Experimental Binding Energies for the Metal Complexes [Mg (NH3) n

Article pubs.acs.org/JPCA

Experimental Binding Energies for the Metal Complexes [Mg(NH3)n]2+, [Ca(NH3)n]2+, and [Sr(NH3)n]2+ for n = 4−20 Determined from Kinetic Energy Release Measurements E. Bruzzi,† G. Raggi,† R. Parajuli,‡ and A. J. Stace*,† †

Department of Physical and Theoretical Chemistry, School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, U.K. ‡ Department of Physics, Amrit Campus, Tribhuvan University, Kathmandu, Nepal ABSTRACT: A supersonic source of clusters has been used to prepare neutral complexes of ammonia in association with a metal atom. From these complexes the following metal-containing dications have been generated: [Mg(NH3)n]2+, [Ca(NH3)n]2+, and [Sr(NH3)n]2+, and for n in the range 4−20, kinetic energy release measurements following the evaporation of a single molecule have been undertaken using a high resolution mass spectrometer. Using f inite heat bath theory, these data have been transformed into binding energies for individual ammonia molecules attached to each of the three cluster systems. In the larger complexes (n > 6) the results exhibit a consistent trend, whereby the experimental binding energy data for all three metal ions are very similar, suggesting that the magnitude of the charge rather than charge density influences the strength of the interaction. From a comparison with data recorded previously for (NH3)nH+ it is found that the 2+ charge on a metal ion has an effect on the binding energy of molecules in complexes containing up to 20 solvent molecules. Although subject to comparatively large experimental errors, the results recorded for Ca2+ and Sr2+ when n ≤ 6 show evidence for the formation of an inner solvation shell containing up to 6 molecules. However, Mg2+ exhibits relatively low binding energies when n = 5 and 6, which suggests that a second shell starts to form before there are 6 ammonia molecules bound to the metal ion. This conclusion is supported by DFT calculations and it is proposed that these complexes could take the form [Mg(NH3)4(NH3)]2+ when n = 5 and either [Mg(NH3)4(NH3)2]2+ or [Mg(NH3)5(NH3)]2+ when n = 6. In each case, additional molecules are hydrogen bonded to one or more molecules in the inner solvation shell.

1. INTRODUCTION Very many gas-phase studies of the chemical and physical properties of metal ions have concentrated on singly charged species because of their ease of formation.1 This situation contrasts markedly with condensed-phase metal ion chemistry, where the +2 charge state is the one most frequently encountered. Difficulties with studying metal dication chemistry arise in the gas phase because of the very high probability of charge transfer; a situation that is easy to appreciate when the second ionization energy of a metal is typically ≥15 eV, whereas the first ionization energy of an attached molecule or ligand is ≤10 eV. Despite these difficulties, significant progress has been made on the development of techniques for both generating and studying the thermochemistry, chemistry, and spectroscopy of solvated metal dications.2 One aspect of metal dication chemistry where quantitative data is of particular significance concerns ion solvation and the determination of individual metal−molecule binding energies. Such information not only contributes toward a better understanding of the behavior of metal ions in bulk solvents but also can provide a benchmark against which quantum mechanical and molecular mechanics calculations can be judged. To date, progress on the determination of solvent © 2014 American Chemical Society

binding energies has been restricted to water in the form of [M(H2O)n]2+ complexes and where n is ≤11. Contributions to these measurements have come from the thermodynamic equilibrium experiments of Kebarle et al.,3−6 the BIRD experiments of Williams et al.,7,8 and the collisional activation experiments of Armentrout et al.9−13 Although an up limit of 11 most probably places some solvent molecules in a second solvation shell, there is evidence from the experiments of Armentrout and co-workers that the +2 charge continues to have an influence on binding energy even for the 11th molecule.9−13 In contrast, comparable experiments on singly charged metal ion complexes of the form [M(H2O)n]+ show that influence of the +1 charge on binding stops at n = 6, which probably corresponds to the first solvation shell.1 In the experiments reported here, complexes of the form [M(NH3)n]2+, where M is Mg, Ca, or Sr, have been generated using the pick-up technique followed by electron impact Special Issue: A. W. Castleman, Jr. Festschrift Received: March 5, 2014 Revised: June 24, 2014 Published: June 25, 2014 8525

dx.doi.org/10.1021/jp5022642 | J. Phys. Chem. A 2014, 118, 8525−8532

The Journal of Physical Chemistry A

Article

Figure 1. Examples of peak profiles recorded for precursor and fragment ions following the loss of a single ammonia molecule in the 2ff r region of a VG ZAB-E mass spectrometer: (a) [Mg(NH3)7]2+; (b) [Ca(NH3)14]2+; (c) [Sr(NH3)12]2+. In each case peak intensity is plotted as a function of laboratory-frame kinetic energy (eV/z), where the precursor ion has been extracted from the ion source at a nominal potential of 5 kV. Also given are the Gaussian fitting parameters w and R2 that have been derived from the curves. w is related to the fwhm of the peak, and R2 is the goodness of fit, where 1.0 is a perfect fit. For (b) and (c), there is evidence of an artifact peak to the right of the signal for the fragment ion.

ionization. Using f inite heat bath theory14−18 the binding energies of single ammonia molecules for n ≤ 20 have then been extracted from data recorded on the unimolecular fragmentation of each of the complexes as a function of n. The results show that the +2 charge continues to have an influence on binding even in complexes where the second solvation shell is firmly established.

effusion cell (DCA Instruments, EC-40-63-21) operating between 400 and 650 °C. Neutral metal atoms (magnesium, calcium, or strontium) collide with the molecular cluster beam to produce various neutral clusters including some with of form M.Arm(NH3)n, where M is a metal atom. Del Mistro and Stace21 have shown from a molecular dynamics simulation that in the simpler case of colliding Ar20 with a single acetonitrile molecule, the cluster first melts and the molecule then moves below the surface within 40 ps of the collision; the mixed cluster then achieves stabilization through the evaporation of argon. It is quite clear for previous experiments19,20 that argon atom evaporation is an essential part of the “pick-up” and facilitates the dispersion of energy on addition of a metal atom and after electron impact ionization. Neutral clusters, some of which contain (on average) a single metal atom enter the ion source of a high resolution, reverse geometry, double focusing mass spectrometer (VG-ZAB-E), where they are ionized by high-energy electron impact (∼70−100 eV). Because only ions

2. EXPERIMENTAL SECTION The apparatus used for the generation, identification, and detection of gas-phase multiply charged metal−ligand complexes has been described extensively in previous publications.19,20 Briefly, the first step is to produce mixed neutral clusters by adiabatic expansion through a pulsed supersonic nozzle of a 5% ammonia/argon gas mix (BOC specialty gases). Neutral clusters of varying composition including Arm, Arm(NH3)n, and (NH3)n, then pass through a region where metal vapor vapor (∼10−2 mbar) is generated by a Knudsen 8526



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correction to the laboratory-frame kinetic energy spread of the fragment ion has been made using the relationship

rather than neutral complexes are detected in the experiment, it is likely that extensive evaporation of ligands, predominantly argon, but also ammonia molecules, takes place to reduce the internal energy of the complexes to a relatively stable level. Accordingly, under most experimental conditions no ion complexes of the form [M(Ligand)n(Ar)m]z+ are ever detected. The resulting ion beam was then extracted from the source at 5 kV into the flight tube of a sector mass spectrometer and the mass-analyzed ion kinetic energy (MIKE) technique used to study fragmentation occurring in the second field free region (2nd f f r) of the mass spectrometer between the magnetic and electric sector.22 A particular [M(NH3)n]2+ cluster dication of mass (m1) was selected using the magnet, and the electric sector field voltage was scanned while the accelerating voltage and magnetic field remained constant. The following equation then provides a means of identifying fragment ions from the magnitude of the electric sector voltage necessary to transmit them zm E* = 1 2 E 0 z 2m1 (1)

⎞2 ⎛ m2 (ΔE) = (ΔE2) − ⎜ ΔE1⎟ ⎠ ⎝ m1 2

2

(2)

where ΔE is now the laboratory-frame kinetic energy spread from which an average center-of-mass kinetic energy release for a Gaussian profile has been calculated using the equation22 2 z 2 2m12eV ⎛ ΔE ⎞ ⟨εt ⟩ = 2.16 ⎜ ⎟ 16z1m2m3 ⎝ E0 ⎠

(3)

where eV is the kinetic energy of the parent ion in electron volts and m3 is the mass of the neutral fragment. Up to six laboratory-frame energy measurements were made for each fragmentation pathway, and an error for the average laboratory-frame width, ΔΔE, was determined from the following relationship, where m is the number of measurements: m

where E0 is the initial parent ion kinetic energy (5000 eV in the present experiment), E* is the laboratory-frame kinetic energy after fragmentation, and m2 is the mass of the fragment ion. z1 and z2 are the number of charges on the parent and fragment ions, respectively, and for this particular series of experiments, both have a value of 2. The detection system consists of a Daly scintillation detector that has been modified to extend the sensitivity range by enabling photon counting techniques to be used when signals are particularly weak. Ion counting is achieved using a fast photomultiplier (EMI 9324) at a cathode voltage of −1 kV in conjunction with a photon counter (Stanford Research SR 400). During the course of these experiments, the background pressure in the second f f r remained 12) there is some evidence of an artifact peak to the right of the main fragment peak, and where there was significant overlap with the peak of interest the artifact contribution to the overall peak shape has been deconvoluted by fitting both profiles separately. The persistent presence of artifact peaks in cluster ion mass spectra has been discussed previously24 and their influence ultimately determines the upper limit to measurements of this nature. The standard deviation of a Gaussian profile, w/2, is related to the full width half-maximum by fwhm = w(2 ln 2)1/2, and for most of the examples discussed here, experimental measurements of peak widths were only accepted when the goodness of fit to a Gaussian profile, R2, was >0.9, where 1.0 is a perfect fit. To minimize the effects of a kinetic energy spread in precursor ions, the energy resolving capability of the mass spectrometer has been improved in comparison to experiments where just fragmentation is being detected. In these new measurements, the laboratory-frame fwhm peak widths of precursor ions (ΔE1) were, for the most part, ≤2 eV, which is to be compared with a typical fragment ion laboratory-frame energy width (ΔE2) of >4 eV. Although previous energy release measurements have been undertaken at a higher energy resolution,23 a compromise has to be made when signal intensities are lower. A mass-weighted

ΔΔE = max ΔEj = 1,..., m −

∑ j = 1 ΔEj (4)

m

Error bars in subsequent figures reflect the magnitude of ΔΔE in terms of a quoted accuracy for each binding energy determined from m experimental peak width measurements. Table 1 presents the kinetic energy release data recorded for all three metallic systems together with the calculated error limits. Table 1. Measurements of the Average Kinetic Energy Release, ⟨ετ⟩ (meV), Associated with the Unimolecular (Metastable) Decay of Each Cluster Iona n

[Mg(NH3)n]

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

23 19 20 21 19 19 19 17 16 15 13 14 14 13 11 13

2+

3.9 2.2 0.9 6.0 1.2 0.6 1.4 1.1 0.5 1.9 8.7 0.6 3.6 2.5 2.3 2.9

[Ca(NH3)n] 51 46 33 22 20 20 19 18 18 17 17 15 14 14 13 14 14

2+

2.8 2.1 3.4 1.1 2.6 1.5 0.7 0.5 0.2 1.5 1.4 1.9 1.4 1.9 2.3 1.1 0.7

[Sr(NH3)n]2+ 59 49 37 23 16 17 19 19 17 15 14 13 15 13 13 11 13

8.9 6.7 1.5 1.8 2.7 2.2 5.3 1.0 0.5 2.6 2.5 2.3 2.1 0.2 0.7 0.7 1.5

a

Each value is derived from an average of six separate measurements of the laboratory-frame kinetic energy spread (ΔE) and the error, ±Δ⟨ετ⟩, reflects the spread in uncertainty of these experimental measurements.

3. THEORY SECTION Quantum calculations has been carried out on small complexes (n ≤ 7) using the Q-Chem quantum chemistry package.25 For magnesium/ammonia complexes, optimized geometries and vibrational frequencies were calculated at the PBE/6-311+ +G** level of theory using Baker’s eigenvector algorithm.26−30 8527



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For complexes containing either calcium or strontium with ammonia, calculations were performed using the Becke threeparameter hybrid exchange functional and Yang’s gradient (B3LYP) functional,31,32 with a 6-311++G** basis set for calcium,28,33 and a Def2-SVPD basis set with effective core potential (ECP) of the Stuttgart−Bonn pseudopotential (SRLC) for strontium.34−37 Binding energies were calculated as Eb = E[M2+(NH3)n+1] − E[M2+(NH3)n] − E[NH3] with M = Mg, Ca, and Sr, and the results were then corrected for basis set superposition error and zero point energy. The binding energies for clusters containing n + 1 ammonia molecules can be calculated as follows Eb = E[M2+(NH3)n+1] − E[M2+(NH3)n] − E[NH3] for M = Mg, Ca, and Sr. However, added to Eb were two corrections: (i) for basis set superposition error (BSSE) the equation is modified to the form EBSSE = E[M2+(NH3)n+1] − EBSSE[M2+(NH3)n] − EBSSE [NH3] where the energies are now counterpoise corrected; (ii) a zero point vibrational energy correction was determined from the equation EZPE = EZPE[M2+(NH3)n+1] − EZPE[M2+(NH3)n] − EZPE[NH3]; the frequencies were not scaled. The total binding energy with corrections was then given by Ebc = EBSSE + EZPE, and these results are summarized in Tables 2−4.

Table 4. Experimental and Calculated Binding Energies (kJ mol−1) for Small [Sr(NH3)n]2+ Complexesa

configuration

4 4 5 5 6 6 7 7

[Mg(NH3)4]2+ [Mg(NH3)3(NH3)]2+ [Mg(NH3)5]2+ [Mg(NH3)4(NH3)]2+ [Mg(NH3)6]2+ b [Mg(NH3)5(NH3)]2+ [Mg(NH3)5(NH3)2]2+ [Mg(NH3)4(NH3)3]2+

calcd binding energy (Ebc) 186.6 75.2 117.9 64.2

exptl binding energy (Eb)

62 ± 10

43 ± 2

3 4 4 5 5 6 6 7

[Ca(NH3)3]2+ [Ca(NH3)4]2+ [Ca(NH3)3(NH3)]2+ [Ca(NH3)5]2+ [Ca(NH3)4(NH3)]2+ [Ca(NH3)6]2+ [Ca(NH3)5(NH3)]2+ [Ca(NH3)6(NH3)]2+

160.5 159.6 46.7 127.0 64.1 105.7 59.0 42.4

160.0 140.8 57.80 115.0 61.8 95.3 50.6 44.1

⟨εt⟩ = 1.5kBT #

193 ± 29.1 129 ± 17.7 86 ± 3.7 50 ± 3.9

(5)

where kB is Boltzmann’s constant. Taken in this form, eq 5 assumes there is no reverse activation barrier, which is expected to be the case here where a neutral molecule is interacting with a charged core. For each value of T# an isokinetic bath temperature, Tb, can be defined for the cluster ensemble from the equation

Table 3. Experimental and Calculated Binding Energies (kJ mol−1) for Small [Ca(NH3)n]2+ Complexesa calcd binding energy (Ebc)

[Sr(NH3)3]2+ [Sr(NH3)4]2+ [Sr(NH3)3(NH3)]2+ [Sr(NH3)5]2+ [Sr(NH3)4(NH3)]2+ [Sr(NH3)6]2+ [Sr(NH3)5(NH3)]2+ [Sr(NH3)6(NH3)]2+

4. DATA ANALYSIS AND RESULTS To transform measured kinetic energy releases into binding energies, use has been made of the evaporative ensemble statistical model of Klots.14−18 In an earlier publication,38 binding energy results were presented following an application of f inite heat bath theory to the systems: (H2O)nH+, (NH3)nH+, and (CH3OH)nH+, where n was in the range 3−30. From those results it was concluded that each cluster ion fragmented via the breaking of a single hydrogen bond. For each of the values of ⟨εt⟩ determined from eq 3 a temperature for the transition state, T#, corresponding to the evaporation of a single molecule from a cluster, can be determined from the following equation14−18,39

Structures that give the closest match between experiment and theory are shown in bold. bCalculations would not converge to give a stable configuration with six ammonia molecules in the first solvation shell.

configuration

3 4 4 5 5 6 6 7

exptl binding energy (Eb)

40−50 kJ mol−1 difference in binding energy between the two types of site. This value does not differ significantly if there are one or two molecules in the outer shell, and similarly, there are no significant variations with regard to the relative positions of molecules within an outer shell.

a

n

calcd binding energy (Ebc)

Structures that give the closest match between experiment and theory are shown in bold.

45 ± 5 58.4 55.5 59.7

configuration

a

Table 2. Experimental and Calculated Binding Energies (kJ mol−1) for Small [Mg(NH3)n]2+ Complexesa n

n

exptl binding energy (Eb) 169 ± 9.4

Tb = T

122 ± 5.7

#

( C −γ 1 ) − 1

exp

γ /(C − 1)

(6)

where C is the heat capacity of a cluster (C is expressed in units of kB) and γ is the Gspann parameter.40 Each cluster has been assigned a value C = 6(n − 1), where n is the number of molecules present. This expression assumes that none of the intramolecular vibrations in any of the molecules are active and that overall cluster rotation and translation do not contribute to the heat capacity. There is also no contribution from intermolecular modes that involve the central metal ion. These assumptions regarding contributions to C from ammonia molecules match the conclusions reached by Sundén et al.41 following a detailed analysis of the heat capacities of water clusters. There are no analogous data available for ammonia clusters. The Gspann parameter, γ, in eq 6 was taken as 23.5, which ±1.5 appears to be the value most frequently used in calculations of the type discussed here.40 The binding or

77 ± 7.9 48 ± 2.3

a

Structures that give the closest match between experiment and theory are shown in bold.

As will be seen below, the experimental error bars on data recorded for values of n ≤ 6 are large; therefore, it was not considered necessary to calculate binding energies to a high accuracy. The primary purpose of these calculations has been to differentiate between the binding energies of molecules bound directly to the metal ion and binding energies of those molecules residing in a secondary or outer solvation shell. The calculations achieve that objective in that there is found to be a 8528



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evaporation energy, Eb, of a single molecule with respect to a cluster can then be calculated from the expression E b = γkBTb

Table 5. Binding Energies, Eb, Determined for Single Ammonia Molecules Bound to the Metal Complexes [Mg(NH3)n]2+, [Ca(NH3)n]2+, and [Sr(NH3)n]2+ a

(7)

[Mg(NH3)n]2+

The magnitude of the binding energy is going to depend quite critically on the environment of the molecule that is being lost from a complex. For a molecule bound directly to a metal dication, Eb is going to be large, possibly too large for the loss of such a molecule to be recorded as a metastable process. In contrast, molecules occupying the second and third solvation shells will be bound by hydrogen bonds to molecules in closer proximity to the metal ion. The presence of a charge may increase the strengths of these hydrogen bonds, but they should still be amenable to measurements of the type being undertaken here. For hydrogen-bonded molecules in an outer solvation shell there are two possible bonding configurations, they are bound either by two such bonds, which is the case for water in its most stable environment, or by one hydrogen bond, which is most probably the case for a typical ammonia molecule. Following a detailed analysis of the kinetics of their metastable fragmentation, it was concluded, for (H2O)nH+, (NH3)nH+, and (CH3OH)nH+ complexes, that decay would only be observed following the breaking of a single hydrogen bond, which was confirmed from data recorded out to n = 30.38 Therefore, for the examples being studied here, Eb might be expected to converge toward a value of between 12 and 16 kJ mol−1 as n in [M(NH3)n]2+ increases. Calculations on ammonia clusters show that, as a function of size, there is considerable variation in values calculated for the binding or evaporation energies of single molecules.42,43 Because all of the calculations concentrate on the most stable structures, there are not data for the breaking of just a single hydrogen bond; the above range comes from dividing calculated binding energies by the number of bonds being broken. This distinction between calculated results for the most stable hydrogen-bonded structures and what is being derived from these experiments emphasizes the fact that the latter records data from the least stable of the structures available to a complex. Table 5 presents experimental values of binding energies for the dications [Mg(NH3)n]2+, [Ca(NH3)n]2+, and [Sr(NH3)n]2+, derived from the f inite heat bath analysis given above, and a graphical summary as a function of n is given in Figure 2. There is a very marked drop in signal intensity for all three metal complexes when n is less than 4, and therefore no measurements were possible. For the case of [Mg(NH3)4]2+, this ion exhibits a very strong Coulomb fission signal,44 which also significantly reduces the possibility of observing unimolecular loss of a neutral molecule. As expected, values for the binding energy show a steep variation when n is small but then decline less rapidly beyond n = 6. For n < 6 the error bars on some of the data points are significantly larger than those seen when n > 6; this is due to the reduced probability smaller ions have of fragmenting in the second f f r, which means that signal strengths are low and the peak profiles are less reproducible. For the small complexes, a consequence of these large error bars is to give binding energies for Sr2+ that are comparable to those recorded for Ca2+ (see below), which is probably not going to be the case. In contrast, the larger cluster ions benefit from the appearance of reproducible peak profiles with excellent signal-to-noise ratios (Figure 1), which in turn lead to consistent trends across the data sets. From Table 5 and Figure 2 it can be seen that there is a marked difference between values of binding energies

n 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Eb 62 45 43 44 38 37 36 32 28 27 23 24 24 22 19 22

[Ca(NH3)n]2+

[Sr(NH3)n]2+

(NH3)nH+ b

±ΔEb

Eb

±ΔEb

Eb

±ΔEb

Eb

±ΔEb

10 5.2 1.9 12.0 2.4 1.1 2.6 2.0 0.9 3.3 15.0 1.0 6.1 4.3 4.0 5.0

169 122 77 48 41 39 36 35 33 31 30 27 27 26 23 23 23

9.4 5.7 7.9 2.3 5.4 2.9 1.3 0.9 0.5 2.8 2.5 3.3 2.5 3.4 0.8 1.9 1.1

193 129 86 50 34 34 36 36 31 28 26 24 26 23 23 19 21

29.1 17.7 3.7 3.9 5.5 4.4 10.1 1.9 0.9 4.8 4.6 4.1 3.7 0.2 1.2 1.2 2.5

85 52 29 20 19 18 17 17 17 17 16 16 16 16 16 17 17

14 3.7 1.5 1.4 1.4 1.9 0.4 0.9 1.0 0.7 0.4 0.3 0.9 0.7 0.9 0.2 0.8

a

These values have been calculated from the experimental data given in Table 1, and ±ΔEb is the average error associated with the experimental measurements. All energies are in units of kJ mol−1. Also given for reference purposes are comparable data recorded for (NH3)nH+ clusters that have been taken from ref 38. bTaken from ref 38.

Figure 2. Binding energies determined from the application of f inite heat bath theory to experimental data recorded following fragmentation of the metal dication complexes [Mg(NH3)n]2+, [Ca(NH3)n]2+, and [Sr(NH3)n]2+ and plotted as a function of n. The data have been taken from Table 2 and are shown together with error bars.

determined for [Ca(NH3)n]2+ and [Sr(NH3)n]2+ complexes when n is in the range 4−6, and the corresponding values determined for [Mg(NH3)n]2+ complexes; in fact, this difference amounts to a factor of 2. A possible reason for this observation can be identified from earlier work by RodriguezCruz et al.7,8 on alkaline earth metal dications complexed with water, [M(H2O)n]2+, where M is Mg, Ca, Sr, and Ba, and n = 6. From their BIRD (blackbody infrared radiation dissociation) experiments they identified a pattern of behavior that equated with the formation of a structure where one water in the 8529



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it possible to identify such configurations from comparisons between experiment and theory, and indeed, for [Mg(NH3)5]2+ and [Mg(NH3)4(NH3)]2+ the energy difference between the two sites strongly favors the latter configuration. For n = 6, it was not possible for the calculations to converge on a stable structure for [Mg(NH3)6]2+; therefore, the possible choices are either [Mg(NH3)4(NH3)2]2+ or [Mg(NH3)5(NH3)]2+. The experimental result for n = 6 is sufficiently low as to rule out the loss of a molecule that is directly bound to the metal ion; therefore, the measurement most probably corresponds to the loss of a molecule from an outer shell. In addition, comparisons with the equivalent data for Ca2+ and Sr2+ show the experimental result for [Mg(NH3)6]2+ to be anomalously low, which again suggests the loss of a hydrogen-bonded molecule. If, for n = 7, possible structures build on the smaller units identified above, then there are two obvious choices, [Mg(NH3)5(NH3)2]2+ and [Mg(NH3)4(NH3)3]2+, but neither calculated binding energy offers a good match to the experimental result. For the Ca2+ data the level of agreement between experiment and theory is better than that for Mg2+. For Ca2+, fragmentation is observed at n = 4 and the calculated binding energy lies within experimental error of the measured value. For n = 5, the results support a structure where all five molecules are bound to the central metal ion, which contrasts with the conclusion reached regarding the Mg2+ data. However, for n = 6, there is evidence to support a switch in behavior, in that there is now a closer match between the experimental result and a binding energy calculated for [Ca(NH3)5(NH3)]2+ rather than [Ca(NH3)6]2+. However, for n = 7 the underlying structure would appear to have reverted to one where six molecules are bound to the metal dication. Finally, for the strontium dication, the match between the experimental and theoretical results would suggest a progressive solvation of the metal ion through to [Sr(NH3)6]2+, at which point a second solvation shell starts to form. What needs to be borne in mind is that the type of experiment being undertaken here is very selective. It could well be that many of the other structures considered in Tables 2−4 are present in the ion signal; however, their contribution to metastable (unimolecular) decay is ruled out by a process that favors fragmentation via the lowest energy pathway. Overall, the marked difference between inner and outer shell binding energies makes it possible to distinguish between molecules bound to either of the two sites. What is most noticeable from the data plotted in Figure 2 is that the values determined for the binding energies continue to exhibit a gradual decline even when n reaches 20. To emphasize this point, the corresponding data derived for ammonia cluster ions, (NH3)nH+,25 using f inite heat bath theory have been plotted in Figure 3 together with the data for calcium, [Ca(NH3)n]2+. Whereas the ammonia cluster data converge to a steady value of ∼16 kJ mol−1 once n ≥ 7, that is clearly not happening for the case of [Ca(NH3)n]2+, where the results would suggest that the +2 charge on the metal continues to have an influence on the binding energy even when n = 20. Given the approximations present in the theory used to derive these values, the binding energies for the (NH3)nH+ ions are surprisingly close to the anticipated range for the strength of a single hydrogen bond. Moreover, the consistency of the results for both (NH3)nH+ and [Ca(NH3)n]2+ in the range 6 < n < 20 underpins the accuracy of the measurements that have been made on the larger clusters. As can be seen from Figure 3, the [Ca(NH3)n]2+ data are converging toward such a value but may

magnesium complex occupies a site in a secondary rather than a primary solvation shell.7,8 Adopting the notation of Pavlov et al.,45 it was proposed that the magnesium complex switched in structure from [Mg(H2O)6]2+, where each water molecule is bound to the central metal dication, to a structure of the form [Mg(H2O)5(H2O)]2+,7,8 where the latter denotes a water molecule that is held in the second solvation shell and is hydrogen bonded to one or more molecules is the first shell. The promotion of a water molecule was observed to occur at high temperatures (>350 K) and was accompanied by a drop in binding energy.7,8 The temperature(s) of the complexes in the experiments reported here is unknown, but for several reasons it is most likely to be higher than that utilized in the BIRD experiments. First, electron impact ionization can result in extensive excitation and the ions are >10−4 s old when they are observed to undergo decay; therefore, molecular evaporation is most probably the only effective energy loss mechanism; indeed, the Klots evaporative ensemble theory assumes as much.14−18 Second, Table 1 reports results following the decay of complexes where n = 4, which Rodriguez-Cruz et al.7,8 could only achieve using collisional activation. At >1 × 10−7 mbar, the pressure in second f f r is too low for the latter mechanism to be responsible for initiating decay in the present experiments.44 The choice of sites from which fragmentation can occur will be strongly influenced by the pathway with the lowest activation energy. Therefore, in addition to accounting for the fact that just a single hydrogen bond is being broken, the fragmentation pathway could also be sensitive to the location of the molecule being lost. For the most part, this effect is driven by the very narrow time window, within which metastable decay can be observed.38 As a result, if there is a choice between a molecule being lost from a strongly bound site on the central metal ion and a site that is located on a more weakly bound outer solvation shell, it is the latter process that will be observed as metastable decay. To explore the options available to each of the metal complexes being studied here, density functional theory, as outlined above, has been used to calculate binding energies for a range of possible configurations that might be adopted by small complexes. The results for [Mg(NH3)n]2+ complexes for n ≤ 7 are given in Table 2. The calculated binding energy for [Mg(NH3)4]2+ is probably close to the upper limit of what can be measured in this type of experiment; however, that would not apply to [Mg(NH3)3(NH3)]2+, where a single molecule has been promoted to a second shell. However, what is responsible for the absence of any loss of neutral molecules from either of these complexes is the fact that the only decay channel observed for n = 4 (either as [Mg(NH3)4]2+ or as [Mg(NH3)3(NH3)]2+) is Coulomb fission.44 Given the nature of the charged fragments from the latter process, it is highly likely that fission is facilitated by the adoption of structures of the form [Mg(NH3)3(NH3)]2+.46 The first complex to exhibit neutral loss is [Mg(NH3)5]2+ and that is where the measurements in Table 1 start. Taking the results of Rodriguez-Cruz et al.7,8 into consideration, the two most likely structures for the latter ion are either one where all the molecules are coordinated to the central metal ion latter ion or one where a single molecule has been promoted to a second shell, i.e., [Mg(NH3)4(NH3)]2+. Although the calculations are not particularly accurate, the results in Table 2 (and indeed Tables 3 and 4) would suggest that there is a step change in binding energy from +110 down to ∼55 kJ mol−1, for those structures where one or more molecules have moved into secondary hydrogen-bonded sites. This difference should make 8530



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(5) Blades, A. T.; Jayaweera, P.; Ikonomou, M. G.; Kebarle, P. 1st Studies of the Gas Phase Ion Chemistry of M3+ Metal-Ion Ligands. Int. J. Mass Spectrom. Ion Processes 1990, 101, 325−336. (6) Blades, A. T.; Jayaweera, P.; Ikonomou, M. G.; Kebarle, P. Ion− Molecule Clusters Involving Doubly Charged Metal-Ions (M2+). Int. J. Mass Spectrom. Ion Processes 1990, 102, 251−267. (7) Rodriguez-Cruz, S. E.; Jockusch, R. A.; Williams, E. R. Hydration Energies of Divalent Metal Ions, Ca2+(H2O)n (n = 5 − 7) and Ni2+(H2O)n (n = 6 − 8), Obtained by Blackbody Infrared Radiative Dissociation. J. Am. Chem. Soc. 1998, 120, 5842−5843. (8) Rodriguez-Cruz, S. E.; Jockusch, R. A.; Williams, E. R. Hydration Energies and Structures of Alkaline Earth Metal Ions, M2+(H2O)n, n = 5 - 7, M = Mg, Ca, Sr, and Ba. J. Am. Chem. Soc. 1999, 121, 8898− 8906. (9) Cooper, T. E.; Carl, D. R.; Armentrout, P. B. Hydration Energies of Zn(II): Threshold Collision-Induced Dissociation Experimental and Theoretical Studies. J. Phys. Chem. A 2009, 113, 13727−13741. (10) Carl, D. R.; Chatterjee, B. K.; Armentrout, P. B. Threshold Collision-Induced Dissociation of Sr2+(H2O)x Complexes (x = 1 − 6): An Experimental and Theoretical Investigation of the Complete Inner Shell Hydration Energies of Sr2+. J. Chem. Phys. 2010, 132, 044303. (11) Carl, D. R.; Armentrout, P. B. Experimental Investigation of the Complete Inner Shell Hydration Energies of Ca2+: Threshold Collision-Induced Dissociation of Ca2+(H2O)x complexes (x = 2 − 8). J. Phys. Chem. A 2012, 116, 3802−3815. (12) Hofstetter, T. E.; Armentrout, P. B. Threshold CollisionInduced Dissociation and Theoretical Studies of Hydrated Fe(II): Binding Energies and Coulombic Barrier Heights. J. Phys. Chem. A 2013, 117, 1110−1123. (13) Carl, D. R.; Armentrout, P. B. Threshold Collision-Induced Dissociation of Hydrated Magnesium: Experimental and Theoretical Investigation of the Binding Energies of Mg2+(H2O)x Complexes (x = 2 − 10). ChemPhysChem 2013, 14, 681−697. (14) Klots, C. E. Evaporative Cooling. J. Chem. Phys. 1985, 83, 5854−5860. (15) Klots, C. E. Temperatures of Evaporating Clusters. Nature 1987, 327, 222−223. (16) Klots, C. E. Evaporation from Small Particles. J. Phys. Chem. 1988, 92, 5864−5868. (17) Klots, C. E. The Reaction Coordinate and its Limitations − An Experimental Perspective. Acc. Chem. Res. 1988, 21, 16−21. (18) Klots, C. E. Thermal Kinetics of Small Systems. J. Chem. Phys. 1989, 90, 4470−4472. (19) Walker, N. R.; Wright, R.; Stace, A. J. Stable Ag(II) Coordination Complexes in the Gas Phase. J. Am. Chem. Soc. 1999, 121, 4837−4844. (20) Walker, N. R.; Dobson, M.; Wright, R. R.; Barran, P. E.; Murrell, J. N.; Stace, A. J. A Gas-Phase Study of the Coordination of Mg2+ with Oxygen- and Nitrogen-Containing Ligands. J. Am. Chem. Soc. 2000, 122, 11138−11145. (21) Del Mistro, G.; Stace, A. J. Cluster-Molecule Collisions − A Molecular Dynamics Analysis of a Pick-up Experiment. Chem. Phys. Lett. 1992, 196, 67−72. (22) Cooks, R. G.; Beynon, J. H.; Caprioli, R. M.; Lester, G. R. Metastable Ions; Elsevier: Amsterdam, 1973. (23) Woodward, C. A.; Stace, A. J. Measurements of Kinetic-Energy Release Following the Unimolecular and Collision-Induced Dissociation of Argon Cluster Ions, Arn+, for n in the Range 2−60. J. Chem. Phys. 1991, 94, 4234−4242. (24) Lethbridge, P. G.; Stace, A. J. Reactivity-Structure Correlations in Ion Clusters − A study of the Unimolecular Fragmentation Patterns of Argon Ion Clusters, Arn+, for n in the Range 30 − 200. J. Chem. Phys. 1988, 89, 4062−4073. (25) Shao, Y.; Molnar, L. F.; Jung, Y.; Kussmann, J.; Ochsenfeld, C.; Brown, S. T.; Gilbert, A. T. B.; Slipchenko, L V.; Levchenko, S. V; O’Neill, D. P.; et al. Advances in Methods and Algorithms in a Modern Quantum Chemistry Program Package. Phys. Chem. Chem. Phys. 2006, 8, 3172−3191.

Figure 3. Comparison between experimental binding energies determined for [Ca(NH3)n]2+ and for (NH3)nH+ plotted as a function of n. The data for (NH3)nH+ have been taken from ref 38.

not reach it until n ∼ 24−25, at which point molecules might be expected to be populating a third solvation shell. What is quite clear is that the +2 charge has an influence on binding energy even when there are 20 molecules surrounding a central metal ion.

5. CONCLUSION Finite heat bath theory has been used to derive binding energies for ammonia molecules bound to the alkaline earth metal dications Mg2+, Ca2+, and Sr2+. It is found that the +2 charge has an influence on the binding of molecules out to, at least, n = 20, and that this influence may not stop until a third solvation shell starts to develop around each metal dication. The results also provide evidence for the presence of structures where molecules are promoted to a second solvation shell once the first shell contains four or more molecules.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS E.B. thanks the University of Nottingham for a scholarship, G.R. thanks the Mexican Government for a scholarship, and R.P. thanks the Royal Society for the award of a travel grant. Financial support for this program of experiments from the University of Nottingham is also acknowledged.

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REFERENCES

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Experimental Binding Energies for the Metal Complexes [Mg (NH3) n

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