ends of virgin PP, primary βscissions always start with 3 C + , and thus there are no type-B1 β-scissions (Scheme 3). In contrast, primary C-C bond cleavage in hydrogenolysis does not discriminate against C1-3, and sequential C-C cleavage, if the desorption is slow, favors CH4 formation. Second, hydrocracking is more suitable for low-PH2 operation. When PH2 decreases from 30 to 5 bar, the PP conversion drops much less significantly on the bifunctional Ru/TiO2-A-SG (37% drop in Figure ) than on monofunctional Ru catalysts (70%, 80%, and 75% on 0.125%, 2% Ru/CeO2, and 5% Ru/C, respectively), and the former converts PP at least 7-fold faster at 5 bar. Third, hydrocracking is accompanied by isomerization, producing more branched alkanes from LDPE (Figure ) and likely aromatics (implied by the yellow color of products). Fourth, hydrogenolysis requires noble metals (Ru, Rh, or Pt with polyolefin substrates), while the non-noble metal Ni can catalyze hydrocracking even more efficiently than Ru (Figure ). Despite the superior efficiency and selectivity with PP, hydrocracking on Ni/TiO2-A-SG is not as effective as hydrogenolysis on Ru/TiO2-A-SG with less branched substrates (Table ), as the virgin structure with minimal 3 C requires extensive isomerization before β-scissions, and has less steric hindrance for hydrogenolysis. Thus, hydrogenolysis might be more suited for the upcycling of PE, particularly HDPE. Another undesired feature of PP hydrocracking on M/TiO2-A-SG is the strong tendency to produce C4-6 (Figure , observed at low PP conversion as well, Figure , C6 yield underestimated due to the fast evaporation). The high C4-6 yields on nonmicroporous catalysts are signs of significant secondary cracking, i.e., consecutive β-scissions before desorption, which will stop when the substrate does not have 7 C atoms (Scheme 3). This usually occurs because the dehydrogenation ability of the catalyst is too low to establish the alkane/alkene equilibrium, leading to low free alkene concentration that cannot displace products from BAS. Replacing Ni with Pt, which has better dehydrogenation ability, enhances the rate (Figure ), confirming that on Ni/TiO2-A-SG, dehydrogenation is the slow step. This also increases chances for type-B β-scissions and thus C3 formation. Type-A β-scissions require three branches in the α, α, γ-configuration (Scheme 3), which is absent in virgin PP/LDPE. |
62fbfe7e08a44bb1a2735acc | 15 | Therefore, isomerization is required prior to type-A β-scissions, which was known to be favored by high free alkene concentration. The weak dehydrogenation ability is caused by the low metal loading (0.07 M/nm 2 ), and one should be able to alleviate the problem and shift the selectivity towards higher-valued heavier products by increasing the metal loading. In Figure , Pt/TiO2-A-SG yields less C3-6 than Ni/TiO2-A-SG despite higher PP conversion, confirming that enhancing the dehydrogenation ability suppresses the formation of these light products. |
62fbfe7e08a44bb1a2735acc | 16 | As for less branched substrates, hydrocracking on Ni/TiO2-A-SG also generates no C1-2 products (Figure , for the same reason with PP), but less C4-6. This could be explained as these substrates have less C with high steric hindrance, leading to faster dehydrogenation, higher free alkene concentration, and thus less secondary cracking. We note that LDPE and n-C16H34 both have 2 C at chain ends in the virgin structure, which allows type-B1 β-scissions. C3 yields are still low, suggesting that the isomerization -type-A β-scission sequence is preferred over type-B βscission, consistent with the literature. We also noticed that in the hydrocracking of PP (on Ni/TiO2-A-SG), the hardness of the solid residue does not seem to change with the PP conversion. This echoes with previous report that the average MW (GPC-based) of the solid does not decrease significantly with hydrocracking reaction time, and implies that hydrocracking preferentially converts smaller products over large polymers, opposite of hydrogenolysis. This could be due to the secondary cracking, which is enhanced by the mass transfer limitation in the viscous environment trapping products around BAS and causing re-adsorption, and/or the slower diffusion of large polymers preventing it to reach BAS after dehydrogenation. |
62fbfe7e08a44bb1a2735acc | 17 | Another intriguing result from this work is the unexpected Brønsted acidity of TiO2-A-SG associated with the carboxylate layers auto-adsorbed from the air (Table ). It has long been known in surface science studies that hydrocarbon layers are formed under air on TiO2, altering its surface properties. The chemical identity of the layers was recently elucidated as mixed formate/acetate, formed by the strong dissociative adsorption of formic/acetic acids ubiquitously present in the air at ppm levels. They are removed by UV radiation or H2/air at ≥ 350 ℃, but stable during laboratory storage, and their presence is detected by XPS (Figure ) and IR as shown in our previous work. TiO2 is widely used in thermo-catalysis as the catalyst or the support, and it is not always treated in-situ at high temperature prior to the reaction. |
62fbfe7e08a44bb1a2735acc | 18 | We believe that certain requirements exist for the carboxylate layers on TiO2 to exhibit Brønsted acidity. All three types of TiO2 we tested have the carboxylate layers (Figure ), but only TiO2-A-SG shows hydrocracking activity. Rutile, or even anatase from the commercial source do not. The observations resonate with our previous report that the layers on TiO2-Acomm deactivate Pt/Al2O3 in CO2 hydrogenation while those on TiO2-R do not. We propose two possible structures of the BAS on TiO2-A-SG: 1) the surface -OH formed along with the carboxylates in the dissociative adsorption of acids; 2) the re-protonation of carboxylates under reaction conditions (≥ 5 bar H2, 260 ℃). Because physisorbed acetic acids are much less active for PP hydrocracking than the chemisorbed carboxylate layers (Table ), we suggest that the first possibility is more likely. Regardless, the properties of the carboxylate layers should be sensitive to the strength and configuration of their chemisorption, which vary with the properties of TiO2. |
62fbfe7e08a44bb1a2735acc | 19 | This would impact their catalytic behaviors, such as Brønsted acidity or deactivating Pt/Al2O3, leading to the varying results among the three TiO2. We also note that three batches of TiO2-A-SG were synthesized for this work, which all exhibit hydrocracking activity with Ni, but the rate varies to a minor extent (two batches shown in Table , the third batch between them). This could be due to the subtle structural difference among the batches in surface area, exposed facets, and/or defects. This novel discovery invokes complicated questions on the structure and property of the carboxylate layers and BAS on TiO2, which are fundamentally intriguing and practically appealing as they can serve as a new type of Brønsted-acid catalysts under proper conditions for reactions beyond polyolefin hydrocracking. While this work focuses on polyolefin upcycling over M/TiO2-A-SG, we will attempt to address these questions with more detailed spectroscopic studies and simpler probe reactions in the future. |
62fbfe7e08a44bb1a2735acc | 20 | In this contribution, we report that low-loading Ru on a sol-gel anatase TiO2 (TiO2-A-SG) can upcycle polyolefin into small hydrocarbons under H2 through hydrocracking, in addition to hydrogenolysis that is common on Ru catalysts. Compared to hydrogenolysis, hydrocracking shows more desired product selectivity in minimal low-valued C1-3, liquids with narrower carbon distribution, more isomers, and can be achieved on Ni with efficiency close to on noble metals. |
62fbfe7e08a44bb1a2735acc | 21 | Between the two pathways, hydrocracking is more favored at lower hydrogen pressure (PH2) and with more branched substrates. It accounts for the majority of polypropylene conversion at PH2 ≤ 30 bar on Ru/TiO2-A-SG, while is only important at 5 bar with low-density polyethylene and nhexadecane. With low dehydrogenation ability, hydrogenolysis suppresses hydrocracking by reducing free alkene concentration. The hydrocracking activity of Ni/TiO2-A-SG is higher than a Ni/SSZ-13 we tested, and its evolution with air exposure and calcination suggest that the source of the Brønsted acidity is the carboxylate layers TiO2 chemisorbs from the air. The investigation of the simultaneous polyolefin hydrocracking and hydrogenolysis on a metal-acid bifunctional catalyst enhances our understanding of the depolymerization chemistry, and guides decisions in process development. The unexpected Brønsted acidity on TiO2-A-SG revealed in this work also carries significant potentials in other acid-catalyzed reactions. |
60c741260f50db24b7395a73 | 0 | Smal l Molecules Interacting with RNA (SMIRNAs) have the potential to be broadly deployed to affect biology, to help study the biological roles of RNA, and to develop novel RNA-targeted therapeutics. The most common way to target RNA is via its sequence by using antisense oligonucleotides. RNA, however, folds into 3dimensional structures that often affect its biology, including causation of disease. Thus, SMIRNAs can serve as an alternative approach to target RNA, affording distinct target sites and potential advantages. |
60c741260f50db24b7395a73 | 1 | The sequence-based design of SMIRNAs have been developed by correlating RNA 3-dimensional folds with empirically derived interactions with small molecules. These interactions are identified via a library-versus-library selection strategy dubbed two-dimensional combinatorial screening (2DCS). Our lead identification strategy, Inforna, searches for overlap between binding partners and 3-dimensional folds in cellular RNAs, directly and quickly informing design of bioactive ligands. This approach has potential to be a general and scalable way to design bioactive ligands targeting RNA, a challenge in medicinal chemistry and chemical biology. |
60c741260f50db24b7395a73 | 2 | Herein, we investigated the scalability of 2DCS to study the RNA-binding capacity of a reasonably large subset of compounds found within the pharmaceutical industry and if the resulting data could be applied to a pre-determined target. To address scalability, we deployed various technologies to probe quickly over 60 million interactions between small molecules from the AstraZeneca compound library (n = 2947) and RNA folds. These studies defined not only the SMIRNAs themselves but also features within the small molecules and the bound RNAs that afford molecular recognition. We then applied our privileged RNA motif-small molecule interactions to enhance VEGFA expression. Upregulation of VEGFA is a promising strategy for management of diseases such as coronary artery disease, a significant societal burden with few therapeutic options. |
60c741260f50db24b7395a73 | 3 | Defining small molecule-RNA fold interactions and studying features in small molecules that bind RNA. An in silico analysis of the AstraZeneca corporate collection (2M compounds) generated a diverse compound subset comprised of 1967 members with RNA-binding potential based on chemical similarity with previous SMIRNAs deposited in the Inforna server. These compounds were then studied for binding to libraries of 3-dimensional RNA folds. The RNA motif libraries comprise a unimolecular hairpin that displays various structural elements, including 32 (32 ILL; n = 1024 unique RNAs), 33 (33 ILL; n = 4096 unique RNAs), and 43 (43 ILL; n = 16384 unique RNAs) internal loops (ILs) respectively (Fig. ). To facilitate studying the binding interactions of the RNA motif and AstraZeneca small molecule libraries, we used an approach dubbed AbsorbArray, where the small molecules are absorbed onto agarose-coated microarrays allowing for spatial encoding. The arrays were then probed for binding to radiolabeled RNA motif libraries in the presence of 100-fold excess of unlabeled competitor oligonucleotides that mimic the constant regions in the library (1-5), DNA (6,7), and tRNA (8) (Fig. ). Due to the combinatorial nature of a library-versuslibrary screen, this experiment probed 43 million RNA fold-small molecule binding interactions simultaneously. Of the 1967 small molecules studied, 23 selectively bound the unique 3-dimensional folds displayed by the RNA libraries providing a hit rate of 1.2%. |
60c741260f50db24b7395a73 | 4 | An analysis of calculated molecular properties further emphasized the difference between the starting library and the compounds that are bona fide RNA binders (Table ). The RNA binders were on average more lipophilic (ClogP = 1.3) and less flexible in terms of having fewer rotational bonds (4.3 vs. 5.7). RNA-binding small molecules also had on average two additional hydrogen-bond donors and have greater polar surface area. Many of the descriptors suggest a planar-like shape preference for the RNA binders. That is, the hits include an additional ring, an increased occurrence of aromatic atoms at the expense of fewer aliphatic atoms as well as fewer chiral centers. The average fraction-sp 3 (a measure on carbon bond saturation) was 0.11, compared to 0.24 for the starting small molecule library. Finally, a large number of RNA binders, 50%, included a basic functionality. These preferences were used to select compound nearest neighbors from the AstraZeneca collection, providing an additional 980 RNA-focused small molecules that were studied by AbsorbArray and 2DCS. [Collectively, the two screens studied a total of 2947 small molecules and >62 million potential binding events.] In this second screen, ten selective RNA-binding small molecules were obtained, providing a hit rate of 1.1%. Tanimoto analysis revealed four additional conserved scaffolds, that avidly bind RNA including 2-guanidino thiazoles, 2-amino quinazolines, 2,4-diamino pyrimidines, and phenyl benzimidazoles, which also includes phenyl-bis-benzimidazoles. (Fig. and). |
60c741260f50db24b7395a73 | 5 | Studying the features in RNA folds that bind small molecules. To identify the RNA 3-dimensional folds that bind each small molecule, bound RNAs were excised from the corresponding position on the microarray surface, amplified via RT-PCR, and sequenced. To define high affinity and selective or privileged interactions, we used a bioinformatics analysis tool previously developed in our laboratory. Coined high throughput-structure activity relationships through sequencing, HiT-StARTS calculates the enrichment of a particular SMIRNA-bound RNA fold in 2DCS sequencing data as compared to the sequencing data derived for the starting RNA motif library; and then calculates the statistical significance of that enrichment reported as a Z-score (Zobs). This approach allows precise definition of: (i) the number of RNA folds that each small molecule binds selectively; (ii) the relative affinity of each of the selected interactions; and (iii) a rich source of RNA fold-small molecule binding partners that can be used to design small molecules that target three dimensionally folded RNAs by using Inforna. We have previously shown that the RNA 3-dimensional motifs that bind small molecules avidly have a Zobs > 8 and that the relative affinity of the selected interactions directly correlates with Zobs. Hence, small molecules with higher Zobs are more fit for binding a SMIRNA than those with lower scores. In summary, these studies defined an encyclopedia of 41,000 RNA fold-small molecule interactions that were deposited into Inforna, an increase of 20-fold over the current Inforna server (Table ). Interestingly, some small molecules only bound members of certain RNA libraries while some bound members from all three. For example, 43 ILL bound 18 compounds (n = 3 unique) while 32 ILL bound 16 (n = 1 unique) and 33 ILL bound 15 small molecules (n = 1 unique). Perhaps, 43 ILL bound a larger subset of the small molecules because of the greater diversity in the RNA motif library. A detailed analysis of the types of RNA folds that bind small molecules is presented in the Supporting Information, including a LOGOS analysis (Figs. S2 to S6). Some interesting observations include that single nucleotide bulges bind a variety of small molecules (Table and Fig. and D); randomized regions with additional base pairs, and higher GC pairing appear more frequently in RNAs selected to bind small molecules than those that do not bind; and U-rich internal loops have lower small molecule binding capacity. |
60c741260f50db24b7395a73 | 6 | Dynamics has been shown to be a key determinant in a variety of RNA functions and local dynamics could affect ligand binding capacity broadly. If the structure of a target RNA is too dynamic, ligand binding potential could be diminished. That is, a defined small molecule binding pocket may not be present, or the affinity of an ill-defined pock could be low due to energetic and entropic penalties associated with locking out multiple conformations. Previous studies have provided some insight into RNA structural dynamics such as smaller loops are not typically as conformationally dynamic as their larger counterparts and U-rich motifs can have dynamic character. We were therefore interested in if the SMIRNAs studied herein had a preference for dynamic or structurally well-defined loops. Fortuitously, a set of structurally related small molecules had overlap in the RNAs that they preferred to bind and those that they discriminated against. We studied the structural dynamics of these loops by nuclear magnetic resonance (NMR) spectroscopy. As shown in Figure , RNAs that bind small molecules have defined structure, as evidenced by the presence of all possible imino proton peaks. |
60c741260f50db24b7395a73 | 7 | In contrast, various peaks from imino protons were absent in the spectra of RNAs that generally do not bind small molecules (Fig. ). Our data suggest that a defined RNA structure is a contributing factor for SMIRNA binding, at least for the scaffolds studied herein. That is, binding is not observed to RNA motifs that are overtly dynamic and SMIRNA binding to them with sufficient affinity and selectivity could be a challenge. |
60c741260f50db24b7395a73 | 8 | A lead small molecule that targets pre-miR-377 and inhibits its processing in vitro and in cells. We next sought to identify a compound capable of upregulating VEGFA from our 2DCS dataset. Although there are multiple drugs that inhibit VEGFA and its receptor's activity, there are no known compounds that increase its levels. |
60c741260f50db24b7395a73 | 9 | VEGFA expression could be regulated in various ways, including via an internal ribosome entry site (IRES) in its 5' untranslated region (UTR) and multiple miRNA binding sites in its 3' UTR, among others (Fig. ). Small molecule binding to the IRES or 5' UTR would most likely repress VEGFA expression, however inhibition of a miRNA targeting the transcript would likely increase expression. |
60c741260f50db24b7395a73 | 10 | Previous studies showed that miR-377 was overexpressed in failing hearts, and bioinformatic analysis revealed that VEGFA is a direct target of miR-377. Further studies revealed that repression of miR-377 by an antisense oligonucleotide derepressed VEGFA and stimulated angiogenesis, validating that inhibition of miR-377's biogenesis using a small molecule is a promising method for stimulating VEGFA expression (Fig. ). Inforna was mined for binders to pre-miR-377's Dicer site, identifying nine novel binders with high fitness from the AstraZeneca collection. The binding affinities of these compounds for a model RNAs containing the 5'AAU/3'U_A bulge were measured and compared to a control RNA in which the bulge was mutated to an AU base pair. These studies showed that compound C1 avidly bound to the RNA with the pre-miR-377 Dicer site (Kd = 65 ± 10 µM) and did not bind to the control RNA. Compound 1's ability to inhibit Dicer processing of pre-miR-377 in vitro. Treatment with C1 inhibited processing by Dicer with an IC50 of 50 ± 10 μM, mirroring its Kd (Fig. ). To assess selectivity of this inhibition, the Dicer processing and C1 binding site was mutated. Pre-miR-377 has two A bulges, one at the Dicer site and another upstream. |
60c741260f50db24b7395a73 | 11 | One mutant has a single nucleotide insertion that converts the A bulge at the Dicer site to an AU pair, while the other has two single nucleotide insertions such that replaced both A bulges with AU pairs. Both mutated targets are properly processed, however C1 is unable to inhibit Dicer processing of either mutant (Fig. ). These data support that C1 targets the Dicer site, as designed, to inhibit processing. |
60c741260f50db24b7395a73 | 12 | To study if C1 can inhibit the cellular biogenesis of miR-377, its effect was studied in HUVECs, as they differentiate into tubules in a miR-377-and VEGFA-dependent manner, which can be used to measure angiogenic capacity directly. 27 C1 reduced mature miR-377 levels in a dose-dependent fashion, with an IC50 of ~5 μM (Fig. ). |
60c741260f50db24b7395a73 | 13 | To gain insight into compound mode of action, C1's effect on pre-miR-377 levels. As expected, an accumulation of pre-miR-377 was observed, suggesting that Dicer is unable to process the RNA and confirming our in vitro data (Fig. ). We next measured if repression of miR-377, de-repressed the Vegfa mRNA. RT-qPCR showed that indeed, C1 caused an ~30% increase in Vegfa levels with a concomitant increase in VEGFA protein (Fig. and). |
60c741260f50db24b7395a73 | 14 | Silencing VEGFA inhibits the formation of tubules in HUVECs when grown on a Matrigel matrix. To investigate the pro-angiogenic potential of compound C1, HUVECs treated with C1 were differentiated on a Matrigel support. These studies showed that treatment with C1 stimulated angiogenesis by increasing tubule branching density. Furthermore, a stable HUVEC cell line was generated to ablate Vegfa mRNA via expression of a short hairpin (sh)RNA targeting this transcript. The shRNA expressing cell line had reduced ability to differentiate into tubules as the number of tubules was reduced by >60% as compared to wild type, non-shRNA expressing cells (Fig. ). |
60c741260f50db24b7395a73 | 15 | enhanced affinity and specificity. Inforna defined that C1 can target pre-miR-377, however it also identified eight other miRNA precursors with the A bulge that C1 binds in pre-miR-377 (Fig. ). Such RNAs we have dubbed RNA isoforms. Six of these miRNAs are expressed in HUVECs (Fig. ). Thus, the effect of C1 on the levels of each of the miRNAs was studied. Only levels of miR-377 and miR-421 were affected (40 -50% inhibition) at 5 M. Notably, of the six RNA isoforms, the C1-targetable motif is only present in a functional (Dicer processing) site in pre-miR-421 (Fig. ). These results mirror previous studies that show that the binding of SMIRNAs to functional sites are an important determinant of small molecule selectivity. Because of the dual targeting nature of C1 it is henceforth referred to as Targapre-miR-377/421, (TGP- |
60c741260f50db24b7395a73 | 16 | Analysis of the structures of pre-miR-377 and pre-miR-421 identified a 5'G_G/3'CAC bulge adjacent to pre-miR-377's Dicer site, not found in pre-miR-421 (Fig. ). Mining Inforna identified compound C2 (Fig. ) that bound selectively to this site over a mutated base paired control with a Kd of 4 μM (Fig. ). Thus, linking TGP-377/421 and C2 with appropriate spacing could provide a ligand selective for pre-miR-377 (Figs. and). To provide compounds that can be linked together to allow for modular assembly, derivatives of each of these two modules were synthesized; a carboxylic acid was added to TGP-377/421 (C1-COOH) and an alkyne moiety was added to C2 (C2-Ak). C1-COOEt and C2-Ak bound selectively to their respective RNA targets with Kd's of 0.8 and 1.6 M, respectively, with no measurable affinity to a mutant base paired RNA control (Fig. and). Binding was measured with the acylated acid to mimic the dimerized compound. |
60c741260f50db24b7395a73 | 17 | To assemble these compounds to bind to the two sites in pre-miR-377, peptoid based linkers were synthesized with varying distances between an amine and an azide handle to couple compounds 1A and 2A via an amide coupling and copper-catalyzed click reaction, respectively. The compound series was studied for binding to a mimic of pre-miR-377 and showed that the dimer with four N-n-propyl-glycine spacers bound with the highest affinity (Kd of 5±1 nM) with no measured binding to a base paired mutant RNA (Fig. ). Thus, this compound is referred to as Targapre-miR-377 (TGP-377). In vitro, TGP-377 inhibited Dicer processing of pre-miR-377 with an IC50 of ~500 nM, a 10fold improvement over TGP-377/421. Furthermore, mutation of binding sites for both compounds to base pairs ablated TGP-377's inhibitory effect, demonstrating binding site dependence for activity (Fig. ). TGP-377 is a potent and selective inhibitor of pre-miR-377 processing and stimulates VEGFA production in HUVECs. Delivery of TGP-377 to HUVECs decreased mature miR-377 levels 10-fold more potently than TGP-377/421 (Fig. ). As expected based on its mode of action, TGP-377 increased pre-miR-377 levels by 1.6-fold when HUVECs were treated with 500 nM of compound (Fig. ). |
60c741260f50db24b7395a73 | 18 | The selectivity of TGP-377 was assessed via miRNA profiling. First, we studied the effect of TGP-377 on miRNAs predicted to modulate VEGFA production by Targetscan. These miRNAs include miR-15b, -16, -20a, -20b, -195, -377, and -205. Analysis of their precursor hairpins showed that only pre-miR-377 contains the 5'AAC/3'U_A target site. Analysis of the entire miR-ome produced in HUVEC cells showed that amongst >200 miRNAs, only miR-377 was significantly inhibited by >50 % (p <0.001) upon treatment with TGP-377 (Fig. ). Importantly and in contrast to C1, pre-miR-421 is not affected (orange triangle in volcano plot; Fig. ), demonstrating that TGP-377 is selective for pre-miR-377 and that modular assembly can overcome liabilities of selectivity while at the same time enhancing potency of monomeric compounds. As miR-377 decreases the levels of Vefga mRNA, application of TGP-377 also enhanced the levels of Vegfa mRNA by >50% at 500 nM (Fig. ). |
60c741260f50db24b7395a73 | 19 | proliferative proteins in HUVECs. Treatment of HUVECs with 500 nM of TGP-377 increased levels of excreted VEGFA in HUVEC media supernatants by 2-fold (Fig. ), with a similar effect observed by Western blot of intracellular VEGFA (Fig. ). Global proteomics analysis of the HUVEC proteome (>4000 unique proteins) revelated that only 160 proteins were affected by TGP-377 treatment (p <0.05; Fig. ). A bioinformatic STRING analysis was performed to study protein association networks that are affected by TGP-377. This showed that, as expected, cell proliferative pathways including FGFR, Hedgehog, MAP kinase, and ERK pathways were upregulated. Previous studies have shown that upregulation of VEGFA causes a reduction of Hedgehog interacting protein (HHIP) levels, part of a larger feedback loop for angiogenesis. As expected, levels of HHIP were significantly reduced upon TGP-377 treatment (p<0.01; Fig. ). Of interest, levels of Protein Phosphatase 2 Regulatory Subunit B'Alpha (PPP2R5A) were also significantly reduced upon treatment (p<0.05; Fig. ). PPP2R5A, which is part of a pathway that controls cell survival, has been previously shown to be downregulated upon upregulation of VEGFA. Other affected proteins that are known to be modulated specifically within the VEGFA-mediated pathways can be found in Table . Collectively, these studies show that TGP-377 exerts selective effects on the proteome and indeed broadly affects signaling via the VEGFA pathway. |
60c741260f50db24b7395a73 | 20 | Studying the effects of TGP-377 on VEGFA protein levels and stimulation of a pro-angiogenic phenotype. Because proteomics and miR-ome data show that TGP-377 is selective at the RNA and protein levels, we studied the effect of TGP-377 on phenotype, i.e., tubule branching density. Indeed, treatment of HUVECs with TGP-377 (500 nM) increased tubule branching density by ~50% (Fig. ). Interestingly, the effect of TGP-377 was similar to that observed when recombinant VEGFA protein (10 μg/mL) was added to the cell culture medium or an LNA antagomir against miR-377 (LNA-377) (Fig. ). In contrast, a scrambled LNA control antagomir (50 nM) had no effect on tubule branching (Fig. ). |
60c741260f50db24b7395a73 | 21 | In contrast, exogenous addition of VEGFA (10 μg/mL) to cell culture medium stimulated tubule formation (Fig. ). Collectively, these studies support the hypothesis that TGP-377 affects phenotype via the miR-377-VEGFA circuit (Fig. ). This study further shows that sequence-based design of SMIRNAs via Inforna is a powerful approach to design bioactive compounds targeting RNA to affect a biological pathway specifically. |
60c741260f50db24b7395a73 | 22 | There are potential RNA drug targets in nearly every disease process. Small molecules offer some key potential advantages as chemical probes and lead drug molecules targeting RNA. Small molecules typically target structured regions that often play critical roles in disease biology, and their properties can be more easily optimized compared to oligonucleotides-based therapeutic agents. One of the major challenges SMIRNAs has been the perception that selectivity and potency are difficult to achieve. |
60c741260f50db24b7395a73 | 23 | Evidently, selectivity and potency are indeed possible as now several SMIRNAs have been designed to affect RNA-mediated biology in cells and pre-clinical models of disease. It is likely that as more information emerges on the RNA folds that are bound by small molecules that the number of targets that can be affected by SMIRNAs will increase. In the current study, we designed TGP-377 as a test case to develop approaches to drug a pre-defined RNA target rationally and predictably. A lead compound was quickly identified and then rapidly optimized. Translating lead compounds such as TGP-377 into medicines that reach patients is a more complicated endeavor, however. |
60c741260f50db24b7395a73 | 24 | The class of compounds developed herein could be suitable for the treatment of heart disease and myocardial infarctions by increasing VEGFA production. Both DNA and mRNA delivery are being tested in clinical trials for boosting VEGFA levels, with the mRNA delivery approach having the most promise. Interestingly, TGP-377 is a relatively small molecule compared to an mRNA . Although compounds such as mRNA can be effectively delivered to the failing heart to allow for local expression, the nature of miRNA-targeting may provide selectivity without directly delivering the therapeutic to affected tissues. That is, TGP-377's will only be effective in a limited number of tissues that express both miR-377 and Vegfa mRNA. Further, the increase in VEGFA production will have an upper limit based on the effect of miR-377 on Vegfa's translation, not simply compound dose. Our proteomics studies showed that TGP-377 exerts highly specific effects on the proteome. Although additional studies will be required to progress these compounds into animal models and later clinical studies, our data suggest that the compound shows promise for therapeutic development. There are wide number of indications to which RNA-targeted small molecule medicines will be applicable. Perhaps studies like these will illustrate that molecular design can provide potent and selective small molecules to specifically recognize RNA targets in cells. |
6198b44f9960f38e5bb51ed2 | 0 | Carbazoles are ubiquitous N-heterocycles used throughout medicinal chemistry and the material sciences. From a pharmaceutical perspective, the carbazole core features extensively in drugs and natural products, many of which exhibit potent anti-proliferative activities (Figure ). The breadth of applications has inspired the development of numerous methodologies for their preparation. Pd-catalyzed processes in particular enable a [3+2]heteroannulation via a Pd(0)-catalyzed Buchwald-Hartwig amination, followed by a Pd(II)-catalyzed C-arylation at a late stage in a synthetic workflow. However, a generalized set of guidelines outlining the molecular determinants which define the chemo-and regioselective control of each C-N/C-C bondforming reaction, and the factors which influence Pd(0) versus Pd(II) catalysis in a one-pot process has not been established. This is an important requirement for the formation of tetracyclic carbazoles where a regioselective C-H activation step is required. In this manuscript, we establish reaction guidelines to prepare tri-and tetracyclic carbazoles by controlling the chemoselectivity of the first Pd(0)-catalyzed C-N bondforming step, and the regioselectivity of the second Pd(II)catalyzed C/N-arylation (Figure ). Our rationale was to use chloroanilines (1) to define the A-ring of a carbazole core, and heteroaryl bromides to form the C/D-rings of tricyclic and tetracyclic products. |
6198b44f9960f38e5bb51ed2 | 1 | With conditions for the Pd(0)-catalyzed C-N bond-forming step established, the optimization of the one-pot process was explored (Table ). The optimal ligand/base pairing of HPCy3BF4 with K3PO4 was identified, which formed 9a from 1a and 6a in 78% yield. This highlights that the second C-H activation step is regioselective for the 7-position of 6a. |
6198b44f9960f38e5bb51ed2 | 2 | To further understand how the nature of the chloroaniline and heteroaryl bromide substrates influenced the chemoand regioselectivity of both bond-forming steps, a series of test reactions were undertaken (Scheme 2). Exchanging 6bromoisoquinoline (6a) for isoquinoline (10) formed dimethoxyphenazine (11) and the tertiary aniline (12) in 35% and 25% isolated yield, respectively (Scheme 2a). No dihydrophenazine was isolated from the reaction, which suggests an in situ oxidation occurred. No reaction occurred when isoquinoline (10) was the coupling partner with 1-chloro-3-methoxybenzene (13, Scheme 2b). Only secondary aniline (15) was isolated when para-anisidine (14) was reacted with 6-bromoisoquinoline (6a, Scheme 2c). Taken collectively, these test reactions highlighted the following requirements for the preparation of the tetracyclic core: (i) the aryl bromide is essential and prevents dimerization of the chloroaniline, (ii) whilst the absence of a bromo substituent in the heteroaryl substrate results in C-H activation at the same site, there is little regiocontrol, (iii) a chloro substituent is essential for C-arylation. |
6198b44f9960f38e5bb51ed2 | 3 | The influence of the electron-donating aniline lone pair in the direct C-arylation step was then explored. We surmised that the acetylated substrate (16) would deactivate the Cring and render the C-arylation less efficient. This indeed occurred as highlighted by the formation of deacetylated Carylated regioisomers, 9a and 17, in 27% total yield (1.2:1.0 9a:17). We assume that deacetylation occurs in situ because of the high temperatures and in the presence of base in the reaction mixture. An unexpected result was the formation of the linear tetracyclic carbazole 17, arises from C-H activation of the isoquinoline 7-position of 16. The formation of 17 suggests that C-H activation of the 7-position is favored if the acetyl group is present prior to C-arylation. In contrast, if 7a is present -presumably formed by deactylation of 16 -C-H activation at the 5-position occurs. We speculate that the acetyl group (i.e., 16) directs C-H activation at this site via coordination of a Pd(II) species through the amide carbonyl. This series of reactions have guided us to propose that oxidative addition of the C-Cl bond in 7a occurs first and proceeds via a Pd(0) species to form 18 (Scheme 2e). Pd(II)catalyzed C-arylation forms the palladacycle (19) followed by tautomerization (20). Finally, reductive elimination produces the C-arylated product (9a). |
6198b44f9960f38e5bb51ed2 | 4 | With mechanistic knowledge of the second C-C bondforming step established, the substrate scope of the process was investigated (Scheme 3). The reaction conditions formed 7H-pyrido [3,4-c]carbazole analogues (9a-c). The presence of a nitro group resulted in only trace amounts of 9d formed, with the secondary aniline (7e) isolated in 79% yield. The reaction conditions also tolerated changes in the substituents in the D-ring of the heteroaryl bromide (9e-j). The [3+2]heteroannulation strategy was also compatible with the formation of carbazole-1,4-quinones (21a-f). Access to N-arylated products is also possible, forming a mixture of fused imidazoles (9k-l) via an N-arylation step, alongside tertiary anilines (22-23). |
6198b44f9960f38e5bb51ed2 | 5 | Our [3+2]heteroannulation strategy was extended to the targeted synthesis of biologically-active tetracyclic carbazoles. Carbazole-1,4-quinones (e.g., 21a-f) have established anti-cancer activity via topoisomerase inhibition or by the production of reactive oxygen species. We used 21b as a key intermediary scaffold for the targeted synthesis of a deaza analogue of the natural product 9-methoxyellipticine (Scheme 3b), producing 24 in 3 steps and in an overall yield of 20%. Further exemplification of our strategy was demonstrated by the preparation of alkylated 7H-pyridocarbazoles (e.g. 9a-e) which have well-established anti-cancer activity. Previous preparative methods of this series of compounds have involved a 6-step linear synthesis affording compound 9e in 28% overall yield. Our two-step convergent strategy accessed the 7H-pyrido [4,3-c]carbazole core 9e in a single step (83%), followed by alkylation to produce mono-N-alkylated examples (25-26), and the potent anti-cancer agent ditercalinium (27). In summary, we have established a mechanistic framework for the preparation of fused tetracyclic carbazoles. We envisage that this convergent approach could find application in medicinal chemistry for structure-activity profiling and in broader synthetic applications which require step-efficient access to carbazole scaffolds. |
63f376899da0bc6b333f8612 | 0 | X-ray absorption spectroscopy (XAS) is a powerful too to elucidate structural and dynamical information based on the localized core orbitals of atoms, molecules, solids, and materials. XAS provides element-specific information while maintaining sensitivity to chemical environment, and theoretical calculations of core-to-valence transition energies are invaluable for interpreting such spectra. Available computational models include time-dependent density functional theory (TD-DFT), orbital-optimized excited-state DFT, various correlated wave function models, or the Bethe-Salpeter equation (BSE) approach. Each of these methods is widely used and available in standard electronic structure codes, but there are limitations. Not least among these is cost, as only the DFT-based approaches are scalable to large systems such as proteins or liquid environments. Excitedstate DFT methods, which are based on finding a non-Aufbau solution to the Kohn-Sham equations, require a tedious state-by-state approach if an entire excitation spectrum is desired. TD-DFT can furnish the entire core-level spectrum in a single shot (when used with frozen occupied orbitals for the valence electrons), yet results tend to be much more functional-dependent even as compared to ground-state DFT. Building on previous work, we seek simplified approaches based on Kohn-Sham eigenvalues only, which encode information regarding chemical shifts and may be useful in modeling emerging transient spectroscopies at x-ray and extreme ultraviolet wavelengths. The present work investigates "core-hole constraining" methods for XAS, using time-independent (ground-state) DFT calculations. There are several variants, as described below, but the unifying feature of these methods is that an electron is promoted from a core orbital into a valence virtual orbital and then orbital relaxation is incorporated by solving the Kohn-Sham equations in the presence of a core hole, with the excitation energy ω i→f estimated as the difference between virtual and occupied energy levels, |
63f376899da0bc6b333f8612 | 1 | Thus, the signature of these approaches is that no proper excited-state calculation is performed, but instead the requisite information for XAS is extracted from groundstate molecular orbitals (MOs), albeit possibly involving promotion of a fractional electron, as described below. This description encompasses a variety of eigenvaluebased approaches include Slater's transition method (STM) and its generalizations, along with the transition potential method (TPM) and its generalizations. (The TPM can be viewed as an approximation to Slater's original idea.) Some other approaches such as the full core-hole method (FCHM) fall under this umbrella as well. Some of these methods are based on the use of fractional-electron selfconsistent field (SCF) calculations, and they differ in whether the virtual orbitals are probed one by one, as in Slater's original conception, or whether only the lowest unoccupied MO (LUMO) is used. The latter approach is the basis of TPM and its variants, which afford an entire core-level spectrum (at one particular edge) from a single calculation. These methods have the same computational cost as the ∆SCF approach, in which a full electron is promoted into the virtual space in a state-by-state manner, but without the need for stateby-state calculations. They may hold some advantages for modeling complex systems or experiments insofar as the spectrum is computed in a single shot and is closely tied to initial-state Kohn-Sham eigenvalue information. |
63f376899da0bc6b333f8612 | 2 | Like ∆SCF, however, the eigenvalue-based methods can be expected to depend sensitively on the choice of exchange-correlation (XC) functional. The present work systematically investigates different core-hole constraining approaches using XC functionals on various rungs of Jacob's ladder. It follows a similar investigation of fractional-electron methods for computing core-level electron binding energies, intended for computational xray photoelectron spectroscopy (XPS). In that previous work, we demonstrated that an empirically-shifted version of STM with a single fitting parameter affords more accurate K-shell electron binding energies than even the best ab initio methods, including GW -type methods. A similar empirical shifting procedure is introduced here for core-level excitation energies, and is shown to perform quite well. |
63f376899da0bc6b333f8612 | 3 | where E i is usually the ground state and E f corresponds to a non-Aufbau Kohn-Sham determinant with an electron excited into the virtual space and therefore a hole below the highest-occupied MO (HOMO). Various algorithms have been developed to relax non-Aufbau MOs while avoiding variational collapse. The maximum overlap method (MOM) often works well for the lowest excited state, and has previously been applied to core → LUMO excitations. In our experience, however, more sophisticated methods are often required to converge higher-lying excited states. B. Slater-Type Methods. The use of a fractionalelectron SCF calculation as the basis for computing excitation or ionization energies originated with Slater. Fractional-electron calculations are now widely used to diagnose and correct problems with delocalization error and self-interaction in DFT, but have also been used in conjunction with correlated wave function models. The concept originates in the Slater-Janak theorem, which states that SCF eigenvalues ε i are derivatives of the SCF energy with respect to orbital occupancy, ε i = ∂E/∂n i , which holds for all of the occupied orbitals including lower-lying ones. As a result, the occupied level ε i (1/2) that is computed with n i = 1/2 electrons in occupied MO ψ i approximates the ∆SCF ionization energy. This fact forms the basis of the STM, which has long been applied to both core-level electron binding energies and core-level excitation energies. For K-edge XPS, this method exhibits an accuracy of ∼ 0.5 eV at the Hartree-Fock level but is significantly worse at DFT levels of theory. However, reasonable accuracy can be recovered using DFT via generalized (G)STM approaches that require more than one fractional-electron SCF calculation per ionization energy. In the present work, we examine core-level excitation (rather than ionization), using eigenvalue differences as in eq. 1. In the original STM, transition energies ∆E are computed according to the formula |
63f376899da0bc6b333f8612 | 4 | for virtual (ε v ) and core (ε c ) MO eigenvalues, computed using occupancies n v = 1/2 = n c . In this and subsequent equations, we will use the notation ε r (n c , n v ) to mean the Kohn-Sham eigenvalue for MO ψ r , obtained from an SCF calculation that employs occupancies n c and n v for the core and virtual orbitals, respectively. (We assume spinorbitals in this notation so 0 < n c ≤ 1 and 0 ≤ n v ≤ 1.) As seen in examples below, it may be the case that n v = n c , although this will create a charged excitation. The simple STM in eq 4 is known to overestimate excitation energies. This observation motivated a generalization in which the fractional-electron SCF calculation is mixed with a calculation involving a full core hole, which can be understood as a higher-order extension of Slater's method. For excitation energies, this generalized (G)STM takes the form |
63f376899da0bc6b333f8612 | 5 | where the energy levels ε c (1, 0) and ε v (1, 0) correspond to a full core-hole calculation (n c = 0 and n v = 1), whereas ε c (1/3, 2/3) and ε v (1/3, 2/3) are obtained from a calculation with n c = 2/3 and n v = 1/3. In the early days of molecular DFT calculations, the GSTM approach showed promising accuracy of ∼ 0.3 eV for K-shell electron binding energies, although this was later shown to benefit from some error cancellation with the functionals available at the time. Other GSTM schemes involving different fractional occupancies have been proposed more recently, and we have evaluated some of them using a modern slate of approximate XC functionals. Some of these approaches are tested here for XAS. |
63f376899da0bc6b333f8612 | 6 | C. Transition Potential Methods. As originally formulated, the STM and its generalizations require a separate calculations for each excited state of interest, i.e., for each virtual level ε v into which a fractional electron is promoted. The ∆SCF approach requires the same, with a full electron promoted for each individual state. This is a tedious and inconvenient way to compute an entire spectrum, and promotions beyond the LUMO are prone to variational collapse in the absence of symmetry constraints. Alternatives are to modify the core occupancy (n c ) only, leaving the virtual space empty (n v = 0), or else to promote an electron or fraction of an electron into the LUMO, then use the eigenvalue spectrum from that calculation to estimate excitation energies (∆E = ε v -ε c ). The latter approximation assumes that the potential generated by the LUMO is similar to that generated by the higher-lying virtual orbitals. The widely-used TPM corresponds to the first of these two alternatives, in which no electrons whatsoever are placed in the virtual space. The TPM formula for the lowest excitation energy is |
63f376899da0bc6b333f8612 | 7 | Note that n c = n v so the system becomes charged in the fractional-occupation SCF calculation. This can be a problem for DFT calculations under periodic boundary conditions, and therefore some charge-neutral alternatives have been explored. These are discussed below. A summary of different approximations is provided in Table , given in the form ∆E = F v -F c where F v and F c are simple functions of the virtual and core eigenvalues, respectively, computed from one or more SCF calculations with non-Aufbau occupancies that are allowed to be fractional. The list includes several variants of STM, as this has been tried with different fractions of an electron, as well as some alternatives such as the FCHM, 18,58-60 which is the n c = 0 analogue of the TPM/HCH method in eq 6. In FCHM, a full electron is removed from the core but nothing is placed in the virtual space: |
63f376899da0bc6b333f8612 | 8 | D. Excitation Beyond the LUMO. Each of the methods discussed so far can be extended to transitions into virtual orbitals above the LUMO, but such calculations often suffer variational collapse or other SCF convergence issues. Using the LUMO to stand in for the transition potential generated by the higher-lying virtual orbitals is a way to sidestep this problem, and an especially promising protocol is XCHM, for which the final state is charge-neutral. Excitation energies for XCHM are computed according to |
63f376899da0bc6b333f8612 | 9 | Physically, this approach includes the core-hole relaxation effects in valence states, which is important for relative peak positions and intensities, while ∆E IP helps to incorporate core-hole screening and thus to provide reliable chemical shifts. Both of these IP-TPM approaches can be used both for core → LUMO transitions but also for higher-lying excitations. |
63f376899da0bc6b333f8612 | 10 | To test the various core-hole-constraining approaches that were introduced above, we implemented fractional occupancy methods in a locally-modified copy of Q-Chem. (These methods will be released in Q-Chem v. 6.1.) Several algorithms are available to optimize a non-Aufbau determinant that contains a fractional core hole, but the calculations presented here use either the MOM algorithm 62 or the "initial MOM" (IMOM) algorithm. These differ only in whether overlaps are computed with respect to the previous SCF cycle's occupied MOs (in the MOM procedure) or the initial set of MOs at the first SCF cycle (in IMOM). |
63f376899da0bc6b333f8612 | 11 | Density functionals examined include SCAN, , SCAN0 (with 25% exact exchange), 90 B3LYP, ωB97X-V, Becke's "half-and-half" functional (BH&HLYP) containing 50% exact exchange, CAM-B3LYP with range-separation parameter ω = 0.33 bohr -1 , and the long-range corrected (LRC) functionals LRC-ωPBE (with ω = 0.3 bohr -1 ) and LRC-ωPBEh (ω = 0.2 bohr -1 ), the latter of which includes 20% exact exchange at short range. Finally, we examine the short-range corrected (SRC) functional SRC1-r1, which was parameterized for TD-DFT calculations of K-edge XAS transition energies for the elements C, O, N, and F. The def2-QZVP basis set is used for all calculations, in an effort to separate basis-set errors from methodological errors. Previous results for core-level binding energies indicate that DFT/def2-QZVP values are converged, such that uncontracting the core functions makes negligible difference. (For def2-TZVP, uncontracting the basis set changes electron binding energies by ∼ 0.4 eV. ) For generalized gradient approximations (GGAs) we use the SG-1 quadrature grid, 100 whereas SG-2 is used for meta-GGAs. For symmetry-equivalent atoms, Boys localization 102 is applied prior to the fractional-electron and ∆SCF calculations. |
63f376899da0bc6b333f8612 | 12 | Element-specific relativistic corrections have been included, as in previous work. These were taken from Ref. 103 and they are 0.14 eV for C(1s), 0.28 eV for N(1s), 0.51 eV for O(1s), and 0.85 eV for F(1s), which are close to values reported elsewhere. . These corrections are added to the non-relativistic excitation energy so that the corrected excitation energy is larger than the non-relativistic result, e.g., by 0.14 eV for carbon K-edge excitation energies. |
63f376899da0bc6b333f8612 | 13 | A. K-Edge Transitions. We first examine 1s → LUMO transitions. Table reports the mean absolute errors (MAEs) versus experiment for a data set that is taken from Ref. 87. These correspond to excitation at the elemental K-edge for carbon (14 data points), nitrogen (8 data points), oxygen (11 data points), and fluorine (4 data points). |
63f376899da0bc6b333f8612 | 14 | When a calculation of just the elemental K-edge is desired (and not any higher-lying states), then ∆SCF procedure is usually straightforward and ∆SCF results therefore serve as a baseline for evaluating methods that are based on Kohn-Sham eigenvalues. At the ∆SCF level, several functionals afford results within ∼ 0.3 eV of experiment, when atomic relativistic corrections are included as described in Section 3. These functionals include SCAN, SCAN0, and B3LYP, whereas BH&HLYP, CAM-B3LYP, and ωB97X-V afford slightly larger errors but still exhibit MAEs below 0.5 eV. Interestingly, the SRC1-r1 functional affords the largest errors (MAE = 1.1 eV), despite having been parameterized for TD-DFT calculations of K-edge transitions for these same secondrow elements. Clearly, cancellation of some other errors in TD-DFT is folded into the parameterization of this functional. We previously observed that SRC1-r1 also affords poor results for ∆SCF calculations of Kshell electron binding energies, with a MAE of 1.5 eV as compared to 0.2 eV for functionals such as SCAN and B3LYP. Together, these results suggest that SRC1-r1 is only appropriate for use in conjunction with TD-DFT, not with ∆SCF or eigenvalue-based methods. |
63f376899da0bc6b333f8612 | 15 | The LRC-ωPBE and LRC-ωPBEh functionals do not perform particularly well at the ∆SCF level but afford the smallest MAEs for the STM approach. Note that LRC functionals have been used in the past to improve the agreement between valence Kohn-Sham energy lev-els and ionization energies, 72,104,105 but these functionals are inferior to B3LYP for K-edge excitation energies in TD-DFT. It is possible that "optimal tuning" of these functional, 107 by adjusting ω such that ε HOMO = -∆E IP , might improve the performance even further. We have not pursued this, however, in the interest of obtaining a black-box method that does not need to be adjusted for each new molecule. (Optimally-tuned values of ω are often strongly dependent on system size, even for homologous systems. ) With other functionals, MAEs of 1-2 eV are observed and this includes CAM-B3LYP, which uses range separation but sacrifices correct asymptotic behavior in its parameterization. In previous work on core-level binding energies, we showed that STM is not competitive with ∆SCF but that GSTM results can approach the accuracy of ∆SCF. This can be understood based on the fact that GSTM amounts to a higher-order Taylor series approximation (as compared to Slater's original method), or as a higher-order quadrature scheme in a form of thermodynamic integration. The same is true for these Kedge excitations, where all functionals tested except for SRC1-r1 afford MAEs smaller than 1 eV at the GSTM level. Using B3LYP, the GSTM and ∆SCF results are quite similar. |
63f376899da0bc6b333f8612 | 16 | We next consider the transition potential approaches, TPM and GTPM. These methods modify only the core occupancy n c and do not put any electrons into the virtual space, resulting in underestimation of electron-hole attraction and a shift to higher excitation energies. This is evident in the data presented in Table , where GTPM errors are generally smaller than those exhibited by TPM yet even the GTPM errors remain larger than 2 eV for all functionals tested. FCHM, which likewise does not place electrons into the virtual space, affords similarly larger errors. Given that these methods also create a charged system, and are therefore problematic under periodic boundary conditions, neither TPM nor GTPM can be recommended. The XCHM approach (eq 9) creates a charge-neutral excitation but we find that results are erratic, improving somewhat with respect to other TPMtype methods for certain functionals (e.g., SCAN and CAM-B3LYP), yet seriously degraded for other functionals (e.g., BH&HLYP, for which the XCHM error exceeds 7 eV). The magnitude of these absolute errors is disturbing, given the continued use of TPM approaches in modern DFT. The performance of IP-TPM@1/2 and IP-TPM@1/3, on the other hand, is quite interesting. For a given functional, these methods typically afford smaller errors as compared to any of the TPM-based approaches that do not place electrons in the virtual space, and they also perform better than XCHM in many cases. The IP-TPM@1/3 method, in particular, is consistently better than other eigenvalue-based approaches. In conjunction with SCAN, SCAN0, or B3LYP, the IP-TPM@1/3 method affords MAEs below 1 eV. For B3LYP the MAE is 0.3 eV, essentially identical to the MAE for the ∆SCF approach based on the same functional. |
63f376899da0bc6b333f8612 | 17 | B. Higher-Lying (Near-Edge) Transitions. Table 3 reports error statistics for a data set of 20 higherlying, dipole-allowed transitions originating from 1s orbitals for the elements C (8 transitions), N (6 transitions), and O (6 transitions). These are "higher-lying" (or near-edge) transitions in the sense that the final state is not the LUMO. Experimental excitation energies are taken from various sources and details are provided in the Supporting Information. For each of the methods except ∆SCF, the full XAS spectrum is evaluated by populating the LUMO (only) with a fractional electron. As discussed before, these eigenvalue-based approaches easily avoid variational collapse and other convergence issues that can plague higher-lying near-edge calculations pursued by the ∆SCF approach. Furthermore, a stateby-state calculation is not required. |
63f376899da0bc6b333f8612 | 18 | That said, the accuracy obtained for these higher-lying transitions is not as good as what we reported for Kedge (1s → LUMO) transitions, and this conclusion holds across a variety of XC functionals. It also holds for the ∆SCF approach, where the best-performing functionals (SCAN, SCAN0, and B3LYP) see their MAEs increase from 0.3 eV for 1s → LUMO transitions to 1.2 eV for the higher-lying excited states. The two LRC functionals actually see their errors become slightly smaller for the higher-lying transitions. |
63f376899da0bc6b333f8612 | 19 | For the eigenvalue-based methods the MAEs are 2 eV, even when using SCAN, SCAN0, and B3LYP, and even for the IP-TPM@1/3 that performed well for 1s → LUMO transitions. The lone exception to this trend is XGTPM used in conjunction with B3LYP, for which the MAE is 1.0 eV, but in view of the other statistics this much lower error does not seem reliable. At some level, these larger errors for higher-lying transitions may not be surprising given that we are using a ground-state theory to simulate excited states, and it is possible that DFT simply cannot describe higher-lying states very well, absent some additional constraints or a different strategy. Thus we turn to an empirical shifting scheme that proved quite successful for core-level electron binding energies. C. Empirically-Shifted Method. In previous work, we demonstrated that introduction of a single, functional-specific shifting parameter turned the primitive STM approach into the most accurate electronic structure method for K-shell binding energies, outperforming both ∆SCF but also more expensive methods including variants of GW . In a similar spirit, we introduce an empirically-shifted version of the XTPM approach (eq 11): |
63f376899da0bc6b333f8612 | 20 | where m stands for a virtual MO index and β is an empirical parameter, which might be positive or negative but in practice is negative in most cases. This corrects for excitation energies that are overestimated by XTPM. The shift δ m is similar to the one introduced for XPS in Ref. 37, however for XAS one needs to consider virtual a Same data set as in Table . |
63f376899da0bc6b333f8612 | 21 | To determine β, we use the same data set of 20 higherlying excitation energies that were to obtain error statistics in Table . Fitted values of β, along with errors resulting from this approach, are summarized in Table . All functionals except BH&HLYP and SRC1-r1 afford considerable improvement over the unshifted XTPM approach. (For SRC1-r1, the improvement is almost 1 eV yet the MAE itself remains large, whereas for BH&HLYP the improvement is only 0.25 eV and the error also remains large.) Using B3LYP, the shifted XTPM approach yields a MAE of 0.3 eV, as compared to 1.8 eV without the shift. Thus, the shifted-XPTM approach based on B3LYP is more accurate than ∆SCF with the same functional, for which the MAE is 1.2 eV. In conjunction with other functionals (including SCAN, SCAN0, CAM-B3LYP, LRC-ωPBE, LRC-ωPBEh, and ω97X-V), the shifted-XTPM procedure is also a significant improvement with respect to either ∆SCF or fractional-electron procedures without the shift. In contrast, for BH&HLYP and SRC1-r1 we do not find any value β > 0 that can improve over unshifted XTPM results with the same functional. This is probably due to the large fraction of exact exchange, which may lead to over-localization. |
63f376899da0bc6b333f8612 | 22 | The 1s → LUMO data were not used to fit β so the performance of shifted-XTPM for these K-edge transitions constitutes a true test of the method. Error statistics error [eV] for that data set, obtained without refitting β, are listed in Table . By the standards of other Slater-type approaches, all methods perform reasonably well and the SCAN and B3LYP functionals achieve MAEs of only 0.3 eV. Consider both 1s → LUMO and also higher-lying near-edge transitions, B3LYP is probably the best overall functional and its accuracy is comparable to that of both ∆SCF and IP-TPM approaches. Shifted-XTPM using B3LYP is therefore recommended for full-spectrum XAS calculations. |
63f376899da0bc6b333f8612 | 23 | To put the accuracy in context with other state-ofthe-art approaches, Fig. illustrates the errors alongside some of the competing alternatives, including BSE@G 0 W 0 results from Ref. 35. We compare 29 K-edge and near-edge excitation energies, corresponding to the data set for which the BSE@G 0 W 0 results are available. Those results are compared alongside ∆SCF and four As compared to BSE@G 0 W 0 calculations (MAE = 0.7 eV), we observe that each of the eigenvalue-based methods exhibits larger errors, including XTPM (MAE = 1.6 eV), XGTPM (MAE = 0.8 eV), and IP-TPM@1/3 (MAE = 1.3 eV). The ∆SCF approach is also slightly less accurate, with MAE = 0.9 eV. However, shifting reduces the error associated with XTPM by more than 1 eV, affording a MAE of 0.5 eV that is comparable to what is obtained by shifting TD-DFT results based on a single ∆SCF calculation. MAEs for this same data set, using the shifted-XTPM approach in conjunction with other density functionals, are 0.6 eV for SCAN0, 0.7 eV for CAM-B3LYP, and 0.8 eV for both SCAN and LRC-ωPBEh. D. Other Applications. As illustrative applications, we use several B3LYP-based methods to compute carbon, oxygen, and nitrogen K-edge excitation energies for the thymine and oxazole molecules. Errors (relative to experiment) in several K-edge transitions are listed in Table , using a variety of methods but all based on the B3LYP functional. The transitions in question represent the lowest dipole-allowed excitation from each indicated 1s orbital. In the case of thymine, all methods except XTPM perform well, with MAEs ≤ 0.5 eV. The smallest errors (0.3 eV) are obtained from the ∆SCF and shifted-XTPM approaches. For oxazole, the same two methods afford MAEs of 0.2 eV, as does the IP-TPM@1/3 technique. The advantage of the shifted-XTPM approach over IP-TPM@1/3 is that the former uses a charge-neutral excitation whereas the latter does not. |
63f376899da0bc6b333f8612 | 24 | Oscillator strengths for the eigenvalue-based methods can be implemented based on eq 2. Figure shows XAS spectra computed in this way (and compared to experiment), for both the shifted and unshifted XTPM proce-dure. Empirical shifting corrects the peak positions into good agreement with experiment, for both molecules, whereas the original XTPM procedure overestimates the transition energies. (Note that none of the thymine or oxazole transitions are in the data set used to obtain the shift parameters.) This suggests that shifted XTPM might be a useful approach for large systems where even TD-DFT might be inconvenient. |
63f376899da0bc6b333f8612 | 25 | The performance of various XC functional approximations has been tested for K-shell excitation energies (1s → virtual) involving 1s orbitals of the elements C, N, O, and F. These methods include both the "full corehole" approach, otherwise known as the ∆SCF method or excited-state Kohn-Sham theory, but also fractionalelectron approaches that originate in Slater's transition state idea and several variants thereof. The overall conclusions are as follows. |
63f376899da0bc6b333f8612 | 26 | • For ∆SCF calculations, the SCAN, SCAN0 and B3LYP functionals can be recommended, as each exhibits a MAE of 0.3 eV as compared to experiment when an atomic relativistic correction is applied. Both the LRC-ωPBE functional (which is widely used in TD-DFT calculations) and and the SRC1-r1 functional (which was parameterized for K-edge excitations in TD-DFT) exhibit MAEs greater than 1.0 eV and are not recommended for ∆SCF calculations. |
63f376899da0bc6b333f8612 | 27 | • Other methods including TPM, GTPM, FCHM, and XCHM afford larger errors and cannot be recommended, despite their continued widespread use. For example, the smallest MAE that we are able to achieve with XCHM (over all of the XC functionals that were tested) is 1.6 eV using SCAN, which is much larger than the ∆SCF error of 0.3 eV that is obtained using the same functional. For TPM the smallest MAE is 2.9 eV (using B3LYP), for GTPM it is 2.2 eV (again using B3LYP), and for FCHM it is 1.8 eV (in conjunction with BH&HLYP). In each case, this is significantly larger than the corresponding ∆SCF error. |
63f376899da0bc6b333f8612 | 28 | • To improve these results, we introduce a simple shifting procedure for XTPM that requires only a single fractional-occupancy SCF calculation per ex-citation energy. When used with B3LYP, this approach is accurate for both 1s → LUMO transitions (MAE = 0.3 eV) as well as higher-lying excitations (MAE = 0.6 eV), and is as accurate as the much more expensive BSE@G 0 W 0 method. Reasonable results for full XAS spectra (at several elemental K-edges) are obtained for the thymine and oxazole molecules, which were not in the data set used to determine the empirical shift parameter. |
63f376899da0bc6b333f8612 | 29 | Overall, the shifted-XTPM approach for K-edge excitations, like the shifted-STM procedure for K-shell ionization energies, is competitive with the best ab initio techniques yet requires only a single SCF calculation per spectrum, based on an easy-to-converge fractional electron procedure. These should be useful tools for simulating core-level spectroscopy in complicated environments and large molecular systems. |
623497af13d4787e8992f7fb | 0 | The interaction between molecular excitations and nanoconfined photons can produce the requisite strong interactions for polaritonic chemistry . Motivated by a desire to provide a realistic picture of the molecular structure under the influence of strong photonic interaction, there has been a recent surge in activity focused on merging ab initio molecular electronic structure theory with cavity quantum electrodynamics (ab initio CQED) to provide an accurate and predictive model of polaritonic chemistry . Such efforts include combining CQED with density functional theory (DFT) or it's time-dependent extension (TDDFT) , reduced density matrix mechanics , and wavefunction theory using the coupled-cluster ansatz . These approaches can provide access to potential energy surfaces, couplings, and other properties of interest for simulating the structure and reactivity of polaritonic chemical systems. |
623497af13d4787e8992f7fb | 1 | The role of photonic dissipation or cavity losses on polaritonic structure and dynamics has recently been discussed in a number of studies utilizing model Hamiltonians , though to our knowledge the effort to pursue ab initio CQED methods has not explicitly included photonic loss. In this context, photonic dissipation refers to the finite lifetime of occupied photonic modes that exist within a cavity. Photonic dissipation occurs because the photons confined within a cavity can couple to the material degrees of freedom that exist in the cavity itself (which can be significant when considering plasmonic cavities), and also to the continuum of modes that exist outside the cavity (which causes leakage of photons in Fabry-Perot cavities, for example) . In this work we present a simple ab initio CQED method for treating ground and excited polaritonic states with explicit inclusion of photonic lifetimes via a non-Hermitian cavity quantum electrodynamicsconfiguration interaction singles approach (NH-CQED-CIS). This approach provides a simplification for the couplings between photon and material degrees of freedom that contribute to photon dissipation, and subsumes these complicated interactions into a complex frequency of the photon that quantifies the sum of all photon dissipation rates . Setting the imaginary part of the frequency to zero in this approach implies a lossless photonic mode that is perfectly isolated from the environment and returns the formulation to a Hermitian CQED-CIS theory. We implement this approach in the coherent state basis which results from solution of the CQED-Hartree-Fock (CQED-HF) equations. Both the Hermitian and non-Hermitian formulations of CQED-CIS in the CQED-HF basis contain additional couplings to the CQED-HF reference that are not present in canonical CIS theory, and as a results, our method also provides both ground-and excited-state information about the molecular system coupled to a cavity mode. We endeavor to provide a detailed picture of the key equations and algorithmic considerations for both the CQED-HF and NH-CQED-CIS approach, and therefore provide detailed equations of NH-CQED-CIS in the main text, detailed equations for CQED-HF in the appendix, and reference implementations of both methods through the Psi4Numpy project . We apply both methods to the analysis of several paradigmatic systems, including the ground-state polaritonic structure of formaldehyde coupled to cavity modes that can modify the symmetry of the ground-state wavefunction, and the polaritonic potential energy surfaces of the magnesium hydride ion coupled to a lossy photonic mode. We also compute the photon occupation of ground-states obtained from NH-CQED-CIS in the ultra-strong coupling regime for a variety of loss rates, showing qualitative agreement with analysis found in Ref. 6. |
623497af13d4787e8992f7fb | 2 | with Te (x i ) denoting the electronic kinetic energy operator for electron i, VeN (x i ; X A ) the (attractive) coulomb operator for electron i and nucleus A, Vee (x i , x j ) the (repulsive) coulomb operator for electrons i and j, and V NN is the total (repulsive) coulomb potential between all of the nuclei. Within the Born-Oppenheimer approximation, V NN is a constant, the nuclear kinetic energy is neglected, and the electron-nuclear attraction depends parametrically on the fixed nuclear coordinates. The photonic contribution is captured by the complex energy |
623497af13d4787e8992f7fb | 3 | In the above, b † and b are the bosonic raising/lowering operators for the photonic degrees of freedom, and ω = ωi γ 2 is a complex frequency of the photon with the real part ω being related to the energy of the photon, and the imaginary part γ/2 being related to the dissipation rate of the photonic degree of freedom . The term µ represents the ground state molecular dipole expectation value which has Cartesian components ξ ∈ {x, y, z}. A given ξ -component of the dipole operator has the form μξ = ∑ N e i μξ (x i ) + µ ξ nuc where μξ (x i ) is an operator that depends on electronic coordinates and within the Born-Oppenheimer approximation, we treat the Cartesian components of the nuclear dipole moment µ ξ nuc as functions of the nuclear coordinates rather than a quantum mechanical operator. Note that the shift of the Hamiltonian by µ results from the transformation to the coherent state basis . In the NH-CQED-CIS theory we present, we will utilize an orbital basis that arises from solving the CQED-RHF equations arising from a Hermitian total Hamiltonian where only the real part of ω is retained. The CQED-RHF method has been described elsewhere , though we provide a brief outline in the Appendix. Also provided in the Appendix is an expansion of the Ĥdse term that explicitly shows where the 1-electron dipole, 1-electron quadrupole, and 2-electron dipole operator terms that appear in the NH-CQED-CIS matrix elements come from. We also note that the formulation presented here considers only a single photonic mode; generalizations to multiple photonic modes can be formulated by introducing additional frequencies and coupling parameters for each additional modes in the Ĥp , Ĥep , and Ĥdse terms. In particular, the multimode version would read |
623497af13d4787e8992f7fb | 4 | A mean-field description of the excited states of the molecular system strongly interacting with photonic degrees of freedom, and a correction to the ground-state that contains coupling between the CQED-RHF reference and simultaneous electronic and photonic excitations, may be obtained through a configuration interaction singles (CIS) ansatz. Here we formulate a non-Hermitian version of such an ansatz, NH-CQED-CIS, that incorporates the dissipative features of the photonic degrees of freedom. In our presentation, we formulate NH-CQED-CIS in the coherent state basis using the orbitals that result from the CQED-RHF approach outlined in the appendix. |
623497af13d4787e8992f7fb | 5 | The polaritonic energy eigenfunctions for state I in the NH-CQED-CIS ansatz can be written as a linear combination of the CQED-RHF reference and products of all possible single electron excitations out of the CQED-RHF reference. The CQED-RHF reference involves the product of an electronic Slater determinant with the photon vacuum state |Φ o |0 , so single excitations can occur as electronic excitations from an occupied orbital φ i to a virtual orbital φ a , the raising of the photon number state from |0 → |1 , or both. We therefore write the NH-QED-CIS wavefunction for state I as |
623497af13d4787e8992f7fb | 6 | where the coefficients c denote the contribution of a given term to the wavefunction and we have denoted the electronic excitations in the subscript and the photonic excitations in the superscript of these coefficients. For the case of multiple modes, the photonic basis states will be augmented to consider all possible combinations of the occupations of those modes within a maximum photon number. These coefficients, and the corresponding energy eigenvalues for a given NH-CQED-CIS state I, may be obtained by diagonalizing the Hamiltonian matrix built in the basis shown in Eq. 6. We spin adapt this basis such that |
623497af13d4787e8992f7fb | 7 | , where α and β label the spin orbitals as being occupied by spin-up and spindown electrons, respectively. There are three classes of matrix elements that contribute to the Hamiltonian matrix, and we we write each class of matrix elements after shifting the total Hamiltonian in Eq. 1 by E CQED-RHF . The matrix elements involving the CQED-RHF electronic Slater determinant |Φ 0 and photonic states |s and |t , where s,t ∈ {0, 1} involve only the (complex) photonic energy, |
623497af13d4787e8992f7fb | 8 | Because this NH-CQED-CIS Hamiltonian is non-Hermitian, the left and right eigenvectors, which we will denote Ψ L I and Ψ R I for the left and right eigenvectors for the NH-CQED-CIS state I respectively, are not simply complex conjugates of each other. However, the left and right eigenvectors can be chosen to be biorthogonal, where biorthogonality implies 45 |
623497af13d4787e8992f7fb | 9 | We provide reference implementations using Psi4Numpy , which provides a simple NumPy interface to the Psi4 46 quantum chemistry engine. The code for these reference implementations can be freely accessed in the hilbert package and in the Psi4Numpy project . Furthermore, to provide a no-installation option for interested users to experiment with these implementations, we utilize the ChemCompute project to host the illustrative calculations discussed in the Results section below. Interested users can navigate to to register for a free ChemCompute account. Following registration, interested users can run calculations described in Table in the results section using the link in Ref. 50, the calculations described in Figure using the link Ref. 51, the results described in Table and Figure using the link in Ref. 52, the results illustrated in Figure using the link within Ref. 53, the results illustrated in Figure using the link within Ref. 54, and the results in Figure and 6 in the Appendix using the link within Ref. 55. |
623497af13d4787e8992f7fb | 10 | We apply the CQED-RHF and NH-CQED-CIS approaches to a few simple polaritonic chemical systems. First we examine the ground-state of formaldehyde strongly coupled to a single photon mode, which has been explored by several groups that have been developing density functional theorybased ab initio-QED methods . We optimize the geometry of lone formaldehyde at the RHF/cc-pVDZ level and perform all calculations at that geometry (see Ref. 50). At this level, the RHF ground-state has a dipole moment oriented purely along the z-axis with µ z = -1.009 atomic units. The CQED-RHF equations are solved for a fixed magnitude of the coupling vector |λ | = 0.1 atomic units with the following three polarizations: λ y = (0, |λ |, 0), λ z = (0, 0, |λ |), and |
623497af13d4787e8992f7fb | 11 | This value of λ is quite large and leads to a coupling energy scale hg ≈ h ω 2 λ µ ≈ 1eV , which is approximately 10 times larger than the single molecule coupling strength reported by Baumberg and co-workers . However, as in Ref. 31 where the same coupling magnitude was considered to illustrate cavity modifications to intermolecular interactions, we note that such coupling strengths could be conceivable considering that experimental cavities will have many modes and the effective coupling arises as the norm of all the mode coupling parameters. |
623497af13d4787e8992f7fb | 12 | The ground-state energy, as predicted by the CQED-RHF method, departs from the RHF energy in all three cases, with the largest deviation coming from λ z case (see Table ), which would be expected given the permanent dipole moment is oriented along the z-axis. However, the deviations seen by the λ y and λ yz cases point to subtle effects arising from the quadrupolar terms in the quadratic self energy and the 2-electron contribution to the quadratic self energy. To quantify these various contributions, we look at the changes in the various contribu-tions to the CQED-RHF energy with and without coupling to the photon field. For example, we define the change in the canonical RHF 1-electron energy resulting from the photon field in the λ yz case as |
623497af13d4787e8992f7fb | 13 | where D λ yz µν are elements of the converged CQED-RHF density matrix in the λ yz case and D µν are elements of the CQED-RHF density matrix in the absence of coupling to a photon (i.e., the canonical RHF density matrix). We tabulate the changes in these various CQED-RHF contributions for the λ z , λ y , and λ yz cases in Table . The 1-electron quadrupolar and 2-electron dipolar terms that arise from Ĥdse typically comprise the largest changes to the CQED-RHF energy from the three polarizations considered in Table . However, the changes in the canonical RHF 1and 2-electron terms (denoted ∆ 1E and ∆ 2E ) suggest changes to the ground-state electron density via the CQED-RHF orbitals arise from coupling to the cavity modes. Although these changes largely cancel each other in the total energy (i.e. ∆ 1E ≈ -∆ 2E in all three cases), it is nevertheless interesting to view the impact of cavity coupling on the CQED-RHF orbitals. The RHF orbitals for the HOMO (2B 2 ) and LUMO+1 (6A 1 ) of formaldehyde uncoupled to a photon are compared to their corresponding CQED-RHF orbitals for the λ yz case ( 7A and 8A ) where the orbitals are noticeably distorted (see Figure ). The reshaping of the CQED-RHF orbitals in the λ yz case results in a loss of symmetry from C 2v to C s and impacts both ground-state energy and properties. As seen in Table , there is no 1-electron dipole contribution to the energy shift in the λ y case since the ground state dipole moment is oriented purely along the z-axis. However, in the λ yz case, the distortion of the ground-state orbitals results in a reorientation of the dipole moment to point along the yz axis with value µ = (0, -0.025, -1.16) atomic units. We see that this reorientation of the ground-state dipole moment is accompanied by changes in the ground-state energy specifically attributable to the 1-electron dipolar terms CQED-RHF Fock operator (see Table ). In principle, this change in ground-state dipole moment could be experimentally confirmed through rotational spectroscopy. In particular, because the oscillator strength of a given transition involves integrals over the dipole moment |
623497af13d4787e8992f7fb | 14 | and the dipole moment in the cavity-coupled case takes on an orientation dependence compared to the lone molecular case, the oscillator strengths in the cavity case would be modified in turn. Turning to the NH-CQED-CIS Hamiltonian, it can be seen that unlike the canonical CIS method, the NH-CQED-CIS method couples single excitations of the electronic and photonic terms to the CQED-RHF reference state. Specifically, it can be seen in Eq. ( ) that the CQED-RHF wavefunction can couple to states which involve singly-excited electronic configurations and singly-occupied photon states. This coupling can lower the energy of the lowest energy eigenstate of the NH-CQED-CIS Hamiltonian relative to the ground-state determined by the CQED-RHF method (see Table ). The cavity-induced modification to the symmetry of the CQED-RHF wavefunction has important consequences for which singly-excited configurations can contribute to the ground state. We examine the impacts of this cavity effect again with formaldehyde coupled to a lossless photon with ω = 0.382 atomic units (10.4 eV), which is approximately resonant with the first two dipole allowed transitions at the CIS/cc-pVDZ level of theory (see Ref. 52). We consider the same coupling magnitudes as before, this time focusing only on the λ z and λ yz cases. The polarization vector in the λ z case belongs to the A 1 irrep of the C 2v point group, while the polarization vector in the λ yz case belongs to the A irrep of the C s point group. In Figure , we present the dominant singlyexcited contributions to the NH-CQED-CIS ground-state in the λ z and λ yz cases. We indeed see slightly more permissive mixing of singly-excited configurations into the NH-CQED-CIS ground-state in the λ yz case due to the lower symmetry of the wavefunction. We report the changes in the ground-state energy as predicted by the NH-CQED-CIS method relative to the canonical RHF method and the CQED-RHF method in As a second illustrative example of the NH-CQED-CIS method, we consider the upper-polariton (|UP ) and lowerpolariton (|LP ) states that emerge from coupling MgH + to a photon resonant with the ground to first singlet excited state (|X → |A ) transition . We consider the photon to be polarized along the z axis, in alignment with the relevant transition dipole moment, with λ z = 0.0125 atomic units. This time, we allow the photon to have a complex energy where the imaginary part accounts for photonic dissipation, which can also be related to the energy uncertainty of the photonic mode . We consider the real part of the photon energy to be 4.75 eV, and the imaginary part to be either 0 eV or 0.45 eV. This value of λ leads to a coupling energy scale hg ≈ h ω 2 λ µ ≈ 0.1eV , which is comparable to the single molecule coupling strength reported by Baumberg and co-workers . Similarly, the dissipation energy scale of 0.45 eV corresponds to approximately a 10 fs lifetime, which is shorter but on a similar order to the lifetimes of the plasmonic resonances reported in Ref. 4. We specifically chose this value because it represents the γ = 4g threshold at which the Rabi splitting of polaritonic surfaces associated with strong coupling dissapears |
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