J. Phys. Chem. 1996, 100, 6445-6450
6445
Complexing of the Ammonium Ion by Polyethers. Comparative Complexing Thermochemistry of Ammonium, Hydronium, and Alkali Cations Michael Meot-Ner (Mautner)* and L. Wayne Sieck Chemical Kinetics and Thermodynamics DiVision, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
Joel F. Liebman Department of Chemistry and Biochemistry, UniVersity of Maryland Baltimore County, Baltimore, Maryland 21228-5398
Steve Scheiner Department of Chemistry and Biochemistry, Southern Illinois UniVersity, Carbondale, Illinois 62901-4409 ReceiVed: May 31, 1995; In Final Form: January 2, 1996X
The binding energies of NH4+ to polyethers, and for comparison, to acetone molecules, were measured by pulsed high-pressure mass spectrometry. The binding energies in the polydentate complexes increase with increasing ligand size and number of available oxygen groups. However, the binding energies are smaller than in complexes with free Me2CO molecules, reflecting the geometrical constraints in the polydentate ligands. The binding energy of NH4+ in various polydentate complexes is similar to that of K+ and smaller than that of H3O+ by 105 ( 12 kJ/mol (25 ( 3 kcal/mol). Based on the H3O+ to crown ether binding energies, these relations can be used to estimate the binding energy of NH4+ and K+ to 15-crown-5 of 248 ( 12 kJ/mol (59 ( 3 kcal/mol) and to 18-crown-6 of 296 ( 12 kJ/mol (71 ( 3 kcal/mol). The order of binding energies of oxygen-containing ligands to H3O+ > Na+ > NH4+ ≈ K+ is reproduced by ab initio calculations on complexes with MeOCH2CH2OMe. The amount of calculated charge transfer to the ligands follows the order of binding energies. The difference between the binding energies of H3O+ and NH4+ to oxygen-containing ligands in the gas-phase complexes is similar to the condensed-phase aqueous heats of solvation of these ions.
Introduction H+
In a recent study, we compared the complexing of and H3O+ by monodentate and polydentate ligands.1 We found that, for an equal number of electron-donor ligand groups, monodentate ligands can optimize their geometry about the ion bond better than constrained, polydentate ligands. For example, two Me2CO molecules can optimize their geometry about H3O+ and bind to this ion by 308.4 kJ/mol (73.7 kcal/mol), substantially more strongly than the binding energy of 245.2 kJ/mol (58.6 kcal/mol) with MeOCH2CH2OMe, where the geometry is constrained. However, assembling a cluster from several free ligand molecules involves a large negative ∆S°, compared with the preassembled polydentate ligand. Ultimately, in large complexes the T∆S° contributions can render a polydentate ligand more favorable in terms of ∆G°, relative to an equal number of monodentate ligands. We shall examine whether similar effects apply also in the NH4+ clusters. In another previous paper, we examined the solvation energies of NH4+ and K+.2 We found that the solvation energies of the two ions were comparable in a variety of environments, from gas-phase clusters to liquid solutions and crystals. This finding shows that the thermochemistry of binding of the ammonium ion with ligands is similar to the isotropic and spherical cation K+, which has a similar ionic radius in condensed-phased matrices. An electrostatic calculation showed that this is due to summed effects of partial charges on the various atoms of NH4+, which make the ion appear at the distance of a ligand atom as a spherical entity with unit charge.2 X
Abstract published in AdVance ACS Abstracts, March 15, 1996.
0022-3654/96/20100-6445$12.00/0
In the present work, we shall examine the complexing of polyethers with NH4+, to serve as a model for the binding energies of K+ with the polydentate ligands. To extend the analogies, we shall also compare the complexing energies of H3O+, NH4+, and Na+ with various ligands, to examine whether H3O+ also behaves thermochemically similarly to spherical cations. These comparisons are made possible due to the existing data for the complexes of these cations, largely from the Kebarle and Castleman groups and from the present authors.3-17 Furthermore, since the binding energies of H3O+ to crown ethers were also measured by Sharma and Kebarle,10,15 these comparisons can permit estimation of the binding energies of NH4+ and K+ to crown ethers. The present study also includes a comparison of the enthalpies of formation and of aqueous solutions of a series of Na+ and H3O+ salts, from which a comparison is made of the interaction energies for Na+, H3O+, K+, and NH4+ in the condensed phase. Experimental and Computational Methods The measurements were performed using the NIST pulsed high-pressure mass spectrometer.18 Reaction mixtures of CH4 carrier gas with trace CHCl3 for electron capture, at total source pressures of 2.4-3.8 mbars, with 2 × 10-5 to 5 × 10-4 mole fraction NH3 and 1 × 10-6 to 2 × 10-4 mole fraction Me2CO or polyethers were used. The low concentrations of polyethers were required to allow equilibrium measurements at the lowest possible temperatures, to minimize potential problems of ether pyrolysis. We demonstrated in the previous study that equilibrium is obtained under these conditions.1 Varying reactant © 1996 American Chemical Society
6446 J. Phys. Chem., Vol. 100, No. 16, 1996
Figure 1. Van’t Hoff plots for association reactions.
concentrations up to a factor of 4 showed that the measured equilibrium constants were independent of the concentration. Electron pulses of 1-2 keV and of 1-2 ms duration were used to ionize the mixtures. In most experiments, equilibrium ion distributions were achieved during the pulse and were followed to 5-10 ms after the pulse. In some reactions, the approach to equilibrium was observed during 1-2 ms after the pulse and was observed for another 2-4 ms. Ab initio calculations were carried out using the Gaussian92 computer program.19 The 4-31G basis set was chosen because its computational efficiency allows a thorough search of the conformational space, which is important in hydrogenbonded complexes where the surfaces may be very flat in some dimensions.20 This basis set was applied successfully for various hydrogen-bonded systems.21-23 The 4-31G basis set was used for the hydrogen-bonded species, 6-31G for Na+ and 3-21G for K+.24 Atomic and group charges were calculated by the standard Mullikan scheme25 and by a natural population analysis.26 Results and Discussion 1. Complexation by Monodentate and Polydentate Ligands. Van’t Hoff plots for the association reactions studied are shown in Figures 1 and 2, and the thermochemical results are summarized in Table 1. The complexation thermochemistry of H3O+, Na+, NH4+, and K+ in monodentate to hexadentate complexes are compared in Table 2. The binding energies with polydentate ethers increase with the increasing molecular size and number of hydrogen-bonding sites in the ligand, similar to the binding of H+ and H3O+ by such ligands.1,22,23 With the smallest diether in the NH4+(H2C(OMe)2) complex, the binding energy and entropy are similar to that of NH4+(Me2CO), and these values are consistent with what may be expected for a comparable size monoether such as n-Pr2O from correlations of binding energies and proton affinities.24 This shows that the geometry of this small diether is not suitable for bidentate bonding. As noted above, in complexes where H+ or H3O+ bind to polydentate ethers with n oxygen donor atoms, the binding is significantly weaker than with n monodentate molecules.1 In the present case, we compare the binding of NH4+ to polydentate ethers vs free Me2CO molecules. Note that we use Me2CO as a model for unconstrained free ether ligands, since Me2CO has similar proton affinity and therefore similar expected hydrogenbonding properties to a large ether-like n-Pr2O. Therefore, the differences between the binding energies to Me2CO molecules
Meot-Ner et al. and polyether oxygen groups represent primarily the effects of geometrical constraints in the polydentate complexes. The present experimental data extend to bi-, tri-, and tetradentate complexes. The binding energies of the free Me2CO molecules are always significantly larger than the comparable polydentate ligands: in 2Me2CO vs MeOCH2CH2OMe (glyme, denoted as G1) by 42.7 kJ/mol (10.2 kcal/mol); in 3Me2CO vs MeOCH2CH2OCH2CH2OMe (diglyme, denoted as G2) by 73.6 kJ/mol (17.6 kcal/mol); and in 4Me2CO vs 2MeOCH2CH2OMe by 70.7 kJ/mol (16.9 kcal/mol). Using an estimated binding energy of 6Me2CO from the usual clustering trends, a similar difference applies also in the hexadentate ligands, a difference of about 85 kJ/mol (20 kcal/mol) vs 3MeOCH2CH2OMe or 2MeOCH2CH2OCH2CH2OMe. The entropy effects make an opposing contribution to the stabilities of the complexes, and at 300 K the T∆S° term favors the polydentate ligands by 18.8 kJ/mol (4.5 kcal/mol), 52.2 kJ/ mol (12.5 kcal/mol), and 40.0 kJ/mol (9.6 kcal/mol) in the above di-, tri-, and tetradendate complexes, respectively. As in the complexes of H3O+, these effects can be related to the geometry. The free Me2CO can arrange in the optimized, presumably tetrahedral geometry about NH4+, whereas the hydrogen bonds in the complexes with the polydentate ethers are constrained, as shown below by the ab initio calculations. The opposing entropy terms result from the fact that assembling the complex from a larger number of free molecules involves more negative entropy changes than addition to the already assembled polydentate ligand. 2. Comparative Complexing Energetics of H3O+, NH4+, Na+ and K+: Gas-Phase Results. First, we note that the ∆H° values for NH4+ and K+ in all the complexes in Table 2 from solvation by single solvent molecules to bulk H2O are equal to within experimental error. Similar results were found in our previous study, which included also different ligands, such as MeCN and C6H6, and crystal lattice energies.2 The present results extend these comparisons for the complexes of the two ions with Me2CO ligands. This further demonstrates that NH4+ behaves in its bonding properties similar to an isotropic ion with a comparable condensed-phase ionic radius. The only exception is the comparison between the complexes of NH4+ and K+ with MeOCH2CH2OMe. We note in Table 2 that the differences between the ab initio and experimental ∆H° values for the other complexes are 34-42 kJ/mol (8-10 kcal/ mol), while only 21 kJ/mol (5 kcal/mol) for NH4+(MeOCH2CH2OMe). These and other trends (see below) suggest that the experimental binding energy for this complex may be too high by 8-18 kJ/mol (2-4 kcal/mol), and that for K+(MeOCH2CH2OMe) may be too low by a similar amount. We note that measurements for NH4+(MeOCH2CH2OMe) had to be done in the temperature range where the protonated diether (MeOCH2CH2OMe)H+ undergoes pyrolysis. Although this ion does not play a direct role in the association equilibrium, possible reaction cycles involving its decomposition products and proton transfer from them to regenerate NH4+ can possibly lead to artifacts in the equilibrium measurements. Next, we compare the complexes of H3O+ with other ions. These comparisons are meaningful only if the core ion is indeed H3O+, i.e., if the proton remains on this ion despite the higher proton affinities of the Me2CO and polyether oxygens. Previous calculations on the analogous H3O+(nMeCN) system and on H3O+(MeOCH2CH2OMe) and recent calculations on the diketone complex NH4+(MeCOCH2CH2COMe) all suggest that the proton can indeed remain on the H3O+ core, due to the canceling effects of the ligand polar groups as they attract protons in opposing directions.1,27,28
Complexing of the Ammonium Ion by Polyethers
J. Phys. Chem., Vol. 100, No. 16, 1996 6447
Figure 2. Van’t Hoff plots for association reactions NH4+(Me2CO)n-1 + Me2CO a NH4+(Me2CO)n.
TABLE 1: Thermochemistry of Association Reactionsa -∆H° NH4+ + Me2CO 0, 1 1, 2 2, 3 3, 4 4, 5 NH4+ + H2C(OMe)2 NH4+ + MeOCH2CH2OMe 0, 1 1, 2 2, 3 NH4+(MeOCH2CH2OMe) + NH3 (MeOCH2CH2OCH2CH2OMe)H+ + NH3 (MeOCH2CH2OCH2CH2OMe)H+ NH3 + MeOCH2CH2OCH2CH2OMe
-∆S°
kJ/mol
kcal/mol
J/mol K
cal/(mol K)
118.4 (6.3) 84.9 (2.9) 66.1 (1.3) 54.8 (6.2) 42.3b 121.8 (15.1)
28.3 (1.5) 20.3 (0.7) 15.8 (0.3) 13.1 (1.5) 10.1b 29.1 (3.6)
110.5 (10.9) 104.2 (7.1) 108.9 (29.7) 102.1 (23.0) (100)b 105.4 (25.9)
26.4 (2.6) 24.9 (1.7) 26.0 (0.8) 24.4 (5.5) (24)b 25.2 (6.2)
16 (12)c 97.1 (5.4) 60.3 (5.0) 58.6 (3.4) 127.2 (4.2)
38 (3)c 23.2 (1.3) 14.4 (1.2) 14.0 (0.8) 30.4 (1.0)
152 (30)c 140.2 (14.2) 114.2 (19.7) 81.2 (9.2) 116.7 (75)
36 (8)c 33.5 (3.4) 27.3 (4.7) 19.4 (2.2) 27.9 (1.8)
127.6 (3.4)
30.5 (0.8)
213.0 (8.4)
50.9 (2.0)
a Uncertainty estimates, in parentheses, are derived from the standard deviations of the slopes and intercepts of the van’t Hoff plots of n points multiplied by the 95% confidence interval coefficients from Student’s t-distribution for n - 2 degrees of freedom. b From ∆G° (215) ) -4.5 kcal/mol, ∆S° estimated. c Large uncertainty due to possible ether decomposition; see text.
Drawing the comparison between the thermochemistry of H3O+ and Na+ in complexes with one to six H2O molecules, this pair shows a constant difference in ∆H° of 34 ( 8 kJ/mol (8 ( 2 kcal/mol), similar to NH4+ vs K+, where the difference is a constant 0 ( 8 kJ/mol (0 ( 2 kcal/mol). Again, this would be consistent with H3O+ not engaging in strong specific interactions with the H2O ligands, especially in the outer solvent shells, after a small shell-filling effect with three H2O molecules.3,7 In most environments, including the condensed phase (see below), H3O+ seems to act thermochemically as an isotropic core ion with an ionic radius somewhat smaller than Na+. However, the complexes of the two ions with two and three molecules of MeOCH2CH2OMe show substantial deviations from this trend, suggesting possible experimental error in these values (probably in the Na+ complexes rather than in the H3O+ complexes with this ligand, since the latter fit the overall H3O+ vs NH4+ trend; see below). 3. Comparative Complexing Energetics of H3O+, NH4+, Na+ and K+ in the Condensed Phase. The preceding thermochemical comparison of NH4+ and K+ was facilitated by the fact that the enthalpies of formation in the gas phase and in aqueous solution are known for numerous salts of these ions. There are likewise many sodium salts NaX for which the desired enthalpies are known, but there exist few salts of H3O+. Consequently, we will focus on species of the type H2O·HX, where HX is a strong acid. We are also forced to compare solid salts of NaX mainly with liquid monohydrates except for the solid HClO4 derivative. Additionally, these monohydrates will be taken to be the desired H3O+ X- salts:
the enthalpy of formation of liquid H2O·HX is taken as either that value per se or the sum of 1 mol of liquid water and of HX in 1H2O. Table 3 presents the desired enthalpies of formation, where all otherwise unreferenced thermochemical data in this discussion is taken from ref 29. (See ref 30 on the enthalpy of formation of H2O‚HI.) Table 3 shows that the enthalpies of formation of condensed phase NaX and H3O X are equal to within (8 kJ/mol (ca 2 kcal/mol). The enthalpy of formation of Na+(g) is known to be 12 kJ/mol (ca 3 kcal/mol) higher than that of H3O+(g).31 This suggests that the lattice energy of NaX is ca. 12 kJ/mol (3 kcal/mol) higher than that of H3O X. It would appear that Na+ and H3O+ are thermochemical mimics in the energetics of condensed-phase salts. With respect to the enthalpies of solution of these two ions, Table 4 shows that the enthalpy of solution of aqueous H3O X salts is ca. 40 ( 10 kJ/mol (10 ( 2 kcal/ mol) more negative than the corresponding NaX salt. (The NaHSO4/H3O HSO4 comparison is not applicable here).32 Since the lattice energies of H3O+ salts are some 12 kJ/mol (3 kcal/ mol) more positive than the corresponding sodium salts, we conclude that the solvation energy of H3O+ is some 28 kJ/mol (7 kcal/mol) more negative than Na+. Consequently, it would appear that there is a more or less uniform, but significantly nonzero, difference between the interaction of H3O+ and Na+ with lattice vs aqueous environments, unlike NH4+ vs K+, where the energies were similar. It is generally agreed that the aqueous solvation enthalpy of K+ is ca. 85 kJ/mol (20 kcal/mol) less negative than that of Na+.33 Therefore, the aqueous solvation enthalpy of K+ is some
6448 J. Phys. Chem., Vol. 100, No. 16, 1996
Meot-Ner et al.
TABLE 2: Complexation Thermochemistry of Ions by Oxygen Ligands, from the Present and Literature Dataa ∆H° monodentate H 2O Me2CO bidentate 2H2O 2Me2CO G1 G1 (calc) tridentate 3H2O 3Me2CO G2 tetradentateg 4H2O 4Me2COc 2G1 hexadentate 6H2O 6Me2CO 3G1 2G2 18-crown-6 liquid H2O
∆S°
H3O+
Na+
NH4+
K+
H3O+
Na+
133.1b
100.4c
77.8d 118.4
74.9e 108.8f
100.4b
90.0c
139.7d 203.3 160.7 (181.6)
142.3e 196.6f 128.9j (163.6)
187.9b 239.7h 125.5 (140.2)
193.3d 269.4 195.8
197.5e 263.6f
301.2b 364.0h 208.4h
274.5c
241.4d 324.3 257.7
246.9c
384.5b (429)k 264.0h
379.1c
322.2d (402)k 318.0 323.4 (296)m 363.2n
333.5e
586.6b (673)k 373.6h 364.8h 233.5l 126.4n
605.4c
212.5b 308.4h 245.2h (278.7)
183.3c 197.5i (242.7)
286.2b 385.8h 309.6h
249.4c
334.3b (418)k 348.1h
307.1c
425.5b (485)k 409.6h 414.2h 387.0l 461.5n
403.3c
344.3i
441.4i 451.0n
(296)m 366.5n
NH4+
K+
110.5
90.4e 100.4f
214.6 151.9 (141.0)
191.6e 209.2f 112.1j (107.5)
182.8c 144.8i (118.4)
323.4 149.4
314.2i
490.8i 107.9n
287.9e 309.6f 391.2e
425.5 292.0 604.2e (632)k 406.3 362.3 95.4n
71.1n
a ∆H° and ∆G° in kJ/mol, ∆S° in J/mol K. b Data for H O+ (nH O), ref 3. c Data for Na+ (nH O), ref 6. d Data for NH + (nH O), refs 4 and 5. 3 2 2 4 2 Data for K+ (nH2O), ref 7. f Data for K+ (nMe2CO), ref 12. g This means a total of four solvating molecules or groups, which may be directly + h + + coordinated to the ion or partially coordinated to each other, as in H3O (4H2O). Data for H3O (nMe2CO), H3O (nG1), and H3O+ (nG2), refs 8 and 9. i Data for Na+ (nG1), ref 11. j Data for K+ (G1), ref 13. k For H3O+ (nMe2CO), in ref 2 we used the experimental data for n ) 1-3, and for n > 3 we assumed ∆H° ) -34 kJ/mol and ∆S° ) -105 J/mol K, on the basis that clustering thermochemistry usually approaches the bulk condensation thermochemistry. l Data for H3O+ (18-crown-6), ref 10. m Estimated from H3O+ (18-crown-6), using the difference of 91 kJ/mol (22 kcal/mol) between the solvation energies of H3O+ and NH4+ by three G1 and two G2 molecules, and equating K+ with NH4+. n Data for liquid H2O, ref 14. e
TABLE 3: Enthalpies of Formation of NaX(s) and the Corresponding Condensed-Phase H3OX Species NaCl(s) NaClO4(s) NaBr(s) NaI(s) NaHSO4(s) NaNO3(s) NaHSeO4(s) a
-411.1 -383.3 -361.1 -287.8 -1125.5 -467.9 -821.4
H3O Cl(l) H3O ClO4(s) H3O Br(1) H3O I(1) H3O HSO4(1) H3O NO3(1) H3O HSeO4(1)
-407.4 -382.2 -358.6 -296a -1127.6 -473.5 -820.5
See footnote 30.
TABLE 4: Enthalpies of Aqueous Solution of NaX(s) and the Corresponding Condensed-Phase H3OX Species NaCl(s) NaClO4(s) NaBr(s) NaI(s) NaHSO4(s) NaNO3(s) NaHSeO4(s) a
+3.9 +13.9 -0.6 -7.5 -2.0 +9.3 -0.3
H3O Cl(1) H3O ClO4(s) H3O Br(1) H3O I(1) H3O HSO4(1) H3O NO3(1) H3O HSeO4(1)
-45.6 -22.9 -48.8 -45a -67.5 -19.7 -51.5
See footnote 30.
113 kJ/mol (27 kcal/mol) less than that of H3O+. Having earlier suggested that the interaction enthalpies of K+ and NH4+ are nearly equal regardless of the media,2 we conclude that H3O+ is solvated 113 kJ/mol (27 kcal/mol) more strongly than NH4+. This value is consistent with what is shown elswehere in this paper from the analysis of gas-phase species. This value is similar to the difference in the solvation energies derived from gas-phase proton affinites and thermochemical cycles, which give a difference of 100 kJ/mol (24 kcal/mol).34,35 4. Comparison of H3O+ with NH4+ and Estimation of the Binding of NH4+ and K+ to Crown Ethers. For all the tetradentate and higher complexes of the two ions, including solvation by bulk H2O, the complexation energy of H3O+ is greater than that of NH4+ by 94 ( 8 kJ/mol (23 ( 2 kcal/mol).
In particular, for hexadentate complexes, with 2MeOCH2CH2OCH2CH2OMe or 3MeOCH2CH2OMe molecules, the difference between the complexation energies is equal, 91 kJ/mol (22 kcal/ mol). These observations suggest that a similar difference will apply to the binding energies with crown ethers. On this basis, using the binding energies of crown ethers to H3O+,10 the binding energy of NH4+ to 15-crown-5 is estimated as 248 ( 12 kJ/mol (59 ( 3 kcal/mol) and to 18-crown-6 as 296 ( 12 kJ/mol (71 ( 3 kcal/mol). From the similarity of NH4+ and K+ bonding energies to all ligands, the same values are estimated for the binding energies of K+ to these crown ethers. Note that the proton affinities of the crown ethers are higher than that of NH3,15,16 and as with H3O+,10 equilibrium determinations of the binding energies would have to be obtained from thermochemical cycles involving the crown ether (Cr) reactions CrH+ + NH3 f NH4+ + Cr; NH4+ + Cr f (CrH+)NH3; and CrH+ + NH3 f NH4+(Cr). Using the proton affinities,36 and the (NH4+)Cr binding energies estimated above, the ∆H° for the association of (15-crown-5)H+ and (18-crown6)H+ with NH3 can be estimated as 152 kJ/mol (-36 kcal/mol) and -172 kJ/mol (-40 kcal/mol), respectively. These values are probably too large for equilibrium measurements, since at the required temperatures above 700 K, the neutral or protonated ethers may be expected to pyrolyze.37,38 Ligand-switching reactions at lower temperatures using ligands of known binding energy to NH4+ could be useful. 5. Ab Initio Structures and Charge Distributions. To examine the structural basis of the differential binding energies of polyethers to the four ions, we performed ab inito calculations on their complexes with MeOCH2CH2OMe. The geometries of all structures were fully optimized, and frequency calculations revealed all to be true minima in the potential energy surface. Atomic charges were computed through a standard Mulliken
Complexing of the Ammonium Ion by Polyethers
J. Phys. Chem., Vol. 100, No. 16, 1996 6449 of the hydrogen bonds illustrate the geometrical constraints that weaken hydrogen bonding to the polydentate ligands. Turning to the charges on the various atoms, the K+ ion retains nearly the full unit charge in the complex, and the charge decreases when going to Na+ in both the Mullikan and natural population analysis. The group charges of H3O+ and NH4+ are also both above 0.8. However, H3O+ shows the largest amount of charge transfer to the ligand, which follows from the ability of the O-H bond to form a stronger hydrogen bond and thereby accept electron density from the proton acceptor diether molecule. The normal pattern, that formation of a hydrogen bond enhances the electron density on the protonaccepting atom, leads to the large negative charges on O1 and O3 in the H3O+ complex. Overall, the atomic or group charges on the ions in all the complexes are above 0.8, showing that the ions retain most of charge in all the complexes. However, the amount of charge transfer to the ligand is not negligible and follows the order of binding energies. This is manifested both by the positive charges on the ions and by the negative charges on the ether oxygen atoms in the complexes. Comparing the charges on the K+ vs NH4+ complexes illustrates the various factors that add up compensatingly to produce the observed similar binding energies. The charge on K+ is largest, but it is centered on the nucleus farthest removed from the ether oxygens. On NH4+, there is a large negative charge on the N atom,2 but the positive charges on the hydrogenbonding H atoms are much closer to the negative ether oxygens. These differences in geometries and partial charges result in similar bond energies for K+ and NH4+. This further illustrates the complex electrostatic forces that were analyzed previously,2 which results in H3O+ and NH4+ behaving in a thermochemically similar manner to spherical cations. Conclusions
Figure 3. Ab initio geometries and charge distributions for complexes of MeOCH2CH2OMe with the ions shown. Atomic and group charges without parentheses are from Mulliken analysis and in parentheses from natural population analysis.
analysis25 and by a natural population analysis.26 The geometries and charge distributions in the four complexes are shown in Figure 3. The complexes of Na+ and K+ belong to the C2 point group. The COCCOC framework of the diether is nonplanar and can be characterized by the dihedral angle φ(OCCO). Replacement of the metal ions by H3O+ and NH4+ permits the formation of hydrogen bonds to the ether oxygen atoms. The calculated binding energies are shown in Table 2. The results reproduce the observed experimental trends, in that H3O+ binds more strongly, followed by Na+, and there is little difference between NH4+ and K+. The entropy loss is greatest for the hydrogen-bonding ions, due in part to the decrease in the vibrational freedom of the hydrogens when bonded to the ether, as well as loss of the overall molecular rotational freedom of H3O+ and NH4+. The Na+ ion is closest to the O atoms, with R(Na-O) ) 2.19 Å. The larger size of K+ keeps it at 2.62 Å from the oxygens, which turns out to be quite similar to the r(N-O) distance in the NH4+ complex. Note that the two hydrogen bonds in the latter complex deviate from linearity by 30o, with Θ(NH-O) ) 154o. The same nonlinearity occurs in the complex with H3O+; however, the proton-donating ability of the OH bond shortens the hydrogen bond, so that r(O1-H) ) 1.69 Å for NH4+ but only 1.43 Å for H3O+. The nonlinearity
The present results, together with literature data, allow a comparison of the binding of H3O+, NH4+, Na+, and K+ to monodentate and polydentate ligands. The observed trends show that the binding thermochemistry of H3O+ and NH4+ to various ligands, from single solvent molecules and clusters to the condensed phase, are similar to the trends in the thermochemistry of isotropic, spherical core ions (a discrepancy between NH4+(MeOCH2CH2OMe) and K+(MeOCH2CH2OMe) possibly due to experimental artifact should be investigated further). We showed before that this is due to the sum of electrostatic effects of the partial charges on the atoms of NH4+. At the distance of a ligand molecule, the sum of these field effects resembles the electrostatic forces arising from a spherical ion at the same distance.2 We observe that binding strengths to polydentate ligands are weakened by strained geometries, as illustrated by the ab initio nonlinear hydrogen bond geometries, compared with an equal number of free ligand molecules. However, opposing entropy effects can partially or fully compensate for this difference. The trends in the gas-phase binding energies allow an estimate of the binding energies of NH4+ and K+ to crown ethers, which may not be accessible to direct equilibrium measurements. Acknowledgment. This work was funded in part (L.W.S.) by the Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. Department of Energy. J.F.L. wishes to thank the Chemical Science and Technology Laboratory of the National Institute of Standards and Technology for partial support of his research. The work at SIU was supported by the National Institutes of Health (GM29391).
6450 J. Phys. Chem., Vol. 100, No. 16, 1996 References and Notes (1) Meot-Ner (Mautner), M.; Sieck, L. W.; Scheiner, S.; Duan, X. J. Am. Chem. Soc. 1994, 116, 7848. (2) Liebman, J. F.; Romm, M. J.; Meot-Ner (Mautner), M.; Cybulski, C. M.; Scheiner, S. J. Phys. Chem. 1991, 95, 1112. (3) Meot-Ner (Mautner), M.; Speller, C. V. J. Phys. Chem. 1986, 90, 6616. (4) Payzant, J. D.; Cunningham, A. J.; Kebarle, P. Can. J. Chem. 1973, 51, 3742. (5) Meot-Ner (Mautner), M. J. Am. Chem. Soc. 1984, 106, 1625. (6) Dzidic, I.; Kebarle, P. Can. J. Chem. 1969, 47, 2619. (7) Searles, S. K.; Kebarle, P. Can. J. Chem. 1969, 47, 2619. (8) Meot-Ner (Mautner), M.; Scheiner, S.; Yu, W. O. Submitted. (9) Meot-Ner (Mautner), M.; Sieck, L. W.; Scheiner, S.; Duan, X. J. Am. Chem. Soc. 1994, 116, 7848. (10) Sharma, R. B.; Kebarle, P. J. Am. Chem. Soc. 1984, 106, 3913. (11) Castleman, A. W.; Peterson, K. I.; Upschulte, B. L.; Schelling, F. J. Int. J. Mass Spectrom. Ion Phys. 1983, 47, 203. (12) Sunner, J.; Kebarle, P. J. Am. Chem. Soc. 1984, 106, 6135. (13) Davidson, W. R.; Kebarle, P. Can. J. Chem. 1976, 54, 2594. (14) Meot-Ner (Mautner), M. J. Phys. Chem. 1987, 91, 417. (15) Sharma, R. B.; Blades, A. T.; Kebarle, P. J. Am. Chem. Soc. 1984, 106, 510. (16) Meot-Ner (Mautner), M. J. Am. Chem. Soc. 1983, 105, 4906. (17) Meot-Ner (Mautner), M. J. Am. Chem. Soc. 1984, 106, 1265. (18) Meot-Ner (Mautner), M.; Sieck, L. W. J. Am. Chem. Soc. 1991, 113, 4448. (19) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, G. G. Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Bomperts, R.; Andres, J. L.; Ragavachari, K.; Binkley, J. S.; Gonzalez, G.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92; Gaussian, Inc.: Pittsburgh, PA, 1993. (20) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971, 54, 724. (21) Scheiner, S. Acc. Chem. Res. 1985, 18, 174. (22) Desmeules, P. J.; Allen, L. C. J. Chem. Phys. 1980, 72, 4731. (23) Scheiner, S.; Harding, L. B. J. Am. Chem. Soc. 1981, 103, 315. (24) Dobbs, K. D.; Hehre, W. J.; Pople, J. A. J. Comput. Chem. 1986, 7, 359.
Meot-Ner et al. (25) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833. (26) Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1985, 83, 735. (27) Deakyne, C. A.; Meot-Ner (Mautner), M.; Campbell, C. L.; Hughes, M. G.; Murphy, S. P. J. Chem. Phys. 1986, 90, 4648. (28) Yamabe, S.; Hirao, K.; Wasada, H. J. Phys. Chem. 1992, 96, 10261. (29) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. The NBS Tables of Chemical Thermodynamic Properties: Selected Values for Inorganic and C1 and C2 Organic Substances in SI Units. J. Phys. Chem. Ref. Data 1982, 11, Suppl. 2. (30) For the two halogens X and Cl, we find the difference of the enthalpies of formation to be the same within 3 kJ/mol for the following “systems” (a) of HX (neat) and of HX in 1H2O, (b) of HX in 1H2O and in 2H2O, (c) of HX in 2H2O and in 3H2O, (d) of HX in 3H2O and in 4H2O, (e) of HX in 4H2O and in ∞H2O. The “difference enthalpies” (c), (d), and (e), are likewise nearly the same for X ) Cl, Br, and I. This suggests that near equality will also be seen for the enthalpy difference (a) for the three halogens. For X ) Cl and Br, the difference is -39.2 and -36.3 kJ/mol respectively. Assuming the difference for I ) -36 ( 3 kJ/mol, then the enthalpy of formation of HI in 1H2O is -10 ( 3 kJ/mol and, accordingly, that of H3O I is -296 kJ/mol. (31) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17, Suppl. 1. (32) The NaHSO4/H3O HSO4 comparison is not applicable here because HSO4- can be exothermically dissociated by the solvent to form H3O+ + SO42-, a process that has no counterpart for NaHSO4 or any other sodium or hydronium ion salt discussed in this study. (33) Coe, J. V. Chem. Phys. Lett. 1994, 229, 161. (34) Meot-Ner (Mautner), M. J. Phys. Chem. 1987, 91, 417. (35) Taft, R. Prog. Phys. Org. Chem. 1983, 14, 247. (36) Lias, S. G.; Liebman, J. F.; Levin, R. D. J. Phys. Chem. Ref. Data 1984, 13, 695. (37) Sieck, L. W.; Meot-Ner (Mautner), M. J. Phys. Chem. 1984, 88, 5324. (38) Sieck, L. W.; Meot-Ner (Mautner), M. J. Phys. Chem. 1984, 88, 5328.
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