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65f04fd966c1381729d79a16 | 3 | Next, all generated mutants were screened for their dehalogenation and epoxide ring-opening activity in 96-well format. To this end, well-established model substrates for both the dehalogenation (dichloropropanol 1f for HheC and chlorocyclohexanol 2f for HheG) and the ring-opening reaction (epichlorohydrin 1 for HheC and cyclohexene oxide 2 for HheG) were used. For fast activity screening, we employed pH-based assays which have previously been reported in literature and make use of either phenol red or bromothymol blue as pH-indicators to detect qualitatively the amount of released (dehalogenation) or consumed free protons (epoxide ring opening) during catalysis (Figure and Table ). For the exchange of the threonine (T7 in HheC and T13 in HheG) and glycine (G14 in HheC and G20 in HheG) in both enzymes only mutants carrying a chemically similar amino acid (serine instead of threonine, alanine instead of glycine) still exhibited detectable activity. In contrast, F12 in HheC displayed a much higher variability (Figure ) with HheC mutants F12G, F12A, F12C, F12S, F12Q, F12H, and F12Y being active in both dehalogenation and epoxide ring opening reactions. Interestingly, this was not the case for position Y18 of HheG. Here, only the exchange of tyrosine by phenylalanine yielded a mutant with significant activity. Those activity data are in full agreement with our results regarding the soluble expression of the generated mutants, with the only exception that not all soluble HheC F12X mutants were indeed also active. For all further tests, active HheC and HheG mutants of motif 1 were produced in larger scale and applied as FPLC-purified proteins (for yields see Table ). |
65f04fd966c1381729d79a16 | 4 | It should be noted here that Tian et al. do report a few active HheG mutants with amino acid exchanges at position Y18 of motif 1, which they obtained during protein engineering of this enzyme with the aim to improve enantioselectivity. In their case, however, only whole-cell reactions have been performed, while we have been working with isolated enzymes instead. Thus, it is possible that those HheG mutants exhibit even more reduced stability or yield much less soluble enzyme compared to wild-type HheG, which is why we could have lost them during enzyme isolation and/or purification in our study. At the same time, this would reinforce our assumption that position 18 in HheG impacts protein folding and stability. |
65f04fd966c1381729d79a16 | 5 | To facilitate more detailed kinetic analyses of the epoxide ring-opening reactions catalyzed by HHDHs in high throughput, we developed a quantitative pH indicator assay inspired by work from Gul and colleagues. This assay relies on the conversion of a strong acid (e.g. azide) to a weak acid (e.g. an alcoholate) during epoxide ring opening, which increases the net pH value of the reaction mixture while the reaction progresses. Using bromothymol blue (BTB, an indicator with sweeping absorption spectra giving light yellow to dark blue mixtures) and dilute MOPSbuffered reaction mixtures, we typically followed ring-opening reactions starting at around pH 7. Unlike previously described assays using pH indicators, our system returns quantitative conversion data by employing isometric normalization. Using the isosbestic point of the deprotonation of BTB, we traced the deprotonation equilibrium of the indicator back to a concentration of consumed protons via the buffer strength (see the SI for details and mathematic operations). This assay proved readily compatible with high-throughput experimentation in 96-well plates and allowed straightforward monitoring of more than 20 reactions in parallel. Although we primarily used the assay for HHDH-catalyzed epoxide ring-opening reactions in our study, we expect it to be applicable to other protonconsuming or -liberating (biocatalytic) reactions as well. A) Crystal structures of HheC (green; PDB: 1PWX) and HheG (blue; PDB: 5O30) wild type with conserved residues of sequence motifs 1 and 2 highlighted. B) Solubility data of motif 1 mutants of HheC and HheG according to SDS-PAGE analysis (Figure ). C) Activity screening data (dehalogenation and epoxide ring opening) of motif 1 mutants of HheC and HheG using qualitative pH indicator-based assays. High activity or solubility is represented by purple color, whereas no activity or insolubility is represented by yellow color. Grey color represents HheC mutants that could not be generated on genetic level. |
65f04fd966c1381729d79a16 | 6 | Following the initial qualitative activity screen, we studied the epoxide ring-opening activity of active mutants with azide and various epoxides in more detail to gain further insights into the kinetic implications of motif 1 mutations on a broader range of substrates. Specifically, we used structurally diverse epoxides to cover relevant chemical space by employing epichlorohydrin (1), cyclohexene oxide (2), styrene oxide (3), phenyl glycidyl ether (4), limonene oxide (5), and trans-1-phenylpropylene oxide (6) (Figure ) and followed their conversion with our quantitative BTB-based pH assay. This analysis revealed that the introduction of mutations in motif 1 significantly impacted overall enzymatic activity (Figure ), even though the substrate spectra of the HheC and HheG mutants did not change compared to the wild type. Indeed, most mutants exhibited considerable reductions of their specific activities with all model substrates compared to the respective wild-type enzyme. The only variant in this panel which gained significant activity was HheC mutant F12Y, displaying a 3-to 5-fold increase in specific activity with 1 and 3. Otherwise, even very conservative mutations, as for instance HheC mutant G14A and HheG mutant G20A, resulted in drastic losses of activity. This observation is in general agreement with the report of Jörnvall et al. on the mutagenesis of the corresponding conserved glycine residue in motif 1 of an SDR enzyme. Replacement of this glycine by alanine resulted in a 69% decrease in activity, while mutations G14V and G14N yielded almost inactive enzymes. The activity trends observed for the epoxide ring-opening direction generally carried over to the dehalogenation catalyzed by the motif 1 mutants. We examined this with the haloalcohols 1,3-dichloro-2-propanol (1f), 2-chlorocyclohexanol (2f) and 1,3-dibromo-2-propanol (7g) (Figure ), whose conversion could be followed discontinuously with a previously reported halide release assay. While the specific activities of nearly all mutants were significantly reduced compared to the wild-type enzymes, HheC F12Y displayed considerably increased activity with the haloalcohols 1f and 7g (Figure ), mirroring the trends observed for the ring-opening activities. A higher activity of HheC mutant F12Y in the dehalogenation of 1,3-dichloro-2-propanol (1f) has previously been observed during thermostabilization of HheC by directed evolution. Reactions were performed in duplicate in a total volume of 1 mL with 10 mM epoxide and 20 mM azide in 2 mM MOPS buffer, pH 7.0 at 30 °C (HheC) or 22 °C (HheG) using 20-400 µg mL -1 purified enzyme (Table ). Samples were taken after 30, 60, 180, 270 and 360 s. Chemical background of negative control reactions without enzyme addition was subtracted. The resulting specific activities exhibit standard deviations between 0.00 and 0.13 U mg - 1 . C) Specific activities of HheC and HheG mutants as well as wild-type enzymes in the dehalogenation of haloalcohols 1,3-dichloro-2-propanol (1f), 2-chlorocyclohexanol (2f) and 1,3-dibromo-2-propanol (7g) determined via halide release assay. Reactions were carried out in duplicate in a total volume of 1 mL with 10 mM haloalcohol in 25 mM Tris•SO4 buffer, pH 7.0 at 30 °C (HheC) or 22 °C (HheG) using 10-400 µg mL -1 purified enzyme (Table ). Samples were taken after 30, 60, 180, 270, and 360 s. Chemical background of negative control reactions without enzyme addition was subtracted. The resulting specific activities exhibit standard deviations between 0.00 and 0.21 U mg -1 . |
65f04fd966c1381729d79a16 | 7 | To unveil if the observed activity increase of HheC mutant F12Y is induced by an improved substrate binding or rather a significantly elevated reaction rate, we measured kinetic data for the dehalogenation of haloalcohol 1f and the ring opening of epoxide 1 with azide using the halide release assay as well as our BTBbased pH assay, respectively. Interestingly, this kinetic analysis revealed that the F12Y mutation only slightly impacted KM or K50 for the substrates 1f and 1 (Table ). In contrast, the maximal reaction rates were considerably increased -3.5-fold for the dehalogenation of 1f and at least 5-fold in the azidolysis of 1 (rate improvement varies when either the kinetics for epoxide or azide are considered). Thus, the improved performance of HheC F12Y in dehalogenation and epoxide ring opening is solely caused by an enhancement of reaction velocities. For comparison, the corresponding K50 values of HheC mutants T7S and G14A for binding of epoxide 1 were increased by a factor of 2 or more compared to the wild type and mutant F12Y, indicating a lower substrate affinity of those motif 1 mutants in HheC. Moreover, HheC T7S exhibited an at least two-fold higher kobs,max compared to wild type, while the respective kobs,max of HheC G14A in the azidolysis of 1 was drastically reduced, both in line with our determined specific activities. Unfortunately, true kcat values could not be determined in this epoxide ring opening reaction due to the high K50 values of all HheC mutants towards azide and the strong chemical background azidolysis of 1 occurring at azide concentrations above 100 mM. Therefore, kinetic measurements with varied epoxide concentration were performed at non-saturating azide concentration, yielding significantly lower kobs,max values compared to kinetic measurements with fixed epoxide and varying azide concentrations (Table ). Importantly, all three HheC mutants do also exhibit higher K50 values as well as a considerably stronger cooperativity in azide bindingbased on higher Hill coefficients nHthan the corresponding wild-type enzyme (Table ). Thus, those conserved residues in sequence motif 1 of HheC are indeed influencing nucleophile binding to a great extent. In contrast, changes in the kinetic parameters of HheG mutants compared to wild type in the azidolysis of epoxide 3 are less dramatic (Table ), which is again in agreement with respective specific activities of HheG mutants determined for this reaction. The observed cooperativity for azide binding, however, again varies significantly depending on the introduced mutation. Table . Kinetic parameters of selected HheC mutants in the dehalogenation of 1,3-dichloro-2-propanol (1f) (determined by halide release assay) as well as the azidolysis of epichlorohydrin (1) (determined by our BTB assay). For the latter reaction, first the epoxide concentration was varied while keeping the azide concentration constant at 100 mM; afterwards the azide concentration was varied fixing the epoxide concentration at 100 mM. The Michaelis-Menten equation was used to fit the resulting data for the dehalogenation of 1f, whereas the Hill equation was used for fitting the experimental data obtained for the ring opening of 1 with azide. Next, we probed the enantioselectivity of our motif 1 mutants in epoxide ring opening reactions with azide to test if motif 1 mutations affected also the selectivity of these enzymes. For variants of HheC, we selected the terminal epoxides 1 and 3 as substrates, while we used 3 and the cyclic epoxide 2 for HheG variants. Our choice of epoxide 3 was primarily motivated by the opposite regioselectivity of HheC and HheG in their ring opening of this substrate (Figure ). The non-catalyzed reaction preferentially yields 2-azido-2-phenylethan-1-ol (3a.1) through nucleophilic attack at the benzylic α-carbon. While HheG enforces this inherent preference, HheC exhibits selectivity for attack at the terminal β-position. Biotransformations analyzed by chiral GC revealed that most of the motif 1 mutations in HheC decreased enantioselectivity significantly compared to the wild-type enzyme, independently of the epoxide substrate (Table ). In contrast, mutants T7S and F12Y displayed a greatly increased enantioselectivity in the conversion of 1 with azide, while the extremely high enantioselectivity of the wild type enzyme with 7 was maintained. This indicates a considerable impact of motif 1 residues on the enantioselectivity of HheC. On the other hand, the enantioselectivity of the studied HheG mutants in the ring opening of 2 and 3 hardly changed compared to HheG wild type (Table ). For comparison, mutations at the central aromatic residue Y18 in the homologous HheG enzyme from Acidimicrobiia bacterium did affect enantioselectivity in the ring opening of 3 with cyanate. Apart from this overall varying influence of motif 1 residues on enantioselectivity, all herein studied HheC and HheG mutants retained the wild-type enantiopreference for the conversion of (S)-1 and (R)-3. Following these activity and enantioselectivity studies, we also examined the thermal stability of active motif 1 mutants of HheC and HheG by differential scanning fluorimetry (also known as thermofluor assay), as a positive impact of mutation F12Y on the thermostability of HheC has previously been reported. Our analysis revealed a considerable stabilizing effect for mutations F12H (+10.5 K), F12Y (+10.1 K) and G14A (+7.3 K) in HheC (Figure ). The latter is especially surprising as this mutation heavily decreased enzyme activity. In contrast, the opposite trend in thermal stability has previously been reported for the exchange of the equivalent glycine residue in SDR motif 1 of Drosophila alcohol dehydrogenase, and was also observed in our study for the corresponding mutation G20A in HheG. The herein reported stabilizing effect of mutation F12Y in HheC was previously attributed to the formation of an additional hydrogen bond with residue T131 compared to wild-type HheC, which we could confirm based on our computational results (see below). A slight increase (+2.8 K) in the apparent melting temperature of HheG upon exchange of the corresponding tyrosine 18 by phenylalanine becomes apparent from Figure as well. a Reactions were carried out in a total volume of 1 mL in 50 mM Tris•SO4, pH 7.0, at 30 °C (HheC) or 22 °C (HheG) and 900 rpm using 10-400 µg mL -1 purified enzyme. Samples were taken after 15 min (epoxide 1) or 1 h (epoxide 3), extracted with an equal volume of tert-butyl methyl ether and analyzed by achiral and chiral GC. b Conversion and enantioselectivity towards formation of product 2-azido-1-phenylethan-1-ol (3a.2) through nucleophilic attack at the terminal β-position. c In the non-catalyzed chemical background reaction, formation of product 2-azido-2-phenylethan-1-ol (3a.1) through nucleophilic attack at the benzylic α-carbon is preferred. d Conversion and enantioselectivity towards formation of product 2-azido-2-phenylethan-1-ol (3a.1) through nucleophilic attack at the benzylic α-carbon. |
65f04fd966c1381729d79a16 | 8 | Taking into account that HheC mutant F12Y is not only more active in the dehalogenation and epoxide ring opening of several tested substrates, but exhibits also higher enantioselectivity and thermal stability compared to wild-type HheC, the question arises why mutation F12Y was not selected during natural evolution of this enzyme. For comparison, other native HHDHs such as HheB or HheG carry a tyrosine instead of a phenylalanine at the respective motif 1 position. One possible hypothesis might be that mutant F12Y is not superior in combination with HheC's natural substrate(s), as the epoxides and haloalcohols tested by us probably do not represent natural substrates of HheC. In agreement with this hypothesis, mutant F12Y is not generally more active independent of the used substrate, but was found to display a lower specific activity in the azidolysis of glycidyl phenyl ether. On the other hand, the gene of HheC is organized in an operon together with an epoxide hydrolase-encoding gene in the genome of A. radiobacter. Both enzymes were predicted to act together in the detoxification of harmful haloalcohols. Thus, HheC's activity in A. radiobacter likely needs to be harmonized with the respective activity of the epoxide hydrolase to prevent an accumulation of the epoxide intermediate, which is harmful itself due to its high reactivity with e.g. primary amines of lysine residues. A too high activity of HheC might therefore not be evolutionary beneficial. |
65f04fd966c1381729d79a16 | 9 | Since amino acids of sequence motif 1 line the nucleophile-binding pocket of HHDHs, we also expected a possible impact of those residues on nucleophile binding, as already observed for the nucleophile azide during our kinetic studies of motif 1 mutants. Thus, we further focused on a potential change in nucleophile acceptance after mutagenesis of motif 1 residues using a broader range of nucleophiles. In this regard, mutants T7S, F12Y and G14A of HheC as well as HheG mutants T13S, Y18F and G20A were applied in epoxide ring opening reactions of phenyl glycidyl ether (4) using azide, nitrite, cyanide, cyanate, thiocyanate as well as the halides chloride and bromide as nucleophiles. Those nucleophiles have previously been demonstrated to be accepted by HheC and HheG wild type. To cover an activity range as large as possible, conversions of enzyme-catalyzed transformations were determined after short (1 h) but also extended (24 h) reaction times (Figure ). These experiments revealed that the overall nucleophile acceptance of HheC and HheG was not altered considerably upon mutagenesis. However, a few interesting results stand out. For instance, HheG mutant G20A displayed surprisingly high activity with the nucleophiles thiocyanate and bromide, almost in the range of wild-type HheG, while it was virtually inactive with all other tested nucleophiles. However, the same effect was not noticed for HheC G14A, which might be related to the overall much lower activity of HheC with thiocyanate. As reported earlier , epoxide ring opening with thiocyanate can occur via S-and N-nucleophilic attack yielding two different product isomers, which were also observed in our study. Their ratio, however, did not change depending on the applied enzyme variant (Figure ). In contrast, the ratio of formed diol and nitroalcohol product in the ring opening of 4 with nitrite as nucleophile indeed varied to some extent depending on the respective motif 1 mutation. In this case, the diol product occurs due to O-nucleophilic attack at the epoxide and subsequent hydrolysis of the formed nitrite ester. Interestingly, especially the preference of HheC mutant T7S and HheG mutant G20A for diol formation was increased in comparison to respective wild-type enzymes (Figure ). Those results again underscore the impact of 1 residues on nucleophile binding and selectivity. ) with 20 mM nucleophile (azide, nitrite, cyanide, cyanate, thiocyanate, chloride, bromide) in 50 mM Tris•SO4 buffer, pH 7.0, at 30 °C (HheC) or 22 °C (HheG) and 900 rpm using each 150 µg mL -1 purified enzyme. Reactions were carried out in a total volume of 1 mL. Samples were taken after 1 h and 24 h, extracted with an equal volume of tert-butyl methyl ether and analyzed by achiral GC. "NC" represents negative control reactions without enzyme addition. B) Ratio of formed products in reactions with nucleophiles nitrite and thiocyanate. |
65f04fd966c1381729d79a16 | 10 | Intrigued by how the central aromatic residue in motif 1 enhances HheC activity towards the epoxide-ring opening reaction, we decided to computationally evaluate HheC wild-type and mutant F12Y by means of Quantum Mechanics (QM) and Molecular Dynamics (MD) simulations. Considering the proximity of position F12 to the catalytic residues (Figure ) and the big impact on reaction rate (Table ), we hypothesized that the additional hydroxyl group could potentially establish hydrogen bonds with either the catalytic and binding residues, the nucleophile binding pocket and/or the substrates epichlorohydrin (1) and azide to promote catalysis. To elucidate whether mutation F12Y directly impacts the activation barrier for the epoxide ring-opening reaction, we generated a cluster model of the active site and used DFT as done previously by the group of Himo (Figure , 5B). We observed that both in the reactant complex (RC) (Figure ) and the transition state (TS1) the additional hydroxyl group thanks to mutation F12Y can establish a hydrogen bond with azide, which helps to retain the nucleophile in the nucleophile binding pocket and more importantly positions azide in a good orientation for epoxidering opening (Figure , left panel). The terminal nitrogen of azide establishes a hydrogen bond with the backbone of L178 and the hydroxyl group of Y12, whereas the nitrogen involved in the nucleophilic attack is hydrogen-bonded to a crystallographic water molecule (Figure , left panel). This hydrogen bond network impacts the charge distribution at the azide and favors the accumulation of more negative partial charge at the nitrogen responsible for the nucleophilic attack (Table ). The activation barrier at this conformation towards the epoxide ring opening 1 is ca. 9 kcal/mol at the M06-2X/Def2-TZVPP level of theory. We located another TS2 that does not present the F12Y-azide interaction, instead the terminal nitrogen of azide makes a hydrogen bond with both the crystallographic water molecule and L178 (Figure , right panel). This difference in the hydrogen bond network with respect to TS1 slightly modifies the negative charge on the nucleophilic nitrogen of the azide, thus leading to an activation barrier for TS2 ca. 6 kcal/mol higher than for TS1 (the activation barrier for TS2 is ca. 16 kcal/mol). This additional TS2 is extremely similar to the one found for HheC wild type (Figure ). In the wild type, the activation barrier for the ring opening of 1 is ca. 14 kcal/mol as found for TS2 in the case of F12Y. The computed barriers are in line with the previously reported barriers for HheC with azide and other epoxides reported by Himo and coworkers. It should be mentioned that the large differences in the activation barriers found for HheC F12Y and wild type are overestimated as compared to the experimental kinetic constants, but in line with the observed big impact of mutation F12Y on the catalytic turnover (minimum 5-fold increase in kobs,max). We observed in the DFT-optimized RC as well as TS2 that F12Y makes a hydrogen bond with the carbonyl backbone of P175 (the distance between the hydrogen of the hydroxyl group of Y12 and the oxygen of the backbone of P175 is ca. 2 Å in all cases, see Figure and). The carbonyl group of P175 was found to provide electrostatic stabilization to C, which favors the attack at this position. The hydrogen bond established between the hydroxyl group of F12Y and P175 induces a slight bend of the carbonyl backbone. HheC mutant F12Y therefore also favors the proper positioning of the P175 backbone close to the epoxide substrate and favors the attack at the less substituted carbon. |
65f04fd966c1381729d79a16 | 11 | We hypothesized that mutation F12Y could also help in the preorganization of the active site pocket, thus impacting and favoring the productive binding of the azide (and epoxide) in place for the ring-opening reaction to occur. To that end, we ran nanosecond timescale MD simulations for both HheC wild type and mutant F12Y in the absence of any substrate, and in the presence of epoxide 1 and azide in the active site. The analysis of the MD simulations in the absence of any ligand indicated that F12Y establishes a hydrogen bond with the backbone of T131 that is adjacent to the catalytic S132 (Figure ). This interaction established between the hydroxyl group of Y12 and T131, which is obviously not possible in HheC wild type, has some important implications for the active site preorganization. Thanks to this interaction, the loop containing F12Y is slightly more rigid (Figure ), which helps in retaining azide in place for the epoxide-ring opening reaction (Figure , right panel). In HheC wild type, such an interaction is not possible, thus the side chain of F12 is substantially more flexible and clearly affects the binding of the azide in the nucleophile binding pocket (Figure , left panel). Moreover, this newly established hydrogen bond between Y12 and T131, and the resulting loop rigidification likely contribute to the observed higher thermal stability of HheC mutant F12Y as well, as suggested previously. Although the kinetic constant (kobs,max) for mutant F12Y is substantially improved, the mutation at the same time affects the binding of azide and induces stronger cooperativity (Table ). The higher K50 value found for azide in mutant F12Y can be explained by the distance between azide and position F12Y (Figure ). In F12Y, azide can adopt two different binding modes: the catalytically productive pose as shown in Figure , and an additional one in which azide displaces the epoxide and interacts with both the catalytic S132 and F12Y. This additional, catalytically non-productive binding mode likely causes the higher K50 value found experimentally for azide in mutant F12Y (Table ). We additionally applied our correlation-based tool Shortest Path Map (SPM) to investigate how the communication network between subunits might be altered through mutation F12Y (Figure ). Interestingly, we observed a much more interconnected network in mutant F12Y, thus suggesting that the establishment of the Y12-T131 interaction enhances the intramolecular interactions and the allosteric communication between subunits. This is in line with the higher Hill coefficient of HheC F12Y found experimentally (Table ). |
65f04fd966c1381729d79a16 | 12 | In summary, the QM and MD simulations of HheC wild type and F12Y in complex with epoxide 1 and azide indicate that mutation F12Y changes the network of hydrogen bonding with azide, which has a big impact on the activation barrier, but also on the preorganization of the active site and the retention of both epoxide and azide at their required optimal positions for enhanced activity. In comparison, the equivalent tyrosine 18 in HheG wild type is not able to establish similar hydrogen bonding interactions with azide or T151 (equivalent to T131 in HheC) due to the much wider active site pocket of HheG. The latter might explain why mutation Y18F in HheG affects enzyme activity only slightly (vide infra). The extra flexibility of residue F12 in WT (highlighted with a double arrow) affects the productive binding of azide in the active site pocket, thus hampering the epoxide-ring opening reaction. |
65f04fd966c1381729d79a16 | 13 | Overall, we have demonstrated that important enzyme properties of HHDHs, such as activity, selectivity and stability, are influenced by the conserved residues threonine, phenylalanine/tyrosine and glycine of sequence motif 1 (T-X4-F/Y-X-G), which lines the nucleophile binding pocket of HHDHs. Despite the fact that those three residues appear to be highly conserved among naturally occurring HHDHs (please note that two highly homologous natural variants with sequence motif variation at the threonine position have been reported very recently ), we could show that especially the aromatic residue (phenylalanine/tyrosine) and the threonine position can be mutated to adjust enzyme properties, as exemplified for HheC. Only the conserved glycine residue of motif 1 proved quite invariable in both studied HHDHs as even the exchange by alanine resulted already in drastic activity losses toward most tested dehalogenation and epoxide ring opening reactions. |
65f04fd966c1381729d79a16 | 14 | Even though the actual effect of individual mutations is mainly enzyme dependent, mutagenesis of motif 1 residues can yield greatly improved enzyme variants such as HheC F12Y. This mutant features not only a higher thermal stability as reported earlier , but displays also much higher activity in the dehalogenation and epoxide ring opening of most substrates tested herein, as well as an impressive enantioselectivity improvement in the ring opening of epichlorohydrin (1), making this variant highly attractive for biocatalytic applications. Moreover, the detailed molecular insights into the activity improvement induced by mutation F12Y, which have been gained through QM and MD simulations in this study, will facilitate further protein engineering campaigns of HheC starting from mutant F12Y in the future. |
65f04fd966c1381729d79a16 | 15 | Escherichia coli BL21(DE3) was used for heterologous protein production as outlined before. All genes were expressed from vector pET-28a(+) (Merck) under control of the T7 promoter, resulting in the addition of an Nterminal hexahistidine (His6)-tag to the heterologously produced proteins. HheC and HheG mutagenesis Amino acid positions for mutagenesis were selected based on the respective motif 1 sequences of HheC (T-X4-F-X-G) and HheG (T-X4-Y-X-G). For each conserved amino acid position within motif 1, variants carrying all 19 possible amino acid exchanges were generated using site-directed mutagenesis (see Table for a list of used primers). In case of positions T13, Y18 and G20 of HheG as well as T7 and G14 of HheC, a Golden Gate mutagenesis protocol was used (see supplementary Table for details regarding the composition of the PCR reaction). The PCR protocol for plasmid amplification while introducing the mutation consisted of an initial denaturation (98 °C, 30 s), 30 cycles of denaturation (98 °C, 10 s), annealing (Tm-5 °C, 30 s) and elongation (72 °C, 30 s kb -1 ), followed by a final elongation step (72 °C, 120 s). After successful generation of mutated linear plasmids, one-pot restriction and ligation was performed using 1x cut smart® buffer (NEB), 1x T4-ligase buffer, 2 U BsaI, 400 U T4-ligase and 150 ng PCR product in 20 µL, and was incubated for 2 h at 30 °C, followed by heat inactivation of the reaction for 20 min at 65 °C. Resulting plasmids were transformed into Escherichia coli BL21(DE3) cells via heat shock method. Correct insertion of desired mutations was confirmed by sequencing. For position F12 of HheC, a MEGAWHOP mutagenesis protocol was used. Respective MEGA-primers were generated using QuikChange® mutagenic reverse primers in combination with a T7 forward primer (Table ). Reaction conditions (see Table ) as well as the PCR protocol were the same as for Golden Gate mutagenesis except for the used annealing condition, which was set to 57 °C for 30 s. For the subsequent MEGAWHOP mutagenesis, 300 ng of purified MEGA-primer, 30 ng pET28a(+)-hheC and PfuUltra II Hotstart PCR Mastermix (Agilent Technologies, Santa-Clara, CA, United States) were applied. The PCR protocol consisted of an initial denaturation step (98 °C, 30 s), 30 cycles of denaturation (98 °C, 10 s), annealing (55 °C, 30 s) and elongation (68 °C, 2 min kb -1 ), followed by a final elongation step (72 °C, 120 s). |
65f04fd966c1381729d79a16 | 16 | Small-scale production of all HheC and HheG mutants was performed in 50 mL reaction tubes in a total volume of 15 mL of Terrific Broth (TB) (per liter: 4 mL glycerol, 12 g peptone, 24 g yeast extract, 0.17 M KH2PO4, 0.74 M K2HPO4) supplemented with 50 µg mL -1 kanamycin and 0.2 mM isopropyl-β-D-thiogalactopyranosid (IPTG), and inoculated with 10% (v/v) preculture. After incubation for 24 h at 22 °C and 220 rpm, cells were harvested by centrifugation (20 min, 3488 g, 4 °C) and the resulting cell pellets were stored at -20 °C until further use. For smallscale purification via N-terminal His-tag, cell pellets were resuspended in 2 mL buffer A (50 mM Tris•SO4, 300 mM Na2SO4, 25 mM imidazole, pH 7.9), supplemented with 1 mg mL -1 lysozyme and one Pierce Protease Inhibitor Mini Tablet (EDTA-free, Life Technologies, Thermo Fisher Scientific). Cells were disrupted by sonication on ice for 3 min (6 cycles of 10 s pulse and 20 s pause). Cell debris were removed by centrifugation (30 min, 21 000 g, 4 °C). The resulting cell-free extracts were loaded on 0.8 mL Pierce® centrifuge columns with a column volume (CV) of 0.6 mL Ni Sepharose TM 6 fast flow (GE Healthcare, Freiburg, Germany), pre-equilibrated with buffer A. After protein binding, columns were washed with each 10 CV of buffer A to remove non-specifically bound proteins. Elution of His6-tagged target proteins was performed using 1.5 CV of buffer B (50 mM Tris•SO4, 300 mM Na2SO4, 500 mM imidazole, pH 7.9) and fractions of each 1 mL were collected. For desalting, 1 mL elution fraction was loaded onto PD MidiTrap TM G-25 desalting columns (GE Healthcare), pre-equilibrated with TE buffer (10 mM Tris•SO4, 4 mM EDTA, pH 7.9, 10% (v/v) glycerol), and eluted with 1.5 mL TE-buffer. Protein concentrations were determined based on absorbance at 280 nm using a NP80 nanophotometer (Implen, München, Germany) and respective molar extinction coefficients obtained by Protparam . |
65f04fd966c1381729d79a16 | 17 | Selected active mutants of HheC and HheG as well as wild-type enzymes were produced in larger scale in shake flasks using the same protocol as mentioned above but 500 mL TB medium. Cells were harvested by centrifugation (20 min, 3494 g, 4 °C) and resulting cell pellets were stored at -20 °C until further use. For purification via N-terminal His-tag, cell pellets were resuspended in 30 mL buffer A, supplemented with 1 mg mL -1 lysozyme and one Pierce Protease Inhibitor Mini Tablet, and disrupted by sonication on ice for 7 min (14 cycles of 10 s pulse and 20 s pause). Cell debris were removed by centrifugation (45 min, 18000 g, 4 °C) and resulting cell-free extracts were filtered through a 0.45 µm syringe filter. Cell-free extracts were loaded (2 mL min -1 flow rate) on a 5 mL HisTrap FF column (GE Healthcare, Freiburg, Germany), pre-equlibrated with buffer A, using an ÄktaStart FPLC system (GE Healthcare). Afterwards, the column was washed with 10 CV of buffer A to remove non-specifically bound proteins. His6-tagged target protein was eluted using a gradient from 0 to 100% buffer B in 60 mL while collecting fractions of each 1 mL. Fractions with highest UV absorbance at 280 nm were combined and concentrated to a volume of 2.5 mL using Vivaspin Turbo 15 centrifugation units (Sartorius, Göttingen, Germany) with 10 kDa molecular weight cut-off. For desalting, the concentrated protein solutions were loaded onto PD10 desalting columns (GE Healthcare), pre-equilibrated with TE buffer, and eluted with 3.5 mL TE-buffer. Respective yields of purified HheC and HheG variants are listed in Table . |
65f04fd966c1381729d79a16 | 18 | For determination of specific activities in epoxide ring opening with epoxide substrates 1, 2, 3, 4, 5, and 6 using azide as nucleophile, reactions of 1 mL total volume contained 10 mM epoxide, 20 mM azide, and 10-400 µg mL -1 purified enzyme in 2 mM MOPS•SO4 pH 7.0. Reactions were incubated at 22 °C (HheG wild type and mutants) or 30 °C (HheC wild type and mutants) with shaking at 900 rpm in a ThermoMixer C from Eppendorf (Hamburg, Germany). Samples of each 100 µL were taken after 30-360 s and transferred to a 96-well plate containing already 100 µL quenching solution (40 µg mL -1 BTB in 100% methanol) per well. Afterwards, absorbance at 616 nm and 499 nm was measured using a ClarioStar microplate reader. Activities were calculated using equations S8, 10, 15, 17, 18 in the supplementary. This assay was also used for the determination of kinetic parameters in epoxide ring opening reactions. For kinetic measurement of HheC and its mutants, reactions were carried out in 2 mM MOPS•SO4 using 1-150 mM epichlorohydrin (1) while keeping the azide concentration fixed (60 mM for HheC WT, T7S, F12Y, 100 mM for HheC G14A) or using 1-300 mM azide while keeping the concentration of epoxide 1 constant at 100 mM. Reactions were incubated at 30 °C. Samples were taken after 30-360 s to ensure determination of initial velocities. For HheG and its mutants, reactions were performed in 2 mM MOPS•SO4 using 1-150 mM cyclohexene oxide (2) while keeping the azide concentration fixed (60 mM for HheG WT, T13S, Y18F, 100 mM for HheG G20A) or using 1-300 mM azide while keeping the concentration of epoxide 2 constant at 100 mM. Reactions were incubated at 22 °C. Samples were taken after 30-360 s to ensure determination of initial velocities. Analysis of the resulting kinetic data was performed as previously described for specific activity calculation and kinetic data was fitted using the Hillequation ( ) in Origin Pro2021 (see Figures ). |
65f04fd966c1381729d79a16 | 19 | Specific activities (U mg -1 ) in the dehalogenation of haloalcohols 1,3-dichloro-2-propanol (1f), 2chlorocyclohexanol (2f) and 1,3-dibromo-2-propanol (7g) based on initial reaction rates were determined using the halide release assay . Reactions were performed in duplicate in a total volume of 1 mL containing 10 mM haloalcohol in 25 mM Tris•SO4 buffer pH 7.0 at 30 °C (HheC and its mutants) or 22 °C (HheG and its mutants) using 10-400 µg mL -1 purified enzyme. Sample of 100 µL volume were taken after 30, 60, 180, 270 and 360 s and mixed with 100 μL assay reagent comprising equal volumes of solution I [0.25 M NH4Fe(SO4)2 in 9 M HNO3] and solution II [saturated solution of Hg(SCN)2 in pure ethanol]. Absorbance at 460 nm was measured using a ClarioStar microplate reader. Specific activities were calculated using standard curves for halides Cl -and Br -in the range of 0 to 3.3 mM. Chemical background of negative control reactions without enzyme addition was always subtracted. This assay was also used for the determination of kinetic parameters in the dehalogenation of 1,3-dichloro-2propanol (1f) by HheC mutants. Fir this, the same reaction conditions were used as described above with the substrate concentration ranging from 0.01-20 mM. Resulting kinetic data was fitted using the Michaelis-Menten equation (2) in Origin Pro2021 (see Figure ). |
65f04fd966c1381729d79a16 | 20 | Melting temperature determination Thermal shift assays were performed using a QuantStudio 1 Real-Time-PCR system (Thermo Fisher Scientific) in MicroAmp Optical reaction tubes (Thermo Fisher Scientific) containing 20 µg protein and 10 µL 50x concentrated SYPRO orange as fluorescent dye (Thermo Fisher Scientific) in TE buffer in a total volume of 50 µL. Fluorescence (excitation: 580±10 nm, emission: 623±14 nm) was monitored upon increasing the temperature from 10 to 90 °C in 0.5 °C increments. The temperature at which the maximum fluorescence change was observed, representing the melting temperature Tm, was calculated using the Protein Thermal Shift software (version 1.4, Thermo Fisher Scientific). |
65f04fd966c1381729d79a16 | 21 | Mutants of HheC and HheG were analyzed in epoxide ring opening of glycidyl phenyl ether (4) using azide, nitrite, cyanide, cyanate, thiocyanate as well as chloride and bromide as nucleophiles. Each 1 mL reaction contained 10 mM epoxide 4, 20 mM nucleophile and 150 µg of purified enzyme in 50 mM Tris•SO4 buffer, pH 7.0. Reactions were carried out at 22 °C (HheG and its mutants) or 30 °C (HheC and its mutants) with shaking at 900 rpm in an Eppendorf ThermoMixer C. Samples were taken after 1 h and 24 h, extracted with an equal volume of tert-butyl methyl ether containing 0.1% (v/v) n-dodecane as internal standard. Organic phases were dried over MgSO4 and samples were analyzed by achiral GC (see Table for details regarding temperature programs and retention times). |
65f04fd966c1381729d79a16 | 22 | To determine the regio-and enantioselectivity of HheC and HheG mutants in epoxide ring opening of epichlorohydrin (1), cyclohexene oxide (2) and styrene oxide (3) in comparison to respective wild-type enzymes, reactions of 1 mL volume were performed in 50 mM Tris•SO4, pH 7.0 containing 10 mM epoxide, 20 mM azide and 10-200 µg purified enzyme. Reactions were incubated at 22 °C (HheG and its mutants) or 30 °C (HheC and its mutants) with shaking at 900 rpm in an Eppendorf ThermoMixer C. Samples were taken after 15 min for epoxide 1, 30 min for epoxide 3 and 2 h for epoxide 2, and extracted with an equal volume of tert-butyl methyl ether containing 0.1% (v/v) n-dodecane as internal standard. Organic phases were dried over MgSO4 and samples were analyzed by achiral and chiral GC (see Table for details regarding temperature programs and retention times). |
65f04fd966c1381729d79a16 | 23 | Parameters for substrates 1 and azide were generated with the antechamber and parmchk2 modules of AMBER20 using the 2nd generation of the general amber force-field (GAFF2). Partial charges (RESP model) were set to fit the electrostatic potential generated at the HF/6-31G(d) level of theory. The charges were calculated according to the Merz-Singh-Kollman 61,62 scheme using the Gaussian16 software package. The protonation states were predicted using PROPKA. The enzyme structures were obtained from the PDB with the code (1PWZ) and cleaned from other non-peptidic molecules to obtain the wild-type (WT) system in a tetrameric oligomerization state. The single mutation F12Y was introduced using the Pymol mutagenesis tool. Proteins were solvated in a equilibrated truncated octahedral box of 12 Å edge distance using the OPC water model, resulting in the addition of ca. 21.300 water molecules, and neutralized by the addition of explicit counterions (i.e., Na + ) using the AMBER20 leap module. All MD simulations were performed using the amber19 force field (ff19SB) in our in-house GPU cluster, GALATEA. The Pmemd.cuda program from Amber20 was used to perform a two-stage geometry optimization. In the first stage, solvent molecules and ions were minimized, while solute molecules were restrained using 500 kcal•mol -1 •Å-2 harmonic positional restraints. In the second stage, an unrestrained minimization was performed. The systems were then gradually heated by increasing the temperature by 50 K during six 20 ps sequential MD simulations (0-300 K) under constant volume. Harmonic restraints of 10 kcal•mol -1 •Å-2 were applied to the solute, and the Langevin equilibration scheme was used to control and equalize the temperature. The time step was kept at one fs during the heating stages to allow potential inhomogeneities to self-adjust. Each system was then equilibrated without restraints for 2 ns at a constant pressure of 1 atm and temperature of 300 K using a 2 fs time step in the isothermalisobaric ensemble (NPT). After equilibration, five replicas of 250 ns were run for each system (i.e., 1.25 μs per system and 5 μs in total simulated time) in the canonical ensemble (NVT). MD simulations were analyzed by monomers to make it easier to study, multiplying the simulated time by four. All analysis was done using available Python libraries (pyemma , mdtraj , and mdanalysis ) in a jupyter lab environment. |
65f04fd966c1381729d79a16 | 24 | For the QM cluster model, the atom selection was done following the previous work of Himo's group. The only difference is that we added all backbone atoms for residue 12 (the position that is mutated in variant F12Y), allowing for additional flexibility and ring rotation. Geometry minimizations were performed using Gaussian16 63 , using the hybrid density functional theory method B3LYP , and the 6-31G(d,p) basis set. All energies were calculated by performing single-point calculations on the optimized B3LYP/6-31G(d,p) geometries using the M06-2x functional and Def2TZVPP basis set (M06-2X/Def2TZVPP//B3LYP/6-31G(d,p)). Solvation effects were considered using the SMD solvation model, a variation of Truhlar's and coworkers' integral equation formalism variant (IEFPCM) , using diethyl ether as solvent. |
65f04fd966c1381729d79a16 | 25 | The Shortest Path Map (SPM) analysis was performed using the MD simulations of HheC wild type and variant F12Y. For SPM calculation, the MD simulations are used to compute the inter-residue mean distance and correlation matrices. A simplified graph is created using both matrices, in which only the pairs of residues that show a mean distance of less than 6 Å along the MD simulation are connected through a line. The edge connecting both residues is weighted to the Pearson correlation value (dij=-log |Cij|). The residues with more correlated motions, will be connected through a shorter line. The generated graph is further simplified to identify the shortest path lengths. Following this strategy, the residues whose lines in the graph are shorter (i.e., with more correlated movements) and thus, play an important role in the conformational dynamics of an enzyme, are detected. Finally, the generated SPM graph is drawn on the 3D structure of the enzyme. |
650398fc99918fe537f6e6f3 | 0 | Hence, isolated gas-phase TM(CO)n models and the chemisorption of CO on metal surfaces are often investigated to shed light on their catalytic potencies. The fact that the dominant binding mode of CO with electropositive metals is via the less electronegative C rather than the more electronegative O is at first glance surprising. This unique characteristic of CO arises from the two-electron s lone pair present on the C, making it the strongest ligand in the spectrochemical series. Often, M•••CO interactions are further supported by the superior π-acceptor ability of CO that induces metal-to-ligand π back-donation. However, the electron flow through the π-frame (or to π* orbitals of CO) simultaneously weakens the C-O bond. To date, a majority of transition metal CO studies are focused on the first-and second-row TMs, with less attention on the heavier third-row TMs. For example, according to the Cambridge Structural Database (CSD, 2021.1.0) there are 164 first-row (TM = Sc-V) and 185 second-row (TM = Y-Nb) crystal structures available with the TM-CºO bonding configuration, whereas the number of complexes for the corresponding search for third-row structures (TM = La-Ta) is only 97. Among the third-row TMs, one of the least studied systems is Hf, of which only 9 hits are obtained from the CSD for a Hf-CºO search. While this analysis does not include a review of the solution or gas phase chemistry studies for third row structures, it nevertheless gives a sense of the proportion of studies that have been dedicated to third-row complexes. |
650398fc99918fe537f6e6f3 | 1 | In reviewing the literature, we were only able to locate two experimental gas-phase studies on Hf(CO)n systems, which are related to infrared spectra analysis. Work by Zhou and Andrews provides evidence for the existence of all Hf(CO)1-4 and Hf(CO)2 -species. They also report the stretching frequency of CO of HfCO to be 1869 cm -1 (obtained from laser-ablated hafnium in solid neon) and a trend of greater d → π* back-donation going from TiCO to HfCO. This trend is consistent with the spectroscopic study of M(CO)6-8 + (M = Ti-Hf) by Brathwaite and Duncan. Computational modelling is vital in understanding the chemistry of systems that are challenging to handle under laboratory conditions. For example, Hf compounds are known to be highly toxic, motivating theoretical studies. 17, 18 However, selection of appropriate computational tools is crucial to make accurate predictions. In general, unsaturated TM(CO)n complexes have several close-lying electronic states, which make them challenging to model accurately with computation. High-level multi-reference theories provide a platform for predictions of systems with many low-lying electronic states. The gold-standard coupled cluster level of theory can also deliver predictions with higher precision relative to most computationally tractable MR methods as long as the targeted states are sufficiently singlereference in nature. However, both multi-reference and coupled cluster levels of theory require a great deal of quantum chemical expertise and computing power, which makes them less widely used, especially in larger systems. On the other hand, density functional theory (DFT) is widely popular due to its black box nature and reasonable accuracy at low computational cost. However, a practitioner must select an appropriate exchange-correlation functional because the best-performing functional depends on the system and property. In this work, we probe the interactions between between Hf and CO with high-level multireference configuration interaction theory (MRCI), coupled cluster singles doubles and perturbative triples [CCSD(T)], as well as with DFT. Specifically, numerous low-lying electronic states of HfCO are analysed with MRCI and their potential energy profiles, equilibrium electronic configurations, corresponding chemical bonding patterns, and various energy-related properties are reported. The single-reference electronic states are investigated with CCSD(T) and used as benchmarks for evaluating DFT errors associated with 23 exchange-correlation functionals that span multiple rungs of "Jacob's ladder". We assess whether performance trends are transferable to solid-state systems by studying the chemisorption of one CO on a Hf surface with a set of DFT functionals. |
650398fc99918fe537f6e6f3 | 2 | Internally contracted multi-reference configuration interaction (MRCI) and coupled cluster singles doubles and perturbative triples [CCSD(T)] 26 correlated wavefunction theory (WFT) calculations were carried out with the MOLPRO 2015.1 code. These calculations used the largest Abelian subgroup, C2v, of the parent C∞v point group associated with the linear species HfCX (X = O, S, Se, Te, Po). |
650398fc99918fe537f6e6f3 | 3 | First, at the MRCI level we obtained full potential energy curves (PECs) of HfCO arising from Hf( 3 F)+CO(X 1 Σ + ), Hf( 3 P)+CO(X 1 Σ + ), Hf( 1 D)+CO(X 1 Σ + ), and Hf( 5 F)+CO(X 1 Σ + ) interactions as a function of Hf•••C distance. For each potential energy scan, the C-O distance was kept fixed to the experimental bond distance (i.e., 1.128 Å) of the isolated CO molecule. This choice was made to simplify the scans, although we had previously noted backbonding could weaken the CO bond. Hence, we do not attempt to compute fundamental frequencies from these potential energy curves since they would be purely approximate. We nevertheless expect the effect on the bond distance to be modest and comparable across all species and electronic states compared. MRCI calculations were initiated from reference complete active space self-consistent field (CASSCF) wavefunctions. Specifically, the CASSCF wavefunctions were constructed by placing 4 electrons in 6 active orbitals [CAS (4,6)]. At long Hf•••C distances (> 5 Å), the selected orbitals are purely 6s and all 5d atomic orbitals of Hf, corresponding to the four active electrons. |
650398fc99918fe537f6e6f3 | 4 | [5dyz], and 1a 2 [5dxy] in symmetry. All valence electrons were correlated in the subsequent MRCI calculation. A full MRCI geometry optimization was performed only for the ground triplet and lowest-lying quintet electronic states of HfCO. Davidson-corrected MRCI (MRCI+Q) energies obtained at the ground state MRCI geometry were also used to compute the dissociation energy (De) and the excitation energies (Te) of the HfCO. At the MRCI level spin-orbit coupling effects were evaluated by a single point calculation of the MRCI ground state geometry using the Breit-Pauli Hamiltonian as implemented in MOLPRO. |
650398fc99918fe537f6e6f3 | 5 | For WFT calculations of HfCO, correlation-consistent cc-pVXZ-PP 38 basis sets were chosen for Hf and aug-cc-pVXZ for C and O, where X = T, Q or 5. Specifically, only a quadrupleζ quality (X = Q) basis set was used for all MRCI analysis, but we also compared results from triple-ζ, quadruple-ζ, and quintuple-ζ quality sets for CCSD(T) calculations. The plain cc-pVTZ(- PP) basis set was also tested for all atoms of HfCO and exclusively employed for its isovalent HfCS, HfCSe, HfCTe, and HfCPo species to reduce the computational expense. In all cases, the inner 60 electrons of Hf (1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 4d 10 4f 14 ) were substituted with the Stuttgart relativistic pseudopotential (ECP60). HfCO, HfCS, and HfCSe WFT energetics were used to investigate density functional theory (DFT) errors associated with 23 density functional approximations (DFAs) that fall into six rungs of "Jacob's ladder" using the Psi4 43 package. The 23 DFAs corresponded to semi-local generalized gradient approximations (GGAs) (BLYP, BP86, and PBE), meta-GGAs (TPSS, SCAN, M06-L, and MN15-L), global GGA hybrids (B3LYP, B3P86, B3PW91, and PBE0), meta-GGA hybrids (TPSSh, SCAN0, M06, M06-2X, and MN15), range-separated hybrids (LRC-ωPBEh and ωB97X), and double hybrids (B2GP-BLYP and PBE0-DH, DSDBLYP-D3BJ, DSD-PBEB95-D3BJ, and DSD-PBEP86-D3BJ) functionals, as implemented in a recently introduced workflow. In this workflow, the density of a B3LYP calculation is converged first and used as the starting point for all other DFA calculations. Starting from CCSD(T) geometries, the results from these DFAs were used to evaluate the single-point De for HfCO, HfCS, and HfCSe. In the past we have applied def2-XZVP (X = T, Q) basis sets to study TM based systems and in this work the larger X = Q set was applied for all DFT calculations. The dissociation energy of CO from a periodic Hf(001) surface of hexagonal Hf was determined using Quantum-ESPRESSO (ESI Figure ). For all calculations, a norm-conserving pseudopotential with a kinetic energy cutoff of 70 Ry was employed. The Hf surface was approximated as a 3x3x1.5 slab and the CO molecule was placed vertically on top of an Hf atom. |
650398fc99918fe537f6e6f3 | 6 | The positions of the Hf atoms in the top layer and the vertical distance of CO were optimized using the BLYP functional and a 3x3x1 k-point mesh. Subsequently, the dissociation energy was calculated with BLYP, PBE, BP86, B3LYP, and PBE0 through single-point calculations on the BLYP-optimized geometry at the Γ point of both the slab with CO present and the slab without CO along with an isolated CO molecule. |
650398fc99918fe537f6e6f3 | 7 | To understand bonding in HfCO, we start by analyzing the electronic structure of the individual Hf atom and CO molecule. The 3 F ground electronic state of Hf has a valence 5d 2 6s 2 electron configuration. Simple electron promotions within the 5d shell produces its first two excited electronic states, which are experimentally only 16-26 kcal/mol higher in energy (i.e., 3 P at 15.8-25.7 kcal/mol, 1 D at 16.1 kcal/mol). As a result of the low-lying electronic states of the isolated atom, Hf is expected to form complexes with a variety of chemical bonding configurations. We investigate the reaction between the aforementioned electronic states of Hf with the ground state of the CO ligand (X 1 Σ + ). The first excited state of CO (a 3 Π) lies well separated from the ground state (by 139.2 kcal/mol) and hence its interaction with Hf was not pursued in this work. The combination of Hf( 3 F)+CO(X 1 Σ + ), Hf( 3 P)+CO(X 1 Σ + ), Hf( 1 D)+CO(X 1 Σ + ), and Hf( 5 F)+CO(X 1 Σ + ) produce 7 triplet, 3 triplet, 5 singlet, and 7 quintet spin electronic states of the HfCO molecule, respectively. In total, we have studied 10 triplet, 5 singlet, and 7 quintet spin PECs of HfCO at MRCI level of theory to identify its low-lying electronic states (Figure ). Note that all quintet states except b 5 Δ are high in energy and are not shown in Figure . |
650398fc99918fe537f6e6f3 | 8 | Analyzing the results of the MRCI potential energy scan, we observe that the Hf( 3 F)+CO(X 1 Σ + ) fragment produces three attractive states, X 3 Ʃ -, A 3 Φ, B 3 Π, and one strongly repulsive 3 Δ state. X 3 Ʃ -, A 3 Φ, and B 3 Π are the ground state and the third and fourth lowest-lying electronic states of the molecule, respectively. The first excited state (i.e., a 1 Δ) dissociates to the Hf( 1 D)+CO(X 1 Σ + ) asymptote. We analyzed the electron configurations of the electronic states and the associated molecular orbitals (Table and Figure ). These electron configurations highlight the σ-dative bonding between Hf and CO. Specifically, the dative interaction between these fragments is described by the doubly occupied 1σ orbital, which arises from 5d ! ! (Hf)+σ(CO) hybridization (Figure and ESI Figure ). The occupied 6s atomic orbital of Hf polarizes away from CO to facilitate an efficient σ-dative attack (2σ orbital of Figure ). Other than the σ-dative bond, a strong metal-to-ligand π back-donation (dxz/dyz of Hf to πx * /πy * of CO) was also observed in all electronic states. This π back-donation is evident from the 1πx and 1πy molecular orbitals of HfCO, which are occupied in all cases (Figure ). Specifically, according to natural bonding orbital analysis, 24% of the two electrons has back-donated from Hf to the two π* orbitals of CO in the ground state. On the other hand, only A 3 Φ, B 3 Π, b 5 Δ, and d 1 Π excited states occupy non-bonding 1dxy (1δxy) and 1d " ! #$ ! (1δ " ! #$ ! ) orbitals (Table and Figure ). We next analyzed the relationship between electron configuration and bond order expected in these complexes. The single-reference ground state of HfCO (X 3 Σ -) has a 1σ 2 2σ 2 1πx 1 1πy 1 (= 1σ 2 2σ 2 1π 2 ) dominant electron configuration. Based on its 1σ 2 1π 2 electron population, a double bond (i.e., Hf=C) can be expected for the ground state (Table and Figure ). Indeed, its calculated effective bond order based on the CASSCF weights is ~1.8, which agrees well with our qualitative expectation. The first excited state of HfCO (a 1 Δ) has the same electronic configuration as the ground state but with a different spin configuration. Indeed, the coupling of two π electrons in symmetrically equivalent 1πx and 1πy orbitals produces this multi-reference singlet electronic state. |
650398fc99918fe537f6e6f3 | 9 | The destabilization of a 1 Δ compared to X 3 Σ -is rationalized by Hund's rule. The highly excited c 1 Σ + state carries the same multi-reference electronic configuration as a 1 Δ but is likely higher in energy due to potential mixing with other excited states. The heavily multi-reference A 3 Φ, B 3 Π, and d 1 Π states are generated by promoting one electron from a 1π orbital of X 3 Σ -to 1δ orbitals (1dxy and 1d " ! #$ ! ) with various compositions ( HfCO is the b 5 Δ state that has the unique 1σ 2 2σ 1 1π 2 1δ 1 configuration. Similar to the ground state, we can expect a bond order of two for b 5 Δ, which in fact is almost identical to its effective bond order, 1.9, as could be expected based on its 98% single-reference nature. |
650398fc99918fe537f6e6f3 | 10 | We carried out CCSD(T) geometry optimizations with the ATZ and AQZ basis sets, but to overcome the great computational cost of larger basis set calculations, we performed only a singlepoint quintuple-ζ basis set calculation at the geometry obtained with our quadruple-ζ basis set. We do not expect a significant structure variation from AQZ to A5Z basis sets, as the difference in bond length observed is less than 0.005 Å by improving from the ATZ to AQZ basis sets. |
650398fc99918fe537f6e6f3 | 11 | Generally, it is expected that larger basis sets will predict shorter bond lengths, and our results are consistent with that expectation (Table ). Our MRCI-optimized bond distances and CCSD(T) values agree within 0.02 Å. In terms of experimental references values, the experimental C-O stretching frequency has been reported with co-deposition of laser-ablated hafnium with 0.1% CO in neon at 4-10K. 12 This value 12 is 1869 cm -1 , which differs by 26 from our CCSD(T) value for ). |
650398fc99918fe537f6e6f3 | 12 | We also evaluated the ionization energy (IE) of the single-reference ground state at the CCSD(T) level of theory. The removal of an electron from the doubly occupied 2σ molecular orbital of HfCO (X 3 Σ -) produces the HfCO + (X 2 Σ -) cation. At the CCSD(T) level this IE is 6.974 eV, which is slightly higher compared to the first IE of the Hf atom (i.e., 6.825 eV) and could be due to the slightly ionic Hf +0.53 -[CO] -0.53 charge distribution. No experimental reference value is available for comparison to this quantity, so we will use the CCSD(T) reference value for subsequent evaluation of the accuracy of various DFAs in DFT. |
650398fc99918fe537f6e6f3 | 13 | Recently, we observed that the De of the HfX (X = O, S, Se, Te, Po) series decreases moving from lighter HfO to heavier HfPo, which correlates with the binding elements' electronegativity (i.e., O > S > Se > Te > Po). Building upon our prior work, we also analyze the HfCX (X = O, S, Se, Te, Po) series. Because the metal-binding atom C is the same for all HfCX, it is somewhat difficult to make a prediction on the De trend for the HfCX series based on our knowledge on HfX series. Indeed, we observe a reversed trend for HfCX, where De increases moving from lighter HfCO to heavier HfCPo. This opposite trend does follow expectations based on the dipole moment (μ) of the ligand (i.e., CO < CS < CSe < CTe < CPo). The relationship between De(Hf-CX) vs. μ(CX) is linear with R 2 = 0.991 (Figure ). To confirm the generality of this relationship, at the same level of theory we computed the De of the isovalent ZrCX and TiCX series and related it to the dipole moment of the CX species. Note that the ground states of ZrCO and TiCO are both 5 Δ. For both metals (M = Zr and Ti ), the De increases moving from MCO to MCPo and importantly the near-linear De vs. μ relationship is preserved (R 2 values 0.992 and 0.995, Figure ). Notably, the slope of the relationship decreases moving from HfCX to TiCX by about 25%. This can be rationalized by the fact that a decrease of De was observed moving from HfCX to TiCX, while the dipole moments are necessarily unchanged. |
650398fc99918fe537f6e6f3 | 14 | De, IE, and the ΔET-Q (X 3 Σ -and b 5 Δ) values to evaluate DFT functional errors. Specifically, we assessed 23 functionals that span multiple rungs (GGAs, meta-GGAs, global GGA hybrids, meta-GGA hybrids, range-separated hybrids, and double hybrids) of "Jacob's ladder" (see Computational Details). We generally expect higher accuracy from the functionals that are in higher rungs of the ladder that comes with higher computational cost. However, our most expensive double hybrids have large De errors compared to less expensive functionals (Figure ). We next extended our comparison to the evaluation of errors in HfCS and HfCSe (ESI Figures and). The DFA errors are 7-24% higher for HfCO compared to the errors of HfCS and HfCSe for all functionals except for the B3LYP, SCAN0, and ωB97X functionals that have < ~7% errors (ESI Tables ). On the whole, the dissociation of all three systems is predicted |
650398fc99918fe537f6e6f3 | 15 | well by the meta-GGA hybrid M06-2X with less than 8% error. This observation is in line with our past DFT analysis of HfB, which had almost identical De predictions for M06-2X and CCSD(T). Although it should be noted in contrast to HfCX (X 3 Σ -) and HfB (X 4 Σ -), which have unpaired valence electrons, M06-2X was previously observed to perform the worst at predicting De for the closed-shell ground state of HfO (X 1 Σ + ). For both HfCS and HfCSe, the two bestperforming functionals of HfCO (B3LYP and ωB97X) also provided small errors (~5-8%), reinforcing our suggestion of the use of these functionals. Notably, all the studied functionals preserved the linear De vs. μ trend that we observed earlier (Figure and ESI Figure ). At first the agreement of CCSD(T) and B3LYP on HfCX dissociation is surprising. For example, according to the work by Wilson et al., B3LYP underestimated dissociation of CO from coordination complexes with first row transition metals, including Fe(CO)5 and Cr(CO)6, and this trend was reversed in FeCO, where B3LYP overestimated dissociation. Nevertheless, it was suggested B3LYP predicted a higher error for the dissociation with Fe due to stronger multireference character of this system, whereas HfCO studied here is single reference. In our previous work we observed B3LYP errors of 7 and 35.4% for dissociations of single-reference ionic HfO (closed-shell X 1 Ʃ + ) and HfB (X 4 Ʃ -) systems, respectively. Note that it is rather difficult to come to a firm conclusion of which family or functional is best for all Hf-complexes especially if the degree of metal-organic bonding is quite different in each case. |
650398fc99918fe537f6e6f3 | 16 | We also evaluated the DFT errors associated with the ΔET-Q and IEs of HfCO (Figures and and ESI Tables and). Among all the functionals considered, for these quantities, the double hybrids (DHs), with the exception of PBE0-DH, yield the closest results to CCSD(T). This result differs from the De analysis where DHs performed poorly. Specifically, the DHs display values within 0-3 kcal/mol of the CCSD(T) reference for ΔET-Q and 0-0.11 eV for IE. |
650398fc99918fe537f6e6f3 | 17 | Surprisingly, the second-best performing family is GGA. Despite the well-known underestimation of ΔET-Q by GGA, the average deviation from the CCSD(T) value is smaller than the other functional families. Overall, several functionals performed well for predicting the ΔET-Q and IE of HfCO (Figures and). Importantly, the best-performing functionals for HfCO De, the GGA hybrid B3LYP and the range-separated hybrid ωB97X, also had small errors for the IE (1.7 and 5.1%, respectively). The same cannot be said for ΔET-Q, where these functionals had 24.4 and 42.3% errors, respectively. Thus, our overall recommendation remains for the use of B3LYP and ωB97X based on De and IE despite some caveats regarding the spin state ordering. Nevertheless, it is noteworthy that all functionals correctly identify the ground state, despite in some cases underestimating (e.g., B3LYP) or overestimating (e.g., ωB97X) the quantitative value of the ΔET-Q gap (Figure ). values in molecules and provide a consistent result between the surface and the molecular complex. |
650398fc99918fe537f6e6f3 | 18 | In conclusion, we studied potential energy curves, dissociation energies, excitation energies, harmonic vibrational frequencies, and chemical bonding patterns of several low-lying electronic states HfCO. We found seven bound electronic states of HfCO with respect to the Hf( 3 F)+CO(X 1 Σ + ) dissociation. Among these, all but the X 3 Ʃ -and b 5 Δ are multi-reference in nature. We adopted larger augmented quadruple-and quintuple-ζ basis sets to obtain highly accurate CCSD(T) results for the two single-reference electronic states. Our analysis on MCX (M = Hf, Zr, Ti and X = O, S, Se, Te, Po) demonstrated a linear relationship between the dissociation energies of these complexes and the dipole moments of the CX species, where De increases moving from lighter MCO to heavier MCPo. |
650398fc99918fe537f6e6f3 | 19 | Importantly, these two functionals displayed higher errors for predicting ΔET-Q hence they might not be ideal for predicting excited-state properties. We further studied the interaction of a CO molecule with a Hf surface with BP86, BLYP, PBE, B3LYP, and PBE0 functionals and observed that the GGAs consistently predicted smaller chemisorption energies (by ~8 kcal/mol) compared to their gas-phase Des but the global hybrids yielded more consistent results. Taken together with our analysis of benchmarks on the molecular systems, this encourages us to suggest B3LYP as a promising functional for both molecular and solid-state models of Hf-C interactions. |
615d8f44be107438db93b345 | 0 | Negatively charged Nitrogen-Vacancy centers (NV -) can be used as probes for ultrasensitive detection of magnetic and electric fields , temperature , and nuclear spins at the nanoscale . NV -centers can be optically polarized with continuous irradiation of laser light at room temperature and at Earth's magnetic field , thus paving the way for applications in biomedical assays , as intracellular thermometers , optical magnetic imaging in living cells or optical magnetic detection of single-neuron action potentials . Moreover, optical pumping of NV -centers has been proposed as an alternative to dynamic nuclear polarization (DNP) for the hyperpolarization of nuclear spins . |
615d8f44be107438db93b345 | 1 | These applications rely on ensembles of NV -centers in the vicinity of the diamond surface . Due to their large surface area, NV-rich, fluorescent nanodiamonds (NDs) are promising candidates for such applications . Moreover, NDs are biocompatible, and their surface can be functionalized to target specific cells or proteins . NDs can be internalized by living cells, thus probing the microenvironment in subcellular compartments . Furthermore, 13 C enrichment of NDs is desirable to improve the hyperpolarization efficiency for contrast agents, quantum sensing and magnetic resonance signal enhancement . |
615d8f44be107438db93b345 | 2 | Several techniques have been proposed for the production of NDs, including nanomilling of bulk diamond, detonation diamond and high-power laser ablation . Detonation NDs tend to be small (5-10 nm) and rich in impurities . High-power laser ablation can produce fluorescent NDs in a single-step process , but the yield is insufficient for practical application. Conversely, nanomilling of bulk diamond makes it possible to control concentration of defects and NV centers, as well as particle size, with good production yield . |
615d8f44be107438db93b345 | 3 | Increasing the surface area of the material by nanomilling can improve exposure of shallow NV centers to the external environment. However, it inevitably affects NV -charge stability , as surface effects tend to favor the NV 0 charge state, which does not present useful spin properties . As a result, NDs present larger relative concentration of NV 0 in NDs compared to the starting material. |
615d8f44be107438db93b345 | 4 | Laser light used to polarize and interrogate NV -centers can also induce charge switching between NV -and its neutral form NV 0 . Photoconversion depends on the presence of nitrogen defects and surface acceptor states, and thus both NV -→ NV 0 and NV 0 → NV -photoconversion routes have been observed in different diamond samples. Recently, we have shown that increasing laser power can substantially increase the availability of shallow NV -produced by nitrogen implantation in ultrapure CVD diamond . However, it is unclear whether a similar strategy may be advantageous in NDs. |
615d8f44be107438db93b345 | 5 | Here, we prepared NDs of various sizes by nanomilling of highly-fluorescent 13 C-enriched diamond. Fluorescence spectra and optically detected magnetic resonance (ODMR) spectra were acquired at different laser powers for the native bulk diamond, and for NDs of 156 nm and 48 nm. Additionally, we internalized NDs in macrophage cells to study the effects of laser power under the typical conditions of a bioassay and in the cellular environment. Experiments were performed with a house-built wide-field microscope at sub-micrometric spatial resolution (1 pixel in the image equals 160 nm) to account for the intrinsic heterogeneity in NDs behavior and to study the microenvironment in different cellular compartments. Our findings highlight the importance of surface effects on photoconversion and provide useful information on the optimization of experimental conditions for biosensing or polarization transfer applications involving fluorescent NDs. |
615d8f44be107438db93b345 | 6 | Bulk 13 C-enriched diamond grown by the high-pressure, high-temperature (HPHT) technique was acquired from ElementSix. These samples have a concentration of NVs of ≈10 ppm, and 13 C enrichment ranged from 5 to 10% (≈5 * 10 4 -10 5 ppm), depending on the position within the diamond stone; concentration of substitutional nitrogen (P1 centers) was approximately 200 ppm. The fraction of 13 C was provided by the vendor, while the concentrations of nitrogen and NV centers were estimated through spectroscopic measurements on the bulk diamond before milling . Attrition milling was used to prepare samples with varying size distribution with a procedure adapted from . The whole process is exemplified in Fig. . The sample material (62 mg) was added to a stainless steel milling cup, which was filled up to one third of its height with 5 mm stainless steel milling balls. The bottom third of the milling cup was then filled with isopropanol that had been dried using molecular sieve. The sample was milled for six hours at 50 swings per second. After milling, the sample contained a significant amount of metallic debris caused by the milling. To clean the diamond material, the sample was flushed out of the milling cup with distilled water into a 250 ml round bottom flask. The remaining steel balls were removed using a magnet. To dissolve metallic impurities, 50 ml of concentrated hydrochloric acid was added. The mixture was stirred overnight at room temperature. After settling, the supernatant was decanted and 50 ml 96% of sulfuric acid was added. The resulting mixture was heated to 120 °C bath temperature without a reflux condenser to remove any remaining isopropanol. After one hour, a reflux condenser was attached to the flask and 20 ml of nitric acid (65%) slowly added while monitoring the reaction mixture carefully to prevent a violent reaction. It is important to note that any remaining isopropanol might violently react with concentrated nitric acid, thus it is important to remove it carefully before adding HNO3! The solution was stirred overnight at 120 °C. After the solution had cooled down to room temperature, the supernatant acid mixture was removed using a pipette and the solution was transferred to centrifugation tubes. To wash the diamond material, centrifugation at 15000 rpm was used over one hour to settle the diamond material at the bottom. The supernatant was removed and replaced with distilled water. The diamond material was then dispersed using sonication. This process was repeated until the supernatant showed a neutral pH. After reaching neutral pH, centrifugation was used to separate the particles by size. Two fractions were separated, and their size distribution measured using dynamic light scattering, giving a D50 value (volume distribution) of 156 nm and 48 nm, respectively. NDs were suspended in deionized water and stored in glass vials. Data of DLS and scanning electron microscopy can be found in the Supplementary Material. |
615d8f44be107438db93b345 | 7 | For uptake experiments, RAW 264.7 cells were seeded in an Ibidi at a density of 3 × 10 4 cells/ well and incubated at 37° C for 24 h, to allow them to adhere to the slide surface. Incubation of cells with NDs (size 156 nm and 48 nm) was performed for 24 h at 37 °C in a humidified atmosphere with 5% CO2. At the end of the incubation, cells were washed three times with PBS and fixed in 4% PAF at room temperature for fifteen minutes. |
615d8f44be107438db93b345 | 8 | Cells were rinsed twice with phosphate buffered saline (PBS) and permeabilized with 0.1 % Triton in PBS for ten minutes. Actin filaments were stained with phalloidin fluorescein isothiocyanate (FITC) (Sigma) for thirty minutes at room temperature. After washing twice with PBS, nuclei were counterstained with 4′,6-diamidino-2-phenylindole (DAPI). Coverslips were mounted with a glycerol/water solution (1/1, v/v). Observations were conducted under a confocal microscopy (Leica TCS SP5 imaging system) equipped with an argon ion and a 561 nm DPSS laser. Cells were imaged using a HCX PL APO 63×/1.4 NA oil immersion objective. NDs were excited by 561 nm laser, while the emission was collected in the 570-760 nm spectral range. Phalloidin was imaged using 458 nm laser and the emission collected in the 498-560 nm range. DAPI was imaged using 405 nm laser and the emission was collected in the 415-498 nm range. Image analysis was performed using ImageJ software. |
615d8f44be107438db93b345 | 9 | Wide-field ODMR imaging was performed with a modified Nikon Ti-E inverted wide-field microscope [Fig. ] equipped with a microwave channel and a high-sensitivity CMOS camera (Hamamatsu ORCA-Flash4.0 V2) . A 532 nm continuous-wave laser (Model: CNI laser mod. MGL-III-532/50mW) was used as excitation source, delivering on the sample a power of ~30 mW through a 40X (NA=0.75 and working distance of 0.66 mm) refractive objective. The laser power was modulated by inserting neutral density filters on the optical path. To avoid backscattering of laser light, we used a custom made dichroic beamsplitter. FL was collected in a spectral window ranging from 590 to 800 nm. |
615d8f44be107438db93b345 | 10 | The home-built instrument used for these experiments makes it possible to extract ODMR spectra pixelwise with sub-micrometric spatial resolution, thus enabling analysis of heterogeneously distributed samples. Indeed, the deposition procedure can result in a nonuniform distribution of NDs, with region-dependent concentration and size of aggregates. NDs uptake from cells is also inhomogeneous, and cells with varying amount and clustering of NDs inside were observed. |
615d8f44be107438db93b345 | 11 | This modified wide-field microscope was used to perform spatially-resolved Continuous Wave ODMR (CW-ODMR), a technique to determine the sublevel structure of the ground state. The ground state of the NV center is a spin triplet, with the |𝑔, 𝑚 𝑠 = ±1⟩ state levels upshifted by 2.87 GHz with respect to the |𝑔, 𝑚 𝑠 = 0⟩ state. Continuous irradiation with a 532 nm laser polarizes the |𝑔, 𝑚 𝑠 = 0⟩ ground state level through spin dependent transitions from the excited state through the metastable singlet states. Different laser power levels in the range 1-30 mW are used for this experiment. MW frequency is swept in the 2.75-3.00 GHz region at a fixed power output of 15 dBm to detect 13 C sidebands and NV -central resonances. In fact, when the MWs are resonant with the |𝑔, 𝑚 𝑠 = 0⟩ ↔ |𝑔, 𝑚 𝑠 = ±1⟩ ground state transition, the darker states |𝑔, 𝑚 𝑠 = ±1⟩ become populated, and a drop in the fluorescence (a "dip" in the ODMR spectra) is recorded. The ODMR contrast provides a measure of spin polarization of the |𝑔, 𝑚 𝑠 = 0⟩. However, the ODMR spectrum is also affected by the relative contribution from NV 0 fluorescence, which is not modulated by MW and offsets background fluorescence. An increase in ODMR contrast may thus indicate increased polarization of NV -, or decreased concentration of NV 0 s. The sequence of laser and MW irradiation to perform the ODMR experiments is described in the box of Fig. . |
615d8f44be107438db93b345 | 12 | Fig. show the fluorescence (FL) spectra from the bulk diamond, the 156 nm and the 48 nm NDs. Each NV charge state is characterized by its characteristic fluorescence spectrum, with zero-phonon lines (ZPL) at 575 nm and 638 nm for the NV 0 and NV -, respectively. In addition, a phonon sideband, peaked around 620 nm for the NV 0 and 700 nm for the NV -, is observed, extending up to ≈850 nm in both cases. On average, the two NDs samples presented a lower overall FL than bulk diamond (not apparent in figure , where the spectra are normalized to the NV -ZPL for comparison). Moreover, NDs showed a larger component from the NV 0 s with respect to the bulk diamond (represented as black and light red curves, respectively). This is consistent with the idea that surface effects favor the NV 0 centers, thus affecting the relative concentration of the different charge states. |
615d8f44be107438db93b345 | 13 | Fig show the ODMR spectra of the bulk diamond and NDs at different laser powers (from 1 to 30.5 mW) at constant MW power of 15 dBm. The ODMR spectra show the NV -central lines (AL and AR) and two side bands (BL and BR), the latter related to the hyperfine interaction between the NV -spins and the 13 C nuclear spins . The 13 C sidebands are separated from each other by ~130 MHz, consistently with previously reported values . For all samples, the linewidth of the resonance bands decreases with laser power, in agreement with the linenarrowing effect described by Jensen et al. . Alongside with the increase in signal-to-noise (SNR) ratio, this phenomenon improves resolution of the NV -strain-split doublet (central dips AL and AR). We did not observe any detectable temperature effect on the position of the ODMR resonance that may be caused by absorption of MW or laser power . |
615d8f44be107438db93b345 | 14 | In bulk diamond, a monotonic increase in ODMR contrast with laser power was observed, consistent with increasing NV -polarization levels [Fig. and]. Contrast was calculated as the mean value from the central resonances AL and AR. Interestingly, in NDs, a non-monotonic behavior was observed, as shown in Fig. . Up to 8.1 mW of laser power the ODMR contrast increases. At the highest power levels, the trend is the opposite, with a decrease in contrast systematically observed in different sample regions and for both ND sizes [Fig. ]. |
615d8f44be107438db93b345 | 15 | The inversion in the dependence of ODMR contrast in NDs appears paradoxical, as it would indicate a reduction in NV -spin-polarization with increasing laser power. However, this phenomenon is likely to reflect the different contributions of NV 0 centers in the bulk and ND samples under the various experimental conditions explored here. In fact, we notice that both NV-and NV 0 signals are collected by the broad bandpass filter with a spectral window of 590-800 nm (see Methods). The ODMR contrast is defined as 𝐶 𝑠 = (𝐼 𝑜𝑓𝑓 -𝐼 𝑜𝑛 ) 𝐼 𝑜𝑓𝑓 ⁄ , where 𝐼 𝑜𝑓𝑓 and 𝐼 𝑜𝑛 are the NV -FL intensities with MWs off-and on-resonance, respectively. However, the FL contains a contribution (𝐼 0 ) from the NV 0 centers, which is not modulated by MWs and reduces the contrast by a factor 𝐼 𝑜𝑓𝑓 (𝐼 𝑜𝑓𝑓 + 𝐼 0 ) ⁄ . This reduction factor contrast is very different for bulk and NDs. In the bulk, the vast majority of the NV centers are negative, as shown in Fig. , and remain stable under laser irradiation. Therefore, a stronger laser irradiation results in a better spin initialization and improved ODMR contrast, without impacting on the NV charges (I0 negligible). On the contrary, NDs tend to have higher relative concentrations of NV 0 centers as a result of surface effects (Fig. ). Moreover, under laser irradiation, NV -→ NV 0 photoconversion might be more efficient in NDs due to presence of surface acceptor states that can take a photoexcited electron from NV -. Higher laser powers then result in increasing relative concentrations of NV 0 in NDs, and in a reduction in ODMR contrast. This phenomenon competes with NV -polarization, which increases with laser power, resulting in the non-monotonic behavior shown in Fig. . Therefore, in NDs there is an optimal laser power that should be used to prepare the NV -spin states. Stabilization of the NV -might shift the maximum of curve of Fig. b,c to higher laser power. ) show ODMR spectra at different laser power with fixed MW power. In the ODMR spectra, the NV -central lines (AL and AR) provide a measure of the spin polarization of the |𝑔, 𝑚 𝑠 = 0⟩ ground state. The MW range was set to 2.75-3 GHz to show the NV -central lines and the 13 |
615d8f44be107438db93b345 | 16 | A practical difficulty in assessing the properties of ensembles of NDs is the large variability of the optical response in heterogeneous samples . This has been ascribed to inter-aggregate interactions, size distribution and different efficiency in NV center initialization in ND aggregates . To circumvent this problem, we resorted to use a wide-field fluorescence microscope to spatially resolve ODMR spectra in different parts of the sample. The heterogeneity in ND deposition is apparent in Fig. , where FL images clearly inhomogeneous aggregation and concentration of NDs. ODMR contrast in these samples depends on the selected ROIs, characterized by different levels of FL [Inset Fig. ], with lower variability observed in the 156 nm NDs compared to the 48 nm NDs. Conversely, the ODMR contrast from the bulk diamond is uniform throughout the image. Despite region and sample dependent contrast, our data show consistent trends for NDs in different samples and ROIs, thus suggesting that the effect is robust and reproducible. Charge dynamics and spin properties of NVs also depend on the ND microenvironment. To explore the effects described above in a typical bioassay, we incubated the NDs in cell cultures of macrophages (RAW 264.7). Internalization in macrophages is described in the Methods and illustrated in Fig. . The composite figures on the right show the NDs (orange) internalized in the cells, together with the actine filaments (green) and the nuclei (blue), for both 156 nm NDs (top row) and 48 nm NDs (bottom row) The concentration of the 156 nm NDs in liquid is much higher than that of the 48 nm NDs, resulting in a greater internalization of the larger NDs. Thus, only the results of 156 nm NDs are reported in the following section. |
615d8f44be107438db93b345 | 17 | Fluorescence images were taken to evaluate the different amount of internalization of NDs in different cells. To this end, we extracted the ODMR contrast from ROIs of different size and location [Fig. . Representative examples of ODMRs curves extracted from single-cell ROIs (~6x6 µm) or a cell-aggregates ROI (from ~40x40 µm to ~100x100 µm) are shown in Fig. and Fig. , respectively. Despite some line broadening, compared to the bare NDs, the NV -central bands and 13 C sidebands can still be resolved. As for the previous samples, when increasing the laser power, the linewidth of the resonances decreases with the laser power, while the SNR increases, therefore improving the resolution of the NV -strain split doublet. Also in this case, we do not observe any variation depending on the temperature (i.e., no shift of central resonances), despite a possible MW absorption from the water in the cells or in the biological environment. Fig. shows the evolution of ODMR contrast with laser power for different ROIs. While qualitatively similar, the ODMR contrast dependence on laser power is more variable than the one observed in the bare NDs of Fig. , ranging from a small reduction at the highest laser power, to a plateau-like behavior or even a slight increase. We speculate that this wider heterogeneity may be due to differences in the microenvironment, and particularly to the different pH of various cellular compartments (e.g., pH≈5 in lysosomes compared to pH≈7.2 in the cytoplasm). |
615d8f44be107438db93b345 | 18 | Indeed, pH can affect the functional groups at the ND oxidized surface (carboxylic acids, ketones, alcohols, or esters), thus changing the properties and charge stability of shallow NV centers. At low pH, e.g., carboxylates will be protonated to a much higher extent than under physiological conditions at pH≈7.2, with potential effects on charge state of nearby NV centers. While plausible, this hypothesis requires further investigation. |
615d8f44be107438db93b345 | 19 | We also studied the heterogeneity of the optical properties of NDs in cell in greater detail (Figure e,f), with the help of a simple procedure. Here we acquired two FL images, with MW on-and off-resonance. Taking their difference and then normalizing pixelwise, it is possible to reconstruct an ODMR contrast image (Fig. ). In this ODMR contrast mapping, an average 4.5% contrast is observed. Moreover, parts with a high (red) and a low (blue) ODMR contrast can be imaged within the cell. These regions of low ODMR contrast correspond to cellular compartments where NDs cannot easily access, such as the nuclei. We selected a 1% contrast threshold in the ODMR mapping to cut down the noise. Therefore, wide-field ODMR mapping demonstrates the detection of NV centers in cells with a subcellular spatial resolution that is important for mapping the internalization of NDs in cellular compartments. These results pave the way for real-time, fast, and non-invasive mapping of single and ensemble of NV-enriched NDs in vivo and in vitro cellular environments. |
615d8f44be107438db93b345 | 20 | Our results show markedly different dependencies on high-laser power for the ODMR contrast in bulk diamond and NDs. While contrast and NV -spin polarization steadily increase with laser power in the bulk diamond, with little to no variation across the sample, they show a more complex and heterogeneous behavior in the NDs. In bare as-deposited NDs we observed a decrease in the ODMR contrast at the highest power, reflecting a more efficient NV -→ NV0 photoconversion compared to the bulk, and implying a reduction in the pool of NV -centers. The non-monotonic behavior in NDs is likely to be determined by the interplay between spin and charge dynamics under continuous laser illumination. NDs showed a high tendency to aggregate, forming much more heterogeneous systems than in the homogeneous bulk diamond. For NDs internalized in cells we observed a qualitatively similar trend as in the bare NDs, with a different, more variable behavior at the highest laser power, suggesting that the cellular environment may have a role in the dynamics of NV charges, perhaps due to the different pH or to surface interactions with different proteins in the cytosol. |
615d8f44be107438db93b345 | 21 | In conclusion, the large exposed surface area of NDs is greatly beneficial for sensing applications, e.g. in bioimaging assays, but the effects of surface states and surface interactions on the NV charge stability and photoconversion dynamics must be taken into account. Increasing laser power in the native bulk diamond increases ODMR contrast, a measure of the spin polarization of the ensemble of NV -. Conversely, in NDs, surface effects may limit the benefits of stronger laser power due to photoconversion between different charge states. The effects reported here highlight a trade off in the use of NDs for sensing and polarization transfer applications. |
64e8160b79853bbd785d064b | 0 | Solvatochromism, where the absorption and emission spectra of a chromophore change from gas-phase to solution and from one solvent to another, is a well-known phenomena experimentally. It is a significant factor to consider in the design of organic solar cell materials, fluorescence, chemiluminescence, photoacoustic imaging probes, and other functional organic dyes. Theoretically, it is common to ascribe the spectral changes to various types of chromophore-solvent interactions, especially electrostatics, polarization, and charge-transfer. Computationally, these interactions are described -to a varying degree (as detailed below and in the Appendices) -with continuum solvent models, combined quantum mechanical molecular mechanical (QM/MM) models, and various quantum embedding schemes. In terms of the electrostatics, solvent atoms (both nuclei and electron density) interact Coulombically with the ground-and excitedstate electron density of the chromophore, ρ ref m (r), and the nuclei at their reference environment (such as gas-phase). The polarization effects include (a) the "forward" (i.e. solvent→chromophore) polarization, where solvent charges polarize the chromophore molecular orbitals, ψ ref i (r) + δ ψ i (r), and the ground-and excited-state electron density, ρ ref m (r) + δ ρ m (r), and (b) the "backward" (i.e. chromophore→solvent) polarization, where the chromophore polarizes the solvent electronic structure. As summarized in Appendices A and B, these electrostatic and polarization interactions are captured, implicitly or explicitly, by continuum solvent models and QM/MM models. |
64e8160b79853bbd785d064b | 1 | Beyond electrostatic and polarization interactions between the chromophore and solvent molecules, charge transfer can also occur upon the chromophore excitation/de-excitation. One can imagine two mechanisms for such a charge transfer to occur: (a) The frontier orbitals of the chromophore can entangle with solvent orbitals, causing them to spread over to the solvent (similar to the spillover of chromophore orbitals to substituent groups ) and introducing partial charge transfer if the solvent involvement differs between the initial and final electronic states; and (b) An electronic transition within the chromophore (i.e. local excitation/deexcitation) gets superimposed with a chromophore→solvent or solvent→chromophore electronic transition. Clearly, these mechanisms, with one based on the mixing of one-electron fragment orbitals while the other on the superposition of many-electron electronic configurations, are not mutually exclusive. Neither mechanism, however, has been accounted for in existing continuum solvent or QM/MM models, because no orbitals are placed on the solvent molecules within these models. |
64e8160b79853bbd785d064b | 2 | A deeper perspective on the aforementioned charge transfer mechanisms can lead to charge-transfer corrections, if feasible at all, to QM/MM predictions of solvated chromophore excitation/deexcitation. Towards this, we outline our recent deployment of two quantum mechanical embedding schemes -density matrix embedding theory (DMET) and absolutely localized molecular orbitals (ALMO) -to explore mechanism a above (i.e. chromophore-solvent orbital entanglement). The ALMO analysis will also shed light into mechanism b. We stress that many other quantum embedding models have been developed over the years, some of which are potentially also well-suited for a detailed analysis of orbital entanglement and charge transfer. |
64e8160b79853bbd785d064b | 3 | We will use two biochromophores as examples: oxyluciferin (OLU -), which gives rise to firefly's bioluminescence, and phydroxybenzyledene imidazolinone (pHBDI -), a synthesized analog of the chromophore in green fluorescence protein. For both chromophores, a single molecular anion is solvated in a rectangular box with around 1600 water molecules and a counter ion. From a 100 ps NVT simulations (at 300 K), 100 frames are collected at equal intervals. The canonical molecular orbitals (MOs) obtained from KS-DFT calculations 42-44 at the ωB97X-D/6-311++G(d,p) level for a representative configuration of either anionic chromophore together with 30 closest water molecules are shown in Fig. . One can see that HOMO and LUMO of both chromophore-water complexes are located mostly on the chromophore, with a small contribution from a couple of solvent molecules. In contrast, the LUMO+1 of pHBDI -is primarily localized on the solvent molecules with a small contribution from the chromophore. These are the key orbitals involved in the lowest-energy excitation of the respective solvated chromophore based on the time-dependent density functional theory within the Tamm-Dancoff approximation (TDDFT/TDA). Table : Weights of KS-DFT frontier orbitals of OLU -and pHBDI -, both in a representative solvent configuration with 30 water molecules. Full-system DFT calculations were performed using the ωB97X-D functional and 6-311++G(d,p) basis. Weights w and w ′ were computed in the standard and Löwdin-orthogonalized atomic basis, respectively. The subscript A refers to the chromophore, E the solvent molecules, and AE the chromophore-solvent coupling. |
64e8160b79853bbd785d064b | 4 | OLU - pHBDI - To quantify the entanglement of chromophore and solvent atomic orbitals in each of the frontier orbitals (p) of solvated chromophores, we employe equations in Appendix C to obtain the weights of these frontier orbitals from basis functions on the chromophore (w In Table , the weights are clearly more intuitive in the Löwdin basis, for which the values are consistently between 0 and 1. Meanwhile, all chromophore-solvent weights (w ′ AE ) vanish due to the orthogonality between Löwdin basis functions on the chromophore and those on solvent molecules. Essentially, each frontier orbital can be written as |
64e8160b79853bbd785d064b | 5 | where χ p A and χ p E are normalized linear combinations of Löwdin basis functions on the chromophore and solvent molecules, respectively, and properly reflect the phase difference between the two fragments for the p-th molecular orbital. As argued later in Sec. 3.A below, w ′p A w ′p E measures the degree of fragment orbital entanglement for the molecular orbital ψ p . |
64e8160b79853bbd785d064b | 6 | For the two solvated chromophores, one can perform QM/MM calculations with TDDFT/TDA applied to the QM region. Here we investigate two MM descriptions of water: (i) the non-polarizable TIP3P model, and (ii) the effective fragment potential (EFP) for water, which is a polarizable MM model. In the case of EFP, the excitation energies are collected without the polarization correction (denoted as TDA/EFP0) and with the correction (denoted as TDA/EFP). As shown in Fig. , TDA/MM models consistently overestimate the lowest vertical excitation energy with an RMSD of 0.1 eV or greater for both biochromophores in 100 representative solvent configurations. In terms of r 2 value, a better correlation between TDA/MM and full-TDA excitation energies is obtained for OLU -with both MM models, which might be related to the partici- and) pHBDI -anions in 30 water molecules compared against TDA excitation energies for the full chromophore-solvent complexes. TDA/EFP0 and TDDFT/EFP results were obtained without and with the polarization correction. For both biochromophores, 100 solvent configurations were collected from a 100 ps NVT trajectory. TDA calculations were performed using the ωB97X-D functional and 6-311++G(d,p) basis set. The red asterisks indicate the TDDFT/TDA excitation energy of each chromophore in the gas phase. |
64e8160b79853bbd785d064b | 7 | pation of the solvent-delocalized LUMO+1 orbital in the S 1 state of pHBDI -. Additionally, we note that despite the systematic overestimation, TDA/EFP captures the span of the excitation energy better compared to TDA/TIP3P, as indicated by the fitted lines (red) that are more parallel to the diagonals of the parity plots in Fig. . |
64e8160b79853bbd785d064b | 8 | Figure compares the HOMO/LUMO energies and HOMO-LUMO gaps obtained from DFT/TIP3P and DFT/EFP calculations with those from full-system DFT calculations. Overall, the two DFT/MM schemes worked reasonably well in capturing the frontier orbital energies of OLU -in water (see the left two columns in Fig. ). However, as shown in Figs. and, both DFT/MM schemes failed to accurately capture the LUMO energies of the pHBDI --water complexes (and consequently the HOMO-LUMO gaps). Since the pHBDI --water system features relatively closelying LUMO and LUMO+1, we speculate that in some frames, the LUMO of the system may exhibit a greater degree of chromophoresolvent orbital entanglement than indicated by the values of w ′p A and w ′p E in Table , leading to the inadequacy of the DFT/MM models. |
64e8160b79853bbd785d064b | 9 | In the DMET scheme, one adopts an orthonormal atomic basis (such as the Löwdin basis used in here) and divides the basis functions according to the fragment they reside on: those on the impurity (ϕ µ ∈ A, chromophore in the context of this article), and those on its environment (ϕ ν ∈ E, solvent molecules). Let us write the occupied orbitals from full-system KS-DFT calculations as |
64e8160b79853bbd785d064b | 10 | One can regard B ′ AE = ∑ K k=1 λ 2 k (sum of square of singular values in Λ Λ Λ) as the effective degree of chromophore-solvent entanglement associated with the particular density matrix P being analyzed. As shown in Appendix D, B ′ AE is essentially the Mayer "bond order" between the two fragments. |
64e8160b79853bbd785d064b | 11 | Typically, with a large number of solvent molecules, the bath orbitals in Eq. ( ) only span a small subspace of solvent orbitals. The remaining subspace consists of core orbitals ( occupied solvent orbitals that are not entangled with chromophore ones) and virtual orbitals (χ d = ∑ ν∈E V v νd ϕ ν ). With the partitioning of the solvent orbitals into bath, core, and virtual orbitals, the density matrix undergoes a unitary transformation, |
64e8160b79853bbd785d064b | 12 | Using the PySCF software, we would generalize DMET in two ways to facilitate the analysis of chromophore-solvent orbital entanglement. The first generalization is for the density matrix in Eq. ( ) to include extra contributions from the lowest n virtual or-Figure : TDA-ωB97X-D/6-311++G(d,p) excitation energies (in eV) within the embedding orbital (eo) basis for the S 1 state of the OLU - (panels A-F) and pHBDI -(panels G-L) anions, both in 30 water molecules. The embedding orbitals were obtained from the P 0 , P +1 , P +2 , P +5 , P +20 , and P max density matrices, respectively, following the DMET scheme. For P max , the number of virtual orbitals added is equal to the number of nearly zero singular values of P AE 0 . The red asterisks indicate the gas-phase excitation energy for each biochromophore. bitals of the chromophore-solvent complex, |
64e8160b79853bbd785d064b | 13 | where σ and σ ′ are indexes of AO basis functions on either the chromophore or solvent molecules, C σ i and C σ a are coefficients of canonical occupied and virtual SCF orbitals of the chromophoresolvent complex, respectively, namely eigenvectors of the groundstate Fock matrix in Eq. ( ). When n is equal to 0, Eq. ( ) produces the normal ground-state density matrix, P +0 = P 0 . |
64e8160b79853bbd785d064b | 14 | If n is greater than 0, one can interpret the corresponding P +n as the density matrix for the (2n + 1) -anion of the two chromophoresolvent complex, with molecular orbitals taken from DFT calculations for the singly anionic complex. The inclusion of low-lying virtual orbitals of the complex in the construction of the generalized density matrix P +n allows us to not only identify bath orbitals that entangle with the chromophore occupied orbitals but also more precisely capture those entangled with the low-lying virtual orbitals of the chromophore, both of which are expected to be essential for an accurate description of the excitation/de-excitation of a solvated chromophore. |
64e8160b79853bbd785d064b | 15 | The second generalization is to perform TDDFT/TDA calculations in the basis of embedding orbitals. The required occupied/virtual orbitals and their energies can be readily obtained by diagonalizing the Fock matrix in Eq. (11). The corresponding TDDFT/TDA excited states can then be solved for iteratively, where the main computationally intensive tasks are the evaluation of 2-electron repulsion integrals and exchange-correlation response kernel, 56 ∂ 2 f xc ∂ ξ ∂ ξ ′ , (where ξ and ξ ′ refer to alpha/beta electron densities and their gradients, ρ α , ρ β , ρ x α , ρ y α , ρ z α , ρ x β , ρ y β , ρ z β ) based on the ground-state electron density of the entire chromophore-solvent complex, as well as their contractions with the trial vectors. In general, the bath orbitals are expected to be localized on solvent molecules close to the impurity. In our pilot implementation of the eo-TDA method, however, such locality has not been utilized to enable an efficient numerical integration on the atomic grid. |
64e8160b79853bbd785d064b | 16 | As shown in Table , the HOMO energy of both OLU -and pHBDI -are reasonably accurate from eo-DFT calculations, with an error of 2.0-5.0 × 10 -7 eV for the anions in a representative solvent configuration. The LUMO energy, on the other hand, are off by 0.0415 and 0.187 eV, respectively, from eo-DFT(P 0 ) based on a standard ground-state density matrix. As shown in the 3rd and 5th columns of Table , these errors fall to the order of 10 -6 or 10 -7 eV once one or more virtual orbitals of the chromophore-solvent com-plex is added to the computation of the density matrix. LUMO+1, which contributes substantially to the S 1 excitation of pHBDI -, requires the density matrix to be augmented by contributions from at least two virtual orbitals as one would expect. |
64e8160b79853bbd785d064b | 17 | Regarding the excitation energies, an average error of 0.079/0.088 eV and r 2 value of 0.99/0.97 are obtained by eo-TDA calculations based on the ground-state density matrix for OLU - and pHBDI -, respectively, as shown in Figs. and. For these solvated chromophores, eo-TDA(P 0 ) is thus more accurate than TDA/TIP3P and TDA/EFP, which is not surprising because of an improved description of frontier orbitals. [Such an improved accuracy come with a much higher computational cost, though, due to the need of performing first full-system DFT and then eo-TDA calculations with orbitals extending beyond the impurity.] The excitation energy errors of eo-TDA calculations could be further lowered to 0.041 and 0.066 eV (Figs. and), when the eo density matrix is augmented with the contribution from only one virtual orbital. However, these errors decay rather slowly with the further addition of virtual orbitals, reaching only 0.034 and 0.035 eV with the eo-TDA(P +20 ) calculations (Figs. and). This is expected because TDDFT and TDA calculations often involve excitations into higher virtuals with small amplitudes but nevertheless non-negligible perturbations to the excitation energies. As shown in Figs. and, at the limit where a maximum number of virtuals (i.e. the number of nearly zero singular values of P AE 0 ) are included, the net errors are reduced to 0.016 and 0.014 eV for OLU -and pHBDI -, respectively. |
64e8160b79853bbd785d064b | 18 | The generalized DMET scheme and the eo-TDA method introduced above offer a "top-down" approach to understanding the effects of chromophore-solvent orbital entanglement on excitation energies. In this section, we utilize a "bottom-up" alternative based on absolutely localized molecular orbitals (ALMOs) to demonstrate the orbital entanglement effects from a different perspective. Specifically, we employ ALMO-TDA calculations with varying active spaces to assess how the excitations on solvent molecules, as well as the chromophore→solvent and solvent→chromophore charge-transfer excitations impact the S 1 excitation energy of the chromophore when these excitations are superimposed. The ALMO-TDA method, which is the TDDFT/TDA extension of the ALMO-CIS method, was originally proposed to calculate the absorption spectra of large molecular clusters. This method The top row (A) shows the transitions between occupied (O) and virtual (V) orbitals involved in the ALMO-TDA model that gives the results in panels (B) and (C) below, where "C" and "S" denote chromophore and solvent molecules, respectively. In panels (B) and (C), the excitation energies (100 frames for each chromophore) obtained from ALMO-TDA calculations with different active spaces are plotted against the the full-system TDDFT/TDA excitation energies. The root-mean-square deviations (RMSD) and the R 2 values from linear fitting are reported. The ALMO-TDA and full-system TDA calculations were performed at the ωB97X-D/6-31G(d,p) level. |
64e8160b79853bbd785d064b | 19 | has played a central role in the ALMO-based energy decomposition analysis scheme for excited-state intermolecular complexes (i.e., exciplexes and excimers). The reference orbitals for an ALMO-TDA calculation are prepared via the variational optimization of ALMOs, i.e., minimization of the KS-DFT energy with respect to the MO coefficient matrix (C) subject to the constraint that C is block-diagonal by fragments. This procedure is also known as "self-consistent field for molecular interactions" (SCF-MI), and "blocked localized wavefunction" (BLW). With the ALMOs prepared, a singly excited state under the ALMO-TDA framework can be represented as |
64e8160b79853bbd785d064b | 20 | Note that for brevity, the fragment tags of the molecular orbitals have been omitted in the above equation. The S matrix on the right-hand side is defined as the Kronecker product of the o-o and v-v overlap matrices: S ia, jb = S i j ⊗ S ab , which arises from the inter-fragment non-orthogonality of the ALMOs. The A matrix on the left-hand side is defined as |
64e8160b79853bbd785d064b | 21 | where F ab and F i j can be obtained by transforming the AO Fock matrix (constructed using the one-partical density matrix associated with the converged ALMO state) into the ALMO basis. The twoelectron integrals, including the contribution from the XC kernel, can be computed in the same way as in standard TDDFT/TDA calculations. Note that c HF denotes the percentage of exact exchange in the employed functional. For a pure functional, c HF = 0, while in the case of CIS, c HF = 1, and the last term in Eq. ( ) vanishes. |
64e8160b79853bbd785d064b | 22 | In the original ALMO-CIS/TDA formalism, fragment indices X = Y is enforced in Eq. ( ) such that the full-system excitations are represented as the superposition of many absolutely localized on-fragment excitations. An extension that incorporates charge-transfer excitations to or from nearby fragments was proposed later. Here we employ a fully generalized version of this method: taking advantage of the fragment tags of occupied and virtual orbitals, one can include each fragment's occupied and/or virtual orbitals in the active space for single excitations. In the end, the amplitudes t XiYa may include a mixture of on-fragment and interfragment occupied→virtual transitions. This generalized ALMO-TDA scheme, which has been implemented in the Q-Chem software package, allow us to shed light on the orbital entanglement effects from an alternative perspective. |
64e8160b79853bbd785d064b | 23 | 4.B Results of ALMO-TDA calculations for solvated OLU -and pHBDI - Figure shows the comparison of ALMO-TDA results with varying active-space definitions for the water-solvated OLU -and pHBDI - chromophores (100 frames for each; each frame contains 30 water molecules) when plotted against the full-system TDA results. Here the ALMO-EDA calculations with an intuitive partition of the system, with the chromophore being one fragment and all 30 water molecules as the other. Since the ALMO-TDA method is currently limited to systems without inter-fragment linear dependency among the basis functions, a smaller basis set without diffuse functions, 6-31G(d,p), is used for the full-system and ALMO-TDA calculations. |
64e8160b79853bbd785d064b | 24 | , where the local excitation on chromophore is coupled to solvent→chromophore charge-transfer excitations; (v) full ALMO-TDA+CT, where all the possible local and chargetransfer excitations are incorporated. From a bottom-up view, the contrast between (iii) and (i) should be able to indicate the changes in excitation energies due to the entanglement of virtual orbitals (V C and V S ), while the contrast between (iv) and (i) should correspond to the effect of occupied orbital entanglement (O C and O S ). |
64e8160b79853bbd785d064b | 25 | For OLU -solvated in water (Fig. ), schemes (i)-(iii) produce visually similar results, although marginal improvement in the accuracy relative to full-system TDA results is obtained as the active space increases, as indicated by the reduced RMSD values. In contrast, significant improved agreement with the full-system TDA results is obtained by adding the solvent→chromophore chargetransfer excitations to the active space (scheme (iv)), reducing the RMSD from 0.258 to 0.032 eV. Based on our argument above, these results highlight the significance of capturing the entanglement between the occupied orbitals on the chromophore and solvent molecules for the accurate modeling of the S 1 excited state of the solvated OLU -. Interestingly, the "fully entangled" ALMO-TDA+CT model (scheme (v)) systematically overshoots the full-system TDA results, yielding lower excitation energies with a mean-signed error of -0.064 eV and a larger RMSD of 0.065 eV than that given by scheme (iv). While not entirely expected, this is possible since ALMO-TDA and full-system TDA are two linearresponse excited-state methods that use different reference orbitals. There is no variational principle to ensure that the excitation energies provided by full-system TDA must be lower than those obtained from ALMO-TDA. |
64e8160b79853bbd785d064b | 26 | Moving onto the results for solvated pHBDI -(Fig. ), some differences from the OLU -results are observed. While the inclusion of excitonic couplings between the local excitations on the chromophore and solvent molecules results in a similar redshift of ALMO-TDA excitation energies by ∼0.05 eV (comparing scheme (ii) against (i)), the addition of chromophore→solvent charge-transfer excitations to the active space makes a greater difference compared to the previous OLU -case, as indicated by a more substantial reduction in the RMSD by 0.075 eV. On the other hand, incorporating only the entanglement between chromophoresolvent occupied orbitals reduces the RMSD by approximately half, from 0.208 to 0.109 eV, which is not as accurate as the results provided by scheme (iv) for the OLU -case. These results are consistent with our earlier speculation that incorporating the entanglement of virtual models on the chromophore and solvent molecules may play a more vital role in accurately describing the lowest-lying excited state of solvated pHBDI -compared to the OLU -case. With the entanglement of both occupied and virtual orbitals taken into account (scheme (v)), excellent agreement with the full-system TDA results is achieved for pHBDI -in water, with an RMSD of 0.026 eV. |
64e8160b79853bbd785d064b | 27 | • Conventional QM/MM schemes, such as those combining TDDFT/TDA with the TIP3P fixed-charge and the EFP polarizable force fields for the water solvent, tend to systematically overestimate the vertical excitation energies by 0.1 eV or more for these two biochromphores, when compared against full-system TDDFT/TDA values. Such an overestimation is largely caused by the entanglement of both occupied and virtual orbitals of the chromophore to those of nearby solvent molecules. |
64e8160b79853bbd785d064b | 28 | • TDDFT/TDA calculations in the subspace of standard DMET embedding orbitals yield slightly more accurate excitation energies (and higher r 2 values) than TDA/TIP3P and TDA/EFP models, confirming the importance of entangling the occupied orbitals on the chromophore and solvent molecules. However, for a further better description of the virtual space, one needs to utilize a generalized density matrix that is augmented by contributions from full-system virtual orbitals to acquire the DMET bath orbitals, thus highlighting the key role of entanglement between the virtual orbitals on the chromophore and solvent molecules. The entanglement between chromophore and solvent virtual orbitals plays a particularly important role for pHBDI -. |
64e8160b79853bbd785d064b | 29 | • ALMO-TDA calculations with varying active spaces further indirectly reaffirm the key role of the coupling between chromophore and solvent orbitals. In line with the TDDFT/TDA results using the DMET embedding orbitals, occupied-occupied coupling dominates in the case of OLU -, while virtual-virtual coupling plays a more important role in the pHBDI -case. |
64e8160b79853bbd785d064b | 30 | Through sharing these observations, we hope to inspire future employment of DMET with standard and generalized density matrices as a diagnosis tool for thoroughly analyzing the entanglement between chromophore and solvent orbitals. Such analysis can potentially help researchers (i) identify solvent molecules to be explicitly included in the QM region, and (ii) develop empirical models beyond simple electrostatic or polarizable embedding to capture the orbital entanglement and charge transfer effects between chromophore and solvent molecules. These advances will be crucial for further improving the accuracy of TDDFT/MM excitation energies in complex environments. |
64e8160b79853bbd785d064b | 31 | Apparent Surface Charge models (such as PCM, COSMO, and SMD 66 ) adopt a coarse-grained description of solvent molecules as a set of surrogate charges qs -screening charges on the tessellated chromophore molecular surface (s). In an oversimplified interpretation, those screening charges can be regarded as those partially or nearly completely -depending on the solvent optical and static dielectric constants -cancel out the electrostatic potential of the chromophore electron density on the surface ϕ |
64e8160b79853bbd785d064b | 32 | that connects to the Generalized-Born models for solvation, where the Coulombic interaction of one chromophore atomic charge with another is damped by the implicit solvent. To the extent that the optical dielectric constant portion of solvent response (i.e. fast solvent degrees of freedom) is always accounted for in the modeling of molecular absorption and emission, implicit-solvent models also capture the chromophore→solvent polarization (i.e. "backward" polarization) whereby the chromophore polarizes the solvent electron density through the surrogate screening charges. |
64e8160b79853bbd785d064b | 33 | The QM/MM models capture the chromophore-solvent electrostatic interaction and solvent→chromophore polarization explicitly through electrostatic embedding. If a non-polarizable force field description (such as TIPnP) is adopted for the solvent molecules, then each solvent molecule acquire several or more fixed-value point charges. Together, the solvent point charges provide an electrostatic embedding potential that interacts with and polarizes the chromophore electron density. |
64e8160b79853bbd785d064b | 34 | The chromophore→solvent polarization can be enabled by describing the solvent molecules with polarizable force fields, such as Drude oscillator models, induced dipole models, and fluctuatingcharge-and-induced-dipole models, leading to polarizable embedding. Similar to the continuum solvent models, there is a subtlety in polarizable embedding models as to whether the solvent response (e.g. Drude particle positions, fluctuating charges, and in-duced dipoles) is tied to the initial or final electronic state of the chromophore during the electronic excitation/de-excitation. |
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