ARTICLE pubs.acs.org/JPCA
Hydrated Magnesium Cations Mg+(H2O)n, n ≈ 2060, Exhibit Chemistry of the Hydrated Electron in Reactions with O2 and CO2 Christian van der Linde,† Amou Akhgarnusch,† Chi-Kit Siu,*,‡ and Martin K. Beyer*,† † ‡
Institut f€ur Physikalische Chemie, Christian-Albrechts-Universit€at zu Kiel, Olshausenstrasse 40, 24098 Kiel, Germany Department of Biology and Chemistry, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, China
bS Supporting Information ABSTRACT: Ionmolecule reactions of Mg+(H2O)n, n ≈ 2060, with O2 and CO2 are studied by Fourier-transform ion cyclotron resonance (FT-ICR) mass spectrometry. O2 and CO2 are taken up by the clusters. Both reactions correspond to the chemistry of hydrated electrons (H2O)n. Density functional theory calculations predicted that the solvation structures of Mg+(H2O)16 contain a hydrated electron that is solvated remotely from a hexa-coordinated Mg2+. Ionmolecule reactions between Mg+(H2O)16 and O2 or CO2 are calculated to be highly exothermic. Initially, a solvent-separated ion pair is formed, with the hexa-coordinated Mg2+ ionic core being well separated from the O2• or CO2•. Rearrangements of the solvation structure are possible and produce a contact-ion pair in which one water molecule in the first solvation shell of Mg2+ is replaced by O2• or CO2•.
’ INTRODUCTION The activation of water by metal ions and charge-transfer to solvent originating from a metal ion are of fundamental importance for the understanding of hydrogen formation in aqueous environments.14 Among the most widely studied model systems in the gas phase are Na(H2O)n,5,6 Na2m+1+(H2O)n,710 Mg+(H2O)n,1119 and Al+(H2O)n.2026 In the case of Mg+(H2O)n, the formation of MgOH+(H2O)n1 with elimination of atomic hydrogen under the influence of room-temperature blackbody radiation is observed in a transition region n ≈ 1621.15,16 This phenomenon is explained by the presence of a hydrated electron and a solvated doubly charged magnesium center in the cluster.1,1119 When the hydration shell shrinks, the strongly polarizing Mg2+ ion promotes the formation of an OH/H3O+ pair in a salt-bridge arrangement.1,19 Quantum chemical calculations unambiguously show that the maximum of the electron spin density in Mg+(H2O)n is located remote from the metal center, corroborating the solvated electron picture.1719 Experimentally, the hydrated electron hypothesis is also well founded, but one serious issue is yet unresolved. Only three reactions of Mg+(H2O)n with small molecules have been reported so far.16 The behavior of HCl and methanol is consistent with hydrated electrons: With HCl, MgCl+ is formed with elimination of atomic hydrogen, just like Cl is formed together with atomic hydrogen in the reaction of (H2O)n with HCl.27 Methanol in both cases undergoes ligand exchange with water.28 No reaction, however, is reported for Mg+(H2O)n with CO2,16 while hydrated electrons react efficiently with uptake of one CO2 and formation of the hydrated radical anion CO2(H2O)n.29,30 To resolve this apparent discrepancy and to learn more about the r 2011 American Chemical Society
reactivity of Mg+(H2O)n, we have undertaken new reactivity experiments with O2 and CO2, which are known to exhibit an efficient reactivity against hydrated electrons in the gas phase.29,30 Interpretation of the experimental results is supported by quantum chemical calculations.
’ EXPERIMENTAL AND COMPUTATIONAL DETAILS The experiments were performed on a modified Fouriertransform ion cyclotron resonance (FT-ICR) Bruker/Spectrospin CMS47X mass spectrometer with an unshielded 4.7 T superconducting magnet.3033 An external laser vaporization source was used to generate Mg+(H2O)n ions by evaporation of a solid magnesium target (Alfa Aesar, 99.9%) and supersonic expansion of the hot plasma in a helium/water mixture (Helium, Linde 99.996%).22,3437 The frequency doubled Nd:YAG vaporization laser (Continuum Surelight II) was heated by 20 laser shots to avoid changes in the initial distribution, followed by 20 laser shots at 10 Hz and 5 mJ pulse energy to generate the ions. The reaction delay is measured relative to the end of the fill cycle, which means that at nominal t = 0 s, clusters have resided up to 2 s in the cell. Therefore, reaction products are observed at a nominal 0 s reaction delay. O2 (Linde, 99.9991%) and CO2 (Linde, 99.995%) were introduced into the ultra high vacuum region via a needle valve and were present at constant pressure during the experiment, as well as during the fill cycle. Pressures in the range of 5 109 mbar to 5 107 mbar were applied. Received: June 29, 2011 Revised: August 8, 2011 Published: August 09, 2011 10174
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Table 1. Binding Energies of Mg+(H2O), Mg+(CO2), and Mg+(O2) binding energy/kJ mol1 Mg+(H2O)
Mg+(CO2)
Mg+(O2)
De
De
De
D0
D0
D0
this work VASP PW91a PBEb
149 145
74 72
132 109
Gaussian 09c BLYP
134
128
62
60
48
45
BPW91
132
126
58
56
44
40
PW91PW91
144
137
68
66
58
55
PBEPBE
141
134
65
63
50
47
mPW1PW91
141
134
64
62
41
38
PBE1PBE HCTH
143 142
136 136
66 66
64 64
39 60
36 57
M06
138
131
65
62
87
84
131
63
61
55
previous calculationsd B3LYP/6-311+G(2d,p)
137
51
CBS-Q
127
64
90
UCCSD(T)/aug-cc-pVQZ//
127
64
89
B3LYP/6-311+G(2d,p) RCCSD(T)/aug-cc-pCVQZ// 137 B3LYP/6-311+G(2d,p)
131
69
67
94
90
a Energy cutoff for the planewave basis set Ecutoff = 273.894 eV. b Energy cutoff for the planewave basis set Ecutoff = 282.841 eV. c Basis set was 6-31++G(d,p). d Reference 43.
Density functional theory (DFT) calculations were performed for some selected Mg+(H2O)n clusters, namely for n = 3 and 16, and their reactions toward O2 or CO2, using VASP (Vienna Ab initio Simulation Package)3841 and Gaussian 0942 quantum chemical calculation packages. For the calculations with VASP, the local density exchange-correlation functional with the generalized-gradient approximation of PerdewWang 91 (GGAPW91) or PerdewBurkeErnzerhof (GGA-PBE) was used. Spin-polarized formalism was employed for the open-shell electronic structure calculations. The optimized pseudopotentials for the valence electrons of H (1s1), C (2s22p2), O (2s22p4), and Mg (2p63s2), constructed by means of the projector augmented wave (PAW) method supplied by the VASP program, were directly used. A planewave basis set with a cutoff energy (Ecutoff) of 273.894 eV (for GGA-PW91) or 282.841 eV (for GGA-PBE) was used for the electronic wave functions, which were computed by RMM-DIIS minimization for the total electronic energy. Benchmark calculations were performed for the smallest oneto-one Mg+(L) complexes (with L = H2O, CO2, and O2). For VASP, the Mg+(L) complexes and the dissociated products (Mg+ and L) were simulated in a cubic box with a lattice parameter of 10 Å. The binding energies obtained from VASP and from Gaussian 09 with eight DFT functionals using the 6-31++G(d,p) basis set and their literature values43 obtained from higher levels of theory are summarized in Table 1. The binding energies of Mg+(H2O) and Mg+(CO2) obtained from the GGA-PW91 were comparable with those obtained from the GGA-PBE and
Figure 1. Mass spectra of the reaction of Mg+(H2O)n with CO2 at a pressure of 1.1 107 mbar after (a) 0 s and (b) 3 s.
were 517 kJ mol1 higher than the values that were obtained by other DFT functionals performed by Gaussian 09, which were consistent with a previous DFT study for Mg+(H2O)n clusters.19 These values were also comparable with the CCSD(T) values.43 However, much larger discrepancy among levels of theory were observed for the binding energy of Mg+(O2); the binding energy obtained from the GGA-PW91 was significantly larger than the CCSD(T) values, and on the other hand, the values calculated from most DFT functionals performed with Gaussian 09 were underestimated. Among all DFT calculations, M06 produced the values that were closest to the CCSD values for all Mg+(H2O), Mg+(CO2), and Mg+(O2), with a deviation of less than 7 kJ mol1. Structures of larger clusters with n = 3 and 16 were only calculated at the GGA-PW91 level performed with VASP and the BPW91/6-31++G(d,p) and M06/6-31++G(d,p) levels performed with Gaussian 09.
’ RESULTS AND DISCUSSION IonMolecule Reactions. Mass spectra of the reactions of Mg+(H2O)n with CO2 or O2 show that one molecule of the reactant is taken up by the clusters. Figure 1 shows spectra of the reaction with CO2 at a pressure of 1.1 107 mbar after 0 and 3 s reaction delay. In the present study, the mass spectra of Mg+(H2O)n contained MgOH+(H2O)n1 with typically 35%. This made a quantitative analysis of the results complicated, because 25MgOH+(H2O)n1 overlaps with 24Mg+(H2O)n. Since 24 MgOH+(H2O)n1 does not suffer from isobaric overlap, it was possible to calculate the expected contribution of 25MgOH+(H2O)n1 from the natural isotope distribution of magnesium, and to correct the intensity of 24Mg+(H2O)n for isobaric overlap. Figure 2a shows the isobaric overlap-corrected intensities of 24Mg+(H2O)n, 24MgOH+(H2O)n1 and 24MgCO2+(H2O)n, summed over all cluster sizes, as a function of time. The noise level of the summed intensities is obtained from the noise level of each peak from the Gaussian error propagation law. The average cluster size Ænæ of the respective species is shown in Figure 2b. The data unambiguously show that the precursor of 24MgCO2+(H2O)n is 24Mg+(H2O)n. Conversion of 24MgCO2+(H2O)n into 24 MgOH+(H2O)n1 does not take place. Instead, in the size region of n ≈ 1621, 24Mg+(H2O)n is converted to 24MgOH+(H2O)n1 as investigated in detail previously,15,16 and the uptake 10175
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Table 2. Rate Constants kabs (cm3 s1) of the Reactions of Mg+(H2O)n and (H2O)n with CO2 and O2 CO2 O2 a
Figure 2. (a) Reaction kinetics of the reaction of Mg+(H2O)n with CO2 at a pressure of 1.1 107 mbar for long delays. Formation of hydroxide in an intracluster reaction is clearly visible after 6 s. The gray line shows the noise level of the spectra. (b) Development of the average cluster size during the experiment.
Figure 3. Pseudo-first-order kinetics of the reaction of Mg+(H2O)n with CO2 at a pressure of 1.1 107 mbar. The gray line shows the noise level of the spectra.
of CO2 stops with the completion of magnesium hydroxide formation. All three cluster species continuously lose water molecules due to the absorption of room-temperature blackbody radiation.4453 This process slows down considerably for 24 MgCO2+(H2O)n at n = 3, when the internal energy of the cluster at room temperature becomes too small to cause evaporation of a water molecule. After 120 s reaction delay, the presence of 24MgOH+(CO2)(H2O)2,3 is evidence that small MgOH+(H2O)n1 undergo ligand exchange with CO2. The small peak at m/z = 96 is split, indicating that it consists of 25MgOH+(H2O)3 and 24Mg+(H2O)4. The latter ion suggests that CO2 evaporation competes with H2O evaporation from 24MgCO2+(H2O)4. For the first 6 s, these data can be fitted assuming pseudo-firstorder kinetics, as shown in Figure 3. The conversion of 24Mg+(H2O)n into 24MgOH+(H2O)n1 is slow and independent of pressure, which shows unambiguously that hydroxide formation is independent from CO2 uptake. Due to the isobaric overlap, it was not possible to perform a nanocalorimetric analysis30 of the results. Similar results have been obtained for the reaction with O2.
Mg+(H2O)n
(H2O)n a
1.9 1011
1.2 109
9.1 10
11
Derived from previously published data.
5.4 1010 30
A water cluster does not take up O2 or CO2, unless the reactant undergoes a chemical reaction to make solvation by water favorable. The only conceivable reaction pathway here is formation of a radical anion. It therefore seems reasonable to compare the behavior of Mg+(H2O)n with the reactions of hydrated electrons. The pressure-independent second-order rate coefficients are listed in Table 2 and compared with the values of the corresponding hydrated electron reactions. From reanalyzing previously published data we learn that CO2 reacts 23 times as fast as O2 with hydrated electrons,30 while the situation is reversed in the magnesium case, where O2 is a factor of 45 more reactive. Comparing (H2O)n with Mg+(H2O)n, the reactivity of O2 decreases by a factor of 6, and that of CO2 decreases by a factor of 60. The very small rate coefficient of CO2 with Mg+(H2O)n explains why the reaction was not seen in a previous study,16 where a lower reactant gas pressure was used.54 The rate coefficients in Table 2 allow some speculation on the dynamics of the reaction. If the neutral reactant impinges on the cluster surface in a position remote from the hydrated electron, O2 and CO2 desorb quickly from the cluster, rationalizing the overall low rate constant. The different reactivities of O2 and CO2 are much more difficult to rationalize. We suspect that CO2 requires a more extensive rearrangement of the water network than O2, associated with a higher barrier for the formation of the solvated radical anion. This effect is more pronounced in Mg+(H2O)n than (H2O)n, since the hexacoordinated Mg2+ center (vide infra) has a strong structure-building effect on the hydrogenbonded network, while (H2O)n remain more fluxional in the studied size regime. Solvation Structures of Mg+(O2)(H2O)3 and Mg+(CO2)(H2O)3. Experimental observations suggest that Mg+(H2O)n could take up an oxygen molecule or carbon dioxide molecule to form Mg+(O2)(H2O)n or Mg+(CO2)(H2O)n, respectively. Subsequent evaporation of water molecules formed products down to around three water molecules. Figure 4 shows the structures of Mg+(O2)(H2O)3 and Mg+(CO2)(H2O)3 optimized at the M06/6-31++G(d,p) level. Mg+(O2)(H2O)3. DFT calculations at the unrestricted BPW91/ 6-31++G(d,p) and M06/6-31++G(d,p) levels predicted that the lowest-energy structure of Mg+(O2)(H2O)3 has a 3 + 0 structure, in which the Mg is tricoordinated with all three water molecules in the first solvation shell (MgO distances of 2.0422.055 Å) and the 3s1 electron of Mg+ is transferred to the O2 molecule, forming a contact-ion pair (cip) between Mg2+ and O2• (MgO distances of 1.9701.992 Å) (Mg3w-O2-1). A 2 + 1-cip structure (Mg3wO2-2) was located with an energy at 0 K of 37.2 kJ mol1 (BPW91) and 50.5 kJ mol1 (M06) higher than that of Mg3w-O2-1. Migrating a proton from H2O to O2• in Mg3w-O2-1 to form Mg3w-O2-3 is energetically unfavorable by 61.6 kJ mol1 (BPW91) and 92.3 kJ mol1 (M06). A nonelectron-transferred structure (Mg3w-O2-4), in which a triplet O2 molecule is hydrogen bonded to one of the water molecule in the 3 + 0 structure of the doublet Mg+(H2O)3, was also located with the enthalpies at 10176
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Figure 4. Optimized geometries and spin densities of Mg+(O2)(H2O)3 and Mg+(CO2)(H2O)3 calculated at the M06/6-31++G(d,p) level. Energies at 0 K (ΔH0/kJ mol1) and free energies at 298 K in parentheses (ΔG298/kJ mol 1 ) were evaluated at the BPW91/ 6-31++G(d,p) level (upper values) and the M06/6-31++G(d,p) level (lower values).
Scheme 1. Reaction Energies at 0 K (ΔH0/kJ mol1) Evaluated at the BPW91/6-31++G(d,p) and the M06/6-31++G(d,p) Levels
0 K of 205.5 kJ mol1 (BPW91) and 258.9 kJ mol1 (M06) higher than that of Mg3w-O2-1. Mg+(CO2)(H2O)3. Similar to Mg+(O2)(H2O)3, the lowestenergy structure of Mg+(CO2)(H2O)3 is a 3 + 0-cip electrontransferred adduct (Mg3w-CO2-1), in which the CO2• is coordinated to Mg2+ via one of its oxygen atoms (MgOCO distance of 1.942 Å; MgOH2 distances of 2.044 2.047 Å). Mg3w-CO2-2 is a nonelectron-transferred 2 + 1 structure having the neutral linear CO2 (179.7) weakly binding to Mg+ with a MgO distance of 2.296 Å, which is longer than the two MgOH2 distances of 2.089 Å. Proton transfer from H2O to CO2• is again energetically unfavorable and give structures with 41.0 kJ mol1 (BPW91) and 37.4 kJ mol1 (M06) for an HCO2• radical (Mg3w-CO2-3) and 76.6 kJ mol1 (BPW91) and 72.0 kJ mol1 (M06) for a HOCO• radical (Mg3w-CO2-4) higher than that of Mg3w-CO2-1. As illustrated in Scheme 1, the binding energies of O2 toward Mg+(H2O)3 are 207.6 kJ mol1 (BPW91) and 262.9 kJ mol1 (M06), which are significantly larger than the energy required to remove water molecules. For Mg+(CO2)(H2O)3, the CO2 is only weakly bound with the binding energies of 20.8 kJ mol1 (BPW91) and 42.0 kJ mol1 (M06). The low binding energy of CO2 in small clusters is in line with the observed CO2 evaporation from Mg+(CO2)(H2O)4, as discussed above. Solvation Structures of Mg+(H2O)16 and Their CO2 or O2 Adducts. Structural Sampling for Mg+(H2O)16. Some solvation structures for Mg+(H2O)16 were optimized from initial structures where the hydrogen bonding networks were constructed in order to allow the unpaired electron being solvated in different solvation shells away from the Mg center.19 In this work, more structures were sampled from an extensive DFT/molecular
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dynamics (DFT-MD) simulation using the GGA-PW91 method as previously employed and geometry optimizations at the BPW91/6-31++G(d,p) and M06/6-31++G(d,p) levels performed with Gaussian 09. The structural sampling was started from a geometry having the electron solvated remotely from the Mg center.19 The ion was put in a cubic simulation box with a lattice parameter of 20 Å, and the mass of all atoms, including H, O, and Mg, was artificially changed to the mass of a deuterium atom in order to increase the sampling rate. A sampling DFTMD simulation for this mass-modified Mg+(H2O)16 (around 3 times lighter than its nominal mass) was run at a temperature of 500 K for 5 ps with a time step of 0.5 fs for the numerical integration of the equations of motion. Heating the cluster ion to 500 K supplied a kinetic energy (KE) of ∼18 kJ mol1 per each water molecule (an order of energy of a single hydrogen bond) to randomize the solvent structure. The cluster was then cooled in 1 ps from 500 K down to 100 K, at which the KE of a massmodified water molecule (6 Da) was around the value of a water molecule with its nominal mass (18 Da) at 300 K. Ten initial geometries were obtained by repeating the above procedure. A DFT-MD simulation for each of these ten initial geometries (with the mass of all atoms being reset to their nominal masses) was run for 5 ps at a temperature of 300 K being controlled by a NoseHoover thermostat. The geometry at the end of each MD trajectory was optimized at the GGA-PW91 level performed with VASP and the BPW91/6-31++G(d,p) and M06/6-31++G(d,p) levels performed with Gaussian 09. The resulting geometries and relative energies are summarized in Table 3. The geometries of all Mg+(H2O)16 are graphically displayed in Figure S4 (Supporting Information), Cartesian coordinates of Mg+(O2)(H2O)16, Mg+(O2)(H2O)16, and Mg+(CO2)(H2O)16 are available in Tables S1S3. The Mg center of all geometries obtained from the GGAPW91 and the BPW91/6-31++G(d,p) levels are penta-coordinated and carry negligible spin density, except Mg16w-8 (0.18 au) and Mg16w-10 (0.24 au). Optimizing at the M06/ 6-31++G(d,p) level, the solvation structures of some geometries were changed, and more spin density was localized on the Mg center, for instance, to 0.46 au in Mg16w-6. Interestingly, the solvation structure around Mg in the lowest-energy geometries (Mg16w-1 and Mg16w-2) became hexa-coordinated with its unpaired 3s electron being solvated out by the water molecules in the outer solvation shells. For example, in the lowest-energy geometry obtained in this work (Mg16w-1) (Figure 5 and Table 3), the unpaired electron is solvated by three water molecules, namely w2, w20 , and w300 , which are the second, second, and third water molecules away from the Mg center. Mg16w-3 is a penta-coordinated structure with the unpaired electron being solvated by the second, second, and third water molecules away from the Mg center and is slightly higher than Mg16w-1 in energy at 0 K by 6.8 kJ mol1. A previous study on Mg+(H2O)n has demonstrated that the relative energies of different solvation geometries can be significantly affected by the basis set superposition error (BSSE), which overestimates the solvation energy of the geometry having higher coordination of the Mg center.17 To reduce the effect of BSSE, the four lowest-energy geometries (two for hexa-coordinated Mg and two for penta-coordinated) were further optimized at the M06/6-311++G(d,p) level and single-point energy calculations for these optimized geometries were also performed at the M06/6-311++(3df,3pd) level. With the larger basis sets, the energy difference between the lowest-energy hexa-coordinated geometry Mg16w-1 and pentacoordinated geometry Mg16w-3 is only 2.1 kJ mol1. 10177
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Table 3. Relative Energies at 0 K (ΔH0/kJ mol1) and Relative Free Energies at 298 K (ΔG298/kJ mol1) of Some Geometries of Mg+(H2O)16 VASP
Gaussian 09
PW91a
BPW91/6-31++G(d,p)
+
Mg (H2O)16 geometry Mg16w-1
ΔE 0.0
ΔH0 ΔG298 0.0
0.0
M06/6-31++G(d,p)
spin density
position of
on Mg
SOMOb
0.04
second; second; third
M06/6-311++G(d,p)
spin density ΔH0 ΔG298 d
0.0
0.0
spin density
on Mg
position of SOMOb
ΔH0f
ΔG298
on Mg
0.04
second; second;
0.0 (0.0)
0.0
0.08
5.0 (4.4)
9.6
0.09
third (6-coord)c Mg16w-2
14.6
7.1
6.6
0.03
first; second; third
2.4
9.4
0.09
first; second; second (6-coord)c
Mg16w-3
4.9
7.4
5.8
0.04
second; second; third
6.8
5.4
0.04
second; second; third
4.1 (2.1)
0.8
0.25
Mg16w-4
9.4
12.7
12.7
0.01
second; third
13.3
13.4
0.33
second; third
10.3 (7.3)
3.7
0.35
first; second; third
Mg16w-5
12.9
1.6
10.6
0.06
second; third; third
14.2
7.3
0.21
Mg16w-6
0.8
1.1
6.6
0.06
first; second; third
15.2
16.1
0.46
second; third
Mg16w-7
5.4
4.0
4.8
0.05
first; second; secondd
24.0
25.2
0.16
first; second; second
Mg16w-8
28.6
10.2
3.4
0.18
second; second
25.9
15.9
0.36
second; second
Mg16w-9
12.0
2.1
1.4
0.05
first; second; third
27.2
13.1
0.21
first; second; third
Mg16w-10
72.5
43.7
24.4
0.24
first; second; second;
30.2
25.3
0.41
second; second; fourth third; third; third
fourth Mg16w-11
36.2
6.0
8.3
0.01
third; third; thirdd
31.5
27.2
0.31
Mg16w-12
18.3
2.7
15.9
0.03
second; fourth
32.6
18.8
0.10
second; third
Mg16w-13
43.1
15.5
6.0
0.01
third; third; fourthd
33.8
24.1
0.21
third; third; fourthe
Mg16w-14
6.7
8.5
7.7
0.04
second; fourthe
34.4
25.0
0.19
second; fourth
a
Energy cutoff of the planewave basis set Ecutoff = 273.894 eV. b The SOMO is populated at the nth water molecules away from the Mg center. c The Mg center is penta-coordinated if not specified. d Previously published geometries (ref 19). e Geometry with one imaginary frequency. f Single point energy in parentheses are evaluated at the M06/6-311++G(3df,3pd)//M06/6-311++G(d,p) level with zero-point correction at the M06/6-311++G(d,p) level.
Figure 5. Optimized geometries (left-hand side) and spin density (righthand side) of Mg+(H2O)16 calculated at the M06/6-31++G(d,p) level.
Addition of O2 or CO2 to Mg+(H2O)16 leads to the formation of solvated O2• or CO2•, respectively. The reaction energies for the lowest-energy structure of the hexa-coordinated geometry (Mg16w-1) and the penta-coordinated geometry (Mg16w-3) were calculated at the M06/6-31++G(d,p) level. Figure 6 summarizes the geometry and spin density of the products and the reaction energies of the reactions. Reacting O2 with Mg16w-1 produced a solvent-separated ion pair (ssip) Mg16w-1-O2, in which the Mg2+ is remaining hexa-coordinated with six water molecules and the O2• is well-solvated and separated from the
Figure 6. Optimized geometries and spin densities of Mg+(O2)(H2O)16 and Mg+(CO2)(H2O)16. Reaction energies at 0 K (ΔH0/kJ mol1) were evaluated at the M06/6-31++G(d,p) level.
Mg2+ center by 3.765 Å and 4.037 Å. The reaction is highly exothermic by 294.5 kJ mol1, which is sufficient to evaporate around 67 water molecules from the cluster. Addition of O2 to Mg16w-3 resulted in a contact-ion pair (cip) Mg16w-3-O2, which also contains a hexa-coordinated Mg2+ center, but one of the six water molecules in the first solvation shell in Mg16w-1-O2 is replaced by the O2• with Mg 3 3 3 O2 distances of 2.146 Å and 3.126 Å. The cip structure is thermodynamically more favorable than the ssip structure by 13.3 kJ mol1. This indicates that even 10178
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The Journal of Physical Chemistry A if Mg16w-1-O2 is initially formed from the reaction between O2 and the lowest-energy Mg16w-1, rearrangement of the solvation structure is possible to generate Mg16w-3-O2. Subsequent water evaporations will end up with the cip of small Mg(O2)+(H2O)n as the structure of Mg3w-O2-1 in the case of n = 3. A similar process was predicted in the reaction of Mg+(H2O)16 with CO2 to form Mg+(CO2)(H2O)16. The formation of the ssip Mg16w-1-CO2 is exothermic by 128.6 kJ mol1, which is equivalent to the evaporation energy of three water molecules. Unlike Mg+(O2)(H2O)16, solvent displacement in the first solvation shell by the CO2• resulted in a slightly energetically unfavorable ssip Mg16w-3-CO2 by 6.9 kJ mol1. The difference in the calculated exothermicity of ssip formation of Mg+(H2O)16 with O2 and CO2 is 165.9 kJ mol1. The difference in the experimental values for O2 and CO2 uptake by (H2O)n is 208 ( 22 kJ mol1.30 The similarity of both values, despite the considerable changes of the cluster structure imposed by Mg2+, underlines that the picture of both processes is consistent.
’ CONCLUSIONS Mg+(H2O)n, n ≈ 2060, exhibit the chemistry of the hydrated electron (H2O)n in reactions with O2 or CO2, as previously published for HCl.16,27 However, the rate coefficients of the reactions decrease by a factor of 60 for CO2, comparing Mg+(H2O)n with (H2O)n. The qualitative agreement is strong experimental evidence that the picture of a doubly charged magnesium center, with a remote hydrated electron, is correct. Calculations corroborate this interpretation and yield further insight into the mechanistic details of the O2 and CO2 reaction. Solvation structures of Mg+(H2O)16 have been sampled with DFT-MD simulations at the GGA-PW91 level and refined at the M06/6-31++G(d,p) level. The lowest-energy structure of Mg+(H2O)16 contains a hexa-coordinated Mg2+ ion and a hydrated electron that is remote from the ionic core. Ionmolecular reactions of Mg+(H2O)16 with O2 or CO2 are calculated to be exothermic by 294.5 kJ mol1 or 128.6 kJ mol1, respectively, to initially form a solvent-separated ion pair. Rearrangement of this structure into a contact-ion pair is possible with an energy of 13.3 kJ mol1 for Mg+(O2)(H2O)16 or +6.9 kJ mol1 for Mg+(CO2)(H2O)16. Evaporation of water molecules generates the smallest observed clusters with three water molecules, Mg+(O2)(H2O)3 and Mg+(CO2)(H2O)3, which are contact-ion pairs with O2 being strongly bound to the Mg center by 262.9 kJ mol1, while CO2 is only weakly bound by 42.0 kJ mol1, both calculated at the M06/6-31++G(d,p) level. ’ ASSOCIATED CONTENT
bS
Supporting Information. Figures of experimental results of the reaction of Mg+(H2O)n with O2 (mass spectrum Figure S1, kinetics Figures S2, S3). Geometries of all Mg+(H2O)16 are graphically displayed in Figure S4. Cartesian coordinates of Mg+(H2O)16, Mg+(O2)(H2O)16, and Mg+(CO2)(H2O)16 are available in Tables S1S3. This information is available free of charge via the Internet at http://pubs.acs.org/
’ AUTHOR INFORMATION Corresponding Author
*Fax: (+) 852-3442-0522; e-mail:
[email protected] (C.-K.S.). Fax: (+) 49-431-880-2830; e-mail:
[email protected] (M.K.B.).
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’ ACKNOWLEDGMENT Financial support from the Deutsche Forschungsgemeinschaft, Grant Number BE2505/4-2, and DAAD, PPP Hongkong, Project-ID 50750748, is gratefully acknowledged (M.K.B.). The work described in this paper was supported by grants from the Germany/Hong Kong Joint Research Scheme sponsored by the Research Grants Council (RGC) of the Hong Kong and the German Academic Exchange Service of Germany (Reference No.: G_HK006/10) and from the General Research Fund from the RGC of Hong Kong (Reference No.: 9041543) (C.-K.S.). ’ REFERENCES (1) Bondybey, V. E.; Beyer, M.; Achatz, U.; Joos, S.; NiednerSchatteburg, G. Isr. J. Chem. 1999, 39, 213. (2) Fuke, K.; Hashimoto, K.; Iwata, S. Adv. Chem. Phys. 1999, 110, 431. (3) Bondybey, V. E.; Beyer, M. K. Int. Rev. Phys. Chem. 2002, 21, 277. (4) Beyer, M. K. Mass Spectrom. Rev. 2007, 26, 517. (5) Schulz, C. P.; Haugstatter, R.; Tittes, H. U.; Hertel, I. V. Phys. Rev. Lett. 1986, 57, 1703. (6) Schulz, C. P.; Haugstatter, R.; Tittes, H. U.; Hertel, I. V. Z. Phys. D: At., Mol. Clusters 1988, 10, 279. (7) Steinbach, C.; Buck, U. Phys. Chem. Chem. Phys. 2005, 7, 986. (8) Buck, U.; Steinbach, C. J. Phys. Chem. A 1998, 102, 7333. (9) Bewig, L.; Buck, U.; Rakowsky, S.; Reymann, M.; Steinbach, C. J. Phys. Chem. A 1998, 102, 1124. (10) Mundy, C. J.; Hutter, J.; Parrinello, M. J. Am. Chem. Soc. 2000, 122, 4837. (11) Fuke, K.; Misaizu, F.; Sanekata, M.; Tsukamoto, K.; Iwata, S. Z. Phys. D: At., Mol. Clusters 1993, 26, S180. (12) Misaizu, F.; Sanekata, M.; Fuke, K.; Iwata, S. J. Chem. Phys. 1994, 100, 1161. (13) Sanekata, M.; Misaizu, F.; Fuke, K.; Iwata, S.; Hashimoto, K. J. Am. Chem. Soc. 1995, 117, 747. (14) Watanabe, H.; Iwata, S.; Hashimoto, K.; Misaizu, F.; Fuke, K. J. Am. Chem. Soc. 1995, 117, 755. (15) Berg, C.; Achatz, U.; Beyer, M.; Joos, S.; Albert, G.; Schindler, T.; Niedner-Schatteburg, G.; Bondybey, V. E. Int. J. Mass Spectrom. Ion Processes 1997, 167/168, 723. (16) Berg, C.; Beyer, M.; Achatz, U.; Joos, S.; Niedner-Schatteburg, G.; Bondybey, V. E. Chem. Phys. 1998, 239, 379. (17) Siu, C. K.; Liu, Z. F. Chem.—Eur. J. 2002, 8, 3177. (18) Reinhard, B. M.; Niedner-Schatteburg, G. J. Chem. Phys. 2003, 118, 3571. (19) Siu, C. K.; Liu, Z. F. Phys. Chem. Chem. Phys. 2005, 7, 1005. (20) Misaizu, F.; Tsukamoto, K.; Sanekata, M.; Fuke, K. Z. Phys. D: At., Mol. Clusters 1993, 26, S177. (21) Watanabe, H.; Iwata, S. J. Phys. Chem. 1996, 100, 3377. (22) Beyer, M.; Berg, C.; G€orlitzer, H. W.; Schindler, T.; Achatz, U.; Albert, G.; Niedner-Schatteburg, G.; Bondybey, V. E. J. Am. Chem. Soc. 1996, 118, 7386. (23) Beyer, M.; Achatz, U.; Berg, C.; Joos, S.; Niedner-Schatteburg, G.; Bondybey, V. E. J. Phys. Chem. A 1999, 103, 671. (24) Siu, C. K.; Liu, Z. F.; Tse, J. S. J. Am. Chem. Soc. 2002, 124, 10846. (25) Reinhard, B. M.; Niedner-Schatteburg, G. J. Phys. Chem. A 2002, 106, 7988. (26) van der Linde, C.; Beyer, M. K. Phys. Chem. Chem. Phys. 2011, 13, 6776. (27) Siu, C. K.; Balaj, O. P.; Bondybey, V. E.; Beyer, M. K. J. Am. Chem. Soc. 2007, 129, 3238. (28) Balaj, O. P.; Siu, C. K.; Balteanu, L.; Beyer, M. K.; Bondybey, V. E. Int. J. Mass Spectrom. 2004, 238, 65. (29) Balaj, O. P.; Siu, C. K.; Balteanu, I.; Beyer, M. K.; Bondybey, V. E. Chem.—Eur. J. 2004, 10, 4822. (30) H€ockendorf, R. F.; van der Linde, C.; Balaj, O. P.; Beyer, M. K. Phys. Chem. Chem. Phys. 2010, 12, 3772. 10179
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