Threshold Collision-Induced Dissociation and Theoretical Studies of

Article pubs.acs.org/JPCA

Threshold Collision-Induced Dissociation and Theoretical Studies of Hydrated Fe(II): Binding Energies and Coulombic Barrier Heights Theresa E. Hofstetter† and P. B. Armentrout* Department of Chemistry, University of Utah, 315 S. 1400 E. Rm 2020, Salt Lake City, Utah 84112, United States S Supporting Information *

ABSTRACT: The first experimentally determined bond dissociation energies for losing water from Fe2+(H2O)n complexes, n = 4−11, are measured using threshold collision-induced dissociation (TCID) in a guided ion beam tandem mass spectrometer coupled to an electrospray ionization source that forms thermalized complexes. In this technique, absolute cross-sections for dissociation induced by collisions with Xe at systematically varied kinetic energies are obtained. After accounting for multiple collisions, kinetic shifts, and energy distributions, these cross-sections are analyzed to yield the energy thresholds for losing one, two, or three water ligands at 0 K. The 0 K threshold measurements are converted to 298 K values to give the hydration enthalpies and free energies for sequentially losing water ligands from each complex. Comparisons to previous results for hydration of Zn2+ indicate that the bond energies are dominated by electrostatic interactions, with no obvious variations associated with the open shell of Fe2+. Theoretical geometry optimizations and single-point energy calculations are performed using several levels of theory for comparison to experiment, with generally good agreement. In addition to water loss channels, the charge separation process generating hydrated FeOH+ and protons is observed for multiple reactant complexes. Energies of the rate-limiting transition states are calculated at several levels of theory with density functional approaches (B3LYP and B3P86) disagreeing with MP2(full) results. Comparisons to our kinetic energy dependent cross-sections suggest that the energetics of the MP2(full) level are most accurate.

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INTRODUCTION The behavior and interactions between metal ions and solvent molecules are of fundamental importance in the chemical, electrochemical, and biological worlds. To provide fundamental information regarding these interactions, the hydration of metal cations, both singly and multiply charged, has been studied extensively in the gas phase over the past two decades.1−25 For the past few years, the Armentrout group has used threshold collision-induced dissociation (TCID) and theoretical calculations to investigate the qualitative and quantitative affects of microhydration on closed-shell metal dications (M2+), where M = Ca, Sr, Zn, and Cd.26−33 In this experiment, thermalized M2+(H2O)n complexes are collided with Xe as a function of the ion kinetic energy. The resultant absolute cross-sections for loss of water ligands are analyzed to yield the thresholds for loss of sequential water molecules, which can be equated with the hydration energies at 0 K. These studies, which include the first measurements of the complete inner shell hydration energies of any metal dication, show that the sequential bond dissociation energies (BDEs), coordination behavior, and dissociation pathways are all dependent on the metal itself as well as the number of water ligands surrounding the metal. Concomitantly, several other techniques have reported similar findings in the binding energies and dissociation pathways of M2+(H2O)n, using ion equilibria,1,2,7,8,10 blackbody infrared radiative dissociation,16−19 and collision-induced dissociation.3,4,13 The © 2012 American Chemical Society

qualitative structures of these gas-phase hydrated metal dications have also been explored using spectroscopy20−23,31,34,35 and by examining trends in water loss BDEs.26,27,32 The hydration of Fe2+ is important in many biological (e.g., heme proteins) and electrochemical processes (e.g., corrosion). The present study investigates the microhydration of Fe2+ by examining the TCID of Fe2+(H2O)n complexes, where n = 5− 11, the first experimental investigation into its hydration energies for complexes of any size. Similar to previous M2+(H2O)n studies,26−33 the dominant process observed for all n studied is reaction 1 Fe2 +(H 2O)n → Fe2 +(H 2O)n − 1 + H 2O

(1)

followed by a secondary loss in reaction 2 Fe2 +(H 2O)n → Fe2 +(H 2O)n − 2 + 2H 2O

(2)

and then sequential loss of additional water molecules. In addition, particular sized complexes are found to undergo a charge separation process in reaction 3 Special Issue: Peter B. Armentrout Festschrift Received: May 8, 2012 Revised: July 18, 2012 Published: July 19, 2012 1110

dx.doi.org/10.1021/jp3044829 | J. Phys. Chem. A 2013, 117, 1110−1123

The Journal of Physical Chemistry A Fe2 +(H 2O)n → FeOH+(H 2O)m + H+(H 2O)n − m − 1

Article

The measured ion intensities are converted to absolute crosssections with an absolute uncertainty of ±20%, as described previously.36 In addition, the acceleration voltage applied to the ions in the collision cell, Vlab, is converted to the relative kinetic energy in the center-of-mass (CM) frame using ECM = 2Vlabm/(m + M), where m and M are the masses of Xe and the ionic reactant, respectively, and the factor of 2 accounts for the charge on the reactant complexes. The absolute energy zero and kinetic energy distribution of the reactant ions are determined using a retarding potential technique.36 The full width at half-maximum (fwhm) for the Vlab distribution ranges from 0.09−0.14 eV. The absolute uncertainty in Vlab is 0.05 eV. All energies below are reported in the CM frame. Threshold Analysis. Competition between reactions 1 and 3 can be modeled statistically, as discussed elsewhere, using eq 446−48

(3)

The latter reaction is observed as a primary (albeit inefficient) dissociation channel for complexes of n = 5−8. For all these complex sizes, reaction 3 is higher in energy compared to reaction 1 such that the competition between the two pathways does not affect the measured hydration energies, as discussed below. Analysis of the kinetic energy dependence of these reactions provides the first experimental determinations of the hydration energies of these smaller iron dication−water complexes. Comparison with other metal systems shows that, for this size range, the metal identity plays a significant role in the metal hydrate complex dissociation behavior. Similar to our recent studies of hydrated doubly charged transition metals (Zn2+ and Cd2+),27,32 the ground state (GS) structure and coordination number of Fe2+(H2O)n is highly dependent on the level of theory. In infrared multiple photon dissociation (IRMPD) spectroscopy experiments on Zn2+(H2O)n, where n = 6−12,31 the MP2(full)/6-311+G(2d,2p)//B3LYP/6-311+G(d,p) level of theory gave better agreement with experiment compared to similar calculations at the B3LYP and B3P86 levels.31 Consequently, the present thermochemical analysis of the TCID data of Fe2+(H2O)n is based on the GS structures predicted by the MP2(full) energetics.

σ (E ) =

Nσ0 E

∑ gi ∫ i

E

E0 − Ei

PD1(E − ε)N − 1dε

(4)

where σ0 is an energy-independent scaling factor, N is an adjustable parameter that describes the efficiency of collisional energy transfer,37 E is the relative kinetic energy of the reactants, E0 is the threshold for CID of the ground electronic and rovibrational state of the reactant ion at 0 K, and ε is the energy transferred into the reactant ion by the collision such that the energy available for dissociation is E* = ε + Ei. PD1 = 1 − exp[−k(E*)τ] is the probability of dissociation of the energized molecule, EM, where τ is the experimental time-offlight (∼5 × 10−4 s in this apparatus),37 and the rate constant, k(E*), is given by Rice−Ramsperger−Kassel−Marcus (RRKM) theory.49,50 This equation accounts for the fact that the complexes examined in the present study are sufficiently large that their dissociation lifetime near the dissociation threshold can be comparable to the experimental time-of-flight. Thresholds for sequential dissociation of a second water molecule were modeled in conjunction with that of the single water loss channel, reaction 1. A statistical approach to modeling sequential dissociation has recently been developed and proven to provide accurate thresholds for singly charged systems51 and M2+(H2O)n.27,32 This model makes statistical assumptions regarding the energy deposition in the products of the initial CID reaction and ultimately assigns a probability for further dissociation of the product of reaction 1. Rotational constants and vibrational frequencies needed in the analyses are taken from quantum chemical calculations discussed below. For the water loss channels of reaction 1 and 2, the transition state (TS) is loose because the bond cleavage is heterolytic with all the charge remaining on the fragment containing the iron dication.52 This TS is treated at the phase space limit (PSL) in which the TS is product-like, and the transitional modes are treated as rotors.46 This also means that the threshold energies determined for such processes correspond directly to the bond energies for water loss. Because the charge separation process in reaction 3 produces two singly charged species, there must be an associated Coulomb barrier along the reaction coordinate for this dissociation channel, such that the appropriate TS is tight. The rate limiting TSs of reaction 3 are labeled according to the products formed, i.e., TS[m + (n − m − 1)]. Analysis of the data involves using eq 4 (or its extension to sequential dissociation) to reproduce the data over extended energy and magnitude ranges, using a least-squares criterion for

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EXPERIMENTAL AND THEORETICAL SECTION Experimental Procedures. Cross-sections for the collision-induced dissociation (CID) of Fe2+(H2O)n complexes are measured using a guided ion beam tandem mass spectrometer (GIBMS), which has been described in detail previously.36,37 Using electrospray ionization (ESI), hydrated Fe2+ ions are generated from 10−4 M solution of FeSO4 in water. The ESI source38 comprises a stainless steel electrospray needle, a heated capillary, an 88 plate ion funnel,39 and a hexapole ion guide where the ions undergo sufficient thermalizing collisions to bring them to a Maxwell−Boltzmann distribution at 300 K, as shown previously.26,27,29,30,32,38,40−42 An in-source fragmentation technique, described in more detail elsewhere,42 is used to increase the intensity of the Fe2+(H2O)n complexes for n = 5−7 produced by our ESI source. In this technique, the dc voltage on electrodes located between the hexapole rods is increased to form smaller metal hydrate complexes. Importantly, the placement of the electrodes is designed to allow thermalization in the hexapole after fragmentation, as demonstrated previously.26−33 No Fe2+(H2O)n complexes smaller than n = 5 were observed from our source even after increasing the electrode voltage past the intensity peak for the n = 5 complex. In part, this is because the charge separation reaction 3 becomes a preferred dissociation pathway for these smaller complexes, although the results below suggest formation of n = 4 should have been possible. Ions are focused from the source and mass selected using a magnetic momentum analyzer. Fe2+(H2O)n ions are then decelerated to well-defined voltages relative to the ion source, Vlab, and focused into a radio frequency (rf) octopole ion guide, trapping the ions radially.43 A collision gas cell surrounds part of the octopole and contains xenon,5,44 which is introduced to the collision cell at pressures varying between 0.05 and 0.40 mTorr. After collision, reactant and product ions drift to the end of the octopole guide, where they are focused, mass analyzed with a quadrupole mass filter, and detected utilizing a Daly detector.45 1111


The Journal of Physical Chemistry A

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Figure 1. CID cross-sections for the sequential water loss (open symbols) and charge separation processes (solid symbols, ▲ for FeOH+Wm and ▼ for H+Wn−m−1 except in part a where H+W2 and H+W products are also shown as open symbols for clarity) for Fe2+Wn, where n = 5−11 and W = H2O, colliding with Xe at 0.2 mTorr as a function of laboratory voltage (upper x-axis) and center-of-mass energy (lower x-axis). Solid lines show the total cross-section (σtotal) and the total charge separation cross-section. In parts a and g, the reactants include additional species present in the ion beam as indicated in brackets. In parts c−e, cross-sections at 55 m/z are attributable to the isobaric ions H+W3 at low energies and Fe2+(H2O)3 at high energies. 1112



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optimizing the fitting parameters, σ0, E0, and N. The uncertainties in these parameters include variations associated with modeling several independent experimental cross-sections, scaling the theoretical vibrational frequencies by ±10%, varying the optimum N value by ±0.1, scaling the experimental time-offlight up and down by a factor of 2, and the uncertainty in the absolute energy scale. Quantum Chemical Calculations. Calculations were performed using the Gaussian03 and Gaussian09 packages,53,54 using structures found previously27 for Zn2+(H2O)n complexes as starting geometries for the Fe 2+(H2O)n complexes. Geometry optimizations were performed at the B3LYP55,56 level of theory with a 6-311+G(d,p) basis set. Vibrational frequencies and rotational constants were also calculated at this level. Transition state geometry optimizations and frequency calculations of the tight TSs for reaction 3 were performed at a B3LYLP/6-311+G(d,p) level and were each found to have only one imaginary frequency. Frequencies for either the loose or tight TSs were scaled by 0.98957 before being used in the RRKM analysis described above, as well in the calculation of the zero-point energy (ZPE) and thermal corrections. Singlepoint energies were calculated at the B3LYP, B3P86,58 and MP2(full)59 levels with a 6-311+G(2d,2p) basis set. Basis set superposition error (BSSE) corrections were calculated for dissociation of the lowest energy structures in the full counterpoise (cp) limit.60,61

Fe2+(H2O)11 ion. Consequently, the cross-section for loss of two and four water ligands to form Fe2+(H2O)9 and Fe2+(H2O)7 is dominated by formation of the isobaric FeOH+(H2O)2 and FeOH+(H2O) ions formed by water loss from the singly charged hydrated iron hydroxide. This contamination problem does not affect the thermochemical and threshold information derived from the primary water loss product of Fe2+(H2O)11 but will affect the absolute magnitude of the cross-section and resulting σ0 value. In the case of the Fe2+(H2O)5 parent ion, overlap with H+(H2O)4 is the main contaminant and again affects the secondary loss channel, as discussed further below. Finally, the Fe 2+ (H 2 O) 3 and H+(H2O)3 products overlap but have sufficiently distinct energy dependences that makes resolving their contributions straightforward, Figure 1c−e. Such isobaric interferences could potentially be avoided by using Fe2+(D2O)n complexes; however, this requires 100% exchange to be useful and is not easily accomplished because of complications outlined previously.32 Alternative isotopes of iron would be another possibility, but the next most abundant 54Fe isotope (6% natural abundance) is too small to generate Fe2+(H2O)n complexes with sufficient intensity to conduct reliable TCID dissociation experiments. It should also be noted that the magnitudes of the crosssections for the two singly charged product ions formed in reaction 3 must be identical; however, in all cases, the H+(H2O)n−m−1 cross-sections shown are smaller by a factor of two or three compared to the FeOH+(H2O)m cross-sections, although they do have the same energy dependences. In previous work28,32 and verified again here for the hydrated iron system, we have shown that this is a result of the large kinetic energies given to the products after passing over the Coulomb barrier associated with these reactions. Because the hydrated proton products are lighter in mass, they acquire a higher velocity in the kinetic energy release, which makes it more difficult to collect these products as efficiently, primarily because they can now be scattered backward in the laboratory frame. Ion focusing conditions can be found where the H + (H 2 O) n−m−1 cross-sections match the FeOH + (H 2 O) m cross-sections (which are unchanged from those shown in Figure 1), but these also sacrifice intensity of the parent complex thereby reducing the sensitivity and quality of the resulting data. Thus, the hydrated iron hydroxide cation crosssections shown provide our best measure of the charge separation cross-sections. n = 5. The Fe2+(H2O)5 reactant is isobaric with H+(H2O)4, which is formed easily under the source conditions used. On the basis of the magnitudes of cross-sections observed for the H+(H2O)3 and H+(H2O)2 products, Figure 1a, it is apparent that the intensity of the protonated water reactant complex is much larger than that of Fe2+(H2O)5. Indeed, the relative intensity of the H+(H2O)3 product is approximately two-thirds that previously measured for TCID of pure H+(H2O)4.62 Despite this, the Fe 2 + (H 2 O) 4 , FeOH + (H 2 O) 2 , and FeOH+(H2O) products are unique to the Fe2+(H2O)5 reactant, and the energy dependence of their cross-sections is unaffected by the presence of the protonated water complex, although their absolute magnitudes should be increased by about a factor of 3. The observation of Fe2+(H2O)4 demonstrates that Fe2+(H2O)5 dissociates by reaction 1, and the FeOH+(H2O)2 product suggests it can dissociate via reaction 5:

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RESULTS AND DISCUSSION CID Cross-Sections. Experimental cross-sections for the collision-induced dissociation of Fe2+(H2O)n with Xe were acquired for n = 5−11, Figure 1. In all cases, reaction 1 is the dominant process followed by the sequential loss of additional water molecules in reaction 2 and higher order processes as the translational energy increases. The individual products for reaction 1 are shown in all parts of Figure 1. Individual products for reaction 3 are shown in Figure 1a−d, whereas Figure 1e,f shows only the total charge separation cross-section. The onsets of the products of reaction 3 for n = 5−8 exhibit a pressure effect at low energy, such that the exothermic tails observed in Figure 1a−d disappear upon extrapolation to zero pressure of Xe. For n = 5−8, reaction 3 competes with reaction 1 in the dissociation of the parent Fe2+(H2O)n complex; however, because charge separation is higher in energy compared to the water loss dissociation pathway, as described in detail below, it does not complicate the analysis of reaction 1. For larger complexes, the charge separation reaction does not compete with the lowest energy water loss channels. Another difficulty in the results shown in Figure 1 is the presence of several isobaric species formed in the ESI source. For the major isotope 56Fe (92% natural abundance), Fe2+(H2O)n complexes where n = 5, 7, 9, and 11 have the same nominal m/z values as hydrated iron hydroxide cations, FeOH+(H2O)m where m = 0, 1, 2, and 3, respectively, and the n = 3, 5, 7, 9, and 11 complexes have the same m/z values as H+(H2O)p where p = 3, 4, 5, 6, and 7, respectively. Thus, loss of H2O from these monocation contaminants has the same m/z as loss of two water ligands from the dications in reaction 2. The intensity of the Fe2+(H2O)7 and Fe2+(H2O)9 parent complexes are sufficiently large that these contaminants do not affect the results shown. In contrast, for the CID of Fe2+(H2O)11 shown in Figure 1g, only the primary and tertiary water loss channel cross-sections are reliable because the intensity of the FeOH + (H 2 O) 3 parent ion is much greater than the 1113



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FeOH+(H2O)3 complex decreases above ∼1.3 eV, whereas the H+(H2O)2 product continues to increase slowly. The decline in the FeOH+(H2O)3 product appears to be primarily a result of subsequent dissociation to form FeOH+(H2O)2 and at still higher energies to FeOH+(H2O). Likewise, the H+(H2O)2 product cross-section flattens out above 2.5 eV, consistent with its sequential dissociation to form H+(H2O). In addition to these sequential pathways, reactions 5 and 6 can also contribute to the FeOH+(H2O)2, H+(H2O)2, and H+(H2O) cross-sections, although observation of their apparent thresholds is complicated by the sequential dissociation pathways. On the basis of the magnitudes of these charge separation processes relative to the water loss reactions observed in Figure 1a, reaction 5 is a minor contributor to the products, whereas reaction 6 should be more obvious. Indeed, the total charge separation cross-section does increase more rapidly beginning about 2.5−3 eV (more obvious on a linear cross-section scale), consistent with what is expected from the relative energetics of the Fe2+(H2O)5 and Fe2+(H2O)6 reactant ions. Notably, the apparent threshold of the FeOH+(H2O)2 product is now more clearly higher in energy than the Fe2+(H2O)4 product, agreeing with our discussions above on the relative energetics of reaction 5 versus reaction 1. Furthermore, the increase in the charge separation cross-sections near 2.5−3.0 eV seems to fall below the apparent threshold for formation of the Fe2+(H2O)3 product. n = 7 and 8. In the dissociation of Fe2+(H2O)7 and 2+ Fe (H2O)8, the dominant reactions are again reaction 1, followed by the loss of additional water molecules as the collision energy increases, Figure 1c,d. Interestingly, reaction 3 is also observed for both parent ions in addition to the higher order charge separation reactions mentioned above. For n = 7, charge separation occurs via reaction 8:

Fe2 +(H 2O)5 + Xe → FeOH+(H 2O)2 + H+(H 2O)2 + Xe (5)

Previous GIBMS studies of hydrated protonated water clusters62 indicate that the H+(H2O)2 product cross-section from dissociation of H+(H2O)4 reactant begins at ∼1.60 eV, consistent with the main feature observed in this cross-section, Figure 1a. However, there are contributions to this product at lower energies that match equally small observable intensity in the FeOH+(H2O)2 partner product. Both of these cross-section intensities are low (∼0.08 Å2) but clearly above the sensitivity limit of these experiments. Although the small intensity makes the assignment of reaction 5 somewhat tenuous, signal was observed at these lower energies in multiple experimental runs under the higher sensitivity conditions provided by higher Xe pressures. Both product cross-sections have a higher apparent threshold than the Fe2+(H2O)4 product, and their small magnitudes indicate that reaction 5 is energetically and entropically disfavored compared to reaction 1. Importantly, this conclusion also indicates that competition with reaction 5 will have no effect on our determination of the threshold for reaction 1 of n = 5. The FeOH+(H2O)2 cross-section increases by about an order of magnitude by 3 eV. The onset of this increase matches the onset of the H+(H2O) cross-section, suggesting the presence of the higher order charge separation dissociation, reaction 6: Fe2 +(H 2O)4 + Xe → FeOH+(H 2O)2 + H+(H 2O) + Xe (6) +

+

Importantly, the production of H (H2O) from the H (H2O)4 reactant does not begin until ∼3 eV, confirming that the threshold observed here corresponds to reaction 6. The occurrence of this charge separation reaction at smaller values of n agrees with parallel observations in previous studies of hydrated Cd2+ and Zn2+.28,32 In these cases, cross-sections for hydrated metal hydroxide cation products exhibiting two features, such as that for FeOH+(H2O)2, are indicative of a low-energy process (here, reaction 5) that is enthalpically disfavored compared to water loss followed by a higher-energy process (here, reaction 6) for which the threshold now lies below that for water loss. In the present case, the relative energetics for reaction 6 cannot be confirmed directly because the competing Fe2+(H2O)3 product is isobaric with H+(H2O)3. The final product observed, FeOH+(H2O), has a crosssection consistent with formation by loss of water from FeOH+(H2O)2, although contributions from another charge separation reaction from n = 3 could also be present. Verification of the possible charge separation reactions observed here can be obtained from an examination of larger reactant complexes and theoretical calculations, as discussed further below. n = 6. The dominant reaction observed in the dissociation of Fe2+(H2O)6 is the sequential loss of water molecules down to the smallest observable size of n = 2, Figure 1b. The lowest energy charge separation products are a consequence of reaction 7:

Fe2 +(H 2O)7 + Xe → FeOH+(H 2O)3 + H+(H 2O)3 + Xe (8)

which accounts for the very small cross-sections of both product ions below ∼0.8 eV. The apparent thresholds of both products are greater than that for formation of the Fe2+(H2O)6 cross-section once the exothermic tail is removed by extrapolating to zero pressure conditions, showing that reaction 1 is energetically and entropically favored over reaction 8. At energies above ∼0.8 eV, cross-sections for the products of reaction 7 become evident, with much larger magnitudes than those for reaction 8; however, the relative magnitudes of the cross-sections for reaction 7 versus that for formation of Fe2+(H2O)5 remain the same as in Figure 1b (and likewise for Figure 1d). Note that the cross-section for the m/z 55 product is assigned to H+(H2O)3 formed in reaction 8 at low energies, and above ∼3.6 eV, this cross-section significantly increases because Fe2+(H2O)3 is formed. Similar dissociations are seen in the CID of n = 8, Figure 1d. There are now very small contributions from the FeOH+(H2O)4 product of reaction 9: Fe2 +(H 2O)8 + Xe → FeOH+(H 2O)4 + H+(H 2O)3 + Xe (9)

Fe2 +(H 2O)6 + Xe → FeOH+(H 2O)3 + H+(H 2O)2 + Xe

The observation of this larger iron hydroxide cross-section is near our instrumental sensitivity limit; therefore, this crosssection has substantial noise and was observable only when using high pressures of Xe (>0.2 mTorr) in our collision cell. Even with this large noise, the onset to reaction 9 appears to be higher in energy than reaction 1. Notably, the magnitudes of

(7)

Again, the apparent thresholds for the products of reaction 7 appear to be slightly higher in energy than the formation of the Fe2+(H2O)5 complex, so the competition from reaction 7 will not affect the first water loss BDE. The cross-section for the 1114



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Table 1. Relative Calculated Enthalpies (ΔH0) and Free Energies (ΔG298)a in kJ/mol of Fe2+(H2O)n complex (x,y,z) Fe2+(H2O)5

Fe2+(H2O)6

Fe2+(H2O)7

Fe2+(H2O)8

Fe2+(H2O)9

Fe2+(H2O)10

Fe2+(H2O)11

(5,0) (4,1)_A (4,1)_AA (6,0) (5,1)_AA (4,2)_AA,A (6,1)_AA (5,2)_2AA (4,3)_AA,2A (6,2)_2D,DD_2AA (5,3)_2D,2DD_3AA (4,4)_2D,2DD_2AA,2A (6,3)_4D,DD_3AA (6,3)_6D_3AA (5,4)_3D,2DD_3AA,A (5,4)_4DD_4AA (4,5)_D,3DD_2AA,3A (6,4)_4D,2DD_4AA (5,5)_D,4DD_4AA,A (4,5,1)_D,3DD_AA,2A,AAD,AD_AA (6,4,1)_4D,2DD_4AA,AAD_A (6,5)_2D,4DD_5AA (5,6)_5DD_4AA,2A (5,5,1)_D,4DD_3AA,A,AAD_A (4,6,1)_4D_AA,4A,AAD_A

B3LYP

B3P86

MP2(full)

0.0 (0.8) 4.9 (0.0) 5.7 (8.6) 2.6 (3.2) 0.0 (0.0) 8.2 (3.1) 12.0 (11.3) 0.0 (2.5) 9.4 (0.0) 9.2 (7.9) 0.0 (0.0) 15.1 (5.9) 8.3 (9.0) 8.5 (10.1) 2.3 (0.0) 0.0 (3.8) 17.5 (5.2) 12.3 (16.4) 0.0 (0.0) 6.0 (0.7) 11.9 (15.3) 11.3 (24.9) 0.8 (0.0) 0.0 (0.0) 20.6 (4.8)

0.0 (2.2) 3.5 (0.0) 4.6 (8.9) 3.4 (4.0) 0.0 (0.0) 7.4 (2.2) 12.9 (12.7) 0.0 (3.0) 8.9 (0.0) 10.3 (9.1) 0.0 (0.0) 15.7 (6.5) 8.9 (9.6) 8.7 (10.4) 2.3 (0.0) 0.0 (3.8) 18.3 (6.0) 12.9 (17.3) 0.0 (0.3) 5.0 (0.0) 12.4 (15.5) 12.1 (25.4) 2.7 (1.7) 0.0 (0.0) 22.1 (6.1)

0.0 (0.0) 21.3 (15.7) 17.2 (19.4) 0.0 (0.0) 10.2 (9.6) 33.7 (28.0) 0.0 (0.0) 1.5 (4.7) 29.5 (20.8) 0.0 (0.0) 4.7 (5.9) 36.7 (28.7) 0.0 (0.0) 0.3 (1.2) 11.0 (8.0) 5.6 (8.6) 42.7 (29.6) 0.0 (0.0) 4.2 (0.1) 11.0 (1.6) 5.4 (0.0) 0.0 (4.8) 8.3 (0.0) 10.0 (1.4) 48.7 (24.1)

ΔG298 values given in parentheses. Single-point energies calculated at each respective level shown using a 6-311+G(2d,2p) basis set with geometries calculated at B3LYP/6-311+G(d,p). ZPE correction included. Adjustments to ΔG298 are performed using standard formulas and the rigid rotor/ harmonic oscillator approximation. a

Information). Not surprisingly, the iron(II) complexes have similar average metal−oxide bond distances compared to their zinc analogues (within 0.05 Å) and shorter bond lengths compared to their cadmium analogues (by 0.17 Å). These differences in bond lengths are directly related to the differences in the metal ion radius: 0.83 Å for Fe2+, 0.78 Å for Zn2+, and 0.99 Å for Cd2+.66 The Fe2+(H2O)6 complex has C2h symmetry, whereas both Zn2+(H2O)6 and Cd2+(H2O)6 have Th symmetry. In the C2h geometry, a pair of water molecules opposite one another have rotated slightly (∠HOFeO ≈ 13°), and these FeO bond lengths differentially increase from the more symmetric Th geometry in which all hydrogens point directly at adjacent oxygens (∠HOFeO ≈ 0°) and the bond lengths are all equal. This is presumably the result of the aspherical electron distribution around the open-shell Fe2+ (5D, 3d6) ion, which leads to a slight Jahn−Teller distortion as a result of the asymmetric t2g orbital occupation. A previous report64 identified S6 symmetry for this complex, whereas we find this symmetric form is a transition state (degenerate imaginary frequencies of 317 cm−1) for the Jahn− Teller distortion between different axes. In a search to find the global ground state (GS) of each complex, a number of isomers were calculated for all inner shell sizes of the n = 5−11 complexes, several of which are shown in Figure S1, Supporting Information. Similar to previous hydration studies of transition metals,27,32 the relative energies and predicted ground states (GSs) depend on the level of theory used in the single-point energy calculation. In agreement with these earlier studies, the MP2(full) relative energetics tend to predict GSs with a larger coordination number (CN) than those predicted by either the B3LYP or B3P86 levels. The

the cross-sections for primary charge separation reactions 5, 7, 8, and 9 relative to that for reaction 1 decrease as the size of the reactant complex increases, consistent with processes that become increasingly disfavored. The main charge separation process remains reaction 7, as illustrated by the large increase in the FeOH+(H2O)3 and H+(H2O)2 cross-sections beginning concomitantly at ∼1 eV. Note the m/z 55 cross-section again has two distinct features that can be attributed to H+(H2O)3 at low energies and Fe2+(H2O)3 at higher energies (above ∼4.5 eV). n = 9−11. In all cases, reaction 1 is the dominant dissociation pathway followed by the loss of additional water molecules as the collision energy increases, Figure 1e−g. For these three systems, reaction 3 does not complicate the dissociation of the parent ion, and the cross-sections of the observable charge separation products of the higher order processes discussed above are summed into a total charge separation cross-section, Figure 1e,f. No high order charge separation products were observed in the CID of n = 11 because of the overall low counts of the parent ion and complications of the mass overlaps at this complex size, as discussed above. Theoretical Geometries: Fe2+(H2O)n. On the basis of the MP2(full) relative energetics, all water ligands bind directly to the iron dication in the geometries for n = 1−6, in agreement with previous63−65 condensed phase experimental and theoretical works on iron(II) hydration and comparable to Cd 2+ (H 2 O), 3 0, 3 2 Zn 2+ (H 2 O), 2 7 Ca 2+ (H 2 O), 2 6, 3 3 and Sr2+(H2O).29 The Fe2+(H2O)n complexes, where n = 1−6, complexes have C2v, D2d, D3, D2d, C2, and C2h symmetries, respectively (as shown in Figure S1 of the Supporting 1115



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is a (6,1)_AA complex at 0 and 298 K, but DFT predicts the (5,2)_AA to be the 0 K GS by 12−13 kJ/mol compared to the 6-coordinate structure. Here, the DFT 298 K free energy GS is the (4,3)_AA,2A complex, which is 21−30 kJ/mol higher in energy at the MP2(full) level. The relative energetics for n = 8 and 9 have a similar pattern as seen for n = 6, namely, the MP2(full) overall GS is 6-coordinate, the DFT GS is 5coordinate, and the 4-coordinate complex is higher in energy. As complex size increases, the relative differences in energy become increasingly smaller between the low-energy isomers of each inner solvent shell size. For example, the MP2(full) GS of Fe2+(H2O)9 is the (6,3)_4D,DD_3AA, but this complex is within 1 kJ/mol of the more symmetric (6,3)_6D_3AA complex, Figure 3, at all levels of theory, Table 1. With such

relative stability of each isomer is also temperature dependent as entropy effects can change their energetic order. Relative 0 K enthalpies and 298 K free energies for the lowest-energy isomers of different inner shell sizes are presented in Table 1 for results calculated using the B3LYP, B3P86, and MP2(full) levels with a 6-311+G(2d,2p) basis set. Table S1 of the Supporting Information includes a more extensive tabulation of different isomers but is not intended to be a complete survey of all stable isomers. Our (x,y,z) nomenclature describes the different conformations of Fe2+(H2O)x(H2O)y(H2O)z, where x, y, and z are the number of water molecules in the first, second, and third shells, respectively. When needed, this designation is augmented by the hydrogen bonding motif of the isomer: a second shell water molecule that hydrogen bonds to two different inner shell water molecules is a double acceptor (AA), whereas a second shell water molecule that forms only one hydrogen bond to the inner shell is a single acceptor (A). An inner shell water molecule that donates either one or two hydrogen bonds is designated as a single or double donor (D or DD, respectively). Water molecules in the second shell that hydrogen bond to water molecules in the third shell are a combination of both an acceptor and donor water molecule and are named accordingly. In general, the structures and relative energetics are similar to those discussed in detail for Cd2+(H2O)n.30,32 The lowest energy complexes of each inner shell size are discussed below. The effects of the differing levels of theory and temperature is clearly seen in the low energy isomers of the n = 5 complex, Figure 2. The MP2(full) GS at 0 and 298 K is the (5,0)

Figure 2. Low-energy isomers of Fe2+(H2O)5 calculated at the B3LYP/6-311+G(d,p) level of theory. Relative 0 K enthalpies calculated at the MP2(full) level are given in parentheses.

Figure 3. Low-energy isomers of Fe2+(H2O)9 calculated at the B3LYP/6-311+G(d,p) level of theory. Relative 0 K enthalpies calculated at the MP2(full) level are given in parentheses.

complex, with the (4,1)_A and (4,1)_AA complexes lying 16− 21 kJ/mol higher in energy. The (5,0) complex is also the 0 K enthalpic GS using density functional theory (DFT), but entropic effects allow (4,1)_A to become the DFT free energy GS at 298 K. This change is because the (4,1)_A complex has a singly bound water in the second solvent shell that can rotate nearly freely, thereby enhancing the entropic favorability of this complex. In contrast, the (4,1)_AA complex rises in 298 K free energy compared to (5,0) because the double acceptor water molecule constrains the geometry even further. The disparity in GS prediction between the two types of calculations, DFT versus MP2(full), seems to be a common theme for transition metal hydration as it is also seen for both hydrated Zn2+ and Cd2+. Similar patterns are seen for the larger complexes, where MP2(full) tends to predict a CN of 6 and the DFT levels predict a CN of 4 or 5 depending on complex size and temperature. Previous molecular dynamics studies have found CN of 6 to dominate, in agreement with our MP2(full) calculations.65 For n = 6, the MP2(full) GS is the (6,0) complex, the DFT GS is (5,1)_AA, and (4,2)_AA,A is higher in energy at all levels, Table 1. Moving to n = 7, the MP2(full) GS

close relative energetics, both complexes are equally likely to be present in our experiment given a Maxwell−Boltzmann distribution of the isomer population. Likewise, there are several 4- and 5-coordinated structures at this complex size that are all within 6 kJ/mol of each other at 298 K according to DFT results, Tables 1 and S1, Supporting Information. Figure 3 also illustrates an isomer having a cyclic structure in which one water molecule is attached to both a first (D) and second (AD) shell ligand and hence is named (6,3.5,0.5)_4D,DD_ 2AA,AD_AA. Such cyclic species are observed for n = 8−11, Table S1, Supporting Information, but are never the lowest energy species for a particular inner shell size. For n = 10, the overall GS is the (6,4)_4D,2DD_4AA complex at the MP2(full) level; however, the (5,5) _D,4DD_4AA,A and (4,5,1)_D,3DD_AA,2A,AAD,AD_A complexes are within 2 kJ/mol of the 6-coordinate in 298 K free energy. DFT results prefer the (5,5) or (4,5,1) structures with the (6,4) configuration being 12−13 kJ/mol higher in energy. For n = 11, the (5,6)_5DD_4AA,2A, (6,4,1) 1116



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Table 2. Optimized Modeling Parameters of eq 4 from Analysis of CID Cross-Sections of Fe2+(H2O)na n 5 6

reactant (5,0) (6,0) (6,0) (6,0)

7

(6,1) (6,1)

8

(6,2) (6,2)

9

(6,3)_4D,DD_3AA (6,3)_4D,DD_3AA

10

(6,3)_6D_3AA (6,4) (6,4)

11

(5,5) (4,5,1) (6,4,1) (5,6) (5,5,1)

product b

(4,0) (5,0)b (5,0)c (4,0)c (4,0)d (3,0)d (6,0)b (6,0)c (5,0)c (6,1)b (6,1)c (6,0)c (6,2)b (6,2)c (6,1)c (6,2)b (6,3)b (6,3)c (6,2)c (6,3)b (6,3)b (6,4)b (6,4)b (6,4)b

σ0 8 (4) 59 (5) 57 (5) 46 (7) 56 (9) 0.9 (0.3) 71 (10) 68 (6) 52 (4) 81 (8) 73 (3) 63 (5) 92 (7) 88 (3) 43 (7) 93 (7) 108 (8) 103 (2) 72 (8) 109 (8) 107 (8) 4 (3) 4 (3) 4 (3)

a

N 0.9 0.8 0.8 0.8 0.5 0.5 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 1.0 1.0 0.9 0.9 0.8 0.8 0.7

(0.2) (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) (0.2) (0.1) (0.1) (0.2) (0.2) (0.2) (0.2) (0.2)

E0 (eV) 1.12 0.98 0.97 2.16 2.13 3.95 0.81 0.79 1.84 0.72 0.66 1.48 0.57 0.56 1.25 0.57 0.52 0.47 1.07 0.48 0.42 0.48 0.47 0.47

(0.06) (0.06) (0.04) (0.05) (0.06) (0.11) (0.05) (0.06) (0.06) (0.07) (0.03) (0.03) (0.04) (0.03) (0.03) (0.04) (0.06) (0.03) (0.03) (0.06) (0.06) (0.03) (0.03) (0.03)

ΔS†1000 (J/mol K) 56 (5) 57 (5) 57 (5) 50 (5) 55 (4) 55 (4) 53 (8) 53 (5) 56 (5) 54 (4) 57 (5) 39 (5) 40 (5) 17 (5) −2 (5) 30 (4) 24 (4) 30 (4)

Uncertainties in parentheses. bSingle-channel dissociation modeling including lifetime effects. cSequential dissociation modeling. sequential dissociation modeling.

d

Tertiary

assignment of the quintet as the GS is in agreement with previous theoretical studies of hydrated Fe2+.68 Thermochemical Results. Cross-sections for the loss of the first (primary) and second (secondary) water molecule in reaction 2 were analyzed using both the single channel (eq 4) and sequential models in several ways, with Table 2 summarizing the average optimum modeling parameters. The reactant isomer is assumed to be the 298 K GS (as this species should have the dominant population in a thermally equilibrated source) and the product isomer is the 0 K GS (as our threshold analysis is dominated by the lowest 0 K enthalpy species).27 As noted above, the MP2(full) relative energetics have been found previously31 to be more accurate for transition metal dication hydration systems compared to the DFT levels used here. Consequently, we analyze the data using the complexes predicted to be the GS by the MP2(full) singlepoint energies. For the dissociation of each complex, threshold E0 values are given in Table 2 for the primary and secondary (in most cases) dissociations and are obtained using models discussed above that include lifetime effects. As shown previously for similar complex sizes of other hydrated dications,26,27,29,30 the threshold obtained from analysis without lifetime effects included is higher because of a kinetic shift. The kinetic shift gradually increases as the complex gets larger because of the increased dissociation lifetime of these larger complexes. Notably, cross-sections could not be reproduced with fidelity in the threshold region when fitting without including RRKM theory; however, the kinetic energy dependences of the crosssections are reproduced nicely after RRKM theory is incorporated. Table 2 also includes values of ΔS†1000, the entropy of activation at 1000 K, which gives some idea of the looseness of the transition states. Most of these values are in the

_4D,2DD_4AA,AAD_A, and (5,5,1)_D,4DD_3AA,A,AAD_A complexes are also essentially isoenergetic with each other at 298 K according to the MP2(full) level. The (6,5) _2D,4DD_5AA complex is the 0 K GS at the MP2(full) level but is about 6 kJ/mol higher in 298 K free energy. DFT calculations prefer the (5,5,1) or (5,6) complex, whereas the 4coordinate complex is high in energy at all levels of theory. Excited Electronic States. The GS of the Fe2+ ion is 5D (3d6), with the first excited state being 3P (3d6) at 2.406 eV (separation between the lowest spin−orbit levels of each manifold) and the lowest lying singlet state being 1I (3d6) at 3.764 eV.67 MP2(full) (B3LYP) calculations using the 6311+G(2d,2p) basis set find excitation energies of 2.38 (2.40) and 4.63 (3.92) eV. To see how the addition of water ligands affects the relative energetics of these excited spin states, we performed calculations on Fe2+(H2O)4 and Fe2+(H2O)11 in both the singlet and triplet spin states and compared the relative energetics to the respective quintet GS. For n = 4, the DFT levels predict the singlet state to be ∼2.68 eV higher at 0 K, and the MP2(full) level predicts this state to be 3.36 eV higher. The triplet state of n = 4 failed to converge in the optimization step, likely because of the relatively high energies. Calculating the relative 0 K enthalpy on the unconverged structure leads to higher predicted energies at all levels of theory by 1.36−2.00 eV. For the larger n = 11 system, relative energetics are calculated only at the B3LYP/6-311+G(d,p) level. Both the singlet and triplet excited states of (6,4,1) _4D,2DD_4AA,AAD_A are higher in energy compared to the GS by 1.42 and 1.16 eV, respectively. Although the addition of water ligands appears to lower the relative energy of the excited electronic states, a result of the splitting of the degeneracy of the valence d orbitals by the ligand field, both excited states are still much higher in energy than the GS quintet. The 1117



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range determined by Lifshitz69 for simple bond cleavage dissociations, which is consistent with TSs assumed to lie at the centrifugal barrier for the association of Fe2+(H2O)n−1 + H2O. The exceptions are when Fe2+(H2O)10 is analyzed assuming the (5,5) and (4,5,1) structures forming a (6,3) Fe2+(H2O)9 product, where the differences in the inner solvent shell mean the latter is more constrained than the reactants leading to low entropies of activation. As mentioned above, the MP2(full) relative 298 K free energies for different isomers of the n = 9−11 complexes are sufficiently close that multiple isomers could be present in the reactant ion beams. In these cases, the data were modeled using each of these possible isomers individually. Changes in the reaction threshold are a consequence of differences in the kinetic shift of the model, as discussed in detail previously for Zn2+(H2O)n.27 Briefly, if the assumed reactant complex has more outer shell waters with lower torsional frequencies (i.e., more single acceptor water molecules), it has a higher density of states, which lowers the rates of dissociation. This in turn increases the kinetic shift thereby lowering the 0 K reaction threshold. For n = 9, there is no noticeable difference in the threshold if we model assuming the (6,3)_4D,DD_3AA and (6,3)_6D_3AA complexes, consistent with only AA second shell ligands. For n = 10, the (6,4) and (5,5) complexes are nearly isoenergetic with the (4,5,1) structure within 1.6 kJ/mol of the GS. The threshold obtained for the (6,4) reactant decreases by 0.04 eV when the reactant is assumed to be 5coordinate, within our 0.06 eV experimental uncertainty. This decrease is a consequence of the A water molecule found in the (5,5) complex. A larger 0.10 eV threshold difference is found when the (4,5,1) complex is assumed to be the reactant because there are now three water ligands singly bound to inner shell ligands. For the n = 11 complex, the difference between the reaction thresholds when assuming a (6,4,1) or (5,5,1) reactant structure is negligible because both dissociations involve losing an A water molecule from the third solvent shell. Water Loss Secondary Threshold Energies. The secondary water loss thresholds of reaction 2 are fit using the sequential model for n = 6−10, and the results are reported in Table 2. (Because secondary water losses from the n = 5 and 11 complexes have mass overlaps, as discussed above, these processes cannot be analyzed for these two reactant ions.) Similar to the single-channel model, the sequential model assumes the reactant isomer to be the MP2(full) 298 K GS, and the product isomer is the MP2(full) 0 K GS, which goes on to dissociate to the MP2(full) 0 K GS secondary product isomer.27 A representative model is shown in Figure 4 for the sequential dissociation of Fe2+(H2O)7 assumed to be a (6,1) reactant dissociating to (6,0) + H2O and (5,0) + 2H2O. (Notably, the model of the total cross-section is also representative of the fits of the primary dissociation channels discussed above.) The resulting difference between the secondary and primary reaction thresholds predicted by this model is referred to here as the sequential BDE, where the uncertainty of this BDE is typically lower than that calculated from primary and secondary threshold differences because several contributions to the absolute uncertainties cancel in the relative value. The secondary threshold for n = 10 is 1.07 ± 0.03 eV, modeled as (6,4) → (6,3) + H2O → (6,2) + 2H2O, yielding a primary−secondary threshold difference of 0.60 ± 0.03 eV for Fe2+(H2O)8−H2O. This sequential BDE is slightly higher (0.03 ± 0.05 eV) than the primary dissociation threshold for n = 9,

Figure 4. Zero pressure extrapolated cross-sections for the CID of Fe2+(H2O)7 with Xe (symbols). Solid lines show the best fits of the sequential model to the primary, secondary, and total water loss products convoluted over the kinetic and internal energy distributions of the neutral and ionic reactants. Dashed lines show the models in the absence of experimental kinetic energy broadening for reactants with an internal energy of 0 K. Optimized parameters for this model are found in Table 2.

0.57 ± 0.04 eV, but within experimental uncertainty. For n = 9, the sequential model gives a relative threshold value of 0.69 ± 0.02 eV for Fe2+(H2O)7−H2O, as modeled assuming a (6,3) _4D,DD_3AA → (6,2) + H2O → (6,1) + 2H2O process, which is 0.03 ± 0.07 eV lower in energy than the single-channel threshold of n = 8, 0.72 ± 0.07 eV. Similarly, for n = 8, the sequential BDE is 0.82 ± 0.02 eV and is within 0.01 ± 0.05 eV of the primary dissociation for n = 7, 0.81 ± 0.05 eV. For n = 7 and 6, the respective primary−secondary threshold differences for Fe2+(H2O)5−H2O and Fe2+(H2O)4−H2O are 1.05 ± 0.03 eV and 1.19 ± 0.03 eV. These are both higher by 0.07 ± 0.07 eV compared to their primary dissociation counterparts for n = 6 and 5 of 0.98 ± 0.06 eV and 1.12 ± 0.06 eV, respectively. Although the agreement is not as good for these two complexes, it is still within the uncertainty. Overall, thresholds obtained using the sequential model are in excellent agreement with those from the single-channel model, with a mean absolute deviation (MAD) of 0.04 eV, comparable to the typical experimental uncertainty. Similar to our previous hydration studies, the sequential BDEs tend to be slightly higher than the primary values. Because of the mass overlap between the Fe2+(H2O)5 and + H (H2O)4 reactant, the secondary water loss threshold is obscured for n = 5 by the primary water loss from the H +(H 2 O) 4 complex. In an attempt to gain threshold information for the n = 4 complex, we analyzed the tertiary threshold of the n = 6 complex by fitting the Fe2+(H2O)4 and Fe2+(H2O)3 cross-sections using the sequential model to obtain their relative threshold, as described previously for such higher order processes.51 We find that the difference between the tertiary and secondary thresholds for Fe2+(H2O)3−H2O is 1.82 ± 0.11 eV. This process may be influenced by competition with the charge separation reaction 6, as discussed above. Because this is the largest complex size where reaction 3 is energetically favored over reaction 1, there should be a competitive shift. Although we cannot explicitly model this competition because this is a tertiary process, we can apply the competitive shift measured from analogous charge separation processes in our studies of hydrated Zn2+ and Cd2+, 0.08 and 0.09 ± 0.03 eV, 1118



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Table 3. Comparison of 0 K Experimental and Theoretical Hydration Energies (kJ/mol) for Fe2+(H2O)n experimenta n

reactant

product

1 2 3 4

(1,0) (2,0) (3,0) (6,0)

Fe2+ (1,0) (2,0) (3,0)

5 6 7 8 9

(5,0) (6,0) (6,1) (6,2) (6,3)_4D,DD_3AA (6,3)_6D_3AA (6,4) (5,5) (4,5,1) (6,4,1) (5,6) (5,5,1) primary sequential

(4,0) (5,0) (6,0) (6,1) (6,2) (6,2) (6,3) (6,3) (6,3) (6,4) (6,4) (6,4)

10

11

MAD MAD

primary

sequential

175.6 (10.6) 167.4 (11.6)c 114.8 (2.9) 101.3 (2.9) 79.1 (1.9) 66.6 (1.9) 57.9 (2.9)

108.1 (5.8) 94.6 (5.8) 78.2 (4.8) 69.5 (6.8) 55.0 (3.9) 55.0 (3.9) 50.2 (5.8) 46.3 (5.8) 40.5 (5.8) 46.3 (2.9) 45.3 (2.9) 45.3 (2.9) 4.0d

theoryb 334.1 287.1 232.0 167.0

(342.3) (296.7) (241.7) (177.1)

111.7 (122.7) 99.3 (111.1) 77.9 (86.6) 76.5 (84.8) 70.5 (78.6) 69.9 (78.3) 59.2 (67.5) 56.4 (63.3) 48.6 (56.5) 51.3 (56.9) 47.1 (54.0) 46.7 (52.3) 6.8 (14.9)e 5.0 (10.5)e

a

Values from Table 2. Uncertainties in parentheses. bMP2(full)/6-311+G(2d,2p)//B3LYP/6-311+G(d,p) level. ZPE corrected. Values listed with (without) cp correction. cValue includes an estimated competitive shift of 8.2 ± 2.9 kJ/mol. dMean absolute deviation (MAD) between primary and sequential BDEs. eMean absolute deviation (MAD) between experiment and theory with (without) cp correction.

respectively.28,32 Applying the average of these previous competitive shifts lowers our measured sequential BDE for Fe2+(H2O)3−H2O to 1.735 ± 0.12 eV. Note that in previous analyses of higher order dissociations of the K+(NH3)n system, where n = 2 − 5, the absolute tertiary and quaternary thresholds were higher than expected from primary thresholds and the sequential BDEs were also somewhat high, with differences increasing with the order of the process; however, all values were within experimental uncertainties.51 This was confirmed in our recent investigation of Cd2+(H2O)n, where the relative tertiary−secondary threshold for Cd2+(H2O)3−H2O is 1.78 ± 0.14 eV, 0.16 and 0.17 ± 0.15 eV higher than the respective primary and sequential thresholds, just outside the experimental uncertainty.32 Overall, the sequential BDE for n = 4 is conservatively viewed as an upper limit because it is obtained through a third-order process from the n = 6 reactant but should be a reasonable measurement of this BDE. Comparison of Experimental and Theoretical Water Loss BDEs. Theoretical 0 K BDEs including ZPE and counterpoise (cp) corrections are determined from singlepoint energies of reactants and products calculated at the MP2(full) level with a 6-311+G(2d,2p) basis set from geometry optimizations using B3LYP/6-311+G(d,p). As discussed above, there is evidence that our most accurate interpretation of the data comes from the relative energies and low-energy structures predicted at the MP2(full) level;31 hence, a comparison with B3LYP and B3P86 BDEs is not conducted here. A comparison of the MP2(full) results with our experimental hydration energies are provided in Table 3 and Figure 5. As evident from Figure 5, there is generally good agreement between the experimental and theoretical results, except for n = 9, and the qualitative trends in the experimental values are reproduced in the theoretical BDEs. Similar to our previous studies, the best agreement between experiment and theory is found after cp correction. This is quantified by the MADs calculated between both primary and sequential BDEs and the MP2(full) results,

Figure 5. Comparison of experimental (solid symbols) and MP2(full,cp) theoretical (open symbols) bond dissociation energies at 0 K. For n = 11, the values for (5,6) lie on top of those shown for (5,5,1).

Table 3. With counterpoise corrections, the MAD is 5−7 kJ/ mol, whereas without cp corrections, the deviations rise to 10− 15 kJ/mol. The sequential BDE for water loss at n = 4 of 167.4 ± 11.6 kJ/mol is found by modeling the tertiary dissociation of the Fe2+(H2O)6 reactant and applying a 8.2 ± 2.9 kJ/mol competitive shift found in the analogous dissociation in the hydration studies of Zn2+ and Cd2+, as explained above. This higher order sequential process is anticipated to be an upper limit to the BDE for this complex size but agrees nicely (within 1 kJ/mol) with the MP2(full,cp) result. As noted above, the largest deviation between experiment and theory is found for n = 9, which is lower than MP2(full) theory by 9−19 kJ/mol, outside of our experimental uncertainty. However, it can also be seen that the experimental values for n = 10 are also about 9 kJ/ mol below theory for specific structures, Table 3. One possible explanation for these discrepancies is that we are forming some 1119



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Table 4. Comparison of 0 K Transition State Energies to Theory and Water Loss Bond Energies (kJ/mol) n

reactant

4

(4,0)

5

(5,0)

6

(6,0)

7

(6,1)

product (3,0) TS[2 + 1] FeOH+(H2O)2 (4,0) TS[2 + 2] FeOH+(H2O)2 (5,0) TS[3 + 2] FeOH+(H2O)3 (6,0) TS[3 + 3] FeOH+(H2O)3

experiment 167.4 (11.6)

+ H+(H2O) 108.1 (5.8)c + H+(H2O)2 94.6 (5.8)c + H+(H2O)2 78.2 (4.8)c + H+(H2O)3

b

B3LYPa

B3P86a

MP2(full)a

167.5 113.9 −53.9 102.7 66.9 −91.7 90.5 65.8 −81.1 78.2 59.7 −13.0

171.2 116.0 −52.9 105.4 66.6 −93.4 93.4 64.9 −83.5 82.6 60.1 −14.5

167.0 138.2 −20.3 111.7 112.8 −36.5 99.3 116.3 −26.0 77.9 114.2 38.0

a

Single-point energies calculated at the level shown using a 6-311+G(2d,2p) basis set and geometries optimized at a B3LYP/6-311+G(d,p) level. All values are ZPE corrected. bValue taken from Table 3 using the sequential dissociation model to analyze a tertiary threshold with a competitive shift of 8.2 ± 2.9 kJ/mol applied. cValues taken from Table 2 using the primary dissociation channel model.

also indicates is directly bound to the metal center, has a bond energy only 13 kJ/mol weaker than the fifth water. The seventh water drops off even further, by 16−22 kJ/mol, consistent with moving into the second solvent shell. The decreases for the eighth and ninth waters are somewhat smaller and comparable, 9−14 kJ/mol (with the primary and sequential BDEs giving slightly different results), consistent with these also involving water molecules binding in similar positions (all AA according to theory) in the second solvent shell. The 10th and 11th water molecules have similar binding energies that are clearly lower than those for the smaller complexes. This is consistent with these ligands binding via single hydrogen bonds in either the second or a third solvent shell. Note that, if the (4,5,1) is assumed as the GS for n = 10, the BDEs actually increase from n = 10 to 11. This counterintuitive result suggests that this is probably not the ground state structure. This is particularly true given that the MP2(full) GS for n = 9 is clearly 6-coordinate and those for n = 11 are either 5- or 6-coordinate. The decrease in BDEs from n = 5 to 9 is almost linear, which closely resembles the trend found in our Zn2+(H2O)n study.27 Indeed, the primary BDEs for Fe2+(H2O)n, n = 6−9, are within 2 kJ/mol of each analogous BDE for Zn2+(H2O)n, suggesting that electrostatics dominates the interactions rather than subtle distinctions between the open-shell character of Fe2+ versus the closed-shell Zn2+. (Notably, in the study of hydrated Zn2+, only a sequential BDE is available for n = 6, and no experimental BDE was measured for n = 5 because of the limitations imposed by charge separation reactions). The similarities between the BDEs are not surprising considering the similar ionic radii of the two dications and the fact that MP2(full) predicts that the water lost in the dissociations of n = 7−9 is a second solvent shell AA water. Interestingly, for n = 6, MP2(full) predicts a (6,0) structure for both Fe2+ and Zn2+ at 0 K but a (5,1) at 298 K for Zn2+. Charge Separation: Predicted Energetic Barriers. Because of the complications with mass overlaps, overlapping products of the individual charge separation processes, and low signal-to-noise of the products, the cross-sections for reaction 3 could not be analyzed with accuracy using our modeling procedures. Predicted barrier heights for the charge separation of Fe2+(H2O)n, where n = 4−7 corresponds to reactions 5−8, are presented in Table 4. Figure S2, Supporting Information, shows the structures of each of these transition states. Multiple

amount of the 5- or 4-coordinated complexes, which would lower the experimental threshold by their excitation energies, up to ΔΔH0 = 11 kJ/mol, Table 1. In the case of n = 10, this is already accounted for by the spread in the three experimental values obtained assuming different structure. For n = 9, the (5,4) complexes are fairly high in 298 K free energy, ΔΔG298 = 8−9 kJ/mol, such that their thermal population should be small (∼4%). It is possible that they could be formed in our source by an equilibrium with the relatively stable n = 10 (5,5) _D,4DD_4AA,A structure or if these fragile ions undergo dissociation upon extraction from the hexapole. We have made similar suggestions regarding the primary thresholds of similar sized complexes in the hydrated Zn2+ and Cd2+ systems, although here the sequential threshold was higher than the primary threshold by the appropriate excitation energy, indicating that there were different structures in the primary and sequential pathways. In the present system, the independently measured primary and sequential thresholds agree well with one another, suggesting that the experimental binding energy is accurate. Perhaps the discrepancy indicates that both n = 9 and 10 have appreciable populations of the 5coordinate complex or that the theoretical calculations are not as reliable in this size range. For n = 10 and 11, there is an ambiguity as to the structure of predicted GS reactant. There is no way to conclusively assign a structure based on trends in the experimental energetics because the experimental BDEs are self-consistent with theory and reproduce the predicted microtrends at both the n = 10 and 11 complexes. For example, the experimental BDE for the n = 10 complex modeled using the (6,4) reactant is 4 kJ/mol higher than that for the (5,5) reactant and 10 kJ/mol higher than that assuming the (4,5,1) reactant. Similar differences of 3 and 11 kJ/mol, respectively, are found for the theoretical bond energies. A similar microtrend is reproduced for n = 11. In all likelihood, there is a distribution of these structures in the experimental reactant ion beam generated from our thermal ESI source. Trends in Water Loss BDEs. The BDEs for losing water from the Fe2+(H2O)n complexes decrease as the complex size increases. The largest energetic difference is between the n = 4 and 5 complexes, with a value comparable to those calculated for the smaller complexes as well, 47 − 65 kJ/mol, Table 3. This is consistent with all of these waters being bound directly to the metal center. In contrast, the sixth water, which theory 1120



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Table 5. Conversion of 0 K Thresholds to 298 K Enthalpies and Free Energies (kJ/mol) for the Water Loss Dissociations from Fe2+(H2O)n, Where n = 4−11; Uncertainties in Parentheses reactant

product

ΔH0a

(4,0) (5,0) (6,0) (6,1) (6,2) (6,3)_4D,DD_3AA (6,3)_6D_3AA (6,4) (5,5) (4,5,1) (6,4,1) (5,6) (5,5,1)

(3,0) (4,0) (5,0) (6,0) (6,1) (6,2) (6,2) (6,3) (6,3) (6,3) (6,4) (6,4) (6,4)

167.4 (11.6) 108.1 (5.8) 94.6 (5.8) 78.2 (4.8) 69.5 (6.8) 55.0 (3.9) 55.0 (3.9) 50.2 (5.8) 46.3 (5.8) 40.5 (5.8) 46.3 (2.9) 45.3 (2.9) 45.3 (2.9)

ΔH298 − ΔH0b 1.5 2.3 1.5 4.4 2.4 4.2 4.3 1.7 3.7 3.0 2.0 2.9 3.5

(0.4) (0.6) (0.5) (0.4) (0.4) (0.4) (0.4) (0.4) (0.2) (0.1) (0.3) (0.2) (0.2)

ΔH298 168.9 (11.6) 110.4 (5.8) 96.1 (5.8) 82.6 (4.8) 71.9 (6.8) 59.2 (3.9) 59.3 (3.9) 51.9 (5.8) 50.0 (5.8) 43.5 (5.8) 48.3 (2.9) 48.2 (2.9) 48.8 (2.9)

TΔS298b 36.5 42.4 42.5 40.7 40.2 40.8 40.4 37.5 37.2 31.2 34.8 31.4 33.1

(1.3) (1.3) (1.4) (1.0) (1.1) (0.9) (1.0) (1.2) (0.8) (0.7) (1.1) (0.9) (0.8)

ΔG298 132.4 (11.7) 68.0 (5.9) 53.6 (6.0) 41.9 (4.9) 31.7 (6.9) 18.4 (4.0) 18.9 (4.0) 14.4 (5.9) 12.8 (5.8) 12.3 (5.8) 13.5 (3.1) 16.8 (3.0) 15.7 (3.0)

a

Experimental values from Table 3. bValues calculated from the vibrational frequencies and rotational constants calculated at the B3LYP/6311+G(d,p) level. Uncertainties found by scaling the frequencies up and down by 10%.

for the case of Zn2+(H2O)7 dissociating to ZnOH+(H2O)3 + H+(H2O)3.28 Comparison of Charge Separation and Water Loss Energetics. Theoretically predicted energies for water loss dissociation pathways are compared to the predicted barrier heights of the charge separation TSs in Table 4. For the n = 4 complex, all levels of theory predict that the TS[2 + 1] barrier height is lower in energy (by 29−55 kJ/mol) compared to the water loss BDE. This prediction is in line with our experimental observations as discussed above for Figure 1a. Looking at this prediction more quantitatively, we see that the 7-fold increase in the FeOH+(H2O)2 cross-section observed beginning at ∼2.5 eV correlates with the energetics of reactions 1 + 6 starting from the n = 5 complex. The observed threshold for these sequential reactions is consistent with the theoretical energies of 2.2−2.3 (DFT) and 2.6 (MP2) eV, which are obtained by summing the energy of the n = 5 water loss BDE and the TS[2 + 1] barrier height. Given that theory confirms that reaction 6 is energetically favored over reaction 1, our application of a competitive shift to the sequential water loss BDE for n = 4 is prudent. The resulting BDE is regarded as our most accurate at this time. For n = 5, the DFT levels predict the barrier height of TS[2 + 2] to be 36−39 kJ/mol lower in energy than the water loss BDE. In contrast, the MP2(full) level predicts a much higher barrier height for reaction 5, yielding a slight energetic preference for the water loss dissociation pathway (1 kJ/ mol). As discussed above, evidence from Figure 1a suggests that reaction 5 is energetically disfavored over reaction 1, in qualitative agreement with the MP2(full) predictions. This agreement with the MP2(full) level is seen more clearly for n = 6, Figure 1b, where the apparent threshold of the FeOH+(H2O)3 product in reaction 7 is ∼0.2 eV higher in energy compared to the water loss product. Again, DFT predicts the TS[3 + 2] for reaction 7 to be 25−29 kJ/mol lower in energy than reaction 1, whereas MP2(full) predicts charge separation to be disfavored by 17 kJ/mol, in quantitative agreement with the apparent thresholds from Figure 1b. For n = 7, there is only a very small contribution from reaction 8; however, both the FeOH+(H2O)3 and H+(H2O)3 products appear to have thresholds that are higher in energy than the product of reaction 1, and their cross-sections are much too small to correspond to energetically favored reactions. This

attempts were made to calculate the rate-limiting TS of reaction 9, but each failed to give a reasonable structure or frequencies. For n = 4, the predicted barrier heights for TS[2 + 1] are ∼115 (DFT) and 138 (MP2) kJ/mol. For larger complexes, the disagreement in the predicted barrier heights between the DFT and MP2(full) levels becomes even larger. For n = 5−7, TS energies predicted by DFT are similar, ranging from 60−67 kJ/ mol, whereas MP2(full) also predicts consistent barriers but much higher in energy, 113−116 kJ/mol. Similar discrepancies between the levels of theory are seen in the exothermicities of the overall reactions, Table 4, such that the reverse Coulomb barriers exhibit more systematic behavior. (Unfortunately, the present experiments provide no direct information concerning the overall exothermicities for reaction 3. Combined with hydration energies of the hydronium ion and the present Fe2+ hydration energies, measurements of the hydration energies of FeOH+ could provide such data.) Here, the reverse barrier decreases as n increases, i.e., 158 (168), 149 (159), 142 (147), and 76 (73) kJ/mol for n = 4−7, respectively, at the MP2(full) (B3LYP) levels. This trend is in agreement with previously discussed trends for charge separation of hydrated Zn2+ and Cd2+ dications.28,32 Presumably, there is little disagreement between DFT and MP2 levels of theory for the reverse Coulomb barrier because this is dominated by electrostatics. Overall, in the absence of experimental measurements of these TSs, it is difficult to say with certainty which level of theory is more accurate in predicting the barrier height; however, the next section provides a qualitative assessment. A reviewer points out that our observation of the loss of H+(H2O)2 from the (5,0) and (6,0) complexes of Fe2+(H2O)n is interesting given the salt-bridge mechanism for charge separation originally suggested by Beyer et al. for hydrated alkaline earth dications.9 Although complexes larger than M2+(H2O)2 were not explicitly examined, the essence of this work is that charge separation requires rearrangement of the (n,0) complex to the (n − 1,1) isomer followed by loss of H3O+ mediated by a transition state having a M2+−OH−−H3O+ saltbridge structure. The present observations, as well as previous work for Zn2+(H2O)n,28 demonstrate that charge separation can also occur by rearrangement to (n − 2,1,1) isomers for n = 5 and 6 and to (n − 3,1,2) isomers for n = 7 and 8. An example of the detailed mechanism for such a process has been elucidated 1121



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H2O for the dissociation of the n = 4 complex suggesting that this is the critical size (ncrit) according to the energy-dependent definition of critical size.28 This conclusion is in agreement with the assignment of Jayaweera et al. that ncrit = 4,3 although this vallue is smaller than the assignment made by Shvartsburg and Siu (ncrit = 5).13 This disagreement results from a different definition of critical size, which Shvartsburg and Siu reported as the largest observable size n for which reaction 3 occurs. As we have pointed out previously, such a definition is somewhat ambiguous as it depends on the experimental sensitivity of the apparatus. For instance, given this definition, the present results would define the critical size as ncrit = 8 because we clearly observe reaction 9 as well as reactions 7 and 8. However, our method allows for the assignment of critical size based on the quantitative observations from Figure 1. A large discrepancy between the DFT and MP2(full) levels was observed when comparing the predicted energetics for the barrier heights of the charge separation processes for n = 5−7. Comparing these predicted energies and their trends to the kinetic energy dependent cross-sections obtained here indicates that the predictions of the MP2(full) level are more accurate.

again is in agreement with the relative energetics predicted by the MP2(full) level of theory for TS[3 + 3] relative to reaction 1 but disagrees with the DFT results. Finally, the fact that the charge separation reaction becomes increasingly disfavored as n increases at the MP2(full) level explains the observations made above that the magnitudes of the cross-sections for the primary charge separation reactions decrease relative to the corresponding water loss as n increases from 5 to 8. Overall, MP2(full) is more accurate for predicting the trends and relative energetics of the hydrated iron dication compared to either DFT method employed in this study. Conversion to 298 K. By using the calculated frequencies and rotational constants of the transition states, a rigid rotor/ harmonic oscillator approximation was applied to convert the 0 K primary water loss threshold energies of the n = 5−11 complexes and the sequential 0 K BDE for n = 4 to 298 K hydration enthalpies and free energies in Table 5. The uncertainties in these conversion factors are found by scaling the vibrational frequencies up and down by 10%. Similar to the hydration energies, the free energies of hydration decrease as n increases. The enthalpy corrections, ΔH298 − ΔH0, and entropies of dissociation, TΔS298, remain relatively constant with complex size. For the n = 10 and 11 complexes, the entropy of dissociation does change when the inner shell size changes with the biggest differences related to the number of low frequency torsions. It should be realized that, for these noncovalently bound systems, there are a multitude of lowfrequency vibrations that correspond to hindered rotations and translations of the ligands, e.g., 33 vibrations in Fe2+(H2O)6. Treating such vibrations as harmonic oscillators may not be completely accurate, but more exact treatments are beyond the scope of the present study.

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ASSOCIATED CONTENT

S Supporting Information *

Table of relative calculated enthalpies (ΔH0) and free energies (ΔG298) of all isomers found for Fe2+(H2O)n, n = 5−11. Two figures showing the structures of low-energy isomers of Fe2+(H2O)n for n = 1−11 and of the charge separation transition states calculated at the B3LYP/6-311+G(d,p) level of theory. This material is available free of charge via the Internet at http://pubs.acs.org.

■

■

CONCLUSIONS Complementing our previous hydration studies of transition metal dications, the kinetic energy dependent cross-sections for collision-induced dissociation of Fe2+(H2O)n, where n = 5−11, with Xe were examined. For all values of n studied, the dominant processes are the sequential loss of single water molecules from the Fe2+(H2O)n species to form Fe2+(H2O)m complexes where m < n, although charge separation processes yielding FeOH+(H2O)x + H+(H2O)y are also observed as primary reactions for n = 4−8. The data are analyzed to yield primary and sequential bond dissociation energies (BDEs) for the loss of one and two (and, in one case, three) water ligands from the reactant complexes. The BDE for the n = 4 complex was accessible only as a tertiary dissociation, such that competition with the charge separation channel could not be modeled directly. Therefore, a competitive shift of 8.2 ± 2.9 kJ/ mol (determined from analogous dissociations of hydrated Zn2+ and Cd2+ in previous studies) was applied in this case. There is excellent agreement between the primary and sequential BDEs along with good agreement to theoretical energetics calculated at the MP2(full)/6-311+G(2d,2p)// B3LYP/6-311+G(d,p) level including ZPE and counterpoise corrections. These results are the first reported experimental bond energies of the hydrated iron dication. Comparisons to the hydration energies of the closed-shell dication Zn2+, which has a similar ionic radius to Fe2+, indicate that electrostatics dominate the interactions, and subtle distinctions associated with the open-shell character of Fe2+ are not obvious. From experimental observations and theoretical results, the charge separation process is energetically favored over loss of

AUTHOR INFORMATION

Present Address †

Lawrence Berkeley National Laboratory, Chemical Sciences Division, 1 Cyclotron Rd. MS 6-2100, Berkeley, California 94720, United States. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Science Foundation, Grant No. CHE-1049580. In addition, we thank the Center for High Performance Computing at the University of Utah for the generous allocation of computer time. Sloan Roberts and Dr. Damon Carl are thanked for acquiring preliminary data on these systems. The reviewers are thanked for several useful suggestions.

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Threshold Collision-Induced Dissociation and Theoretical Studies of

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