Nanoscale Active Sites for the Hydrogen Evolution Reaction on Low Carbon Steel

. To fully elucidate the structural controls on corrosion-related processes at metal surfaces, experimental measurements should correlate and compare directly structure and activity at the scale of surface heterogeneities ( e.g. , individual grains, grain boundaries, inclusions etc. ). For example, the hydrogen evolution reaction (HER), which usually serves as the cathodic counterpart to anodic metal dissolution in acidic media, may be highly sensitive to surface microstructure, highlighting the need for nanoscale-resolution electrochemical techniques. In this study, we employ scanning electrochemical cell microscopy (SECCM) in conjunction with co-located scanning electron microscopy, electron backscatter diffraction, and energy dispersive X-ray spectroscopy to elucidate the relationship between surface structure/composition and HER activity on low carbon steel in aqueous sulfuric acid (pH ≈ 2.3). Through this correlative electrochemical multimicroscopy approach, we show that the HER activity of the low index grains (slightly) decreases in the order (100) > (111) > (101), with grain-dependent free energy of hydrogen adsorption (calculated for the low index planes of iron using density functional theory, DFT) proposed as a tentative explanation for this subtle structural-dependence. More significantly, we show that the HER is greatly facilitated by sub-micron surface defects, specifically grain boundaries and MnS inclusions, directly identifying these heterogeneities as potential “cathodic sites” during (atmospheric) corrosion. This study demonstrates the considerable attributes of correlative SECCM for identifying nanoscale active sites on surfaces, greatly aiding understanding of corrosion and electrocatalytic processes.


Introduction
Resolving the relationship between surface microstructure (e.g., crystallographic orientation, inclusions and grain boundaries) and electrochemical processes at metals and alloys is vital to advance understanding of corrosion. Although the structural and compositional heterogeneities of metal surfaces are routinely studied using ex situ high-resolution microscopy/spectroscopy, 1 corrosion measurements are often performed with classical macroscopic or "bulk" electrochemical techniques 2 that are unsuitable for assessing heterogeneously active surfaces. 3 Scanning electrochemical cell microscopy (SECCM) provides a means of making nanoscale electrochemical measurements at distinct target sites by using the droplet (meniscus) formed at the end of an electrolyte-filled nanopipet to wet a small area of an electrode surface and create a local electrochemical cell. [4][5][6] SECCM is the next-generation of the well-known electrochemical droplet cell (EDC) technique, 7 and differs from the more widely-used scanning electrochemical microscopy (SECM) [8][9] in that with SECCM only small portions of a surface are exposed to solution, through brief meniscus contact from a nanopipet probe at a series of pixels, and electrochemical properties are measured directly (e.g., by voltammetry, chronoamperometry, etc.) at each point. This attribute is particularly beneficial for highly reactive surfaces that undergo corrosion. In further contrast to SECM, the SECCM response also reveals the corresponding surface topography synchronously, with ≈2 nm vertical resolution having been demonstrated, 10 so that the surface location of nanoscale electrochemical measurements are easily identified. Recently, SECCM has been employed to make local electrochemical measurements on single nanoparticles, [10][11][12] transition metal dichalcogenides, [13][14] polycrystalline metals [15][16][17] and sp 2 carbon materials 18 using nanopipets with diameters as small as ≈30 nm. [10][11] SECCM is a potentially powerful tool for corrosion-related research, as demonstrated by proofof-concept studies that revealed the role of microstructure on the electrochemical (corrosion-related) behavior of low carbon steel in neutral pH solutions. 4 SECCM greatly advances the capabilities of conventional EDC techniques by improving spatiotemporal resolution, throughput (number of measurements on a sample), and the density of data, among other key features. 19 In the present study, we focus on the influence of surface microstructure on the rate of the hydrogen evolution reaction (HER) on low carbon steel in aqueous sulfuric acid (pH ≈ 2.3). Although the HER has traditionally been explored in the context of electrocatalysis, 20 this process serves as the cathodic counterpart to anodic metal dissolution during corrosion in acidic media. 21 In addition to the SECCM "droplet-cell" configuration mimicking the conditions of atmospheric corrosion, 3 low carbon steel is frequently exposed to acid media in many industrial applications, including acid pickling and acid cleaning/descaling. 22 Thus, elucidating the structural-dependency is critical to understanding and further predicting the characteristics of galvanic corrosion cells that are formed on macroscopic metal surfaces during practical use.

5
In the present study, SECCM has been employed in conjunction with the co-located microscopy techniques scanning electron microscopy (SEM), electron backscatter diffraction (EBSD) and energydispersive X-ray spectroscopy (EDS) to explore the role of crystallographic orientation, grain boundaries and MnS inclusions on the rate of HER at low carbon steel. The study significantly advances our previous work, 4 with considerable improvements in spatial-resolution and imaging time, in addition to the implementation of density functional theory (DFT) calculations to support the grain-dependent electrochemical data. Sub-microscale surface defects (e.g., grain boundaries and MnS inclusions) are revealed as important cathodic sites.

Experimental Section
Electrode material and chemical reagents. The low carbon steel sample used in this study (composition detailed in Table 1)  sample was subsequently washed with acetone, soapy water and deionized water, before being blown dry. Sulfuric acid (H2SO4, Merck, 96%) was used as supplied and diluted using ultra-pure deionized water (Integra HP, Purite, U.K.), which has a resistivity of 18.2 MΩ cm at 25°C. Table 1. Chemical composition of the low carbon steel, determined using energy dispersive X-ray spectroscopy.
Surface characterization. SEM, EBSD and EDS characterization was performed with a Zeiss SUPRA FE-SEM (Zeiss, Germany), using a Nordlys EBSD detector (Oxford Instrument, U.K.) and an X-max 50 mm 2 energy-dispersive X-ray spectroscopy (EDS) detector (Oxford Instrument, U.K.). SEM images and EDS data were collected at 10 keV, whereas EBSD images were collected at 20 keV, with the sample tilted at 70° to the detector. Following EBSD characterization, grains selected for further immediately halting the z-approach (e.g., see the Supporting Information, Figure S1). Note that the pipet itself did not make physical contact with the substrate.
Upon meniscus contact with the substrate, chronoamperometric (i−t) measurements were made at a series of predefined locations (i.e., in a grid) to build up an 'electrochemical map' of the surface.
The probe was retracted from the surface after each measurement before being moved to the next location in a chronoamperometric 'hopping mode'. A visible droplet 'footprint' was left on the surface after each i−t experiment, which was visible in FE-SEM and used for subsequent co-located (ex situ) surface analysis with EBSD and/or EDS. Measurements of the droplet 'footprint' sizes are displayed in the Supporting Information, Figure S2.
The entire SECCM apparatus was on mounted on an optical  23 calculations with a plane-wave kinetic energy cut-off of 600 eV, which was found to give converged binding energies to 2 significant figures. Calculated data were also converged with respect to Brillouin zone sampling, using a Monkhurst-Pack grid of 9 × 9 × 1 k-points with no origin shift. 24 To account for the core atomic states, ultrasoft pseudopotentials 25 where EH+bare, Ebare, and EH refer to the energy of the plane with a hydrogen atom adsorbed onto it, the energy of the bare plane and the energy of a hydrogen atom in the center of a vacuum box, respectively.
The same parameters were used for the slab calculations.
Throughout these calculations we used an electronic energy convergence tolerance of 2×10 -6 eV. The Gaussian electronic smearing scheme was used, with a smearing width of 0.1 eV, to account for the metallic nature of this system and the electronic structure was optimized using the Pulay DIIS scheme. 29 We used the BFGS geometry optimization scheme 30 with tolerances of 2×10 -5 eV/atom in energy, 0.05 eV/Å in maximum force, 0.002 Å in maximum atomic displacement and, in the case of the variable-cell bulk geometry optimization, 0.1 GPa maximum stress.

Results and Discussion
SECCM: operational principles. In this study, we employ the single barrel SECCM protocol, detailed in Figure 1a, with a pixel acquisition rate of ≈1 s pixel −1 using a probe diameter of 150 nm. A potential, −Eapp, was applied to a Pd/H2 quasi reference counter electrode (QRCE) inserted into the electrolyte in an SECCM nanopipet probe, with respect to the substrate (working electrode) surface. Note that all potentials herein have been calibrated to the Ag/AgCl (3.4 M KCl) scale, after measurements. The SECCM probe was approached to the substrate at a series of predefined locations, and when meniscus contact was made (without physical contact from the nanopipet), a current, isurf, flowed as the electrochemical circuit was closed (e.g., Supporting Information, Figure S1). This was used as the feedback signal to halt the approach of the probe (and map the surface topography from the corresponding x,y,z coordinates). Upon surface-meniscus contact, electrochemical measurements ( Figure 1b) were carried out within the confines of the wetted area, the 'footprint' of which was visualized, after experiments, using SEM, with example data shown in Figure 1c.
Herein, chronoamperometric (current-time, i−t) measurements were made, by stepping Eapp at each scanning point. The pulse potential was selected after inspection of the linear-sweep voltammogram obtained from low carbon steel in 5 mM H2SO4 using the SECCM configuration, with typical data shown in the Supporting Information, Figure S2. During the approach, Eapp was in the passive region (0.463 V vs Ag/AgCl), which provided a reliable feedback signal for positional control (see Figure S1). Upon meniscus contact of the probe with the surface, the potential was maintained at the approach potential for a further 10 ms which 'preconditioned' the surface by forming a thin passive film. Eapp was then stepped to a driving cathodic potential (-1.337 V vs Ag/AgCl) to quickly reduce the passive film and produce a stable substrate surface current, predominantly from the hydrogen evolution reaction (HER): Note that the oxygen reduction reaction (ORR) only makes a minor contribution to isurf at Eapp = −1.337 V vs Ag/AgCl, confirmed by comparing cyclic voltammograms obtained in the presence and absence of air (Supporting Information, Figure S2). The current-time transient during the preconditioning is at the background level due to the comparatively low magnitude of the currents relative to the reduction pulse, however, it can be viewed in isolation in the Supporting Information, Figure S3. This protocol was preferable to running a full voltammetric (current-potential, i−E) curve in the present study for three main reasons. The first reason was to minimize the scanning time (≈1 s pixel −1 , compared to ~85 s pixel −1 previously). 4 The second reason was that biased steel surfaces promote potential-dependent electrowetting 31 and a potential sweep approach may have introduced uncertainty as to the wetted area, whereas with a fixed potential we were able to measure the wetted area with confidence, after experiments (vide infra). The third reason is that sweeping the potential through the active dissolution region (i.e., the large anodic peak seen in Figure S2) causes significant damage to the surface and loads the near-surface electrolyte region (i.e., the meniscus cell) with soluble Fe-species, which can electrodeposit in the potential-region where the HER occurs, complicating the analysis.
To confirm that any pre-existing passive film was fully reduced upon approaching the steadystate current for the HER (achieved on the 10 ms timescale, vide infra), the total charge passed during the reduction pulse was compared to the approximate charge required to remove a film of Fe2O3, within the confined area of the droplet cell. Taking 5 nm as a conservative estimate of the thickness of the passive film on low carbon steel (in reality, likely to be <5 nm thick, as previously reported 32 ), the charge required to remove the film is <20% of the charge passed during the decaying portion of the reduction pulse, detailed in the Supporting Information, Figure S4. Therefore, it is certain that surface currents arising at the end of the reduction pulse (i.e., beyond 7 ms, vide infra) arise predominantly from the HER. The cathodic potential applied is also −0.85 V beyond where the passive potential range ends (from examination of Figure S2), therefore there is a considerable driving force for any passive film to be removed.
The hopping distance (separation between neighboring pixels) was set conservatively to 800 nm in order to avoid overlap between points of the scan (i.e., to ensure that each measurement was independent of the last; Figure 1c). This distance was much larger than the tip diameter (≈150 nm) due to wetting of the metal surface, consistent with previous reports of the enhanced wetting of microdroplets on steel during cathodic polarization. 31 After identifying the scanned area with SEM, co-located the underlying grain structure (vide infra). Furthermore, the wetted area could be measured to calculate local current densities. The wetted area was ca. 400 nm diameter on all grains, with no grain dependence, as shown in the Supporting Information, Figure S5. For reference, 100 pA detected with the SECCM configuration, herein, corresponds to a current density of ca. 80 mA cm -2 . It should be noted that the individual grains were also identifiable from the z-height (topographical) data, collected synchronously with the spatially-resolved i−t data during SECCM imaging (Figure 1e). The <20 nm height difference between the individual grains is due to surface-orientation-dependent polishing rates, and that surface height variation can be detected by SECCM highlights the excellent topographical imaging capability of the technique.

Hydrogen evolution reaction: crystallographic dependence.
In this section, we investigate the dependence of the HER rate (measured through the catalytic current) on the crystallographic orientation of low carbon steel, where the high spatial-resolution afforded by SECCM allows us to make a statistically significant number of measurements on individual grains presented by a low carbon steel sample in a 'pseudo single-crystal' approach. 33 The average isurf−t response extracted from all scanning points after stepping the potential from 0.463 V to −1.337 V vs Ag/AgCl for 10 ms is shown in Figure   1b. During the first ~6 ms of the pulse, isurf, arising from the HER, is not at steady-state and is also influenced from the finite rise time of the measurement (see Experimental Section for details). After ~6 ms, isurf approaches a steady-state and as a result we focus on this section of the transient for analysis.
Note that the relatively short time to steady-state is expected based on the high diffusion coefficient of the hydronium ion (H3O + ) in aqueous media (9.3 × 10 -5 cm 2 s -1 , measured previously 34 ) combined with the quasi-radial diffusion conditions inherent to the SECCM droplet cell configuration, particularly with the fine probe (ca. 150 nm in diameter) employed herein, as discussed in depth previously. 35 EBSD maps and corresponding spatially-resolved isurf maps taken from two areas of the low carbon steel surface are shown in Figure 2a and b, respectively. Note that the isurf maps displayed in  As alluded to above, the HER has been studied predominantly in the context of electrocatalysis, primarily on Pt-based materials, 36 for which the crystallographic orientation (structure) dependence is hotly debated. [37][38] Due to comparatively poor catalytic activity, Fe-based materials (e.g., steel) have received significantly less attention, which is perhaps surprising considering the important role of cathodic processes such as the HER in the corrosion of steel. The majority of literature concerning hydrogen-related processes on steel focuses on hydrogen embrittlement, and the diffusion of hydrogen into bulk steel. 39 In order to tentatively explain the grain-dependent HER rates on low carbon steel (i.e., Figure   2), we performed DFT calculations, focusing on the low index planes, i.e., (100), (101) and 111) of the body centered cubic (BCC) structure of iron. Given that the iron content of the substrate is ~99.5% (see Experimental Section), iron is considered to be representative of the low carbon steel surface and therefore appropriate for DFT. Figure 3a identifies the grains that possess an orientation within 10° of the (i) (100), (ii) (101) and (iii) (111) low index planes (shown schematically for a BCC unit cell).
Presented in Figure 3b is a histogram showing the average surface currents measured between 7.2 to 9.8 ms for all i−t measurements taken on the low index grains (identified in Figure 3a), which visually emphasizes why making multiple measurements on each grain improves the validity of any grain dependent trends. Evidently, the HER activity of the low index grains of the low carbon steel surface decreases in the order (100) > (111) > (101), albeit only slightly (vide infra), with mean isurf (between 7.2 and 9.8 ms) values of 80 ± 4, 71 ± 2 and 66 ± 3 (mean ± standard deviation), respectively.
Note that although the isurf values between 7.2 and 9.8 ms can be taken as qualitative indicators of relative HER activity, due to the cathodic potential applied (−1.337 V vs Ag/AgCl, see Figure S2) and low bulk concentration of H + ([H2SO4] = 5 mM), there is some contribution from mass transport (i.e., the HER is not purely surface-kinetic controlled). To illustrate this, considering that the diffusional flux in SECCM is approximately 10% of that for the same sized disk electrode, 13,40

22
To explore possible explanations for the grain-dependent HER activities, one must first consider the HER mechanism, which is generally accepted to follow one of two electrocatalytic pathways on metal surfaces in acidic media, Volmer-Heyrovsky or Volmer-Tafel: 20 H * + H + + e − → H 2 + * (3) where * donates an adsorption site on the metal surface, and Equations 2, 3 and 4 refer to the Volmer, Heyrovsky and Tafel step, respectively. The hydrogen adsorption free energy, ΔGH, is generally used as a descriptor of HER activity, 41 where for an optimal electrocatalyst, there is an appropriate balance between the strength of hydrogen adsorption (Volmer, Eq 2) and desorption (Heyrovsky/Tafel, Eqs 3 and 4) from the surface. In other words, if the binding energy is too low (i.e., ΔGH less negative), the adsorption step (Eq 2) will limit the rate of reaction and likewise the desorption step (Eqs 3 and 4), if the binding energy is too high (i.e., ΔGH more negative). Thus ΔGH values for the low index planes of iron were calculated using DFT, as presented in Table 2, for the adsorption sites depicted in the Supporting Information, Figure S6. In order to contextualize these values, a classical volcano-type relationship is assumed, taking value calculated for a Pt(111) surface (also presented in Table 2) as the approximate value for the 'peak' of the volcano. [42][43] Note that the ΔGH values calculated for Pt (111) are consistent with previous DFT studies. [44][45]  The calculated ΔGH values in Table 2 are broadly consistent with previous DFT studies on Fe, [46][47] as well as experimentally calculated Fe-H binding energies. 48 Using the example of the (100) plane, the ΔGH values for different adsorption sites are more (e.g., Bridge) and less (e.g., On Top) negative than the volcano "peak" [i.e., Pt(111)], meaning the different sites will fall on the ascending and descending branches of the volcano plot, 42-43 respectively, likewise for different grains [e.g., compare Fe(101) and Fe (111)]. This suggests that the rate determining step for HER (equations 2 -4, above) may vary between adsorption site on a given low index plane, as well as between different low index planes. In any case, taking Pt(111) as the ideal case, we can assume that sites with ΔGH values closest to Pt(111) will be more facilitative of the HER. Thus, we take the difference between the average ΔGH value (from all adsorption sites) for Pt(111), Δ H Pt(111) , and the average ΔGH value for each low index plane, Δ H Fe(hkl) on Fe as a qualitative indicator of relative HER kinetics, as summarized in Table 3. Table 3. The calculated average ΔGH deviations for each of the adsorption sites on the low index orientations of Fe from the average ΔGH value calculated for Pt(111).  (Table 2) are site-specific, meaning each low-index orientation possesses a range of sites with differing HER activities.

Crystal Plane |Δ
Thus, an important outcome from these findings is that while the classical volcano relationship is a convenient and powerful way for predicting the macroscale activity of different materials, as in HER electrocatalysis, 20 it is perhaps oversimplified when predicting the local (nanoscale) response of a heterogeneous electrode surface (e.g., polycrystalline metal). For example, the data in Table 2 suggest that the different low-index planes, or indeed the different adsorption sites within a given low-index plane of BCC iron may have large (order-of-magnitude) differences in HER activity, whereas the experimentally determined HER rates were found to show only a subtle grain dependence (Figures 2   and 3). In reality, as we show below, the rate of HER (and the susceptibility to corrosion-related phenomena) across a (non-ideal) polycrystalline alloy surface is more likely to be influenced by crystallographic defects, e.g., grain boundaries and inclusions.
HER activity at grain boundaries. We next consider the HER activity at grain boundaries between crystallites on polycrystalline surfaces, for which SECCM is becoming a particularly powerful technique. 17,33 The grain boundaries of polycrystalline metals are critically important in the context of corrosion, serving as sites for well-documented phenomena such as intergranular corrosion. 51 The intergranular corrosion of steels is commonly attributed to metallurgical features such as the enrichment of detrimental impurities or the depletion of beneficial alloying elements at grain boundaries. 52 This change in surface chemistry often results in preferential dissolution or in some cases, an enhancement in the cathodic half-cell process(es) at grain boundaries. 51 EBSD and corresponding spatially-resolved isurf maps of a grain boundary (with misorientation angles marked) that exhibits enhanced HER activity are shown Figure 4a and b, respectively. Evidently, elevated cathodic currents are detected at the grain boundary termination (ca. 50% increase compared to the surrounding grains), are clear from Figure 4b. It should be noted that the difference in HER currents between different low-index grains is on the order of 5−20% (see Figure 3), demonstrating that crystallographic defects such as grain boundaries are likely to be far more influential on cathodic corrosion-processes compared to variations in crystal orientation. A time-resolved video of the isurf response at this grain boundary can also be found in the Supporting Information, Movie S2. A further two examples are also presented in Figure 4c and d. It is interesting to note that not all of the grain boundaries exhibit enhanced HER activity (vide infra), clear from the isurf maps in Figure 4, as well as Figure 2, above. It should also be noted that in all cases, the elevated currents at the grain boundaries cannot be attributed to distortion of the SECCM meniscus cell (i.e., changes in the probed surface area), as the topographical variation between neighboring grains is on the sub-10 nm scale, confirmed through the synchronously obtained z-height data, plotted in the Supporting Information, Figure S7.
Additionally, the Supporting Information, Figure S5, shows that there is no variation in the wetting between scanning points located at positions on and adjacent to grain boundaries.
Several factors may result in enhanced catalytic activity at grain boundaries. Surface defects, such as grain boundaries, comprise coordinatively unsaturated sites (i.e., atoms with low lattice 27 coordinate numbers) that can serve as the "active sites" for electrocatalytic processes. 3,53 Indeed, such an effect was proposed in a recent SECCM study, 17 where enhanced electrochemical CO2 reduction activity was identified at grain boundaries on polycrystalline Au. Another possibility is that changes in the surface chemistry at grain boundaries (i.e., impurity enrichment or depletion) may give rise to a catalytically active surface that can facilitate the HER. Although we cannot distinguish between these possibilities herein, the results in Figure 4 demonstrate unequivocally that certain grain boundaries would be more likely to serve as cathodic sites on a macroscopic surface, during atmospheric corrosion (i.e., in the presence of acid rain).

HER activity at manganese sulfide inclusions. We now consider the response of individual sub-micron
MnS inclusions. Figure 5a shows an SEM image of an area scanned using SECCM, with the corresponding spatially-resolved isurf map shown in Figure 5b. The dark "spots" in Figure 5a, two of which are highlighted by the white box, are MnS inclusions, confirmed by performing EDS; sulfur map and spectra shown in Figure 5c and d, respectively. Focusing on the electrochemical map in Figure 5b, there are two blue pixels indicating off-scale current magnitudes corresponding to the sub-micron MnS inclusions, confirming these sites as local HER "hot spots". Similarly to the case for grain boundaries, the catalytic HER current measured at individual inclusions (up to ca. 100% compared to the surrounding grains) is far more significant compared to the difference in activity observed between grains of different crystal orientation ( Figure 3). Indeed, the exceptionally high activity of these sites is clear to see from the electrochemical activity maps in Figures 2 and 5, which is further supported by the detection of a range of other inclusions, as shown in the Supporting Information, Figure S8.
The EDC technique has previously been used to study the local dissolution of large MnS inclusions in steel [54][55] and we have also used SECCM to observe similar behavior on low carbon steel, in neutral pH media. 4 Here, we have been able to measure the electrochemical (electrocatalytic) activity of inclusions (ca. 0.2 -1 μm in size) more directly (i.e., the inclusions constitute all or most of the probed area). Large MnS inclusions have previously been shown to be responsible for enhanced hydrogen trapping on steel surfaces, which can lead to hydrogen induced cracking, [56][57] and blistering at 30 these sites. 58 Our results further emphasize the importance of inclusions as highly active cathodic sites on polycrystalline low carbon steel.

Conclusions
In this study, we have leveraged recent technical advances in scanning electrochemical cell microscopy (SECCM) to investigate the structure-dependent cathodic activity of low carbon steel in aqueous sulfuric acid (pH ≈ 2.3), in the context of atmospheric (acid rain) corrosion. Focusing on the HER, and using a fine nanopipet probe (diameter ≈ 150 nm) in a fast chronoamperometric (i−t) scan-hopping protocol (ca. 1 s pixel −1 ), we have shown unequivocally that the rate of this reaction varies spatially across the surface of low carbon steel. By combining these spatially-resolved electrochemical data with co-located structural information from SEM, EBSD and EDS in a correlative electrochemical multimicroscopy approach, HER activity on the low-index planes was shown to increase slightly in the order of (100) > (111) > (101), which we attempted to explain through the calculation of grain-dependent ΔGH values. The high spatial-resolution of SECCM also allowed grain boundary terminations and (submicron) MnS inclusions to be directly interrogated; these surface defects exhibit greatly enhanced HER activity compared to the crystallographic planes, indicting them as likely "cathodic sites" during macroscopic (e.g., atmospheric) corrosion. Overall, this study further demonstrates the great potential of SECCM in corrosion science and electrocatalysis. A holistic view of structure-activity of (electro)materials results when local electrochemical maps and movies are combined with co-located microscopy/spectroscopy, and experiments are further supported by theory (e.g., DFT calculations).