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65fc0a5166c138172975afd1 | 10 | The X-ray photoelectron spectroscopy (XPS) measurements were performed directly after exposure of the examined alloys to the 0.05 M NaCl containing 150 mM of the molybdate inhibitor for 1 h. A ThermoFisher Scientific Escalab 250Xi spectrometer, equipped with an Al Kα X-Ray source (spot size 250 μm), operating at a pass energy of 10 eV, was used. Before measurements, samples were thoroughly rinsed with deionized water, air dried, and transferred to a vacuum chamber within 10 min to avoid oxidation. The binding energy values were charge-corrected to the carbon C 1s excitation (284.6 eV). |
65fc0a5166c138172975afd1 | 11 | All solutions for corrosion studies were prepared with NaCl (≥99.5) and Na2MoO4 × 2H2O (≥99.5) received from Chemsolute (Th. Geyer Polska) using deionized water with a resistivity of 18.2 MΩ cm. As a reference corrosion medium, 0.05 M NaCl solution was selected. This concentration of salt prevents rapid degradation of Mg alloys and was previously used in our studies of inorganic corrosion inhibitors of Mg and Al alloys . The effectiveness of the molybdate inhibitor was examined in 0.05 M NaCl with the concentration of the inhibitor varying in the range of 10-150 mM. |
65fc0a5166c138172975afd1 | 12 | Classical electrochemical experiments were carried out on an Autolab PGSTAT302N potentiostat/galvanostat with an FRA32M module for electrochemical impedance spectroscopy (EIS) measurements. The measurements were performed in the following order: the open-circuit potential (OCP) monitoring (1000 s), EIS measurement, low-amplitude polarization resistance measurement, and potentiodynamic polarization measurement. A traditional three-electrode setup with a saturated Ag/AgCl reference electrode and a Pt-mesh counter electrode was used. EIS measurements were carried out at the OCP over a frequency range from 10 5 to 10 -2 Hz using a current sinusoidal perturbation amplitude of 10 mV. The ZView 3.2с software was used for data analysis and spectra fitting. |
65fc0a5166c138172975afd1 | 13 | The multisine dynamic electrochemical impedance spectroscopy (g-DEIS) monitoring was performed using a two-channel Biologic SP-300 potentiostat connected to a PXI-4464 AC measurement card and a PXI-6124 AC/DC signal module. Since the dynamic nature of the g-DEIS measurement, spectra were recorded in a narrower frequency range of 22 kHz-0.7 Hz with 10 points per frequency decade. To evaluate the protective ability of the molybdate inhibitor depending on its concentration, a Lead Fluid peristaltic micropump was used. In this case, during the first 600 s of the experiment, g-DEIS spectra were recorded in a 0.05 M NaCl solution without the inhibitor. After this, the concentrated solution of the molybdate inhibitor was gradually introduced into the measured system by the peristaltic pump for 3000 s to achieve the final concentration of the inhibitor in the examined solution of 150 mM. The measurement was then continued for 600 s in the solution containing 150 mM of the inhibitor (Fig. in Supplementary Information). These data were also used to plot the adsorption isotherms. Further details on the experimental setup and the measurement conditions are reported elsewhere . The fitting of the obtained impedance spectra was performed based on the Nelder-Mead algorithm . |
65fc0a5166c138172975afd1 | 14 | The results of XRD analysis of obtained AZ31-xLi alloys are shown in Fig. . The obtained data indicate that the AZ31-4Li mostly consists of an HCP structured a-Mg phase (α-Mg). An increase in the lithium content leads to a shift of α-Mg reflexes to larger 2θ , and the occurrence of the reflexes corresponding to a BCC β-Li phase, which dominates in the case of the AZ31-12Li alloy. XRD patterns of all alloys also have low-intensity reflexes at 2θ ca. 23 and 40°. The AZseries Mg alloys usually have Mg-Al, Al-Mn, and Al-Mn-Zn IMPs . Recently, Znang et al. The surface microstructure of the obtained alloys was examined by SEM, as can be seen in Fig. . The amount of Li plays a decisive role in the microstructure of the obtained alloys. The direct use of the EDX analysis for the detection of lithium and examination of its surface distribution is not possible as more advanced techniques should be used . Therefore, in the qualitative analysis of the microstructure of the AZ31-хLi alloys, the phase assignments were based on the possibilities of the electron backscattering mode of the SEM. In this case, the lighter areas correspond to elements with a higher atomic number (α-Mg), and the darker areas correspond to elements with a lower atomic number (β-Li) . The principal constituents of the AZ31-4Li alloy are IMPs distributed in the α-Mg alloy matrix (Fig. ). The size of the IMPs does not exceed 10 µm. In the case of the AZ31-8Li alloy (Fig. ), two main phases α-Mg (lighter regions) and β-Li (darker regions) with increased number of IMPs. The AZ31-12Li alloy (Fig. ) mostly contains the β-Li phase with a further increased number of IMPs. The observed microstructures also support the results of the XRD analysis (Fig. ) and the formation of Al-Li-type IMPs in these Mg alloys. In each panel, areas marked with numbers correspond to points of EDX analysis listed in Table The quantitative EDX analysis of the characteristic surface constituents (Fig. , Table ) The difference between the relative electronegativity between Mg and Mn is 0.24. Therefore, the formation of Mg-Mn IMPs is more expected than Mg-Al, which is also supported by the XRD data . |
65fc0a5166c138172975afd1 | 15 | The dynamics of changes in the pH and OCP of the examined alloys in 0.05 M NaCl solutions with varying amounts of sodium molybdate inhibitor are shown in Fig. . In each condition, both parameters were followed for 1000 s. The initial value of pH of the 0.05 M NaCl solution without the inhibitor was around 6.7. In this media, a pronounced increase in the bulk pH with time was observed with an increase in the amount of Li in the alloys. This trend can be associated with the initiation of the corrosion process and the tendency of the alloy to corrode . |
65fc0a5166c138172975afd1 | 16 | After 1000 s of exposure of AZ31-4Li, AZ31-8Li, and AZ31-12Li to the 0.05 M NaCl solution without the inhibitor, the pH values increased to 7.2, 7.7, and 9.2, respectively (Fig. ). The introduction of Na2MoO4 into the 0.05 M NaCl solution increased the initial pH of the solution. This is due to the molybdic acid is a weak acid (pKa = 6) and its salts are hydrolyzed in aqueous solutions. In the presence of 10 and 50 mM of the molybdate inhibitor, pH values were rapidly increasing, suggesting activation of the corrosion process in time. In turn, at higher concentrations of the molybdate in the solution pH remained quite stable in time, which is a sign of improved corrosion resistance and retardation of the corrosion process. |
65fc0a5166c138172975afd1 | 17 | The OCP profiles (Fig. ) showed similar tendencies. The lowest values of the OCP were observed in the 0.05 M NaCl solution without the inhibitor. In the presence of the molybdate inhibitor, the OCP was shifted to more positive values at the outset of the exposure of all alloys, suggesting rapid adsorption of molybdate ions on the surface and the retardation of the anodic process . At low concentrations of the inhibitor (10 mM), some small but distinct potential fluctuations were observed for the AZ31-8Li sample, which might be a sign of a less stable surface film and local corrosion attack. The value of the stabilized OCP increased with increasing the molybdate concentration in the solution. The OCP profiles suggest that at high concentrations the molybdate inhibitor rapidly forms a stable film over the surface of all examined alloys, which shifts the electrode potential in the noble direction. retardation of anodic kinetics and improved corrosion resistance. However, in this case, it was followed with an almost an order of magnitude increase in the icorr values. This inconsistency can be explained by either different phase composition of the alloys' matrix, i.e. different thermodynamic probability of corrosion, or the so-called cathodic activation phenomenon, observed in the course of corrosion of Mg alloys . The comparison of anodic and cathodic Tafel slopes (Table ) shows that corrosion kinetics is mostly controlled by the cathodic process and anodic reaction has little impact on the OCP . The polarization curves obtained in molybdate-containing 0.05 M NaCl solutions showed a notable change in the kinetics of the anodic and cathodic processes. The corrosion potential was shifted towards more noble values in the presence of the inhibitor. This shift was larger as the concentration of the inhibitor in the solution increased and, in this case, was directly associated with the interaction of the molybdate inhibitor with the surface of the alloys and retardation of the corrosion kinetics. The maximum difference between Ecorr in the inhibited and reference solutions decreased as the amount of Li in the alloy increased and was ca. 140, 100, and 65 mV for AZ31-4Li, AZ31-8Li, and AZ31-12Li alloys, respectively. Furthermore, starting from 50 mM of added molybdate it was possible to mark the change in the slope on the anodic branches of the polarization curves recorded for AZ31-8Li, and AZ31-12Li alloys, corresponding to the breakdown potential, Ebr. This provides additional evidence for the formation of a protective layer on the surface under these conditions. |
65fc0a5166c138172975afd1 | 18 | The analysis of the anodic Tafel slope, ba, showed a notable increase in the slope values in inhibited solutions for all studied alloys (Table ). The calculated values of icorr at low concentrations of the inhibitor (10 mM of Na2MoO4) increased for all examined alloys. This indicates that at low concentrations aqueous molybdate is not able to effectively passivate all active surface sites. This results in an increased current density over unprotected areas and, consequently, an increased corrosion rate. The same behavior was previously observed for the WE43 and AZ31 alloys in the case of the molybdate and permanganate inhibitors . At higher added concentrations, Na2MoO4 caused a pronounced decrease in icorr. The highest IE calculated by Eq. ( ) was 93-97% in solutions containing 150 mM of the inhibitor. However, the Tafel analysis of polarization curves in the case of the Mg alloys is not always straightforward. Therefore, to compare the effectiveness of the inhibition by molybdate, the values of the current densities iа and ic were extracted at selected potentials of -1.10 and -1.45 V, respectively, laying on anodic and cathodic branches of polarization curves. The anodic current densities decreased two orders of magnitude (150 mM of Na2MoO4), giving clear evidence of the corrosion inhibition due to the presence of the inhibitor. |
65fc0a5166c138172975afd1 | 19 | The obtained values of Rp and IE values calculated on Eq. ( ) are shown in Fig. . As for the polarization data described above, low concentrations of the molybdate inhibitor (10 mM) resulted in a decrease of Rp. At higher concentrations of Na2MoO4, the values of Rp were gradually increasing reaching the maximum in 0.05 NaCl solution with 150 mM of Na2MoO4. The obtained values of the inhibition efficiency (Eq. ( )) were similar to those of the potentiodynamic measurements. The EIS data were analyzed and fitted following the approach proposed in and used in our previous publications . To minimize the possible overestimation of the corrosion resistance and fitting error, the fitting was performed by the equivalent circuit shown in Fig. . |
65fc0a5166c138172975afd1 | 20 | The inductive response at low frequencies was taken into account in all spectra. In this circuit, Rs is the solution resistance, R1 is the charge transfer resistance, CPE1 is the constant phase element describing the double layer capacitance, R2 is the resistance of surface oxide or adsorbates, and L is the inductance . The constant phase element (CPE) was used to assign the capacitive response of a non-uniform surface. The impedance of CPE can be expressed as: |
65fc0a5166c138172975afd1 | 21 | The results of the spectra fitting are summarized in Table . It can be seen that both R1 and R2 parameters increased significantly compared to the uninhibited solution as the concentration of the inhibitor in the solution was 50 mM or more. Table . Fitting data extracted from EIS measurements with a standard deviation of three measurements and calculated inhibition efficiency Concentration of inhibitor, mM The quantitative assessment of IE based on the EIS data can be performed using Eq. and Rct or Rp values and the difference between them is marked in Fig. and in Table . From EIS spectra, Rct can be assigned as the impedance value when Z" → 0, while Rp can be estimated as the low-frequency intersection of the total impedance with the abscissa when the frequency f → 0. |
65fc0a5166c138172975afd1 | 22 | The classical EIS analysis showed that a low-frequency inductive loop was clearly visible in the Nyquist spectra in all examined conditions, showing a great difference between impedance values based on Rct and Rp. In this case, the inductive property is often associated with the relaxation processes of adsorbed intermediates of the corrosion process . However, to provide a reliable EIS measurement the system must fulfill three main requirements, namely, stationarity, linearity, and causality. Classical EIS measurements of Mg alloys' corrosion are often largely affected by the system's non-stationarity , which might cause the occurrence of the low-frequency inductive tail . Therefore, dynamic g-DEIS measurements were also performed. In the selected frequency interval (22000-0.7 Hz) the measurement time is less than 1 s, which allows to perform the measurement in quasi-stationary conditions . The g-DEIS spectra of AZ31-xLi alloys obtained in the solutions with and without the molybdate inhibitor during 70 minutes of immersion are shown in Fig. . |
65fc0a5166c138172975afd1 | 23 | The results obtained in the 0.05 M NaCl solution (Fig. ) without the inhibitor showed similar behavior for all alloys. At each point of the measurement, the Nyquist spectra display dispersed capacitive loops. The content of Li in the examined Mg alloys to some extent affects the corrosion kinetics, represented by the shape of the impedance spectra, and has a crucial impact on the radii of the Nyquist spectra in time. A comparison of the g-DEIS spectra obtained at the same immersion time revealed higher corrosion resistance of the alloy with lower amounts of Li. For all alloys, the radii of the g-DEIS spectra decreased with immersion time, showing high corrosion rates and low corrosion resistance of the formed surface films of corrosion products. After 2000 s, the radii and shape of the spectra are comparable for all alloys (Fig. ), suggesting that the surface of the alloys is covered with a layer of corrosion products, which to some extinction decreases corrosion rate. To further examine the protective action of sodium molybdate, it was gradually added into the 0.05 M NaCl solution after initial pre-exposure for 10 min in the non-inhibited solution (Fig. ). The introduction of the molybdate inhibitor significantly increases the radii of the g-DEIS spectra of all studied alloys. It suggests rapid adsorption of the inhibitor on the surface with the formation of a protective layer, which suppresses the active corrosion of the alloys. The highest initial increase in the impedance values was observed for the AZ31-4Li alloy. The further increase in the inhibitor concentration results in a monotonous increase in the impedance values, with its rate decreasing in the row AZ31-4Li → AZ31-8Li → AZ31-12Li alloy. Nevertheless, for all alloys, the molybdate inhibitor showed high effectiveness. The inhibition mechanism is concentration-dependent with relatively large concentrations required in the solution. This coincides well with our previous data on the corrosion inhibition of the AZ31 and WE43 Mg alloys by aqueous molybdate in 0.05 M NaCl solutions . |
65fc0a5166c138172975afd1 | 24 | The comparison of the EIS and g-DEIS measurement spectra in the solutions containing the same amounts of the inhibitor (Fig. in Supplementary Information) shows that the impedance values were usually higher in the case of g-DEIS measurements. These results clearly show the effect of the system nonstationarity and exposure time on the classical EIS measurement. |
65fc0a5166c138172975afd1 | 25 | In the case of the classical EIS measurements discussed in the present contribution, lowfrequency inductive loops were considered in the data analysis. However, for the g-DEIS measurement, the low-frequency range was limited to 0.7 Hz to ensure the system stationarity. Therefore, no inductive response was registered in the inhibited solutions and the lowest applied frequencies correspond to the response of the surface film consisting of Mg oxide/hydroxide and Mo-rich species . To analyze the g-DEIS data, the equivalent circuit shown as an inset in Fig. was used. In this circuit Rs is the solution resistance, R1 represents the surface film resistance , and the constant phase element (CPE1) represents a capacitive response of the surface film formed on the electrode surface . The dynamics of the change of the circuit parameters in time is shown in Fig. . |
65fc0a5166c138172975afd1 | 26 | The values of R1 in 0.05 M NaCl without the inhibitor were rapidly decreasing in the first 1000 s of the experiment (inset to Fig. ). Afterwards, the decrease was not so prominent, suggesting passivation of the surface with a layer of corrosion products. After ca. 3000 s the values of R1 in 0.05 M NaCl become stable in time. In the experiments with the gradual addition of sodium molybdate into 0.05 M NaCl solution, the value of R1 corresponds to the resistance of the Mo-rich surface film formed on the surface and it started to increase rapidly when the first portions of the inhibitor were added into the solution. It confirms the rapid adsorption of the inhibitor on the surface of the AZ31-xLi alloys and the passivation of their surface. In the case of the CPE constant Y0 (Fig. ), its values were almost one order of magnitude lower in the inhibited solutions, also supporting the high inhibition efficiency of aqueous molybdate. The n parameter of the CPE element (Fig. ) was generally decreasing with time and its values were in the range of 0. Open markers correspond to 0.05 M NaCl (spectra in Fig. ) and filled markers describe 0.05 M NaCl with molybdate inhibitor (spectra in Fig. ). Top x-axes correspond to concentration profile of Na2MoO4 in solutions and are valid for filled markers only. |
65fc0a5166c138172975afd1 | 27 | Since the rate of the inhibitor supply into the solution was constant, the g-DEIS impedance parameters in the solutions with and without the inhibitor can be correlated with the instant concentration of the molybdate inhibitor in the examined solutions at a given time point. Therefore, inhibition effectiveness, IE, can also be estimated from the g-DEIS data using Eq. ( ) . The calculated values are listed in Fig. . Opposite to polarization ( kinetics. The g-DEIS data also allows to estimate these parameters based on the construction of adsorption isotherms . Several types of adsorption isotherms can be used to calculate the adsorption Gibbs energy 0 G and the adsorption equilibrium constant Kads . These calculations require the knowledge of the surface coverage by the inhibitor, θ. Assuming that the complete coverage of the surface gives a 100% reduction in the corrosion rate, it can be taken that θ corresponds to the IE of the inhibitor, calculated above for the g-DEIS data by Eq. ( ) (Fig. ). |
65fc0a5166c138172975afd1 | 28 | and the inhibitor can be adsorbed on the surface with equal probability, and there is no interaction between inhibitor molecules/ions . In the calculations, it is assumed that the adsorption constant Kads depends on the degree of the surface coverage with the inhibitor θ and the inhibitor concentration Сi according to the equations: |
65fc0a5166c138172975afd1 | 29 | The Temkin isotherm takes into account surface heterogeneity . Its equation is based on the assumption of the heterogeneity of the surface energy distribution and linear decrease of the adsorption heat with the increase in the surface coverage by the inhibitor. The difference between the maximum and minimum adsorption heat is described by the parameter f, which is taken to be positive and increases with an increase in the heterogeneity of the surface. Therefore, in the Temkin model, it is assumed that adsorption occurs on the energy-favorable surface locations and can be expressed as: |
65fc0a5166c138172975afd1 | 30 | The obtained Langmuir and Temkin isotherms are shown in Fig. . For all examined alloys they have several linear sections, each characterized by a different slope. For the proper calculations, it was assumed that only the first section corresponding to the smallest concentrations of the molybdate inhibitor in the solution (10-30 mM) and the lowest surface coverage θ is used in the calculations, corresponding to the conditions when a surface monolayer of the inhibitor is formed. The following regions on the isotherm, characterized with different slopes (are not shown), can be assigned to the processes of molybdate polymerization and further growth of a 3D inhibitor film, as was observed in our previous studies of this inhibitor . |
65fc0a5166c138172975afd1 | 31 | The adsorption equilibrium constant Kads estimated from the isotherm slope can be used to calculate the Gibbs energy of adsorption using the equation: Negative values of the change in the Gibbs energy indicate that in a 0.05 M NaCl solution the adsorption of molybdate ions on the surface of AZ31-xLi alloys proceeds spontaneously and thermodynamically irreversibly. It suggests that adsorption occurs immediately after the injection of the inhibitor into the system, which is also supported by the g-DEIS data. Adsorption processes for which the change in the Gibbs energy is more negative than -20 kJ/mol are usually of a physical nature, while those with change in the Gibbs energy below -40 kJ/mol correspond to chemisorption . The values between -20 and -40 kJ/mol correspond to mixed type of adsorption. However, caution should be taken for this parameter due to the relatively high used concentrations of the inhibitor. |
65fc0a5166c138172975afd1 | 32 | The results of the SEM analysis of the surface of AZ31-xLi alloys after exposure to the 0.05 M NaCl solution without the inhibitor for 1 and 24 h are shown in Fig. . After 1 h of exposure, all samples undergo general corrosion with some local corrosion attack in the periphery of IMPs. The regions around severe local corrosion spots were covered with a rather thick layer of corrosion products. The surface of the alloys' matrix was also covered by a layer of corrosion products and corrosion damage increased with an increase in Li content in the alloy. In the case of the AZ31-8Li alloy, the presence of filiform corrosion was observed, which most probably occurred on the boundaries of α and β phases . In turn, after 24 h of exposure of the samples to the corrosive environment, almost the entire surface was covered with an uneven, thick layer of corrosion products, the structure of which differs somewhat depending on the Li content in the alloy. The difference in the corrosion morphologies between studied alloys is explained by the different phase composition of the alloys (Fig. ) and pH values in the near-surface layer of the electrolyte and, accordingly, different thicknesses and composition of the formed layer of corrosion products. ) |
65fc0a5166c138172975afd1 | 33 | The results of the EDX analysis (Table ) confirmed that the formed surface films primarily contain magnesium, most probably in the form of oxide and hydroxide. Aluminum was also observed in rather high amounts (up to 2.6 at.%) at the majority of examined spots. After 24 h of exposure to the corrosive environment, the oxygen content in the composition of surface films increased, which may be due to the formation of a thick layer of oxide-hydroxide passive films. |
65fc0a5166c138172975afd1 | 34 | Fig. shows SEM images of the AZ31-xLi alloys immersed in the 0.05 M NaCl solution with 150 mM of sodium molybdate for 1 and 24 h. The surface morphology of all examined alloys was quite different compared to the solution without the inhibitor (Fig. ). No regions of severe local corrosion attack were seen on the surface, except for some local pitting on the surface of the AZ31-12Li alloy. The formation of a passivating Mo-containing layer is clearly seen on the surface of all alloys. After 24 h of exposure, the surfaces of AZ31-4Li and AZ31-8Li alloys do not show areas of severe corrosion attack, while some areas are covered with thick precipitate layers reach |
65fc0a5166c138172975afd1 | 35 | in Mo (Table ), forming passive layers, most probably over IMPs. However, the surfaces of 595 AZ31-12Li contained some areas of local corrosion attack around IMPs, which is due to the higher 596 local reactivity of this alloy. Nevertheless, no prominent corrosion attack was observed supporting 597 the high inhibition activity of molybdate. The point EDX analysis (Table ) confirmed the presence 598 of molybdate in the surface layers and the formation of a Mo-rich protective layer over the surface 599 of all examined alloys. The relative Mo/O ratio cannot be estimated from the EDX data since the 600 surface layers also contain hydrated Mg compounds with varying stoichiometry . However, 601 it confirmed that the molybdate inhibitor forms surface protective layers of the surface of AZ31-602 xLi alloys. 603 604 Table . Elemental composition of the surface of AZ31-xLi alloys after 1 and 24 h of exposure to 605 0.05 М NaCl without inhibitor. Point labels correspond to those marked in Fig. Numbers indicate regions analyzed by EDX analysis (Table ) |
65fc0a5166c138172975afd1 | 36 | To further examine the surface chemistry of the AZ31-xLi alloys after corrosion in 0.05 M NaCl without and with 150 mM of the inhibitor, Raman spectra were acquired. Optical images of the surfaces selected for Raman measurements are shown in Fig. and obtained characteristic Raman spectra are shown in Fig. . |
65fc0a5166c138172975afd1 | 37 | Examination of the surface of Mg alloys by Raman spectroscopy was reported in based on the Raman peak at 3652 cm -1 corresponding to the A1g O-H stretching vibrations in Mg(OH)2. In our experiments, the analysis of Mg-containing corrosion products was performed focusing on the low-wave number region (200-1200 cm -1 ), where both Mg(OH)2 and Mo-rich species can be analyzed . Raman spectra of all alloys after exposure to 0.05 M NaCl solution without inhibitor for 1 h were similar and showed two characteristic Raman bands at 280 and 443 cm -1 , corresponding to Mg(OH)2 . After 24 h of the exposure to uninhibited solutions resulted in the appearance of the Raman band at 1094 cm -1 , which was assigned to the formation of magnesium or lithium carbonates on the surface, probably by the reaction with CO2 dissolved in the electrolyte . Moreover, we cannot exclude the formation of surface carbonate layers already after 1 h of exposure. However, the thickness of these layers might be not enough for Raman analysis . Its position is very sensitive to changes in the coordination geometry, the chain length, and the hydration degree of molybdate species . This approach was also utilized in our previous publications . After 1 h of exposure, Raman spectra of all alloys contain Raman bands at 1004, 996, and 265 cm -1 , which are typical for hydrated molybdenum(VI) oxide, MoO3(H2O)3 . The Raman band at 1110 cm -1 can be assigned to polyoxomolybdate species or MoOx oxides, which can be formed due to the reduction of the oxidization state of some Mo . Raman bands at 942 cm -1 originate from Mo O - . Raman bands at 321 and 911 cm -1 were assigned to dimolybdates MoO - . Importantly, no Raman signal assigned to reduced phases of Mo(IV) compounds was observed after 24 h of exposure. The phase composition and amount of Li in the alloys have a significant effect on the shape of the obtained spectra. First, XPS spectra shown in Fig. reveal a progressive negative shift of the Mg 1s peak location from 1303.6 eV (for AZ31-4Li) down to 1303.2 eV (for AZ31-12Li), a feature revealing that the alloy surface is covered with the growing amount of Mg hydroxide that probably displaces or covers dense inner MgO layer . At the same time, the Mg moieties share at the surface increases rapidly, tripling its value. . Its share is the highest in the case of the AZ31-4Li and AZ31-8Li alloys, reaching approx. 12 at.% and drops down to 5.3 at.% for theAZ31-12Li alloy (Table ). Additionally, other molybdenum species, Mo(V) and Mo(IV) have been detected in the composition of the surface layers, which share seems to be less affected by the lithium content. |
65fc0a5166c138172975afd1 | 38 | The high-resolution O 1s spectra presented in Fig. support the above observations. The component at 529.9 eV represents Me-O (Me: Mg and Mo) , which dominates at the surface at low Li content and is displaced by hydroxides for AZ31-12Li with Me-OH:Me-O ratio changing from 0.55:1 to 1.22:1 (Table ). The overall observation from the XPS data backs up the electrochemical studies, confirming the higher corrosion susceptibility of the alloys with larger lithium additive, where the passive film is replaced by non-stoichiometric corrosion products (primarily magnesium hydroxides). |
65fc0a5166c138172975afd1 | 39 | This section summarizes the results of the present contribution and attempts to propose the corrosion mechanism of AZ31-xLi alloys in 0.05 M NaCl solutions and their inhibition by aqueous molybdate species. The surface of as-polished AZ31-xLi ions consisted of the alloy matrix and several types of IMPs. The most important difference with the increase of lithium content in AZ31-xLi (x = 4, 8, 12) alloys, is the change of the crystal structure from α-phase hcp (AZ31-4Li) to βphase bcc (AZ31-12Li) through a mixed α+ β phase (AZ31-8Li). Therefore, the corrosion resistance of examined alloys should be mainly defined by the corrosion resistance of the bulk αand β-phases and microgalvanic activity between the alloys' matrix and IMPs. Li et al. reported a decrease in the corrosion rate of Mg-Li alloys in 0.1 M NaCl in the following order Mg-7.5Li > Mg-4Li > Mg-14Li. However, in the present contribution, a linear decrease in the corrosion resistance with increased Li content was observed in an order AZ31-4Li > AZ31-8Li > AZ31-12Li. This difference might be attributed to the additional presence of Al and Zn in the composition of the alloys leading to the differences in the composition of IMPs, variations in the heat treatment, and other structural parameters (grain size, IMPs size, etc.). |
65fc0a5166c138172975afd1 | 40 | The analysis of the track of the OCP of examined alloys and pH of solutions (Fig. ) shows that these processes, especially the selective dissolution of lithium, are very rapid. The intensification of the process of selective dissolution of Li will also be facilitated by the formation of microgalvanic pairs between phases of the alloys with different electronegativity. However, the surface of all alloys is passivated by a layer of corrosion products within a few minutes, as evidenced by the stabilization of the OCP and further confirmed by the results of g-DEIS measurements (Fig. ). The passivation time decreased as the content of Li in the alloy increased, which might be attributed to the formation of a more protective surface films on the surface. In naturally aerated solutions, corrosion products can further react with dissolved carbon dioxide forming relatively stable carbonate surface films on reactions: |
65fc0a5166c138172975afd1 | 41 | The presence of surface carbonates was confirmed by Raman (Fig. ) and С 1s XPS spectra (not shown). The Pilling-Bedworth ratio of Mg(OH)2, MgCO3, LiOH, and Li2CO3 compounds is between 1.26-2.04 , indicating that corrosion resistance of the formed layers would be higher relative to the metallic substrate. Nevertheless, the protective ability of the formed surface layers is not enough, and corrosion attack increased after 24 h of exposure to 0.05 M NaCl solution under the influence of aggressive chloride ions. |
65fc0a5166c138172975afd1 | 42 | Our results demonstrated that the introduction of molybdate ions into 0.05 M NaCl solution dramatically changes the corrosion behavior of all examined AZ31-xLi alloys. Dissolved molybdates retard corrosion attack by forming a protective insoluble film over the active surface areas of all alloys. Nevertheless, as for other Mg alloys , it is essential to achieve a "critical" concentration of molybdate inhibitor in the electrolyte to provide high inhibition effectiveness (Figs. ). Interestingly, the results of instant g-DEIS measurements report inhibition effectiveness even for small portions of the inhibition (Fig. ). However, utilization of low concentrations of molybdates seems to be inefficient at long exposure times. Therefore, in the mechanism below we assume relatively high concentrations of the inhibitor in the solution (above 100 mM) to provide reliable inhibition. |
65fc0a5166c138172975afd1 | 43 | The aqueous chemistry of molybdates is rather complex and several forms of poly-and monomolybdates are present in aqueous solutions depending on their pH . Due to the processes of the alloys' corrosion described by Eq. , the pH in the near electrode area is alkaline. Therefore, mostly monomolybdates will be present in the solution . As supported by the g-DEIS data (Fig. ), the first stage in the corrosion inhibition mechanism is the adsorption of molybdate on the surface of AZ31-xLi alloys. The adsorption preferably occurs on the active areas of the surface. However, it is mostly uniform with time and after 24 h of corrosion, almost the whole surface of all alloys was covered with a Mo-rich layer (Fig. ). |
65fc0a5166c138172975afd1 | 44 | The process results in the formation of insoluble hydroxide forming insoluble hydroxide on the surface, which provides the corrosion protection effect. It should be noted that after 24 h of corrosion experiments, the amount of molybdate on the surface decreased compared to that after 1 h of testing. It might indicate that the high corrosion activity of AZ31-xLi alloys contributes to further local corrosion attack. |
65fc0a5166c138172975afd1 | 45 | In this work, the effect of sodium molybdate on the corrosion mechanism of lithiumcontaining AZ31-xLi (x = 4, 8, and 12 wt.%) magnesium alloy was examined. The corrosion protection effectiveness of molybdate was evaluated depending on its concentration in 0.05 M NaCl solution and correlated with the surface film composition. The following conclusions can be drawn: |
669716cc01103d79c534b99f | 0 | nitrone to generate a Cu(II)-associated zwitterion intermediate, which then undergoes an enantio-determining ring-closing process to form chiral BCHep. To commence the investigation, we selected nitrone (1a) and the pyrazole amide substituted BCB (2a; Table ; see Supplementary Information for details) as standard substrates to evaluate the reaction condition. Surprisingly, of the three Earth-abundant metals tested, copper was the sole catalyst capable of yielding 2oxa-3-aza BCHep (3a) with an isolated yield of 67% (entry 1-3). Even more surprisingly, no ring-opening byproducts were observed, highlighting the high chemoselectivity of the reaction. Next, chiral ligand was employed to control enantioselectivity of the reaction. Except L5, which is known to be a negatively charged ligand in the reaction, all the other electrically neutral ligands can improve the reaction yield (entry 4-11). To our delight, Evans bisoxazoline ligand L6 presented a promising ee value of 71% (entry 9). Modification of bisoxazoline ligand revealed that one with four benzyl groups at the oxazoline ring and bridge carbon gave high ee value (89%, entry 11). Additionally, lowering the reaction temperature to -40 °C further increased the yield and enantioselectivity of the reaction (99%, 96% ee, entry 12). With optimal condition established, we then studied the substrate scope with respect to nitrone (Figure ). The nitrone substrates with methyl or trifluoromethyl group on the benzene ring of nitrones 1 all gave desired products with good yield and excellent enantioselectivity (3a-3c). The halogen substituents on the meta or para position of the benzene ring also didn't adversely affect the outcome of the reaction (3e-3i), which provides an opportunity for further cross-couplings. However, nitrone with an ortho-fluorophenyl gave lower ee value, perhaps due to the steric effect (3d). Moreover, the functional groups with potential for diverse synthetic transformation like nitro, cyano, ester, boric ester, acetoxyl, phenoxy, silyl and sulfonyl group (3j-3q) have no serious harm to the yield and enantioselectivity of the reaction. In addition, trifluoromethoxy (3r) and trifluoromethylthio (3s) groups which often show unusual bio-activities in drug molecules were compatible in the reaction. Except for substituted phenyl groups, the fused aryl rings and hetero-aryl rings in the nitrone substrates also have no negative effect, giving excellent enantioselectivity (3t-3x). Apart from the deviation of R 1 , variations in the N-protecting aryl groups of BCB, including substitutions at the meta or para positions, showed minimal influence on both yield and enantioselectivity (3y-3ab). The substrate scope with respect to BCBs was explored (Figure ). Substitutions on the benzene ring of BCB, regardless of electron donating (3ac and 3ad) or withdrawing (3ae-3ag) groups, all gave gratifying outcomes. Notably, a methylsubstituted BCB can also react with nitrone 1a to form 2-oxa-3-aza BCHep 3ah under standard conditions with high yield and enantioselectivity. To showcase the application potential of this method, we carried out mmol experiment with 1a and 2a under standard condition (Figure ). At 1 mmol scale, 3a was produced with undiminished yield and ee value, highlighting its scalability. Besides, pyrazole amide group of 3a can be readily transformed into several valuable functional groups. Firstly, the NaBH4 reduction of 3a afforded primary alcohol with quantitative yield and unharmed ee value, facilitating subsequent connection through nucleophilic substitution or Mitsunobu reaction. Hydrolysis of 3a produced carboxylic acid 5 with 81% yield and >99% enantio-specificity, granting convenience for further amidation or decarboxylative coupling . Finally, the alcoholysis of 3a converted the amide group to the ester group with 96% yield and 96% ee. In order to elucidate the reaction mechanism, control experiments were performed. Reaction of 2a in the absence of nitrone resulted in >95% recovery of starting material with no observation of ring-opening byproducts, thereby excluding the possibility of a copper-catalyzed ring-opened intermediate (Figure ). Ester substituted BCB 7 was then applied in the cycloaddition and yielded no product, revealing the chelation of bidentated pyrazole amide to copper is indispensable (Figure ). To gain a deeper insight into the activation effect of Cu(II) on pyrazole amide-substituted BCB, we perform DFT calculation to analyze the structural and electronic properties of several relevant species. As illustrated in Figure , the bridgehead carbon adjacent to the phenyl substituent of the free BCB bears a certain amount of positive charge, showing its electrophilic nature. Without the coordination of Cu(II), the strained C-C σ bond of BCB has a bond length of 1.54 Å and a Mayer bond order of 0.64, indicating a weaker bond strength than typical open chained C-C single bond. However, upon coordination with a copper catalyst bearing a bisoxazoline ligand, the strained C-C σ bond of BCB elongated to 1.63 Å with a reduced bond order of 0.49, accompanied by an increased positive charge at the bridgehead carbon. These computational results showed that the coordination of copper(II) catalyst effectively activate BCB. |
669716cc01103d79c534b99f | 1 | The ring-closing step which determines the enantioselectivity of the reaction was also studied by means of DFT calculations (Figure , upper part). In this step, the Cu(II)-coordinated enol produced by the nucleophilic addition of nitrone and BCB connects its electronegative carbon to the electrophilic carbon of imine to form the BCHep scaffold. The Gibbs free energy of the transition state leading to (S)-3a (TS-S) is 1.7 kcal/mol lower than that leading to (R)-3a (TS-R), resulting in the major product with (S)-configuration, which agrees with the experimental observations. To understand the origin of the energy difference between the two transition states, independent gradient model based on the Hirschfeld partition (IGMH) was employed to analyze the weak interaction . As shown in Figure (lower part), both transition states have multiple CH-π interactions between the bisoxazoline ligand and substrate. However, TS-S displays a greater number and stronger intensity of CH-π interactions (highlighted by red circles) compared to TS-R, indicating that enantioselectivity is primarily governed by non-covalent interactions. In summary, we have established an enantio-and regio-selective method for the construction of chiral BCHeps through Cu(II)-catalyzed asymmetric cycloaddition of BCBs with nitrones. The reaction featured with mild condition, high yield, high selectivity, and broad substrate scope. The success of the reaction hinges on the activation of BCB by bisoxazolin-coordinated Cu(II) catalyst, which was verified by DFT calculations. Computational chemistry revealed that the origin of enantioselectivity arises from non-covalent interactions between the ligand and substrate, offering insights for constructing other types of saturated bridged bicyclic bio-isosteres of arenes. Future works will be focusing on the application of this catalytic system to the structurally divergent synthesis of bicyclic skeletons. |
61ecf4171916372d08f148a3 | 0 | In the last several decades, plasmonic metal nanoparticles (MNPs) have generated a great amount of interest due to the dramatic effect of surface localized plasmon resonance. Currently, plasmonic MNPs have been widely used to control and manipulate light at the nanoscale, thus regulating the photophysical and photochemical properties of molecules in their vicinity, such as enhancing molecular optical signals (absorption, Raman, and fluorescence ) and mediating molecular photochemical reactions. Meanwhile, many theoretical and computational methods were developed to unravel the detailed mechanisms of molecular spectral enhancements, plasmon-mediated chemical reactions, as well as plasmon-enhanced resonance energy transfer. In many cases, the plasmon enhancement arises mainly from the electromagnetic mechanism, where an external electric field can be substantially magnified by an MNP around its surface. Accordingly, several classical nonatomistic methods had been widely applied. |
61ecf4171916372d08f148a3 | 1 | The hybrid MNPs-molecular systems represent a challenge for theoretical and computational methods because the cona) Electronic mail: [email protected] b) Electronic mail: [email protected] c) Electronic mail: [email protected] stituents can not be treated on the same footing by the stateof-the-art methods. The properties of molecules require a quantum mechanics (QM) description thanks to the high accuracy of QM methods. However, QM methods are unable to describe the medium to large-sized MNPs due to their steep computational cost. Two kinds of simplified treatments have been usually adopted. One is to simplify the problem by assuming the molecules bonded to very small metal clusters. With this treatment, the optical properties of molecule-metal cluster systems can be described by the QM methods. Small MNPs, however, don't support the bulk plasmon. The other is to adopt the mixed quantum/classical approach, which combines the QM approaches with classical mechanics or electrodynamics, such as the Mie theory, discrete dipole approximation, finite difference time domain, and polarizable continuum models. To more accurately capture the plasmonic effect from MNPs with different sizes, shapes, and compositions, however, atomistic modeling of the MNP-adsorbate system is needed. Specifically, to account for the large polarizability of MNPs, (induced) charges, dipoles, and/or even multipoles would be introduced at each atom site, leading to several (polarizable) force field models for MNPs. These molecular mechanics (MM) methods include the point-dipole interaction model (including its combination with either electronegativity equalization or charge-transfer ), charge-dipole interaction model, discrete interaction model (DIM) and its coordination-dependent variant (cd-DIM), and atomic dipole approximation model. These MM models can be employed in combined quantum mechanics/molecular mechanics (QM/MM) modeling of probe-MNP complexes, where the probe molecule constitutes the QM region so that its vibrational motions (in infrared and Raman spectroscopy) or electronic transitions (in fluorescence) are treated using ab initio QM theories. Mikkelsen et al have investigated the hyperpolarizability changes of organic molecules near gold nanoparticles by a polarizable QM/MM approach recently. The DIM model with induced charges and induced dipoles at each metal atom, in particular, has been combined with QM methods by Jensen and others to model MNP-mediated one-photon and two-photon absorption, Raman, and fluorescence spectra. In parallel to the QM/MM study of MNP-enhanced electronic transitions, Giovannini, Cappelli, and others have combined density functional theory (DFT) and time-dependent density functional theory (TDDFT) with their FQFµ models for water molecules, which are also based on fluctuating charges and induced dipoles. Analytic energy derivatives can provide computational advantages in molecular geometry optimizations, vibrational frequency calculations, and molecular property descriptions. The analytic Raman intensities of the QM method have been derived and implemented decades ago. Recently, the implementations of analytic Hessian and high-order molecular properties (such as IR and Raman intensities) have been extended to several hybrid (polarizable) QM/MM schemes for solvents or protein systems. Here, inspired by the encouraging results of the QM/DIM model from Jensen et al, we present our implementation of this model and its analytic energy derivatives with respect to the nuclear coordinates and perturbed electric field for the study of the adsorbate-MNP systems. Compared to earlier implementations of IR and Raman intensities within a polarizable QM/MM model, our implementation is applicable to polarizable force fields involving both induced charges and dipoles, such as the DIM model for metal clusters. |
61ecf4171916372d08f148a3 | 2 | The paper is organized as follows. Section II briefly recaps the basic theoretical foundation of the polarizable QM/MM model for the ground-state energy of a molecule-MNP system and presents the analytical expressions for high-order derivatives of the energy with respect to the QM nuclear and field perturbations. It is followed by the computational details in Section III. In Section IV, using the pyridine molecule in the vicinity of three gold clusters as testing systems, the computed IR and Raman spectra are presented and discussed. In addition, the SERS of 4,4 -bipyridine on gold and silver MNPs are simulated by QM/DIM method and compared with experimental spectra. Moreover, the effects of nonlinear response of MNP and charge migration to Raman intensity are analysed. Finally, the concluding remarks and potential future improvements are summarized in the last section. |
61ecf4171916372d08f148a3 | 3 | where r i j is the distance between the i-th and j-th MM atoms, and σ is the width of Gaussian functions used to damp the electrostatic interaction between neighboring atoms. The diagonal block of T is formed by the atomic capacitance (c i ) and polarizability (α i ) for charge and dipole self-interactions at i-th MM atom, respectively. F tot is the total external generalized field exerted on the MM sites, including both potentials and fields (-V, E). Using the variational condition, the stationary solution is given by solving a linear equation, |
61ecf4171916372d08f148a3 | 4 | where the Lagrangian multiplier λ is introduced to constrain the net charge for the MM region as Q. 1 refers to a row vector (1, 0, 0, 0, 1, 0, 0, 0, • • • ) with a value of 1 for only the induced charge on each MM atom. When Q is equal to 0 (as for all test cases in this work), the solution to Eq. ( ) could be formally written as, |
61ecf4171916372d08f148a3 | 5 | The last expression for the MM energy will be used in the derivation of the high-order derivatives of the energy. When the MM region is adjacent to the QM region (as described on the DFT level of theory), the total generalized field F tot would include the contributions from the QM region in addition to the external source, |
61ecf4171916372d08f148a3 | 6 | In Eq. ( ), P is the density matrix with elements P µν , Z I labels the I-th QM nuclear charge and T I is the corresponding generalized external field on MM atoms, and R f ext represents the generalized field on each MM atom at position (R jx , R jy , R jz ): |
61ecf4171916372d08f148a3 | 7 | which leads to the interaction between QM and external fields within the dipole approximation. Here M is the dipole moment matrix and R I the I-th QM nuclear coordinate. The corresponding Fock matrix to be used in the SCF cycles could be obtained by differentiating the total energy given by Eq. (10) with respect to the density matrix (P): |
61ecf4171916372d08f148a3 | 8 | will be used for the calculation of the total energy. The last term is the van der Waals (vdW) interaction between QM and MM regions. Here we adopt the distance-dependent variance of the classical Lennard-Jones (LJ) 12-6 potential according to Jensen et al. The expression is presented in Section S1 of the supporting information (SI). |
61ecf4171916372d08f148a3 | 9 | Here P y includes the derivatives of orbital rotations. The first term represents the MM charges and dipoles induced by the seond-order QM potentials and fields with respect to QM nuclear coordinate changes, while the second term is the interaction between first-order QM potentials and fields and MM induced charges and dipoles from another first-order QM potentials and fields perturbed by QM atom displacements. After the construction of the Hessian matrix in the mass-weighted coordinates, and projecting the rotational and translational degrees of freedom out of this harmonic force constant matrix, one could obtain the normal modes and vibrational frequencies by diagonalizing the projected matrix. Note that here the Hessian matrix only includes the QM-QM block, and hence, it is actually partial Hessian within the QM region. |
61ecf4171916372d08f148a3 | 10 | IR and Raman spectra provide information about the molecular vibrations. IR spectra can be obtained from light absorption whereas Raman spectra reflect light scattering process. The IR and Raman spectral intensities are proportional to the squares of nuclear derivatives of molecular electric dipole and polarizability, respectively. When the perturbation is the external field f m , the derivatives of total energy in Eq. ( ) would give the total dipole moment |
61ecf4171916372d08f148a3 | 11 | where F QM,nx • T -1 • R m represents the contribution of the MM part, which indicates that the two perturbations both act on the QM region (i.e., F QM,nx ) in the current framework. It is incorporated into the dipole moment matrix and its derivative matrix in the last line. |
61ecf4171916372d08f148a3 | 12 | The derivatives of density matrix are derived in Appendix A. As in the case of the first-order derivatives of density matrix P x or P n , only the first-order derivatives of orbital rotations are needed in the second-order derivatives of density matrix P nx , which is known as the 2n + 1 rule. The derivatives of orbital rotations are computed by the coupledperturbed Hartree-Fock equation or z-vector equation, which is presented in Appendix B. |
61ecf4171916372d08f148a3 | 13 | The QM/DIM method and its analytic energy derivatives are implemented in a locally modified version of the Q-CHEM package. The parameters used in this QM/DIM method are listed in Section S1 of SI. Pyridine (Py) molecule and two gold clusters including 18 and 32 gold atoms are chosen as the test system. Based on these components, three complex configurations shown in Fig. are formed: surficial Py-Au 18 -S, vertical Py-Au 18 -V, and Py-Au 32 with the nearest N-Au distances being 3, 4, and 5 Å. The geometries are obtained from full QM restrained optimization with a harmonic potential, so that each of the structures has only one imaginary frequency along with the labeled N-Au direction; their coordinates are provided in the SI. Restrained optimizations are also carried out by QM/DIM method and the obtained coordinates show no apparent difference from full QM results (with largest RMSD value as 0.007 Bohr in Table of SI). The IR and Raman spectra are calculated by full QM and hybrid QM/DIM methods. In the latter, pyridine is treated by QM and the gold atoms form the DIM region. The partial Hessian is used in the QM/DIM method, whose potential errors are discussed in Section S3 of SI. To validate the implementation of the analytic derivatives of the QM/DIM method, analytical and finitedifferent approaches are used to compute the frequencies and Raman spectral intensities of the Py-Au 18 -V with the labeled N-Au distance as 3 Å and the values are collected in Tab. S7 of the SI. Furthermore, to demonstrate the capability of current analytic derivatives approaches within QM/DIM, we calculate the normal surface enhanced Raman scattering spectra (SERS) of 4,4 -bipyridine (4,4 -BPy), which is set close to the surfaces of Au 2057 and Ag 2057 icosahedral MNPs, respectively (their geometric arrangements are shown in Fig. of SI). The simulated SERS spectra are compared with experimental ones. All the calculations are carried out with PBE0 functional and 6-31+G(d) for N, C, and H atoms and LanL2DZ ECP and basis set for Au atoms using the locally modified Q-CHEM 5.2 package. B3LYP functional is also used for 4,4 -BPy system for the comparison with previous theoretical works. The convergence thresholds of SCF and CPKS are both 10 -8 au while a 10 -14 au threshold is used for two-electron integrals. SG-1 DFT grid 79 is utilized for DFT numerical integration. The vibrational spectra are plotted using a Lorentz function with a width of 10 cm -1 . |
61ecf4171916372d08f148a3 | 14 | The infrared (IR) spectra of pyridine molecule and three different pyridine-gold complexes (Py-Au 18 -S, Py-Au 18 -V, Py-Au 32 ) computed by QM and QM/DIM methods are displayed in Fig. . The top row shows the IR spectra of the gas-phase pyridine minimum-energy structure, while the other three rows show the spectra calculated using the optimized configurations (with the distances restrained at 3, 4, and 5Å). In these three rows, the green curves correspond to the spectra of the pyridine molecule at the geometry extracted from each of these complexes. Overall, the QM/DIM method (blue curves) reproduces similar trends in the harmonic frequency shifts and comparable IR intensities relative to the full QM profiles (red curves) for the tested systems. |
61ecf4171916372d08f148a3 | 15 | Overall, the harmonic vibrational frequencies of the pyridine molecule are shifted by up to 20 cm -1 from the gas phase to the complexes. Within each of the three complexes, however, the frequencies of the adsorbed pyridine molecule have marginal shifts towards higher frequency (smaller than 7 cm -1 ) upon the binding to Au clusters. This is not surprising because the heavy Au atoms vibrate very slowly and have a negligible effect on the nearby pyridine molecule. For a representative structure, Py-Au 18 -V (3 Å), the numerical values are provided in Table of the SI, and information for several key vibrational modes are collected in Table . |
61ecf4171916372d08f148a3 | 16 | When the pyridine molecule approaches the Au clusters, the IR peaks of three vibrational modes (ring breathing and two C-H wags) within 1000∼1300 cm -1 become increasingly more intense as the distance reduces from 5 to 3 Å. The second C-H wag at 1238 cm -1 is predicted by full QM calculations to have the largest enhancement of 24 times (from 2.7 to 48.7 km/mol) for the S configuration, 33 times for V configuration, and 24 times for Py-Au 32 , as shown in the panels (j), (k), and (l) of Fig. , respectively. In contrast, some peaks are significantly weakened after the binding to Au clusters. This is especially obvious with the two out-of-plane C-H bends at 744 and 780 cm -1 , which have comparable intensities in the gas phase. While only the IR peak at 744 cm -1 is reduced in Py-Au 18 -S (3Å) and Py-Au 18 -V (3Å) complexes, both peaks (744 cm -1 and 780 cm -1 ) lose some strength in the Py-Au 32 (3Å) structure. No. |
61ecf4171916372d08f148a3 | 17 | Freq (cm When the distance is 5 Å, although QM/DIM slightly underestimates the intensity of mode 12, it nearly reproduces the full QM spectra as Figs. ), 3(e), and 3(f) show. As R decreases, however, QM/DIM gives less satisfying Raman profiles. Taking Py-Au 18 -V system with R = 4 Å as an example (see Fig. )), we observe that QM/DIM significantly underestimates the intensity of mode 12 but overestimates this of mode 11 compared with the full QM results. When R is further shortened to 3 Å, the discrepancy between full QM and QM/DIM results in all frequency ranges increases. As shown in Table , QM/DIM significantly overestimates the intensities of all the modes except mode 12. In other words, the QM/DIM approach could provide artificial enhancements for some vibrational modes, which can be attributed to the neglect of chemical enhancement and nonlinear responses of the MNP in the current QM/DIM model. |
61ecf4171916372d08f148a3 | 18 | Moreover, we calculate the normal Raman scattering spectra of 4,4 -bipyridine (4,4 -BPy) in the gas phase, and in the proximity of Au 2057 and Ag 2057 with respect to the DFT XC functional PBE0 and B3LYP, respectively. Fig. and Fig. in SI show the calculated results, where the gas-phase Raman intensities are scaled by a factor of 20. It is noted that the spectra calculated with PBE0 and B3LYP are almost identical, indicating that the impact of functional on the spectra is small. |
61ecf4171916372d08f148a3 | 19 | Fig. demonstrates that, for the adsorbed configurations, QM/DIM predicts a 20 times enhancement for most of the Raman peaks due to electromagnetic enhancement. Both the theoretical calculation and experimental measurement yield a consistent result trend on the MNP-induced changes on the relative spectral intensities. For example, the gold nanoparticle makes the strongest Raman peak of 4,4 -BPy shift to 1678 cm -1 from 1336 cm -1 , the relative intensity at around 1024 cm -1 decrease, and the two Raman peaks in the 600-800 cm -1 range disappear. However, the QM/DIM predictions hardly alter the molecular vibrational frequencies while the experimental frequency shifts could be as large as 18 cm -1 . It is unsurprising because after the 4,4 -BPy is adsorbed on the MNP, the QM/DIM optimization yields a similar geometry as the gas-phase one, thus producing only small changes in the vibrational frequencies. This is in line with the Raman spectra of the Py cases. As shown in Table , the frequencies calculated by full QM and QM/DIM methods have similar values. The large frequency changes after molecule adsorbed on MNP come from geometry differences between Py gas-phase minimum and full QM optimized Py-Au 18 complex. |
61ecf4171916372d08f148a3 | 20 | To shed light on the issue of the QM/DIM approach in the Raman calculations, we calculate the nuclear derivatives of the polarizability through the finite-difference (FD) method based on classical turning points (CTP). Two vibrational modes are chosen: the ring breathing modes around 1020 and 1050 cm -1 (modes 11 and 12). As shown in Fig. , the pyridine nitrogen atom shows little participation in the vibrational pattern of mode 12 while it gets involved in that of mode 11 (the same for other artificially enhanced modes). As Eq. ( ) shows, the molecular electric polarizability α mn is related to the density matrix derivatives with respect to the external field and molecular dipole moment matrix. We can divide the value of α mn into four terms with respect to the atomic basis sets contributed by its two components: the Py molecule and Au cluster. As shown in Table , for mode 11, the Au cluster contributes 8.877 au to the final polarizability change, which largely cancels the other contributions; while the value (-0.519 au) is negligible for mode 12. This distinction could be understood from the vibrational motions of the pyridine. The nitrogen atom plays a major role in the vibration of the ring breathing mode 11 in Fig. (a) and changes the local fields exerted on the Au clusters, which requires the contribution from high-order nonlinear response terms, i.e., the hyperpolarizability-related terms of the Au atoms, to be incorporated. On the other hand, as the vibration of ring stretch mode 12 in Fig. ) is symmetric along the chosen z axis, there is no change in the polarizability of the Au cluster. Furthermore, there is no explicit contribution from the metal atoms to the Raman intensities in the current QM/DIM method, which can be revealed by comparing Eqs. ( ) and (28). |
61ecf4171916372d08f148a3 | 21 | As stated for Eq. ( ), in the current QM/DIM scheme, the contribution of the MM region only comes from the induced charges and dipoles by the second-order potentials and fields of the QM counterpart, where the induced dipole moments are proportional to the first power of the field intensity. MNP may possess a strong nonlinear response, and the induced dipole moments should include the nonlinear terms that are proportional to the second and higher powers of the field intensity. Therefore, it is reasonable to account for the nonlinear response of MNPs. |
61ecf4171916372d08f148a3 | 22 | where R AB is the inter-distance between two fragments, A and B; êk is a unit number at k-th direction; µ A,x is the nuclear derivatives of the ground state dipole moment of A; and β β β B represents the electric hyperpolarizability tensor of B. It corresponds to the event that the incident and scattered photons of the Raman scattering are on the same fragment A, meanwhile one virtual photon is exchanged between the two fragments, i.e., excitation energy transfer (EET) occurs between two locally excited states of the two molecules. We note that to arrive at the hyperpolarizability-dipole interaction expression in Eq. ( ), two approximations are made for the coupling between the two locally excited states: the exchange integrals are ignored and a multipole expansion of the Coulomb interaction operator is adopted. (The third one is that charge-transfer excitations are not into consideration.) This expression, however, is incomplete because the distance could also be differentiable rather than taking the first-order term in dipole moment (shown in Eq. ( )). |
61ecf4171916372d08f148a3 | 23 | Then the interaction of the first term and the hyperpolarizability yeilds Eq. ( ), while the second term is from the derivatives of the distance rather than molecular dipole. The rest contributions to the nuclear derivatives of polarizability α x i j in Eq. ( ) includes the expression β MM mnl f QM l , referring to the first-order change in metal's polarizability induced by QM field. As in the QM/DIM method, each metal atom is induced by QM potential and field by atomic capacitance and polarizability and the induced charges and dipoles interact with each other, it wold be difficult to distinguish this mutual polarization from the contributions in Eq. (36) with the use of molecular hyperpolarizability parameter for metal cluster. Therefore, we use Eq. (35) to account the effect of hyperpolarizability of metal in the following. This correction is sufficient for our purpose because the gold cluster has large hyperpolarizability and it has little participation in the vibrational modes of the Raman spectral region we are interested in. The hyperpolarizability of the Au 18 cluster calculated by the finite-difference method with a field strength of 0.001 au is given in Table . Consistent values are obtained with a smaller field strength (0.0002 au). As demonstrated in Table , the calculated hyperpolarizability of the Au 18 cluster has large components along the z axis, comparable with the values reported in the literature. The corrected QM/DIM Raman intensities of selected modes of Py-Au 18 -V (3 Å) complex is shown in Table . There are five variations (a-e) of the hyperpolarizabilityrelated correction for the QM/DIM method since some arbitrariness arises when only the molecular hyperpolarizability parameter is available rather than the atomic ones. The (a), (b), and (c) columns are calculated by taking the distance R AB in Eq. (32) as the distance between the two centers of mass (COM), the COM of pyridine and the location of the nearest gold atom, and the shortest distance of the two fragments, respectively. In other words, the distance R AB reduces gradually when moving from (a) to (c). The (d) and (e) columns collect the Raman intensities corrected using Eq. ( ) without and with QM induced fields, respectively. Even though the QM/DIM Raman intensity of mode 11 is still larger than the full QM one, it is unsurprisingly reduced with the correction of the hyperpolarizability dependent term. On the other hand, the intensity of mode 12 is also slightly increased by the (a), (b), and (c) corrections. Fig. displays the corrected QM/DIM Raman spectrum of the Py-Au 18 -V (3 Å) complex. For approach (c), even though more correct intensity is reproduced for mode 11, several modes are wrongly enhanced such as 5, 16, and 19. It reflects that the distance is too small within this calculation. When the distance is larger, for instance, in the case of approach (b), the green curve moderately approaches the QM one in Fig. . On the other hand, the (e) profile (blue line) improves the intensities of almost all the vibrational modes except that the intensity of mode 16 is overestimated and that of mode 12 is further reduced relative to the uncorrected QM/DIM result (from 236 to 168 Å 4 /AMU, while the full QM reference is 294 Å 4 /AMU). It is acceptable though that these corrections could not produce overall satisfying intensities for all the modes, because only the molecular hyperpolarizability of the gold cluster is employed in these calculations rather than the distributed atomic hyperpolarizabilities while the fields and their derivatives act on individual gold atoms. |
61ecf4171916372d08f148a3 | 24 | Raman signals can be enhanced by the chemical enhancement and the electromagnetic enhancement. In the current QM/DIM scheme, we don't account for the intermolecular charge transfer (CT) effect, which may be partially responsible for the limited accuracy of the QM/DIM scheme for Raman spectral calculations, especially when the intermolecular distance is short. To check this effect, we calculated the amount of charges on pyridine molecule within the complexes as shown in Table . |
61ecf4171916372d08f148a3 | 25 | Among the four used population methods, only the electrostatic potential (ESP) and fragment-based Hirshfeld (FBH) charge schemes consistently predict the expected trend in the fragment charge population, namely an enhanced CT with a shorter distance between two fragments. These values clearly show that the net transferred charge between Py and Au cluster is almost zero when the nearest distance between these two fragments is 5 Å, while it can be as large as 0.16 e -when the distance shortens to 3 Å in Py-Au 18 -V according to the FBH calculation. It suggests that the ground state charge migration between the Py molecule and Au cluster might also play an important role in the limited accuracy of our current QM/DIM Raman spectral simulations. |
61ecf4171916372d08f148a3 | 26 | In this work, we derived and implemented the QM/DIM method and its high-order energy derivatives for the calculation of noble MNP-mediated molecular vibrational spectra, including IR and Raman scattering. Taking the complexes composed of a pyridine molecule with MNPs consisting of 18 or 32 gold atoms as testing examples, we assessed the accuracy of the current QM/DIM scheme in the calculations of molecular vibrational frequencies and IR/Raman intensities. The QM/DIM method demonstrates the ability to reproduce the molecular vibrational frequencies and IR spectral intensities obtained using the full QM approach. The Raman profiles from QM/DIM calculations behave well for large intermolecular distances such as 5 Å for the tested complexes, while it shows artificial enhancements at shorter molecule-MNP distances for some of the vibrational modes. Even though, with large MNPs such as Au 2057 and Ag 2057 , the simulated normal SERS of 4,4 -BPy by QM/DIM method are comparable with experimental spectra. |
61ecf4171916372d08f148a3 | 27 | The deviation of QM/DIM results from full QM results for small metal clusters, however, can be partially resolved. By incorporating the term that incorporates the first-order nonlinear polarizability of Au clusters and the dipole (or electric field) derivatives of the probe molecule, we can capture the non-negligible three-virtual-photon process of Raman scattering within this hybrid method. With this correction, the Raman spectra for the short-distance configurations of the Py-Au clusters calculated using QM/DIM are improved. We thus suggest that the atomic (distributed) hyperpolarizability of metal atoms should be parameterized within the hybrid QM/DIM method to enable it to describe Raman scat-FIG. . Corrected Raman spectrum of Py-Au 18 -V (3 Å) complex by QM/DIM with PBE0/6-31+G(d)/LanL2DZ. (a-c) variations of QM/DIM method use Eq. ( ) with different distance R AB while (d) and (e) correspond to Eq. ( ) without and with QM induced fields, respectively. TABLE V. Charge populations on the pyridine molecule within the different Py-Au complexes calculated from the Mulliken, ChElPG, ESP, and FBH tering spectra more accurately. Besides, as investigated by Schatz and the coworker, the other high-order properties such as dipole-quadrupole and dipole-magnetic-dipole polarizabilities may also play a rule in the Raman intensity if the electric field derivatives are comparable with the field strength. |
61ecf4171916372d08f148a3 | 28 | Furthermore, at short intermolecular distances, the overlap of wave functions opens the possibility of a charge migration between Py and the Au cluster. In those cases, the effect of intermolecular CT on the Raman signal should not be neglected, which may otherwise limit the applicability of the current QM/DIM scheme for Raman spectral simulations. It is therefore desirable to develop a scheme to account for the CT effect in future QM/MM methods. The use of only QM-QM block Hessian matrix in the current work is also a potential source of small errors in the simulated vibrational spectra. In addition, the vdW interaction between the molecule and MNP could affect the optimized molecular structure and then its vibrational frequencies predicted by using the QM/DIM method. |
61ecf4171916372d08f148a3 | 29 | Finally, we note that the plasmon resonance effect of MNPs has not been taken into account in this work. We expect to include the resonance effect by adopting the frequencydependent parameters for metal atoms in future publications, which requires solving complex-valued response equations. The occupied MO coefficients could be expanded to the second-order in orbital rotations Θ vo as Ref. 90 suggested. |
61ecf4171916372d08f148a3 | 30 | [nx] vo ) are determined using the procedure outlined in the next section. where F = II + Ω Ω Ω + VT -1 V. Note that Ω Ω Ω is the exchangecorrelation portion of the response kernel as defined in Eq. ( ) of Ref. 91. The explicit Fock matrix derivatives, |
611cc248f5c7c37347dd1c61 | 0 | Thermally activated delayed fluorescence (TADF) constitutes a promising route toward creating organic electroluminescent materials with the potential to obtain 100% internal quantum efficiency through the possibility of harvesting both singlet and triplet excitons. On a microscopic level, TADF is governed by the reverse intersystem crossing (rISC) process whereby a nonemissive molecular triplet excited state is converted into an emissive singlet state capable of efficient luminescence. Most prominently, the rISC process depends on the energy gap (∆E ST ) between the lowest excited singlet and triplet states, which enters exponentially into the rate expression and can be seen as an effective activation energy to the TADF process. Other influences are related to spin-orbit coupling (SOC), enabling the formally spin-forbidden rISC process, and the oscillator strength ( f ) of the emitting singlet state. All three properties crucially depend on the state character where enhanced charge transfer (CT) is expected to lower both ∆E ST and f . SOC, on the other hand, is promoted by a difference in state character between the singlet and triplet states. More recently, multipolar systems have been introduced where one acceptor unit is connected to two or more donor units and vice versa. Aside from the above considerations, the possibility of symmetry breaking in the excited state is particularly intriguing in such multipolar systems. The intricate photophysics of TADF emitters poses severe challenges for its computational description while also providing an ideal test bed for evaluating the newest computational tools. The importance of CT states already makes it clear that the application of time-dependent density functional theory (TDDFT) is challenging and expected to affect energies as well as state characters. Suggestions for addressing this problem range from empirical corrections to optimal tuning of range-separated functionals to the avoidance of TDDFT altogether in favour of unrestricted ground-state DFT. Furthermore, state-specific excitedstate solvation effects have to be described at a high level considering that the common linear-response polarizable continuum model (LR-PCM) is inadequate for CT states with large electronhole separation and does not even provide any correction beyond zeroth order to triplet states due to their vanishing transition density. SOC also plays a role, having an intricate dependence on the state character where small amounts of mixed character lead to appreciable coupling. Finally, the importance of vibronic coupling between the locally excited (LE) and CT triplet states has been emphasised providing new dynamical routes to rISC. |
611cc248f5c7c37347dd1c61 | 1 | A common theme in the above discussions is the importance of excited states of different character, in particular LE and CT states. Accurately discussing these states and the mixing between them can become a challenge on its own and a simple discussion of frontier orbitals is often inadequate. Thus, aside from the necessity of choosing an accurate electronic structure method, it becomes exceedingly important to choose a meaningful and reproducible method for analysing the computations. Indeed, a range of tools for categorising excited states are available. |
611cc248f5c7c37347dd1c61 | 2 | Categorisation of excited states occurs prominently via different measures of charge transfer, which are a natural choice for push-pull systems as studied here. However, special care has to be taken for symmetric systems, including the molecules studied here, noting that the dipole moment and related charge displacement metrics are not reliable descriptors for the charge transfer character in symmetric systems. A powerful option to overcome this problem amounts to base the analysis on a correlated electron-hole pair within an effective exciton picture; and this was shown to be particularly suitable even for challenging cases with high symmetry. Aside from categorising excited states, there has been an increasing push toward a rationalisation of the underlying energetics and, in particular, the singlet-triplet gap. The applied approaches range from a formal discussion of the underlying molecular orbital integrals to a direct extraction of computational data from actual electronic structure computations and applying it for energy decomposition and visualisation. It is the purpose of this work to exemplify the above discussion on four different TADF candidates highlighting their intricate photophysics as well as methodological challenges in the computational description. The four molecules studied are shown in and Cz-AQ have been previously synthesised and characterised. We will study these in detail moving on to predicting the properties of Cz-BDT-SO 2 and Cz-BDF. Within this work, we contrast these four related molecules highlighting the profound changes in their observed photophysical properties following seemingly inconspicuous changes in the acceptor unit. |
611cc248f5c7c37347dd1c61 | 3 | The employed acceptor unit BDT is an electron deficient ringfused heterocycle and a synthetic intermediate towards the synthesis of the fully aromatic and strongly-electron donating benzodithiophene moiety which is widely exploited in high performance donor polymers for organic solar cells. While benzodithiophene has seen great utilisation as a donor, BDT itself has received much less attention as an acceptor unit despite its deep LUMO energy which is ca. 0.39 V lower than that of the carbocyclic homologue anthraquinone. Cz-BDT was designed to complement one of the best reported red TADF luminogens at the time, Cz-AQ, and induce a redshift in emission due to the lower LUMO of BDT. This did lead to a >100 nm redshift in emission wavelength compared to Cz-AQ, and TADF was evident from the characteristic double decay in the transient absorbance spectra, however the photoluminescence quantum yield (PLQY) was greatly reduced in both solution and dilute thin film measurements from ≈0.60 for Cz-AQ in solution to <0.10 for Cz-BDT. We note that in the meantime alternative strategies in the design of red TADF emitters have led to high PLQY extending into the near infrared range. Nonetheless, identifying the root cause of the vast drop in PLQY between Cz-AQ and Cz-BDT presents a useful challenge to inform future molecular design and to provide deep insight into the photophysics of TADF emitters along with methodological challenges in its computational description. |
611cc248f5c7c37347dd1c61 | 4 | Here, we also study Cz-BDT-SO 2 where dearomatisation of the fused heterocycles will serve to further reduce the LUMO (and to a lesser extent the HOMO) through inductive effects and remove the influence of the S lone pairs on the electronic properties of the molecule. Oxidation of S to SO 2 serves to stabilise the LUMO and red-shift emission while it is also expected to enhance PLQYs and modulate singlet and triplet energies, ∆E ST , spin-orbit coupling effects, and solvatochromism. Finally, Cz-BDF is studied in order to identify the impact of light vs heavy heteroatoms on molecular geometries, excited state energies, and characters. |
611cc248f5c7c37347dd1c61 | 5 | Within this work, we first explain the methods used discussing the general strategy employed for analysing excited-state wavefunctions and proceeding to specifics of the computational details. The results are presented in some detail starting with general structural parameters and frontier orbitals, proceeding to a discussion of the vertical excitations in terms of the state characters present and the computational description, finishing with an exploration of excited-state minima in solution. Before concluding, we proceed by a compact discussion summarising the photophysics, highlighting general differences between singlet and triplet state wavefunctions, and reviewing the most critical methodological aspects. |
611cc248f5c7c37347dd1c61 | 6 | (1) where Ψ 0 and Ψ I are the ground and excited state wavefunctions and r h and r e represent the coordinates of the excitation hole and the excited electron electron respectively. The excited state described by the 1TDM can be decomposed into local and CT contributions by computing the charge transfer numbers defined as the integral: |
611cc248f5c7c37347dd1c61 | 7 | Eq. ( ) describes a sum over orbital pairs where ψ h t and ψ e t are the NTOs representing the hole and electron, and λ t is the amplitude of the transition. In the specific case that a state can be described by a single transition between two NTOs, in other words, the state is not multiconfigurational, the 1TDM can be factorised into a single pair of NTOs: |
611cc248f5c7c37347dd1c61 | 8 | Thus, for simple transitions involving only one orbital pair, the charge transfer numbers are completely determined by the NTOs and are a product of hole charges on fragment A, q h A , and electron charges on fragment B, q e B . In more general cases, the CT numbers also encode interference effects between the different excited configurations (cf. Ref. 22). |
611cc248f5c7c37347dd1c61 | 9 | The CT numbers constitute a versatile tool and have been ap-plied successfully for, e.g., interacting chromophores, pushpull systems and transition metal complexes. However, a downside of this analysis is that it depends on the a priori definition of a fragmentation scheme. To overcome this problem and obtain a more fundamental measure of charge transfer, we compute an exciton size defined as the root-mean-square separation of electron and hole |
611cc248f5c7c37347dd1c61 | 10 | where the bra/ket notation refers to integration with respect to r h and r e . The exciton size, defined in this way, is a transferable measure that provides insight into charge transfer between isolated molecules, covalently bonded donor-acceptor systems, as well as large conjugated π-systems. Purely local excitations generally have a d exc of 4 Å or less, where anything above this value indicates at least partial CT character. In addition we will utilise the absolute mean electron-hole separation |
611cc248f5c7c37347dd1c61 | 11 | The d he value, which is closely related to the dipole moment, measures the distance between the centroids of the hole and electron distributions. In the present context, d he vanishes if both D units are equally involved in the excitation and only becomes significantly different from zero if there is a localisation of the excitation on one of them. It is, therefore, an ideal tool to monitor symmetry breaking in the excited state. |
611cc248f5c7c37347dd1c61 | 12 | Computations are performed on Cz-BDT, Cz-AQ, Cz-BDT-SO 2 and Cz-BDF as shown in Fig. . The tertiary butyl groups used to improve solubility in the experimental studies have been excluded. Computations in this study are divided into three parts: (i) an initial optimisation of the ground state geometry, (ii) vertical excitations with different functionals, and (iii) excitedstate geometry optimisations in solution. |
611cc248f5c7c37347dd1c61 | 13 | For step (i) the molecular geometries of Cz-BDT and Cz-AQ were optimised at the ωB97X-V/def2-SVP level of theory and confirmed as being minimum energy structures by a vibrational analysis at the same level. For step (ii), to determine an appropriate computational method to describe the excited state character of the molecules, the first 10 vertical excitations are first computed at the ri-ADC(2) level, using the def2-TZVP basis set. The first 10 excited states are, then, recomputed using five different density functionals with TD-DFT in the Tamm-Dancoff approximation (TDA), considering that the TDA is expected to reduce problems associated with triplet instabilities. The density functionals evaluated are PBE, 65 PBE0, 66 ωPBEh, CAM-B3LYP, and ωB97X-V, with the def2-SV(P) basis set. In the case of ωPBEh, we used a range separation parameter of ω = 0.1 a.u. and a global amount of Hartree-Fock exchange of 20% following previous experience on related donor/acceptor systems. The ωPBEh/def2-SV(P) level of theory is selected for step (iii) |
611cc248f5c7c37347dd1c61 | 14 | based on results from density functional benchmarking to the experimental absorption maximum and the ri-ADC(2) state characters. The ground state (S 0 ) structures of all four molecules were optimised using spin-restricted Kohn-Sham DFT (RKS) along with the ωPBEh functional in toluene solution (ε =2.3741) using a conductor-like polarisable continuum model (PCM). Excited singlet states (S 1 ) were optimised using time-dependent density functional theory (TDDFT) along with the ωPBEh functional using a toluene solvent model (ε =2.3741, ε ∞ =2.2403) using a linear response (LR-PCM) approach for excited-state solvation. Excited-triplet states (T 1 ) were optimised at the TDDFT/LR-PCM level of theory along with additional ground-state spinunrestricted Kohn-Sham DFT computations (UKS/PCM). No empirical dispersion correction is used as there is no clear way of choosing appropriate parameters for a manually adjusted functional and since preliminary observations showed that dispersion only has a minor effect on these linear molecules. |
611cc248f5c7c37347dd1c61 | 15 | Based on the S 0 optimised geometries, we compute the TDDFT vertical excitation energies of the first 7 excited states using two different solvation methods, LR-PCM and a perturbative statespecific solvation model (pt-SS). At the excited-state geometries we perform TDDFT computations using the LR-PCM and SS-PCM models. Specifically, the following workflow is used: All three PCM approaches start with a RKS/PCM ground-state calculation. LR-PCM, which is the default approach, proceeds with a TDDFT computation including a correction for non-equilibrium solvation added directly to the TDDFT response matrix. The ptSS approach, on the other hand, starts with a zeroth order TDDFT response matrix -not including any corrections for solvation. It proceeds by computing a state-specific correction term based on the zeroth order response vector and the relaxed ground state density. Oscillator strengths (f) were computed as f = 2/3 × ∆E × µ 2 by combining the original transition dipole moments µ with the perturbatively corrected excitation energies ∆E. Finally, SS-PCM is technically carried out via two subsequent TDDFT jobs: in the first step the solvent field is equilibrated to the state of interest and in the second step the DFT orbital optimisation as well as TDDFT are carried out in the equilibrated solvent field. |
611cc248f5c7c37347dd1c61 | 16 | The D-π-A-π-D molecules studied here are comprised of carbazole (Cz) donor units, phenylene (Ph) ring π bridges, and the acceptor core (BDT or AQ). These molecules have a significant degree of conformational flexibility because rotation is possible around the carbazole-phenyl bonds and the phenyl-core bonds. This gives rise to four independent dihedral angles, denoted as θ 1 /θ 1 and θ 2 /θ 2 (see Fig. ). To restrict the associated number of conform-ers, we will consider only molecules of C 2 symmetry (θ 1 = θ 1 , |
611cc248f5c7c37347dd1c61 | 17 | . Furthermore, we find that the energy difference between the C i and C 2 conformers is negligible (see Table , ESI) indicating that both, along with other conformers, should be present at room temperature. To obtain consistent results, we select C 2 conformers for all subsequent calculations, unless specified explicitly. Optimised ground-state geometries, considering the C 2 case, are presented in Fig. and the geometric data for C 2 and C i are shown in Table . Generally speaking, we find significant twisting for both torsion angles considered. Starting with the discussion of the C 2 geometries, the Cz/Ph twisting angles (θ 1 /θ 1 ) are consistently ≈57 • for both molecules. By comparison, the twisting around the Ph/core junction (θ 2 /θ 2 ) is notably reduced owing to reduced steric hindrance. Twisting in Cz-AQ is larger than in Cz-BDT (39 • vs 26 • ) which can be understood by considering that the AQ group has two hydrogen atoms in the vicinity of the Ph group whereas BDT only has one. Cz-BDT is, thus, expected to allow for enhanced conjugation between the Ph and BDT groups and we will explore the consequences of this on the observed photophysics in more detail below. Proceeding to the bond distances, we find that the Cz-Ph distances (d 1 /d 1 ) are very similar for both molecules (≈ 1.417 Å). For the d 2 /d 2 values however, the bond distance is shorter in Cz-BDT (1.479 Å) than Cz-AQ (1.491 Å) following the same trends as expected for the bond angles, i.e. conjugation is stronger for Cz-BDT. Table also presents results for the C i geometry as well as data from previous work on the two molecules 4,29 using the B3LYP functional. The observed trends between the three data sets are consistent indicating that these geometric parameters are fairly robust with respect to both the precise conformer studied and the functional chosen. |
611cc248f5c7c37347dd1c61 | 18 | To discuss the electronic structure of this system, we start with the frontier molecular orbitals as is usually done for these types of molecules. The highest occupied molecular orbital (HOMO) and lowest unoccupied MO (LUMO) for Cz-BDT are shown in donor units and the LUMO is located on the acceptor core and there are only negligible contributions on the bridging Ph units. |
611cc248f5c7c37347dd1c61 | 19 | A transition from the HOMO to the LUMO would, therefore, produce an excited state with a large amount of charge transfer (CT) character, shifting electron density from the donor to the acceptor. However, HOMO/LUMO plots can only ever provide a very rough picture of the electronic structure and we will proceed to a detailed analysis of the excited states and all orbitals involved, below. |
611cc248f5c7c37347dd1c61 | 20 | Proceeding to the excited states of Cz-BDT and Cz-AQ, we first endeavour to find a computational method that describes their states accurately. To do so, we consider experimental results as well as reference calculations at the ab initio ri-ADC(2)/TZVP level of theory. Experimental results are presented in Table . Cz-BDT is found to have an absorption maximum at 2.65 eV and a strongly red-shifted emission at 1.87 eV. In the case of Cz-AQ both values are about 0.3 eV higher. Table also highlights the considerable difference of the fluorescence quantum yield Φ measured in solution between the two molecules, showing a more than sixfold drop when going from Cz-AQ to Cz-BDT. Whereas, the shift in absorption and emission maxima can be explained by the lowering of the LUMO, it is harder to gain understanding of the drop in quantum yield. |
611cc248f5c7c37347dd1c61 | 21 | The excitation energies for Cz-BDT are presented in the upper panel in Fig. showing that this molecule possesses four lowenergy triplet states (red) before the first singlet state (black). Viewing the lower panel of Fig. (b), we find that T 1 is dominated by local ππ * character on the BDT core, represented in blue, with smaller Ph→BDT CT contributions (green). The corresponding NTOs are shown in panel (c) highlighting that the hole NTO (shown in blue/red) is a π-orbital on BDT with some contributions on the Ph bridge whereas the electron NTO (shown in green/orange) is a π * -orbital located right at the centre of BDT resembling the LUMO shown in Fig. . Proceeding to the next three triplet states, we find that these are a mixture of local ππ * character on BDT (blue) and nπ * character (orange) with increasing nπ * character from T 2 to T 4 . The first singlet state (S 1 ) lies just above 3.0 eV and is similar in character to T 1 albeit with more charge transfer character (red and green). This is also reflected by the dominant hole NTO, shown at the bottom in panel (c), which has extended contributions on the Ph bridges. The vertical gap between T 1 and S 1 is calculated to be 0.42 eV. The S 2 and S 3 states are locally excited states dominated by nπ * character. The S 4 state lying at 3.28 eV is a CT state which contains significant Cz→BDT character (red). For the T 5 and T 6 states, we find a mixture of state characters with roughly 40% of the excitation character attributed to local excitations on Ph and Cz. |
611cc248f5c7c37347dd1c61 | 22 | Reviewing the states in the canonical orbital picture, we find that all states go predominantly into the LUMO, with only the T 5 and T 6 states also containing significant contributions into higher virtual orbitals (LUMO+1 and LUMO+3). Conversely, the HOMO only plays a minor role for the low energy states and of all the states considered here, only S 1 and S 4 and none of the triplet states have notable HOMO-LUMO character (62 % for S 1 , 85 % for S 4 ). This highlights that a simple visualisation of the HOMO and LUMO can by no means explain the photophysics of complicated TADF systems as studied here. |
611cc248f5c7c37347dd1c61 | 23 | The oscillator strengths are represented via the colour shading in the upper panel of 4 (b). At the highly symmetric geometry shown, the first bright state is S 4 at 3.28 eV, with an oscillator strength of 0.45. The lowest ππ * state, S 1 at 3.06 eV, possesses vanishing oscillator strength within the computation. This can be understood by the fact that the analogous state is symmetry forbidden under C i symmetry and assuming that similar orbital interactions are also present at the C 2 geometry. However, once the symmetry is broken, this state is expected to borrow intensity from the bright state suggesting that this state contributes to the lowest energy band in the absorption spectrum, which is found experimentally at 2.65 eV. Next, we move to the second molecule studied here, Cz-AQ. As opposed to Cz-BDT where the lowest state was of local ππ * character, we find in the case of Cz-AQ that the first three states (S 1 , T 1 , T 2 ) are all of nπ * character (orange). The calculated vertical gap between S 1 and T 1 is 0.32 eV which is 0.1 eV smaller than found in Cz-BDT. The T 3 and T 4 states are mixed in character, with mostly local contributions on AQ and smaller amounts of charge transfer from Ph and Cz to the core. The S 2 state is an nπ * state. S 3 and S 4 are both described as charge transfer states with significant Cz→BDT character. Only S 4 has an appreciable oscillator strength, which can, again, be understood in terms of symmetry properties. The S 4 excitation energy is 3.55 eV which is 0.64 eV higher than the experimentally determined absorption maximum, thus ri-ADC(2) overestimates the energy of the bright state by about 0.5 eV for both Cz-BDT and Cz-AQ. Conversely, ri-ADC( ) is expected to underestimate the energies of nπ * states by a few tenths of an eV. Nonetheless, we believe that ri-ADC(2) provides a good reference for the expected state characters involved. In particular, these results indicate that all types of states, i.e., local ππ * /nπ * states and CT states, play a role. |
611cc248f5c7c37347dd1c61 | 24 | Finally, viewing the difference between Figures and, we find that the S 1 and T 1 states of Cz-BDT have significant locally excited ππ * contributions on BDT whereas S 1 and T 1 are dominated by nπ * character for Cz-AQ. Proceeding to the higher excited states, we find enhanced CT (red) for Cz-AQ. Thus, we can already anticipate that the photophysics of Cz-AQ will be dominated by its CT states whereas locally excited ππ * contributions are more important for Cz-BDT. |
611cc248f5c7c37347dd1c61 | 25 | Having described the states at the ab initio ri-ADC(2) level, it is of interest whether an approximate density functional can be used with the aim of both saving computational time, and to find a method that matches closer with experimental absorption wavelengths. For this purpose, the first five singlet and triplet states for Cz-BDT and Cz-AQ are calculated using TDDFT with the PBE, PBE0, ωPBEh, CAM-B3LYP and ωB97X-V functionals. Figures and (ESI) contain the results for Cz-BDT and Cz-AQ respectively, with the state characters assigned as explained in 4 (a). The experimental absorption maximum is shown as a dashed orange line. The exciton size (d exc ) for the excited state [Eq. 6], an alternative measure for charge transfer, is shown in the bottom panel. In Fig. the functionals are arranged according to an effective increase in Hartree-Fock exchange from left to right: PBE (0%), PBE0 (25%), ωPBEh (20-100%, ω=0.1 bohr -1 ), CAM-B3LYP (19-65%, µ=0.33 bohr -1 ) and ωB97X-V (16-100%, ω=0.3 bohr -1 ) where the amount of Hartree-Fock exchange (HFX) and the range-separation parameter (ω/µ) are given in parentheses. Overall, with increasing HFX we find that the state energies, vertical singlet-triplet gaps, and the oscillator strengths of bright states increase. |
611cc248f5c7c37347dd1c61 | 26 | More strikingly, the middle panel in Fig. reveals the dramatic difference in the state characters obtained with the different functionals. In the case of PBE on the left, the first 8 states are almost entirely of Cz→BDT CT character (red). By contrast, any substantial CT is missing for ωB97X-V on the right. Only the three functionals in the middle contain the mixture of local ππ * / nπ * states and CT states as found for ri-ADC (2). The same trend is also found for the exciton sizes in the lower panel. The first eight states for PBE show enhanced charge separation (d exc > 10 Å) whereas no state with an exciton size above 6 Å is found for ωB97X-V. And, again, more diverse values are found for the functionals in between. The difference in state character is reflected by changes in oscillator strength, shown as shading in the top panel of Fig. , which is strongly increased for the functionals with more HFX. These differences highlight the charge transfer problem in TDDFT showing that varying amount of HFX does not only affect the energies but also excitedstate properties. It is noteworthy, here, that a larger amount of "exact" exchange does not necessarily produce better agreement with higher-level computational methods considering that a reduced amount of exchange corresponds to a physically meaningful screened Coulomb interaction, cf. Ref. 7. |
611cc248f5c7c37347dd1c61 | 27 | We proceed to detailed results for the individual functionals. For PBE we find two sets of four almost degenerate CT states (two singlets and two triplets). These can be understood in the sense that they are composed of independent Cz→BDT transitions on the left and right hand side of the molecule, which are effectively decoupled and neither split via Coulomb nor exchange interactions. The exciton sizes are all above 10 Å, which is similar to the distance from the centre of the Cz donor to the centre of the BDT acceptor highlighting that charge transfer between them dominates with no intermediate locally excited contributions playing a role. Considering the global hybrid PBE0, we still find significant amounts of CT character for the first four states but there is already much more structure when compare to PBE. In particular, it is found that the T 1 state has enhanced local character (blue) and an associated reduction in exciton size to 7. glet states around 3 eV with a mixture of local ππ * and nπ * as well as CT character. We find two bright states at 3.01 and 3.06 eV, which possess significant amounts of, both, nπ * and CT character. This should be understood in the sense that there is an accidental degeneracy between an nπ * and CT state, producing this mixing. Moving to the remaining two functionals, we find that the first state with appreciable CT character is above 3.5 eV for CAM-B3LYP and no CT state is found at all for ωB97X-V within the energy window considered (up to 4.5 eV). |
611cc248f5c7c37347dd1c61 | 28 | For Cz-AQ (Figure , ESI), we find broadly the same story: PBE and PBE0 overestimate the amount of CT character of the lowest lying states and underestimate the energy of the bright state, while ωB97X-V underestimates the CT character and severely overestimates the energy of the bright state. The main differences between ωPBEh and CAM-B3LYP are the energy of the bright singlet CT state, with ωPBEh providing a better value relative to the experimental absorption maximum, and the ordering of the states with respect to the state character. With the ωPBEh functional, we find a similar mixture of local ππ * / nπ * and CT states as for ri-ADC(2). The only difference is that the relative energies of the nπ * states are somewhat raised yielding a different ordering of the dark low-energy states. However, as discussed above, ri-ADC( ) is expected to slightly underestimate nπ * state energies, thus supporting the description by ωPBEh. |
611cc248f5c7c37347dd1c61 | 29 | For both Cz-BDT and Cz-AQ, the ωPBEh functional gives a vertical excitation energy for the lowest bright state at a value in close proximity to the experimental value (indicated as dotted orange line in Figures and). Here, experience suggests that due to vibronic effects, the vertical excitation should be about 0.1 eV above the experimental maximum, therefore indicating excellent agreement of the computed values. Furthermore, ωPBEh succeeds in describing the state characters of the low-energy states involved when compared to the higher-level ri-ADC(2) method and is expected to capture the overall photophysics well. Therefore, we will proceed by using the ωPBEh functional in the further course of the study. |
611cc248f5c7c37347dd1c61 | 30 | Having described the vertical excitations and identifying ωPBEh as a method for providing the overall excited state characters effectively, we now turn to an analysis of the excited state minimum geometries in solution for Cz-BDT and Cz-AQ. First, the geometries of the S 0 , S 1 , and T 1 minima are optimised using ωPBEh/def2-SVP within toluene solvation, considering that toluene was used in the experimental studies considered. The S 1 is always optimised with TDDFT whereas, following Ref. 6, we investigate two possibilities for optimising the T 1 minimum, an excited-state optimisation using TDDFT and a formal groundstate optimisation using UKS. The key structural parameters are outlined in Table , and the geometries are shown in Fig. . Generally speaking, we find that upon excitation the molecules planarise, i.e. dihedral angles become smaller, and that the interring distances become shorter. Cz-BDT retains the two-fold symmetry in all computations whereas we observe symmetry-breaking in the excited state for Cz-AQ. Starting with Cz-BDT, we find that variations in the Cz-Ph torsion θ 1 /θ 1 are relatively minor whereas the θ 2 /θ 2 values become close to zero for S 1 and T 1 . This means that the Ph-BDT-Ph system becomes almost planar after photoexcitation, see also Figure , effectively producing one extended π-system, and we will revisit this point below. In Cz-Aq on the other hand, we find clear evidence of symmetry-breaking for the excited state minima: the angles on one side of the molecule (θ 1 and θ 2 ) remain at values close to the S 0 minimum, however θ 1 and θ 2 are reduced. The T 1 minimum for Cz-AQ, optimised with either TDDFT or UKS, has one of the Ph bridges almost in plane with the core, whilst for the S 1 minimum this lies at an intermediate value between the S 0 and T 1 minima. We proceed by discussing the excited states at the individual geometries. For this purpose, we consider two different approaches, the standard LR-PCM method also used for the TDDFT optimisations, as well as a more involved state-specific approach, which is expected to provide an improved description of CT states. For the vertical absorption (S 0 ), we use the perturbative (ptSS) approach whereas for emission (S 1 /T 1 ) we use the equilibrated SS-PCM approach. Starting the discussion with Cz-BDT, we present data for the lowest four triplet and three singlet excited states in Figure . In comparison to the unsolvated model in Fig , we find similar state characters when using the LR-PCM model at the S 0 geometry for Cz-BDT. However, we find that the ππ * states (blue, green, red) are somewhat shifted down in energy producing a different ordering of the states. This shift also removes the accidental degeneracy found between the bright ππ * state and the nπ * state that was seen in the unsolvated calculation. Calculating the same excitations under the ptSS solvation scheme gives stabilisation to states with charge transfer character, and we now find the bright CT-dominated S 2 state at 2.71 eV which is in nearperfect agreement with the experimental absorption maximum of 2.65 eV. |
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