Introduction

Metalloporphyrins play a key role in many biochemical processes and are therefore well studied in condensed phase [1]. Besides this obvious importance, they are also interesting from a purely chemical point of view. Their delocalized π-electron system in combination with their flat structure gives them unique electronic properties. Furthermore, they can be easily functionalized with polar and non-polar groups, and a large variety of metal centers in different oxidation states can be incorporated into the porphyrin ring. Due to this broad chemical flexibility, porphyrins have been studied in many condensed-phase contexts—for example, incorporated into metal-organic-frameworks [2, 3] and used as liquid crystals [4,5,6]. Porphyrins can easily arrange into aggregates in solution phase [2, 7,8,9,10], with the size (distribution) and structures of these aggregates dependent on various parameters including concentration and pH value. In contrast, the number of gas-phase studies on porphyrin ions is rather limited and mostly focused on their reactions with small molecules [11,12,13,14,15,16]. More recently, several groups including ours have also investigated the spectroscopic features of isolated porphyrin ions in gas phase—such as absorption in the Soret- and Q-band regions [17,18,19] as well as in the infrared region [16, 20, 21].

In addition to metalloporphyrin monomers and complexes thereof with small molecules, isolated metalloporphyrin oligomers have also been moving into the focus of gas-phase studies [22]. Understanding the complex conformer space associated with these multi-metalloporphyrin assemblies requires structural characterization. A powerful technique to reveal structural information on gaseous ions is ion mobility spectrometry in combination with mass spectrometry (IMS-MS) [23, 24]. It has been applied to many organic and inorganic compounds, including porphyrins [25,26,27,28]. Siu et al. investigated the gas-phase structure of [Hemin]+ by IMS-MS [25]; Von Helden observed a stacking geometry of protoporphyrin IX aggregates by a combination of ion mobility spectrometry, mass spectrometry, and gas-phase infrared spectroscopy [29]. In a number of recent studies, we have used a combination of IMS-MS and photoelectron spectroscopy to probe the gas-phase structures of several metalloporphyrin oligomers (comprising various different metal centers) [26,27,28]. Specifically, we have assembled solvent-free oligomers consisting of tetrasulfonatophenyl metalloporphyrin building blocks (M-TPPS) by electrospraying them from polar solutions of the corresponding acids or alkali salts. This yields numerous species differing not only in the number of porphyrin units but also in their overall charge states and structure types—as determined primarily by the number of complexed counterions and the oxidation state of the central metal ion.

In previous work, we have generally concentrated on structural systematics as a function of the overall charge while keeping the central metal ion and the type of counterion constant. For oligomers of divalent M-TPPS species, low overall charge states and correspondingly large counterion “loadings” were found to be associated with cofacial (i.e., stacked) structures. In contrast, large overall charge states and correspondingly small numbers of counterions lead to coplanar structures. Interestingly, when aggregating M-TPPS species comprising trivalent metals, a third structure type is observed at the same overall charge states, daisy chain oligomeric structures appear.

In the present study, we focus on how the nature of the counterion (its size and electronic properties) influences the gas-phase structure of metalloporphyrin aggregates. Specifically, we have probed the systematic and sometimes subtle structural changes induced by varying counterion composition in M-TPPS dimers—while holding their overall charge state constant. For this, we have used a combination of IMS-MS, quantum chemical calculations, and sophisticated methods to calculate collision cross sections.

Experimental and Computational Methods

Experimental

The experiments were performed on a SYNAPT G2-S HDMS (Waters Corporation, Manchester, UK) traveling-wave ion mobility mass spectrometer (TWIMS). FeIII- and MnIII meso-tetra(4-sulfonatophenyl)porphyrin chloride were obtained from Frontier Scientific Inc. in the acid form and used as obtained. For each metalloporphyrin, we use solutions of 0.1 mmol/l substance dissolved in methanol/water (5/1). Solutions were electrosprayed using the NanoESI source of the instrument at needle voltages of typically 1.5–2 kV. The mobility measurement runs are obtained with different traveling wave parameters (wave height 20–40 V and velocity 360–1100 m/s, see SI). Resolutions of typically 30–40 were achieved (see Table 1). A Synapt measurement run yields a matrix of arrival times vs. mass-to-charge ratio of all ions in the range probed.

Table 1 Arrival Times Obtained in a Typical Run and Corresponding CCS Values (Calibrated Against the DFT-Optimized Structures of the Zn and Mn Monomers and Zn-Dimers and Using the TM Method As Implemented in Collidoscope)
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Computational

All calculations were performed with the Turbomole package [30] at the DFT level with the BP-86 functional [31, 32] and def-SVP basis set [33]. We investigated possible isomers for each dimeric Fe- and Mn-TPPS species by performing full geometry optimizations for typically 10–20 different topologies. In test calculations, we find that the MnIII center is in a high spin state (four unpaired d electrons) and that in the dimers, the lowest electronic state has eight unpaired electrons. Therefore, we fixed the number of unpaired electrons for the geometry optimizations to eight for the dimers. For each optimized structure, we calculated the N2-collision cross section (CCS) with the trajectory method (TM) and the atomic Lennard-Jones parameters as implemented in the Collidoscope program [34]. Since the Lennard-Jones parameters of the transition metal atoms are not implemented in Collidoscope, we described them with the same parameters as for the main group third row elements. In the TM method, each atom of the drifting ion can have a partial charge assigned to it which in turn influences the charge-induced dipole interaction with the nitrogen buffer gas. We assume the following partial charges: − 1/3 for each of the oxygen atoms, + 1 for the Mn and Fe metal centers (note that the central metal is formally triply charged but replaces two protons in the porphyrin), and + 1 for the hydrogen and sodium counterions. This procedure accounts for the total charge of each ionic species investigated.

Results

Typical mass spectra obtained upon electrospray ionization of solutions of MnTPPS are shown in Fig. 1, FeTPPS mass spectra (not shown) look similar. Note that for the ease of reading, we use in the following the acronym TPPS for the fully deprotonated/desodiated tetra-(sulfonatophenyl)porphyrin trianion. The mass spectra are dominated by metalloporphyrin monomers, [MTPPS]3- with M=Mn,Fe. Dimers such as [(MTPPS)2+nH](6-n)- (n = 0–4) and trimers are present in smaller intensities as well.

Figure 1
figure 1

Mass spectrum of MnTPPS. The monomer intensity is divided by 3. The small peaks around 600 and 750 m/z correspond to trimers in charge state 5− and 4−, respectively

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Due to minute sodium impurities present in the solvents, we can also observe sodiation instead of protonation. The intensities of sodiated species can be easily increased by adding small amounts of NaCl to the solvent; 0.02 mmol/l of NaCl in a 0.1 mmol/l solution of MnTPPS is sufficient to shift the counterion distribution form proton dominated to sodium dominated. This reflects the increased affinity of anionic MTPPS towards Na+ as opposed to H+.

We measured the arrival time distributions (ATD) of the different species drifting through nitrogen buffer gas under the influence of a traveling-wave electric field. These ATD depend on the nitrogen gas pressure in the cell as well as the traveling wave parameters such as speed and amplitude. Therefore, in order to obtain ion mobilities and CCS, a calibration procedure is necessary. Furthermore, the correlation between CCS and structure is not trivial. Linking the peaks observed in the arrival time distribution with the calculated structures is usually performed in a two-step approach: firstly, the ATD is converted into collision cross sections by means of a calibration with species of known CCS. For singly charged species, a widely used calibrant is polyalanine, another system is Agilent tune mix. However, when applying these calibrants to a completely different system such as highly charged porphyrin oligomers, one has to expect significant errors in the extracted CCS values. For us, a better-suited calibration system is ZnTPPS and its dimers, since we have already measured their CCS and identified the structures for ZnTPPS monomers and dimers by combining drift tube measurements and DFT calculations [28]. Note, however, that the measurements on ZnTPPS have been performed on a drift tube instrument in helium instead of nitrogen. Note further that for fully deprotonated ZnIITPPS, the overall charge is now 4−.

The second step is the link between experimental CCS and structure; for each candidate structure, a mobility calculation has to be performed in order to obtain a theoretical CCS that can be compared with experiment. Several levels of sophistication are available for such mobility calculations including the projection approximation (PA) [35], exact hard spheres scattering (EHSS) [36], and the trajectory method (TM) [37]. For mobility measurements in nitrogen, one has to take into account that the polarizability of nitrogen is not negligible. Therefore, the TM prediction should be preferred since PA and EHSS ignore the charge distribution which plays an important role in the interaction with nitrogen, especially in a highly polar multianion such as MTPPS.

In order to minimize the cumulative errors in each of the two steps mentioned above, we calibrated the arrival time distributions against the calculated TM-based nitrogen-CCS of ZnTPPS monomer and dimers as well as MnTPPS3− monomer instead of experimental CCS values. The procedure is as follows: for each experimental run, we measure the unknown oligomer anions of MnTPPS, FeTPPS, and ZnTPPS under identical conditions (wave velocity, wave height). Based on the known structures of the monomers ZnTPPS4− and MnTPPS3− as well as the Zn-dimers [ZnTPPS2+3Na]5−, [ZnTPPS2+4Na]4−, and [ZnTPPS2+5Na]3−, we calculate their theoretical N2-CCS with the TM method. Since the drift time of an ion is expected to be proportional to its CCS-to-charge ratio, the observed arrival times, t, (which includes both the time the ion spends inside and outside the drift tube) should depend linearly on the CCS. This is indeed the case, as can be seen in Fig. 2. Based on the fit we obtain the relation \( \frac{CCS}{z}=a\cdot t+b \) with the parameters \( a=24.5\pm 1.7\ \left[\frac{{\overset{{}^{\circ}}{\mathrm{A}}}^2}{ms\cdot e}\right] \) and \( b=61.5\pm 6.2\ \left[\frac{{\overset{{}^{\circ}}{\mathrm{A}}}^2}{e}\right] \) (for a typical measurement with our regular traveling wave parameters). This simple relation allows us to compare experimental ATD with predictions based on DFT-optimized candidate structures for each of the different unknown dimers of MnTPPS and FeTPPS. Note that while the ATD, and therefore the fit parameters a and b, depend on the traveling wave settings, after calibration, the CCS are not affected significantly by these settings. Furthermore, since all ATD for the different charge states and sodiation degrees are extracted simultaneously from one measurement run (strictly speaking the average over the accumulation time of several minutes), the CCS peak shifts do not depend on the calibration parameters a and b but merely on the arrival time difference. We repeated each measurement run five times and obtained relative errors in the CCS of less than 1% (see SI). Note that the absolute error might be significantly larger since our calibration procedure relies on calculated DFT + TM-based CCS values (validated by He drift tube measurements). This is however not a significant problem, since our goal is not to obtain accurate absolute CCS values, but to assign structure types based on a comparison to structures deriving from calculations with the same method as used for the calibrants.

Figure 2
figure 2

Calibration curve obtained using the data shown in Table 1

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The instrumental resolution can be estimated from the ratio of FWHM (full width half max) and peak position of the arrival time distributions of the calibrants (assuming that only one conformer is present, respectively), see Table 1 and SI. Note that the resolution depends on the ion load and that in contrast to the less abundant dimers, the monomer signals may be broadened due to space charge effects [38].

Based on this calibration procedure we have converted each ATD for the unknown systems into a CCS distribution. In Fig. 3, we present the ion mobility data of a typical run for the protonated and sodiated MnTPPS-dimers in the charge states 5−, 4−, and 3−, respectively. For FeTPPS, we obtain similar arrival time distributions. On average, the peaks obtained for FeTPPS deviate from the manganese data by less than 1%, see Supplementary Information.

Figure 3
figure 3

Typical arrival time distributions (ATDs) of the different dimer anions [(MnTPPS)2+nX](6-n)-, X=H,Na and n = 1–3. The black data points correspond to the ion counts recorded in the respective time bin. The red line is a Gaussian fit to these data. The collision cross section scale is obtained by a calibration procedure according to a linear fit as described in the text (see also Fig. 2)

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Discussion

General Bonding Situation

Before we go on to a more detailed analysis of the data, it is useful to first discuss the bonding situation in MTPPS oligomers in a more general way. MTPPS is highly polar. Upon electrospray, the sulfonic acid groups are easily deprotonated/desodiated leaving up to four negative charges on the perimeter of the molecule. The central metal (FeIII or MnIII) replaces two protons, leaving one positive net charge in the center of the porphyrin. Two or more MTPPS molecules can oligomerize even though they are multiply negatively charged—either by way of the attractive interaction between the central metal of one TPPS-unit with a sulfonic acid group of another TPPS-unit or via (mostly Coulombic) interactions of sulfonic groups with the positively charged counterions (or both).

The situation is illustrated in Scheme 1. The red lines indicate attractive interactions between the positively charged metal center (M=Mn,Fe) of one TPPS unit and the negatively charged sulfonic acid groups of neighboring TPPS units (see Scheme 2, reaction 1). The blue lines illustrate various positions and interactions of the counterions; one counterion close to one sulfonic acid group, one counterion bridging two sulfonic acid groups (see Scheme 2, reaction 2), and two counterions bridging two sulfonic acid groups (Scheme 2, reaction 3). All these attractive Coulombic interactions compete with each other and with the similarly attractive van der Waals interactions. By so doing, they compensate the repulsive Coulomb interactions between isolated sulfonic acid groups.

Scheme 1
scheme 1

Illustration of the different interactions between the negatively charged sulfonic acid groups and the positively charged metal centers (M) and counterions (X)

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Scheme 2
scheme 2

DFT-based reaction energies (without zero-point energies) of the archetypal interactions between metal center, sulfonic acid groups, and counterions

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Next, we have investigated the three archetypal attractive Coulombic interactions (see Scheme 2) more closely by performing DFT calculations. The first of these is the interaction of the porphyrin bound central metal ion (M=Fe,Mn) with a proximal sulfonic acid group. We have modeled this interaction as the energy difference between the adduct, i.e., metalloporphyrin cation (with MnIII and FeIII as metal center) plus benzenesulfonic acid anion, and the separated ions. For this, we have performed full geometry optimizations of both the adduct and the constituting ions. Since MnIII has four 3d electrons, we considered singlet, triplet, and quintet spin states for both the metalloporphyrin and the adduct. As can be seen in Table S1 in Supplementary Information, the high-spin quintet turns out to be lowest in energy. We also allowed for thermal smearing of occupation numbers at 300 K. The total energy obtained did not significantly differ from the energy for the quintet state. From the difference of the ground state energies (without the inclusion of zero-point energies), we calculate an energy difference for adduct formation of − 4.66 eV. For M=FeIII with its five 3d electrons, we similarly consider doublet, quartet, and sextet spin states for both the porphyrin and its adduct with benzenesulfonic acid. The quartet is lowest in energy for both the metalloporphyrin cation and its adduct with one benzenesulfonic acid. For the adduct with two benzenesulfonic acid anions, the low spin doublet is lowest. Again we allow Fermi smearing of the occupation numbers. This yields an energy difference of − 4.90 eV for the formation of the adduct with one benzenesulfonic acid, i.e., the FeIII porphyrin cation binds a benzenesulfonic acid anion slightly more strongly than the MnIII porphyrin.

As illustrated in Scheme 1, monomeric TPPS units can also dimerize by the interaction of perimeter sulfonic acid groups with the counterions that are present (H+ and Na+). As model reactions for this, we consider the interactions between a benzenesulfonic acid anion with a neutral benzenesulfonic acid molecule (X=H) or with its sodium salt (X=Na, Scheme 2, reaction 2). With sodium, the energy gain is significantly larger, 1.96 vs. 1.56 eV. Dimerization of two neutral benzenesulfonic acid units by way of either two H+ or two Na+ counterions is strongly exothermic as well—0.92 eV for hydrogen and 2.25 eV for sodium (reaction 3). However, sodium countercation mediated bridges are significantly stronger than for protons.

Overall, according to these calculations, the FeIII- and MnIIIporphyrins should show very similar Coulombic interactions—in line with their very similar ATDs, see Fig. 3 and Supplementary information. As a consequence, we focus our more detailed analysis on the MnIII-TPPS system.

Dimer Structures

Dimers with One Counterion [(MTPPS)2+X]5−

For the quintuply charged dimers with one counterion [(MTPPS)2+X]5−, we find basically the same arrival time distributions, and therefore similar CCS (between 665 and 680 Å2) independent of the porphyrin metal center (M=Fe,Mn) and counterion (X=Na,H), see Fig. 3 and SI. In most cases, the ATD can be well fit with a single Gaussian function with a peak width corresponding to the experimental resolution. This indicates that either only one isomer is present or several isomers that interconvert on a much shorter timescale than the passage through the drift tube.

In order to assign structures, we performed geometry optimizations at the DFT level for a set of different candidate structures, subsequently calculated their CCS and compared them to experiment. The results are summarized in Table 2 and Fig. 4.

Table 2 Experimental and Calculated CCS for Different DFT-Optimized Candidate Structures for the Fivefold Negatively Charged MnTPPS Dimers, See Fig. 4. The Experimental CCS Are Averaged Over Five Independent Measurements, See SI. The Specified Error Is the Standard Deviation of These Five Measurements
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Figure 4
figure 4

Top: DFT-calculated structures, relative energies, and CCS of the [(MnTPPS)2+H]5− dimer. Below the images of the optimized geometries, we have also included schematic drawings of the topologies of the different isomers. The gray diamonds represent the two TPPS units in each dimer with the four negatively charged sulfonic acid groups at their corners. The red circles represent the porphyrin metal centers (MnIII) which carry one net positive charge, respectively. The green circles represent a proton bound to a sulfonic acid group. The dashed lines indicate bonds between a counterion/metal center and a sulfonic acid group. Bottom: structures, relative energies, and CCS of [(MnTPPS)2+Na]5−. Blue circles represent sodium counterions. XYZ files of all structures are in the Supplementary Information

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We find that in both cases, the CCS of the lowest energy structures (A-I and B-I) agree with experiment to within 1%. Both (very similar) structures can be characterized by three “Coulombic bridges”: two bridges between the metal center of one porphyrin unit and a sulfonic acid group of the other as well as an additional counterion-sulfonic-acid bridge (Fig. 4, structure A-I, and B-I, respectively).

Closely related structures with the counterion bridge or one metal center bridge missing (structures A-II, A-III, A-V and B-II, B-IV, B-V) are between 0.57 and 1.81 eV higher in energy. Their CCS values are between 712 and 716 Å2, more than 5% above the experimental values. Therefore, they can be ruled out (or at most are present in small amounts in a rapidly interconverting mixture with structure A-I).

Linking the two MnTPPS units only by the counterion leads to structures (structure A-IV and B-III, respectively) with even larger cross sections (793 Å2 for hydrogen and 807 Å2 for sodium). They are similarly energetically unfavorable (0.97 and 0.89 eV above structures A-I and B-I).

In analogy to the spin state considerations pertaining adducts of benzenesulfonic acid with MIIITPPS (see the previous section), we performed test calculations with 0, 2, 4, 6, and 8 unpaired electrons to check the description of MnIIITPPS dimers. We found that the “high spin” state with eight unpaired electrons is the lowest in energy; therefore, all geometry optimizations were performed in this state.

Dimers with Two Counterions [(MnTPPS)2+2X]4−

For the quadruply charged dimers with two counterions [(MnTPPS)2+2X]4−, we observed a counterion-dependent structural transition. The doubly sodiated tetraanion (2X=2Na) has a significantly smaller cross-section (617 Å2) than either the doubly protonated (2X=2H) species (636 Å2) or the mixed species (2X=H+Na) (642 Å2), see Fig. 3 and Table 3. As before, we investigated a series of candidate structures by DFT in order to rationalize these findings. The results are summarized in Table 3 and Fig. 5. For the lowest energy isomer of [(MTPPS)2+2H]4−, we find a structure with two M-sulfonic acid bridges and one hydrogen bond between a pair of sulfonic acid groups (structure C-I). This structure has a CCS of 655 Å2, slightly (3%) above the experimental value of 636 Å2. An isomer with two hydrogen bonds between two opposite pairs of sulfonic acid groups (C-II) is only 0.11 eV higher in energy and has a cross section of 611 Å2, 4% below experiment. The dramatic CCS reduction is a consequence of the reduced distance between two sulfonic acid groups, as indicated by red arrows in Fig. 5 (top row). A third structure (C-III) is closely related (one of the hydrogen bonds in C-II opens up) and only 0.24 eV above C-I. With a CCS of 647 Å2, it is 1.7% above the experimental value. All of these three structures are energetically so close to each other that they probably coexist. However, they span a CCS range of 44 Å2, and instead, we only observe one—rather sharp—peak in the arrival time distribution (see Fig. 3). The most plausible explanation is a dynamic equilibrium between these structures which averages out to the observed CCS of 637 Å2. Note that the calculation search for local minima in the potential energy surface, they are performed at 0 K and do not include any vibrational motion.

Table 3 Experimental and Calculated CCS for Different DFT-Optimized Candidate Structures for the Fourfold Negatively Charged MnTPPS Dimers. The Experimental CCS Are Averaged over Five Independent Measurements, See SI. The Specified Error Is the Standard Deviation of These Five Measurements
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Figure 5
figure 5

DFT-Calculated Structures, Relative Energies and CCS of the [(MnTPPS)2+2X]4− Dimers. Below the Images of the Optimized Geometries We Have Included Schematic Drawings of the Topologies of the Different Isomers. The Green Circles Represent Protons, the Blue Circles Sodium Counterions, the Red Ones the Metal Center. XYZ Files of All Structures Are in the Supplementary Information

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Other structures (C-III-VI) can be ruled out on the basis of their relative energies and/or CCS; structure C-V represents a completely different motif, a coplanar arrangement of the porphyrin subunits. This motif has been observed in dimers with a divalent metal center (MII=Zn, Cu, Pd) [28]. Here, it is almost 1 eV higher in energy and has a CCS of 729 Å2, 15% above the experimental value. Structure C-VI is closely related to C-II and C-III in as much as here both hydrogen bonds open up. This leads to an increase in CCS to 699 Å2. From the theoretical point of view, it is interesting to compare the energy gained by forming one (C-VI vs. C-III: 0.76 eV) and two (C-III vs. C-II: 0.13 eV) hydrogen bonds. The energy gained by forming the second hydrogen bond is extremely small, obviously due to the increasing steric strain and electrostatic repulsion of the remaining sulfonic acid groups.

For the mixed dimer [(MnTPPS)2+H+Na]4−, the situation is similar. Structures D-I to D-III, analogous to C-I to C-III, are close in energy and bracket the experimental value (642 Å2), with the structures with one hydrogen bond (D-II 661 Å2 and D-III 657 Å2) being much closer to experiment than D-I (609 Å2). So, if the latter structure is present in a dynamic equilibrium, it is so only in small amounts. Other structures (D-IV, D-V, D-VI) can be ruled out. Note that the arrival time distribution of [(MnTPPS)2+H+Na]4− is wider than that of both [(MnTPPS)2+2H]4− and [(MnTPPS)2+2Na]4− (see Fig. 3 and SI), i.e., there are clearly several conformers present.

For the completely sodiated [(MnTPPS)2+2Na]4−, we find a significant decrease in experimental CCS to 617 Å2 (Fig. 3). This is perfectly reproduced in our calculations; Structure E-I, consisting of two M-sulfonic acid bridges and two bridging sodium ions between opposing pairs of sulfonic acid groups, has a CCS of 613 Å2, within 1% of the experimental value. This structure is analogous to C-II and D-I, with the bridging protons being replaced by sodium ions. Other structures are more than 0.79 eV higher in energy, have much larger CCS, and can therefore be ruled out (Fig. 5, Table 3). So, the structural transition observed between [(MnTPPS)2+H+Na]4− and [(MnTPPS)2+2Na]4− can be rationalized by the formation of an additional sodium bridge between sulfonic acid groups. This bond, much stronger than a hydrogen bridge (see Scheme 2), can easily overcome the increased sterical and electrostatic repulsion.

Dimers with Three Counterions [(MnTPPS)2+3X]3−

For the triply charged dimers with three counterions [(MnTPPS)2+3X]3−, we observe a similar structural transition as before; the protonated species (3X=3H) has a significantly larger CCS (627 Å2) than the sodiated species (594 Å2). The mixed species [(MnTPPS)2+Na+2H]3− has the largest CCS (639 Å2) in the series, and there is a strong decrease in CCS when going to [(MnTPPS)2+2Na+H]3− (605 Å2) and finally [(MnTPPS)2+ 3Na]3− (594 Å2), see Table 4.

Table 4 Experimental and Calculated CCS for Different DFT-Optimized Candidate Structures for the Threefold Negatively Charged MnTPPS Dimers. The Experimental CCS Are Averaged over Five Independent Measurements, see SI. The Specified Error Is the Standard Deviation of These Five Measurements
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As before, we calculated a series of candidate structures for the completely protonated and sodiated as well as the mixed species (see Fig. 6 and Table 4). For [(MnTPPS)2+3H]3−, we find the same motif as lowest energy structure (structure F-I) as for [(MnTPPS)2+H]5− (D-I) and [(MnTPPS)2+2H]4−. The porphyrin units are connected by two Mn-sulfonic acid bonds and one additional hydrogen bond. The cross-section of F-I (641 Å2) is slightly larger (2.2%) than the experimental value (627 Å2). A closely related structure with two hydrogen bonds in trans position (structure F-II) has basically the same energy (+ 0.04 eV), but a CCS that is 5% below the experimental value (597 vs. 627 Å2). As before, a dynamic equilibrium between these two is a plausible assumption. Structure F-III has a CCS similar to F-I, and it is very close in energy too (+ 0.25 eV). So, we cannot rule out that this structure is also present. As a new motif, we find a stacked structure with two porphyrin units connected face-to-face only by three hydrogen bonds (F-V). It is however 0.97 eV higher in energy than structure F-I and has a CCS of 580 Å2, 7% below experiment, and can therefore be ruled out. Other structures such as F-IV or quasi-planar chains (not shown) are even higher in energy, have cross-sections much larger than the experimental value, and can be ruled out as well.

Figure 6
figure 6

DFT-calculated structures, relative energies, and CCS of the [(MnTPPS)2+3X]3− dimers. Below the images of the optimized geometries, we included schematic drawings of the topologies of the different isomers, see Figs. 4 and 5 and text. XYZ files of all structures are in the Supplementary Information

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For the mixed dimer [(MnTPPS)2+2H+Na]3−, we again find two quasi degenerate structures (G-I and G-II) at lowest energies. They represent the same binding motifs as observed before for [(MnTPPS)2+3H]3−. In both cases, the sodium atom favors the bridging position. Structure G-I has a CCS that agrees within 1% with experiment (643 vs. 639 Å2). Structure G-II, with an additional bridging proton, can be ruled out since its CCS is 7% below the experimental value. Structures G-III and G-IV represent variations of the “stack” motif (cf. F-V), but they have cross sections more than 8% below experiment and are significantly (more than 0.88 eV) higher in energy. As before, they can be ruled out.

Replacing another proton by sodium leads to a significant decrease in CCS from 639 Å2 in [(MnTPPS)2+2H+Na]3− to 605 Å2 in [(MnTPPS)2+H+2Na]3−. This can be easily rationalized by structure H-I (analogous to G-II, bridging sodium ion instead of proton). It has a CCS of 601 Å2 within 1% of the experimental value. Other structures, especially the “stack” motif (H-II and H-III), are much higher in energy and can be ruled out.

For the completely sodiated species [(MnTPPS)2+3Na]3−, we obtain experimentally the smallest CCS in the series, 594 Å2. In our calculations, we find two topologically completely different structures: J-I, with two sodium bridges and two center metal bridges (cf. H-I and E-I) and, only 0.08 eV higher in energy, structure J-II with three sodium bridges and no center metal bridges. In the first case, the manganese atoms are fivefold coordinated, and in the second case, they are fourfold coordinated. Both structures have cross sections that agree within 2% with experiment (594 Å2), but J-II fits significantly better (596 Å2). Furthermore, it should be noted that irrespective of the absolute CCS value, the decrease in CCS between [(MnTPPS)2+H+2Na]3− and [(MnTPPS)2+3Na]3− is highly reproducible. This points to another structural transition (replacing a proton by sodium without structural rearrangement should increase the CCS). So, we favor the very compact stacked structure J-II for [(MnTPPS)2+3Na]3−.

Conclusions

By a combination of precise ion mobility measurements in nitrogen, high quality quantum chemical calculations and sophisticated trajectory method CCS calculations, we could rationalize the subtle structural changes in [(MTPPS)+nX](6-n)- (M=MnIII, FeIII; X=H, Na; n = 1–3) induced by replacing the protons by sodium counterions. Specifically for n=2 and 3, we found much more compact dimer structures for sodium—at first glance counterintuitive, since a sodium cation is larger than a proton—but easily rationalized by the stronger interactions of the sodium ions with the sulfonic acid groups of the porphyrins. Ultimately, for [(MnTPPS)2+3Na]3−, the Mn-sulfonic acid bridges are replaced by sodium mediated bridges, i.e., replacing one proton by sodium in a large molecule with 180 atom leads to a topologically different structure.