Introduction

Iron plays an important role in the growth and propagation of many microbes, including several pathogenic and aquatic bacteria (Neilands 1977). When iron availability is low, marine bacteria found in the upper 30 m of sea water (Küpper et al. 2006) produce Fe(III)-chelating siderophores, which allow the microbes to transport extracellular Fe(III) across the cell membrane with greater affinity (Neilands 1977; Harris et al. 1979; Raymond et al. 1980).

Aerobactin (Fig. 1a) and petrobactin (Fig. 1b) are well-studied (Harris et al. 1979; Raymond and Carrano 1979; Barbeau et al. 2002, 2003; Bergeron et al. 2003; Küpper et al. 2006; Zhang et al. 2009) siderophores that contain a central citrate moiety. Aerobactin is known to be produced by marine bacteria such as Vibrio sp. DS40M5 (Haygood et al. 1993), and is also known to be a virulence factor in some pathogenic bacteria, including Aerobacter aerogenes (now Klebsiella pneumoniae subspecies aerogenes) (Gibson and Magrath 1969), Escherichia coli (Neilands 1992) and plant pathogens (Bull 1996). Petrobactin is produced by Marinobacter hydrocarbonoclasticus (Barbeau et al. 2002; Bergeron et al. 2003), a bacterium that breaks down oil.

Fig. 1
figure 1

Chemical structures of siderophores aerobactin (a) and petrobactin (b)

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Fe(III) is a 3d transition metal ion that usually forms high-spin (Raymond et al. 1980) octahedrally coordinated complexes through oxygen with multi-dentate ligands (Balzani 1970). Photoreactivity of Fe(III) citrate complexes is well established (Balzani 1970; Faust and Zepp 1993; Abrahamson et al. 1994). When exposed to UV light they undergo a ligand-to-metal charge transfer (LMCT), reducing Fe(III) to Fe(II), and oxidative decarboxylation through an intermediate radical ligand (Abrahamson et al. 1994). The resulting photoproduct contains a 3-ketoglutarate moiety which can tautomerize to an enol (Figs. 2, 3).

Fig. 2
figure 2

Photochemical formation of photoproducts for FeAB in UV irradiated sea water

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Fig. 3
figure 3

Photochemical formation of photoproducts for FePB in UV irradiated sea water

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Previous experimental work established the structures of uncoordinated aerobactin (Fig. 1a) and petrobactin (Fig. 1b) and their uncoordinated photoproducts (Figs. 2, 3) (Harris et al. 1979; Raymond and Carrano 1979; Barbeau et al. 2002, 2003; Bergeron et al. 2003; Küpper et al. 2006; Zhang et al. 2009).

Aerobactin and petrobactin both coordinate to Fe(III) as hexadentate chelating ligands: aerobactin through peripheral hydroxamate groups and a central citrate group, and petrobactin through peripheral catechols and a central citrate group. Ferric aerobactin (FeAB) (Fig. 5a) and ferric petrobactin (FePB) (Fig. 6a) are complex ions with a 3- charge in sea water (Harris et al. 1979; Barbeau et al. 2002). FeAB shows Λ optical isomerism (Fig. 4a) and cis structural isomerization (Fig. 4b) about the iron atom based on UV–Vis and circular dichroism (CD) spectra (Harris et al. 1979; Raymond and Carrano 1979; Raymond et al. 1980).

Fig. 4
figure 4

Different configurational isomers considered in this work

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Fe(II) is known to oxidize to Fe(III) in the presence of oxygen, allowing for the supply of Fe(III) to be maintained under high siderophore activity (Emmenegger et al. 1998). Aerobactin and petrobactin photoproducts show a similar affinity to Fe(III), with similar binding constants (Küpper et al. 2006; Zhang et al. 2009). The ferric aerobactin photoproduct (FeAB*) (Fig. 5a) and ferric petrobactin photoproduct (FePB*) (Fig. 6a) are complex ions with a 2- charge in sea water (Barbeau et al. 2001; Küpper et al. 2006). 13C-NMR determined that the unchelated photoproduct of aerobactin (AB*) exists primarily in the keto form in DMSO, but undergoes tautomeric exchange of a proton in D2O (Küpper et al. 2006). Potentiometric titration also shows that upon complexation with Fe(III), AB* releases an extra proton (Küpper et al. 2006). This suggests that while the uncoordinated photoproducts likely exist in sea water as both keto and enol tautomers, the enol tautomer likely coordinates with Fe(III) to form the ferric photoproduct since a proton is lost from the enol group when it coordinates to Fe(III). No additional proton would be lost upon coordination with Fe(III) if the keto tautomer formed the ferric photoproduct.

Fig. 5
figure 5

a FeAB and FeAB* enol structures, b FeAB isomers, c FeAB* enol isomers with spectroscopically equivalent structures

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Fig. 6
figure 6

a FePB and FePB* enol structures, b FePB isomers, c FePB* enol isomers with spectroscopically equivalent structures

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It was deduced from spectroscopic, kinetic, and potentiometric equilibrium data for FeAB (Harris et al. 1979; Raymond and Carrano 1979) that after coordination of the four hydroxamic oxygens, the only remaining coordination partners are the citrate carboxyl and hydroxyl groups, which are at the ligand’s central carbon. The relative orientation of the hydroxamate or catechol groups about the central Fe(III) atom leads to distinct cis–cis fac and cis–trans mer configurations (Fig. 4b, c) that place the bidentate ligand groups in four different orientations for FeAB (Fig. 5b) and FePB (Fig. 6b) since the hydroxamate and catechol groups are not symmetric (Raymond et al. 1980). A shorthand naming scheme was developed to easily differentiate the isomers by elucidating the chemical difference between the coordinating oxygens and combining the terminology for the cis–trans isomerism and fac-mer isomerism. For the AB species, the carbonyl and hydroxylamine of the hydroxamate group are represented by “C” and “N” making the four geometric isomers for FeAB cis–cis C-fac, cis–cis N-fac, cis–trans C-mer and cis–trans N-mer (Fig. 5b, c). For the PB species, the two coordinating hydroxyl groups on the catechols are para and meta to the connecting bond of the ligand and are represented as “para-” and “meta-” or making the four geometric isomers for FePB cis–cis para-fac, cis–cis meta-fac, cis–trans para-mer, and cis–trans meta-mer (Fig. 6b, c).

The ferric photoproducts coordinate to an enolic hydroxy group at the central carbon and a carbonyl group at a beta carbon, which leads to eight possible isomers. However, each of four ferric photoproduct geometric isomers has a spectroscopically equivalent structure, so only four unique geometric isomers remain for FeAB* (Fig. 5c) and FePB* (Fig. 6c).

The goal of this study is to resolve the lingering structural uncertainties of FeAB, FeAB*, FePB, and FePB* through computational examination of the cis–cis and cis–trans isomers, specifically by calculating the relative energies and by comparing the calculated and experimental absorbance spectra. The coordination structures of citrate-containing siderophores can be useful in understanding the mechanism of iron chelation, cellular membrane transport, and light-catalyzed decarboxylation. This knowledge can be applied to other biochemical processes, medical treatments (Vichinsky 2001), and environmentally beneficial CO2 capture reactions.

Methods

All electronic structure calculations were performed with Q-Chem 6.0 (Epifanovsky et al. 2021). Geometry optimizations were performed for each structure using density functional theory (DFT). The FeAB and FePB isomers were all calculated with a 3- charge while the FeAB* and FePB* isomers were calculated with a 2- charge. All isomers were calculated with a sextet spin multiplicity. The hybrid generalized gradient approximation (GGA) functional, B3LYP (Lee et al. 1988; Miehlich et al. 1989; Becke 1993), was used with Grimme’s D3 empirical dispersion and the Becke–Johnson (BJ) damping added (Grimme et al. 2011), which is considered one of the best-performing methods for equilibrium bond lengths and equilibrium binding energy (Mardirossian and Head-Gordon 2017). The D3(BJ) empirical dispersion improves the performance of geometry optimizations with little computational cost. The cc-pVDZ basis set (Dunning 1989) was used; at 66 to 96 atoms, the size of the structures prohibits our use of a triple-zeta or larger basis set. Basis sets were obtained for Q-Chem using the Basis Set Exchange repository (Pritchard et al. 2019). The CPCM polarizable continuum model (Barone and Cossi 1998; Cossi et al. 2003) was used to capture solvent effects with a dielectric constant of 78.39 for water. The van der Waals radius for iron was set at 2.44 Å while Bondi radii were used for other elements. A scaling factor of 1.2 was applied to construct solute cavities from the van der Waals radii.

Relative energies were calculated among the four isomers of each compound in the ground electronic state to determine the most stable configuration. To support the validity of this hierarchy, a qualitative comparison of relative energies was made for FeAB with DFT calculations using the hybrid meta-GGA functional, TPSSh (Staroverov et al. 2003), with the D3(BJ) dispersion correction and the cc-pVDZ basis set.

The optimized geometries were analyzed using OctaDist (Ketkaew et al. 2021) to assess the degree of octahedral distortion. Parameters related to the 6 Fe–O bonds of the octahedron are the mean bond length (\(\overline{r }\)), distance distortion (ζ), and tilting distortion (Δ). Angular parameters are average angle distortion (\(\overline{\Sigma}\)), which is the average deviation from 90° of the angles (ϕ) between the 12 cis bonds of the octahedron (Fig. S1a), and average torsional distortion (\(\overline{\Theta }\)), which is the average deviation from 60° of the torsional angles (θ) about the S6 improper rotation axes (Fig. S1b).

$$\overline{r }=\frac{1}{6}\sum_{i=1}^{6}{r}_{i}$$
$$\upzeta =\sum_{i=1}^{6}\left|{r}_{i}-\overline{r }\right|$$
$$\Delta =\frac{1}{6}\sum_{i=1}^{6}\frac{{\left|{r}_{i}-\overline{r }\right|}^{2}}{{\overline{r} }^{2}}$$
$$\overline{\Sigma}=\frac{1}{12}\sum_{i=1}^{12}\left|{90}^{^\circ }-{\phi }_{i}\right|$$
$$\overline{\Theta }=\frac{1}{24}\sum_{i=1}^{24}\left|{60}^{^\circ }-{\theta }_{i}\right|$$

For a regular octahedron, \(\overline{r }={r}_{i}\) and the other parameters are all equal to zero; the larger the values of ζ, Δ, \(\overline{\Sigma}\), and \(\overline{\Theta }\), the more distorted is the octahedron around the Fe(III) atom. These values were compared to parameters for [Fe(H2O)6]3+, which has identical monodentate ligands, and [Fe(C2O4)3]3− (ferric oxalate), which has identical bidentate ligands, to gauge the distortion against minimally distorted or more symmetric structures. Values were also assessed to determine whether there is any correlation between these parameters and configurational preference.

Average computed Fe–O stretching force constants (\(\overline{k }\)) were determined for FeAB, FeAB* enol, FePB, and FePB* enol, as well as [Fe(H2O)6]3+ and [Fe(C2O4)3]3−, from harmonic frequency calculations at the B3LYP-D3(BJ)/cc-pVDZ/CPCM(H2O) level to compare with the calculated Fe–O force constant of ferric-enterobactin at 0.94 N/cm (Zscherp et al. 2021). A force constant less than 1 N/cm is a typical sign of a non-covalent or weak bond.

Electronic absorption spectra were computed with time-dependent DFT (TD-DFT) calculations (Bauernschmitt and Ahlrichs 1996; Furche and Ahlrichs 2002; Dreuw and Head-Gordon 2005; Casida and Huix-Rotllant 2012). Vertical excitation energies were calculated from the B3LYP-D3(BJ) optimized ground state structures using a range-separated hybrid-GGA functional, CAM-B3LYP (Yanai et al. 2004), with the aug-cc-pVDZ (Dunning 1989) basis set. The CAM-B3LYP functional provides a long-range correction to B3LYP that is necessary to adequately model charge-transfer excitations, and it was shown to have the lowest root mean square error (RMSE) for predicting charge-transfer excitations (Liang et al. 2022). The aug-cc-pVDZ basis set adds diffuse functions essential to an accurate description of the anionic electron distribution. The same solvation settings were used as in the geometry optimizations, except that the optical dielectric constant of water (1.78) was used to capture the non-equilibrium solvent response upon the electronic excitation processes. Energies for 100 excited states were calculated in order to simulate the spectrum down to the short wavelength limit of the experimental spectra. To identify the character of the excited states, natural transition orbitals (Martin 2003) (NTOs) for the most intense transitions that contributed to the low-energy charge-transfer band were generated from the TD-DFT calculations and analyzed. Additionally, a qualitative comparison of TD-DFT results was made to show the effects of the TPSSh functional versus CAM-B3LYP on B3LYP-D3(BJ)/cc-pVDZ optimized structures for the FeAB cis–cis C-fac isomer. A qualitative comparison was also made between these two methods for sextet versus quartet spin states.

Calculated spectra were created with Python3 by parsing the excitation transition energy and oscillator strength data from output files and reading them into csv files (Electronic Supplemental Information) using Pandas. Spectra were plotted with Matplotlib (Hunter 2007) using the Cauchy (i.e., Lorentzian) probability distribution function (PDF) in SciPy’s stats module (Virtanen et al. 2020), including an offset for the energy of the nth excited state, \({E}_{n}\) and a tunable linewidth parameter, γ, which was set to 0.3 eV based on comparison to the experimental spectra:

$${\text{PD}}{{\text{F}}_{{\text{Cauch}}{{\text{y}}_n}}} = \frac{1}{{\pi \gamma \left[ 1 + {{\left( {\frac{{x - {E_n}}}{\gamma }} \right)}^2}\right] }}$$

To plot the absorbance, the formula \(f={4.32\times 10}^{-9}\text{M }{\text{cm}}^{2}\int \varepsilon \left(\nu \right)d\nu\) was used to express the oscillator strength f in terms of the molar absorption coefficient \(\varepsilon\). This in turn gives the absorbance A at the peak of the transition through Beer’s law, \(A= \varepsilon cl\), where c is the concentration of the solution, and l is the path length (equal to 1 cm in the experiments). Expressing the energies in eV yields the following relationship between the oscillator strength of the nth transition and the absorbance, \({A}_{n}\)

$${A}_{n}= \frac{c{f}_{n}}{{3.48\times 10}^{-5}\text{M}/\text{eV}}{{\text{PDF}}_{\text{Cauchy}}}_{n}$$

Using the experimental concentrations of 54 μM for FeAB and 22 μM for FePB, and assuming full conversion into photoproduct upon irradiation with UV light, the following expressions were used to determine the absorbance for each transition:

$$\text{FeAB and FeAB*:}\quad{A}_{n}= 1.55 {f}_{n} {{\text{PDF}}_{\text{Cauchy}}}_{n}$$
$$\text{FePB and FePB*:}\quad{A}_{n}= 0.63 {f}_{n} {{\text{PDF}}_{\text{Cauchy}}}_{n}$$

The absorbance spectrum was then created by summing together the PDFs for all 100 excited states for each species and plotting the result versus wavelength.

Results

Raw data for all results can be found in the supplemental information, including absolute energies, bond lengths, harmonic frequencies and force constants of vibrational modes, excited states for each configuration, and Cartesian coordinates for optimized structures.

Relative energies

The cis–cis C-fac configuration of FeAB is predicted to be the most stable by 3.8 kcal/mol (B3LYP-D3(BJ)/cc-pVDZ) (Table 1). However, the next most stable configuration, cis–cis N-fac, optimized to a Δ optical isomer, which is not consistent with experimental findings. Therefore, the most stable structure is at least 8.7 kcal/mol more stable than the cis–trans optimized structures. Similar calculations performed using the TPSSh-D3(BJ) method and the same basis set predicted the same trend of relative energies (Table S1), supporting FeAB cis–cis C-fac as the preferred structure. In the following, we continue our discussion of relative energies based on the B3LYP-D3(BJ) results.

Table 1 Relative energiesa (kcal/mol), octahedral parameters, and average Fe–O force constants (\(\overline{k }\))
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Since the enol tautomer loses a proton upon complexation with Fe(III), giving ferric enol photoproducts one less proton than the ferric keto photoproduct, only the enol tautomer allows for a sextet spin on the central Fe(III) atom with a 2- charge. The keto ferric photoproduct tautomer with a 2- charge allows a singlet, triplet, or quintet spin, corresponding to a central Fe(II) atom. This supports the experimental rationale for the enol tautomer of the ferric photoproducts, assuming that Fe(III) rather than Fe(II) is being re-sequestered by the photoproduct. This is a possible avenue of further exploration, to investigate whether Fe(II) could be sequestered by the photoproduct, allowing both Fe(II) and Fe(III) to be taken into the microbe.

The cis–trans C-mer configuration of FeAB* enol is predicted to be the most stable, with cis–cis C-fac being only 0.7 kcal/mol higher (Table 1), which is within a generally accepted margin of error of about 1 kcal/mol for DFT calculations (Mardirossian and Head-Gordon 2017). The other two configurations, cis–cis N-fac and cis–trans N-mer, are 4.8 kcal/mol and 4.6 kcal/mol higher in energy than cis–trans C-mer, respectively. Given the marginal difference in energy between the two lower-energy configurations, cis–trans C-mer and cis-cis C-fac, a dominant structure cannot be identified based on relative energy alone.

The FePB species shows less structural preference between the configurations, which is likely due to the more uniform chemical environment offered by the two coordinating oxygens of the catechol groups versus the carbonyl and hydroxylamine groups of the coordinating hydroxamate groups of aerobactin. The cis–trans meta-mer configuration of FePB is predicted to be the most stable with cis–cis meta-fac being only 1.1 kcal/mol higher in energy (Table 1). The next lowest configuration, cis–cis para-fac, is 2.8 kcal/mol higher in energy, and cis–trans para-mer is the highest in energy by 3.7 kcal/mol relative to cis–trans meta-mer. The energy differences between each of the configurations is small enough such that a specific ordering cannot be supported through relative energy calculations alone.

The calculations for FePB* enol show slight preference for the cis–cis para-fac configuration by 1.4 kcal/mol (Table 1), but the other configurations are all within 0.4 kcal/mol of each other, making it difficult to identify a preferred configuration.

Octahedral distortion parameters and force constants

Octahedral distortional parameters (Table 1) show that there is significant distortion for all models with little singular or cumulative direct correlation to the lowest energy or best-matching spectrum across all structures. Individual Fe–O bond lengths can be found in the Supplemental Information (Table S5).

The ferric photoproducts appear to be less distorted than FeAB and FePB overall, with \(\overline{\Sigma}\) and \(\overline{\Theta }\) values closer to those for ferric oxalate. Average bond lengths of all siderophore species are at or slightly longer than the 2.036 Å bond length of ferric oxalate. However, the ξ and Δ values are much larger for the siderophores than for ferric oxalate, while no clear pattern is evident in comparing the angular distortion parameters \(\overline{\Sigma}\) and \(\overline{\Theta }\). Not surprisingly, the greater diversity of bonding groups involved in the six Fe–O bonds formed by the coordinated hexadentate ligands lead to a larger contribution to the octahedral distortion from distance considerations than in the more uniform hydrate and oxalate complexes. It is possible that the greater significance of distance distortion increases the correlation with the relative configurational energy. For instance, the smallest \(\zeta\) values among the FeAB and FeAB* configurations are found for the most stable in each case, although this correlation does not hold for the petrobactin species.

The average force constants (\(\overline{k }\)) for Fe–O bonds in selected structures (Table 1) were calculated from an average over the vibrational modes involving Fe–O bond stretches and are all within the range 0.80–0.87 N/cm, which contains the value of 0.85 N/cm calculated for [Fe(H2O)6]3+. These values are less than the value of ferric enterobactin (0.94 N/cm), indicating that these bonds are relatively weak.

Absorbance spectra

The experimental absorbance spectrum for FeAB in sea water (Fig. 7) has an LMCT band in the visible region at 399 nm (\(\varepsilon\)= 2170 L mol−1 cm−1) (Harris et al. 1979; Küpper et al. 2006) and another band in the ultraviolet region at 300 nm (\(\varepsilon\) = 2600 L mol−1 cm−1). Sea water has broad excitations below 300 nm (Armstrong and Boalch 1961), and there are a large number of computed transitions in the UV region below 300 nm, making it difficult to identify individual transitions in the UV range below 300 nm. Therefore, the lower-energy LMCT band was the target for specific matching of transition energies, while the higher-energy region around 300 nm was taken into consideration for overall qualitative matching of spectral shape.

Fig. 7
figure 7

Calculated FeAB spectra, with both absorbance (γ = 0.3) and oscillator strengths for a cis–cis C-fac, b cis–cis N-fac, c cis–trans C-mer, and d cis–trans N-mer compared to experimental FeAB (54 μM) spectrum (grey shading)

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The calculated absorbance spectra for FeAB configurations (Fig. 7) and reported average wavelengths at max absorbance (\({\overline{\lambda }}_{max}\)) (Table 2) reveal that the best match to the experimental spectrum occurs with the cis–cis C-fac configuration, with \({\overline{\lambda }}_{max}\) around 400 nm for the low-energy band and about 305 nm for the high-energy band. While the cis–cis N-fac configuration has \({\overline{\lambda }}_{max}\) values near those of the experimental spectrum, our inability to optimize that configuration to the experimentally observed \(\Lambda\) form argues against its being the likely carrier of the spectrum. Spectra for the two cis–trans configurations have excitations that are significantly red-shifted from experiment and from the best-matching configuration, cis–cis C-fac.

Table 2 Wavelength of max absorbance (\({\overline{\uplambda } }_{max}\)) for the FeAB calculated spectrum at low and high energy transitions compared to experimental absorbance
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Additional analysis of TD-DFT method and spin state on the FeAB cis–cis C-fac conformation shows that the sextet spin state is an accurate representation of the experimental spectrum, and CAM-B3LYP is an accurate method for reproducing the charge-transfer states. The optimized quartet state geometry of cis–cis C-fac FeAB is predicted to lie 16 kcal/mol above the sextet in CAM-B3LYP calculations (12.5 kcal/mol in TPSSh), quite close in energy but still less stable. Applying the TPSSh functional for either spin state strongly redshifts the absorbance bands (Fig. 8) relative to experiment. For both CAM-B3LYP and TPSSh, a quartet spin state blue-shifts the bands from their sextet positions, yielding worse alignment with the experimental spectrum. The sextet spin and CAM-B3LYP functional are thus applied throughout the rest of the TD-DFT calculations.

Fig. 8
figure 8

Comparison of the computed absorbance spectrum for FeAB cis–cis C-fac based on the TD-DFT method and spin (γ = 0.3)

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Further exploration of the FeAB cis–cis C-fac structure reveals that this configuration places CO2 in a position that is favorable for its dissociation from the ligand during decarboxylation (Fig. 9). This further supports the dominance of the cis–cis C-fac configuration of FeAB.

Fig. 9
figure 9

a Geometry of the cis–cis C-fac configuration of FeAB, showing the readiness of CO2 for dissociation, b FeAB cis–cis C-fac structure rotated to view the carboxylate group at the upper left (Humphrey et al. 1996)

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The experimental absorbance spectrum for FeAB* (Fig. 10) has an LMCT band in the visible region at 440 nm (Küpper et al. 2006) and another band in the ultraviolet region at 260 nm. The calculated absorbance spectra for FeAB* enol configurations (Fig. 10) and reported average wavelengths at max absorbance (\({\overline{\lambda }}_{max}\)) (Table 3) show that the cis–trans C-mer configuration is the closest match to the experimental spectrum at 455 nm, despite the average max wavelength being redshifted from the experimental value. Two primary excitations contribute to the calculated low-energy band, with the less intense one at about 415 nm, so additional smoothing of the calculated spectrum would likely give rise to a band that peaks around 440 nm, making this configuration the closest match to the FeAB* experimental spectrum. The cis–trans C-mer configuration was also the most stable configuration in the comparison of relative energies by 0.7 kcal/mol, so the calculated spectrum adds additional support for the cis–trans C-mer configuration as the dominant coordination structure for FeAB*.

Fig. 10
figure 10

Calculated FeAB* enol spectra, with both absorbance (γ = 0.3) and oscillator strengths for a cis–cis C-fac, b cis–cis N-fac, c cis–trans C-mer, and d cis–trans N-mer compared to experimental FeAB* spectrum (grey shading)

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Table 3 Wavelength of max absorbance (\({\overline{\uplambda } }_{max}\)) for the FeAB* calculated spectrum for low and high energy transitions compared to experimental absorbance († No discernible peak in calculated spectrum)
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For all FeAB* configurations, the calculated absorbance spectra reflect the redshift of the lower energy band and blueshift of the higher energy band from the FeAB spectra that is seen in the experimental spectra going from FeAB to FeAB*.

The experimental absorbance spectrum for ferric petrobactin in sea water (Fig. 11) has an LMCT band at 484 nm (ϵ = 2340 L mol−1 cm−1) (Barbeau et al. 2002) and bands in the UV region at 313 nm (ϵ = 14,600 L mol−1 cm−1), 280 nm, and 239 nm (ϵ = 23,200 L mol−1 cm−1).

Fig. 11
figure 11

Calculated FePB spectra, with both absorbance (γ = 0.3) and oscillator strengths for a cis–cis para-fac, b cis–cis meta-fac, c cis–trans para-mer, and d cis–trans meta-mer compared to experimental FePB (22 μM) spectrum (grey shading). Inset plots: calculated absorbance values are halved to facilitate comparison

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In general, the calculated absorbance spectra for different configurations of FePB (Fig. 11) show overestimated absorbance compared to the experimental curve, making it difficult to assess the precision of the fit. A graph has been inset for each spectrum that includes a zoomed-in region for the low-energy band where the calculated absorbance for each exited state was multiplied by 0.5 to reduce the absorbance offset and aid in a better qualitative assessment of the fit. The cis–trans meta-mer configuration has the closest average max wavelength (\({\overline{\lambda }}_{max}\)) at 480 nm (Table 4) to experiment, and this aligns with the lowest relative energy configuration (Table 1). The cis–cis para-fac confirmation has a slightly better fit of the inset spectrum, but it is 2.8 kcal/mol less stable than the cis–trans meta-mer configuration. This makes it difficult to state that one isomer dominates the distribution, although there is mild support for the correlation between the lowest relative energy and the \({\overline{\lambda }}_{max}\) as there is with FeAB and FeAB*.

Table 4 Wavelength of max absorbance (\({\overline{\uplambda } }_{max}\)) for the FePB calculated spectrum for low and high energy transitions compared to experimental absorbance
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The experimental absorbance spectrum for FePB* in seawater (Fig. 12) has an LMCT band at 500 nm (Barbeau et al. 2002) and two bands in the UV region at 309 nm and 239 nm. Similar to the FePB case above, the calculated absorbance spectra for FePB* enol (Fig. 12) also exhibit an absorbance shift of about 0.1 from the experimental curve, making it difficult to assess the quality of the fit. For that reason, the inset graphs have been included for the low-energy band for each configuration with the absorbance multiplied by 0.5. There is little discernible difference in the max wavelengths (Table 5) or the qualitative shape of the calculated spectra of FePB* enol configurations. Considering the marginal difference in the relative energies, with FePB* enol cis–cis para-fac being the most energetically stable by 1.4 kcal/mol, there is little support for any one configuration dominating over another to represent the experimental species beyond the possible association between relative energy and preferred configuration that exists with the FeAB and FeAB* enol models. The redshift of the lower-energy band and blueshift of the higher-energy bands from FePB to FePB* are seen in both experimental and calculated spectra, similar to the trends observed in the FeAB and FeAB* spectra.

Fig. 12
figure 12

Calculated FePB* enol spectra, with both absorbance (γ = 0.3) and oscillator strengths for a cis–cis para-fac, b cis–cis meta-fac, c cis–trans para-mer, and d cis–trans meta-mer compared to experimental FePB* spectrum (grey shading). Inset plots: calculated absorbance values are halved to facilitate comparison

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Table 5 Wavelength of max absorbance (\({\overline{\uplambda } }_{max}\)) for the FePB* calculated spectrum for low and high energy transitions compared to experimental absorbance
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Natural transition orbitals

For each of the configurations, the NTOs for the most intense transitions in the low-energy band are difficult to fully elucidate (Tables S12–S27). What can be said overall is that the major transitions that contribute to the calculated spectra at the low-energy band involve transitions from the highest occupied NTOs (HONTOs) around the hydroxamate or catechol regions of the ligands to the lowest unoccupied NTOs (LUNTOs) that are more centered around the Fe(III) atom and involve the citrate region of the ligand. This supports the low-energy band as being an LMCT band.

Conclusions

This work aimed to resolve the lingering unknowns in the structural configurations of Fe(III)-coordinated aerobactin, petrobactin and ferric-photoproducts by comparing relative energies, exploring octahedral distortion parameters and Fe–O force constants, and matching experimental absorbance spectra.

For FeAB, relative energies show the cis–cis C-fac configuration as the most stable. This configuration is also supported by the good match between the calculated and experimental absorbance spectra. Octahedral distortion parameters show that the ligands coordinating to the Fe(III) center feature a highly distorted octahedral structure and show a possible correlation between the relative energies and the average Fe–O bond lengths. Therefore, the FeAB cis–cis C-fac configuration is well supported as being the primary form observed experimentally. Additionally, structure analysis reveals that the geometry of the cis–cis C-fac configuration of FeAB allows for easy dissociation of the citryl carboxylate upon photoexcitation.

For FeAB* there is strong support for the enol tautomer since the loss of a proton upon complexation with Fe(III) allows for the proper combination of 2- charge and sextet spin. There is also support for the cis–trans C-mer configuration being the primary form observed for the ferric aerobactin photoproduct based on relative energies and spectra comparisons. Octahedral distortion analysis shows slightly less distortion than FeAB, with average bond lengths that are too close to show a correlation with the relative energies.

Ferric petrobactin and ferric petrobactin photoproduct do not have conclusive support from the computed relative energies or from the computed spectra for any single dominant configuration. There is some support for FePB’s cis–trans meta-mer configuration being the primary form of ferric petrobactin based on the relative energy and average wavelength at max absorbance, but the relative energies and max wavelengths of the other configurations fall within a narrow range. However, there is no support for any configuration dominating the ferric petrobactin photoproduct as the relative energies are all close to the estimated error of these methods and the computed spectra are very similar. It appears likely that mixtures of configurations contribute to the experimental observations for FePB and FePB*.

For all configurations, NTOs of the most intense transitions in the low-energy band support its characterization as an LMCT band, involving transitions from the hydroxamate or catechol groups of the ligands to the metal center and citrate group where decarboxylation occurs.

It is hoped that the computational protocol employed in this work will be an effective approach to characterize the structural, energetic, and spectroscopic properties of iron-chelating siderophores and their photoproducts, and to analyze other citrate-containing siderophores.