Cluster Ion Thermodynamic Properties: The Liquid Drop Model Revisited

Journal of Physical Chemistry A

Volumn 103, Issue 15, 1999, Pages 2561-2571

  Peslherbe, Gilles H ^a,b,c   Ladanyi, Branka M ^b   Hynes, James T ^a  

^a UNIVERSITY OF COLORADO   (United States)

^b Department of Environmental and Radiological Health Sciences   (United States)

^c Gina Cody School of Engineering and Computer Science   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000156799     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp983550g     Document Type: Article

References (83)

1. Castleman, A. W.; Keesee, R. G. Acc. Chem. Res. 1986, 19, 413.
2. See, for example, Castleman, A. W., Jr.; Bowen, K. H. J. Phys. Chem. 1996, 100, 12911 and references therein.
3. Rosseinsky, D. R. Chem. Rev. 1965, 65, 467.
4. Desnoyers, J. E.; Jolicoeur, C. In Modern Aspects of Electrochemistry; Bockis, J. O., Conway, B. E., Eds.; Plenum: New York, 1969.
5. Friedman, H. L.; Krishnan, C. V. In Water: A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 3.
6. Dzidic, I.; Kebarle, P. J. Phys. Chem. 1970, 74, 1466. Kebarle, P. Annu. Rev. Phys. Chem. 1977, 28, 445.
7. Dzidic, I.; Kebarle, P. J. Phys. Chem. 1970, 74, 1466. Kebarle, P. Annu. Rev. Phys. Chem. 1977, 28, 445.
8. Klassen, J. S.; Ho, Y.; Blades, A. T.; Kebarle, P. In Advances in Gas-Phase Ion Chemistry; Adams, N. G., Babcock, L. M., Eds.; Jai Press: Greenwich, CT, 1998.
9. See, for example, Kistenmacher, H.; Popkie, H.; Clementi, E. J. Chem. Phys. 1974, 61, 799. Perez, P.; Lee, W. K.; Prohofsky, E. W. J. Chem. Phys. 1983, 79, 388. Sung, S.-S.; Jordan, P. C. J. Chem. Phys. 1986, 85, 4045. Lin, S.; Jordan, P. C. J. Chem. Phys. 1988, 89, 7492. Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1991, 95, 1954, 4236.
10. See, for example, Kistenmacher, H.; Popkie, H.; Clementi, E. J. Chem. Phys. 1974, 61, 799. Perez, P.; Lee, W. K.; Prohofsky, E. W. J. Chem. Phys. 1983, 79, 388. Sung, S.-S.; Jordan, P. C. J. Chem. Phys. 1986, 85, 4045. Lin, S.; Jordan, P. C. J. Chem. Phys. 1988, 89, 7492. Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1991, 95, 1954, 4236.
11. See, for example, Kistenmacher, H.; Popkie, H.; Clementi, E. J. Chem. Phys. 1974, 61, 799. Perez, P.; Lee, W. K.; Prohofsky, E. W. J. Chem. Phys. 1983, 79, 388. Sung, S.-S.; Jordan, P. C. J. Chem. Phys. 1986, 85, 4045. Lin, S.; Jordan, P. C. J. Chem. Phys. 1988, 89, 7492. Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1991, 95, 1954, 4236.
12. See, for example, Kistenmacher, H.; Popkie, H.; Clementi, E. J. Chem. Phys. 1974, 61, 799. Perez, P.; Lee, W. K.; Prohofsky, E. W. J. Chem. Phys. 1983, 79, 388. Sung, S.-S.; Jordan, P. C. J. Chem. Phys. 1986, 85, 4045. Lin, S.; Jordan, P. C. J. Chem. Phys. 1988, 89, 7492. Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1991, 95, 1954, 4236.
13. See, for example, Kistenmacher, H.; Popkie, H.; Clementi, E. J. Chem. Phys. 1974, 61, 799. Perez, P.; Lee, W. K.; Prohofsky, E. W. J. Chem. Phys. 1983, 79, 388. Sung, S.-S.; Jordan, P. C. J. Chem. Phys. 1986, 85, 4045. Lin, S.; Jordan, P. C. J. Chem. Phys. 1988, 89, 7492. Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1991, 95, 1954, 4236.
14. Jorgensen, W. L.; Severance, D. L. J. Chem. Phys. 1993, 99, 4233.
15. See, for example, Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1992, 96, 8268; 1993, 99, 4222. Sremaniak, L. S.; Perera, L.; Berkowitz, M. L. Chem. Phys. Lett. 1994, 218, 377. Dang, L. X.; Garrett, B. C. J. Chem. Phys. 1993, 99, 2972. Dang, L. X.; Smith, D. E. J. Chem. Phys. 1993, 99, 6950. Combariza, J. E.; Kestner, N. R.; Jortner, J. Chem. Phys. Lett. 1993, 203, 423; J. Chem. Phys. 1994, 100, 2851.
16. See, for example, Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1992, 96, 8268; 1993, 99, 4222. Sremaniak, L. S.; Perera, L.; Berkowitz, M. L. Chem. Phys. Lett. 1994, 218, 377. Dang, L. X.; Garrett, B. C. J. Chem. Phys. 1993, 99, 2972. Dang, L. X.; Smith, D. E. J. Chem. Phys. 1993, 99, 6950. Combariza, J. E.; Kestner, N. R.; Jortner, J. Chem. Phys. Lett. 1993, 203, 423; J. Chem. Phys. 1994, 100, 2851.
17. See, for example, Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1992, 96, 8268; 1993, 99, 4222. Sremaniak, L. S.; Perera, L.; Berkowitz, M. L. Chem. Phys. Lett. 1994, 218, 377. Dang, L. X.; Garrett, B. C. J. Chem. Phys. 1993, 99, 2972. Dang, L. X.; Smith, D. E. J. Chem. Phys. 1993, 99, 6950. Combariza, J. E.; Kestner, N. R.; Jortner, J. Chem. Phys. Lett. 1993, 203, 423; J. Chem. Phys. 1994, 100, 2851.
18. See, for example, Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1992, 96, 8268; 1993, 99, 4222. Sremaniak, L. S.; Perera, L.; Berkowitz, M. L. Chem. Phys. Lett. 1994, 218, 377. Dang, L. X.; Garrett, B. C. J. Chem. Phys. 1993, 99, 2972. Dang, L. X.; Smith, D. E. J. Chem. Phys. 1993, 99, 6950. Combariza, J. E.; Kestner, N. R.; Jortner, J. Chem. Phys. Lett. 1993, 203, 423; J. Chem. Phys. 1994, 100, 2851.
19. See, for example, Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1992, 96, 8268; 1993, 99, 4222. Sremaniak, L. S.; Perera, L.; Berkowitz, M. L. Chem. Phys. Lett. 1994, 218, 377. Dang, L. X.; Garrett, B. C. J. Chem. Phys. 1993, 99, 2972. Dang, L. X.; Smith, D. E. J. Chem. Phys. 1993, 99, 6950. Combariza, J. E.; Kestner, N. R.; Jortner, J. Chem. Phys. Lett. 1993, 203, 423; J. Chem. Phys. 1994, 100, 2851.
20. See, for example, Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1992, 96, 8268; 1993, 99, 4222. Sremaniak, L. S.; Perera, L.; Berkowitz, M. L. Chem. Phys. Lett. 1994, 218, 377. Dang, L. X.; Garrett, B. C. J. Chem. Phys. 1993, 99, 2972. Dang, L. X.; Smith, D. E. J. Chem. Phys. 1993, 99, 6950. Combariza, J. E.; Kestner, N. R.; Jortner, J. Chem. Phys. Lett. 1993, 203, 423; J. Chem. Phys. 1994, 100, 2851.
21. See, for example, Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1992, 96, 8268; 1993, 99, 4222. Sremaniak, L. S.; Perera, L.; Berkowitz, M. L. Chem. Phys. Lett. 1994, 218, 377. Dang, L. X.; Garrett, B. C. J. Chem. Phys. 1993, 99, 2972. Dang, L. X.; Smith, D. E. J. Chem. Phys. 1993, 99, 6950. Combariza, J. E.; Kestner, N. R.; Jortner, J. Chem. Phys. Lett. 1993, 203, 423; J. Chem. Phys. 1994, 100, 2851.
22. Lee, N.; Keesee, R. G.; Castleman, A. W., Jr. J. Colloid Interface Sci. 1980, 75, 555.
23. Holland, P. M.; Castleman, A. W., Jr. J. Phys. Chem. 1982, 86, 4181.
24. Thomson, J. J. Application of Dynamics to Physics and Chemistry, 1st ed.; Cambridge: Cambridge, 1888.
25. Mason, B. J. The Physics of Clouds, 2nd ed.; Oxford University Press: London, 1971.
26. Coe, J. V. Chem. Phys. Lett. 1994, 229, 161.
27. Coe, J. V. J. Phys. Chem. A 1997, 101, 2055.
28. See, for example, Chemical Reactions in Clusters; Bernstein, E. R., Ed.; Oxford University Press: New York, 1996.
29. Maroncelli, M.; Fleming, G. R. J. Chem. Phys. 1988, 89, 5044.
30. See, for example, Hummer, G.; Pratt, L. R.; Garcia, A. E. J. Chem. Phys. 1997, 107, 9275.
31. Rips, I.; Jortner, J. J. Chem. Phys. 1992, 97, 536.
32. Makov, G.; Nitzan, A. J. Phys. Chem. 1994, 98, 3459.
33. One might imagine, for example, a cluster version of the integral equation theories that are commonly used for bulk solvation problems. See, for example, the following. Richardi, J.; Fries, P. H.; Krienke, H. J. Chem. Phys. 1998, 108, 4079. Reference 31 and references therein.
34. Serxner, D.; Dessent, C. E. H.; Johnson, M. A. J. Chem. Phys. 1996, 105, 7231.
35. Castleman, A. W., Jr.; Holland, P. M.; Keesee, R. G. J. Phys. Chem. 1978, 68, 1760.
36. Sinanoglu, O. J. Chem. Phys. 1981, 75, 463.
37. For a recent molecular dynamics study of the surface tension of water droplets, see, for example, Zakharov, V. V.; Brodskaya, E. N.; Laaksonen, A. J. Chem. Phys. 1997, 107, 10675.
38. Suck, S. H. J. Chem. Phys. 1981, 75, 5090.
39. Note that solvent-solvent polarizability effects are implicitly included in the LD model via the use of an experimental solvent dielectric constant.
40. A possible route for including nonlinear effects of the ionic field and correcting for dielectric saturation in the vicinity of the ion would be to make the solvent dielectric constant distance-dependent, as was done in early bulk solvation studies. See, for example, ref 31 and references therein.
41. Born, M. Z. Physik 1920, 1, 45.
42. Roux, B.; Yu, H.-A.; Karplus, M. J. Phys. Chem. 1990, 94, 4683.
43. See, for example, Atkins, P. Physical Chemistry, 5th ed.; W. H. Freeman: New York, 1994.
44. Xantheas, S. S.; Dang, L. X. J. Phys. Chem. 1996, 100, 3989.
45. Peslherbe, G. H.; Bianco, R.; Hynes, J. T.; Ladanyi, B. M. J. Chem. Soc., Faraday Trans. 1997, 93, 977.
46. Marcus, Y. Ion Solvation; Wiley: New York, 1985. Marcus, Y. J. Chem. Soc., Faraday Trans. 1 1986, 82, 233; 1987, 83, 339.
47. Marcus, Y. Ion Solvation; Wiley: New York, 1985. Marcus, Y. J. Chem. Soc., Faraday Trans. 1 1986, 82, 233; 1987, 83, 339.
48. Marcus, Y. Ion Solvation; Wiley: New York, 1985. Marcus, Y. J. Chem. Soc., Faraday Trans. 1 1986, 82, 233; 1987, 83, 339.
49. - ion pairs for which the solvation free energy is the same with either choice of ion solvation data.
50. Evans, D. H.; Keesee, R. G.; Castleman, A. W., Jr. J. Phys. Chem. 1991, 95, 3558.
51. As the temperature derivative of the free energy, the entropy is a more delicate and sensitive property to determine in general. Thus, it is difficult to produce both accurate free energies and enthalpies with the same continuum dielectric model. An investigation of the Born model [see ref 31] in fact suggests that the variation of the solvent dielectric constant with temperature is not sufficient to account for the difference between enthalpy and free energy and that the dominant contribution to this difference arises from the variation of the Born radius with temperature, which is not considered here.
52. It should be pointed out that computer simulations are performed by us and others for isolated clusters, whereas the actual experimental measurements do involve clusters of various size in thermodynamic equilibrium with the solvent vapor. The proper definition of the physical cluster has been a long-standing issue in investigations of nucleation and capillarity phenomena, but it is now generally agreed that thermodynamic properties computed for isolated clusters - the only practical approach at this point - give an adequate representation of the properties of clusters in equilibrium with the solvent vapor under realistic experimental conditions. See, for example, Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and Physics: From Air Pollution to Climate Change; Wiley: New York, 1998, p 569. Lee, J. K.; Barker, J. A.; Abraham, F. F. J. Chem. Phys. 1973, 58, 3166. Reiss, H.; Tabazadeh, A.; Talbot, J. J. Chem. Phys. 1990, 92, 1266. Weakliem, C. L.; Reiss, H. J. Phys. Chem. 1994, 98, 6408.
53. It should be pointed out that computer simulations are performed by us and others for isolated clusters, whereas the actual experimental measurements do involve clusters of various size in thermodynamic equilibrium with the solvent vapor. The proper definition of the physical cluster has been a long-standing issue in investigations of nucleation and capillarity phenomena, but it is now generally agreed that thermodynamic properties computed for isolated clusters - the only practical approach at this point - give an adequate representation of the properties of clusters in equilibrium with the solvent vapor under realistic experimental conditions. See, for example, Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and Physics: From Air Pollution to Climate Change; Wiley: New York, 1998, p 569. Lee, J. K.; Barker, J. A.; Abraham, F. F. J. Chem. Phys. 1973, 58, 3166. Reiss, H.; Tabazadeh, A.; Talbot, J. J. Chem. Phys. 1990, 92, 1266. Weakliem, C. L.; Reiss, H. J. Phys. Chem. 1994, 98, 6408.
54. It should be pointed out that computer simulations are performed by us and others for isolated clusters, whereas the actual experimental measurements do involve clusters of various size in thermodynamic equilibrium with the solvent vapor. The proper definition of the physical cluster has been a long-standing issue in investigations of nucleation and capillarity phenomena, but it is now generally agreed that thermodynamic properties computed for isolated clusters - the only practical approach at this point - give an adequate representation of the properties of clusters in equilibrium with the solvent vapor under realistic experimental conditions. See, for example, Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and Physics: From Air Pollution to Climate Change; Wiley: New York, 1998, p 569. Lee, J. K.; Barker, J. A.; Abraham, F. F. J. Chem. Phys. 1973, 58, 3166. Reiss, H.; Tabazadeh, A.; Talbot, J. J. Chem. Phys. 1990, 92, 1266. Weakliem, C. L.; Reiss, H. J. Phys. Chem. 1994, 98, 6408.
55. It should be pointed out that computer simulations are performed by us and others for isolated clusters, whereas the actual experimental measurements do involve clusters of various size in thermodynamic equilibrium with the solvent vapor. The proper definition of the physical cluster has been a long-standing issue in investigations of nucleation and capillarity phenomena, but it is now generally agreed that thermodynamic properties computed for isolated clusters - the only practical approach at this point - give an adequate representation of the properties of clusters in equilibrium with the solvent vapor under realistic experimental conditions. See, for example, Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and Physics: From Air Pollution to Climate Change; Wiley: New York, 1998, p 569. Lee, J. K.; Barker, J. A.; Abraham, F. F. J. Chem. Phys. 1973, 58, 3166. Reiss, H.; Tabazadeh, A.; Talbot, J. J. Chem. Phys. 1990, 92, 1266. Weakliem, C. L.; Reiss, H. J. Phys. Chem. 1994, 98, 6408.
56. Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926.
57. Aqvist, J. J. Phys. Chem. 1990, 94, 8021; 1994, 98, 8253.
58. Aqvist, J. J. Phys. Chem. 1990, 94, 8021; 1994, 98, 8253.
59. In addition - and it will be important in the following - the TIP3P model complemented by our ion - water potentials predicts that surface ion structures are favored over interior ion configurations for iodide ion - water clusters at room temperature, which proves an important requirement of reliable model potentials in studies of these clusters and was at the center of an earlier controversy whether simple pairwise additive potentials could reproduce this feature of halide-water clusters [see ref 9]. The iodide - water interaction potentials used in this work are of the OPLS form, and the parameters were chosen to reproduce the experimental interaction energy and the calculated HF/3-21+G geometry of the ion - water complex, as was done for fluoride and chloride in the following reference. Chandrasekhar, J.; Spellmeyer, D. C.; Jorgensen, W. L. J. Am. Chem. Soc. 1984, 106, 903. The resulting Lennard-Jones parameters are ε = 0.3 kcal/mol and σ = 4.0 Å.
60. Jorgensen, W. L.; Blake, J. F.; Buckner, J. K. Chem. Phys. 1989, 129, 193.
61. Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: New York, , 1989.
62. It should be noted that the ion, not simply its charge, is being annihilated in our Monte Carlo simulations; i.e. both the electrostatic and repulsion - dispersion parts of the solute - solvent interactions are being gradually "turned off", and thus, we are calculating the full solvation free energy of the ion, including the work to transfer the ion into the water cluster, and not only the free energy associated with "charging" the ion, as is customarily done [see ref 59]. However, we expect the work associated with the ion transfer to the water cluster (or the cavity formation) to be negligible [see ref 59]. This assists but does not itself guarantee the important feature that the cluster solvation free energies from our Monte Carlo simulations agree well with the LD model predictions within the statistical uncertainties of the simulations (continuum dielectric-based models only account for the free energy of "charging" the ion).
63. The random-walk Metropolis Monte Carlo method [e.g., ref 44] is employed here. A new configuration is generated by randomly translating one water molecule in all three Cartesian directions and rotating the water molecule around its Euler angles. The range for translational and rotational displacements is chosen to yield typical configuration acceptance ratios of ∼50%.
64. King, G.; Warshel, A. J. Chem. Phys. 1989, 91, 3647.
65. Barnett, R. N.; Landman, U.; Cleveland, C. L.; Jortner, J. J. Chem. Phys. 1988, 88, 4429.
66. Barnett, R. N.; Landman, U.; Cleveland, C. L.; Jortner, J. Chem. Phys. Lett. 1988, 145, 382.
67. Alternatively, if one compares the cluster solvation enthalpies calculated with the DS model and displayed in the top panel of Figure 3 to the asymptotic limit predicted by the model (-106 kcal/mol), one still concludes that the cluster solvation enthalpy is slow to converge to the bulk limit.
68. See, for example, ref 56.
69. solv. In the macroscopic continuum view, the contribution of the former (the interaction free energy) is negative and equal in magnitude to twice the value of the latter positive contribution (the "self free energy of the solvent). Clearly, a LD model does not do justice to the microscopic aspects of this competition.
70. 55 but this may depend strongly on the parametrization of the thermodynamic properties for forming the neutral water clusters.
71. Davidson, W. R.; Kebarle, P. J. Am. Chem. Soc. 1976, 98, 6125.
72. Hiraoka, K.; Mizuse, S.; Yamabe, S. J. Phys. Chem. 1988, 92, 3943.
73. Markovich, G.; Perera, L.; Berkowitz, M. L.; Cheshnovsky, O. J. Chem. Phys. 1996, 105, 2675.
74. We note here that iodide ion clusters may behave differently and exhibit different structural properties, depending on the solvent, and this solvent dependence will prove to play an important role for NaI ion pairs in clusters [see ref 62].
75. Tuckerman, M. E.; Ungar, P. J., von Rosenvinge, T.; Klein, M. L. J. Phys. Chem. 1996, 100, 12878. Tuckerman, M. E.; Marx, D.; Klein, M. L.; Parrinello, M. Science 1997, 275, 817-820.
76. Tuckerman, M. E.; Ungar, P. J., von Rosenvinge, T.; Klein, M. L. J. Phys. Chem. 1996, 100, 12878. Tuckerman, M. E.; Marx, D.; Klein, M. L.; Parrinello, M. Science 1997, 275, 817-820.
77. See, for example, Rashin, A. A.; Honig, B. J. Phys. Chem. 1985, 89, 5588. Jayaram, B.; Fine, R.; Sharp, K.; Honig, B. J. Phys. Chem. 1989, 93, 4320.
78. See, for example, Rashin, A. A.; Honig, B. J. Phys. Chem. 1985, 89, 5588. Jayaram, B.; Fine, R.; Sharp, K.; Honig, B. J. Phys. Chem. 1989, 93, 4320.
79. The very fact that continuum models predict at least the right trends for a variety of more complex solute properties in bulk solution [e.g., Morita, T.; Ladanyi, B. M.; Hynes, J. T. J. Phys. Chem. 1989, 93, 1386] is encouraging in that respect.
80. It is interesting to note that the success of simple dielectric models in describing cluster ion solvation thermodynamic properties over a wide range of cluster sizes suggests that one could evaluate bulk solvation properties from cluster simulations using simple dielectric corrections, at least for simple ions. Cluster simulations do not require the use of periodic boundary conditions, the exact implementation of which remains to date controversial [Aqvist, J.; Hansson, T. J. Phys. Chem. B 1998, 102, 3837. Hummer, G.; Pratt, L. R.; Garcia, A. E.; Garde, S.; Berne, B. J.; Rick, S. W. J. Phys. Chem. B 1998, 102, 3841. Ashbaugh, H. S.; Sakane, S.; Wood, R. H. J. Phys. Chem. B 1998, 102, 3844].
81. It is interesting to note that the success of simple dielectric models in describing cluster ion solvation thermodynamic properties over a wide range of cluster sizes suggests that one could evaluate bulk solvation properties from cluster simulations using simple dielectric corrections, at least for simple ions. Cluster simulations do not require the use of periodic boundary conditions, the exact implementation of which remains to date controversial [Aqvist, J.; Hansson, T. J. Phys. Chem. B 1998, 102, 3837. Hummer, G.; Pratt, L. R.; Garcia, A. E.; Garde, S.; Berne, B. J.; Rick, S. W. J. Phys. Chem. B 1998, 102, 3841. Ashbaugh, H. S.; Sakane, S.; Wood, R. H. J. Phys. Chem. B 1998, 102, 3844].
82. It is interesting to note that the success of simple dielectric models in describing cluster ion solvation thermodynamic properties over a wide range of cluster sizes suggests that one could evaluate bulk solvation properties from cluster simulations using simple dielectric corrections, at least for simple ions. Cluster simulations do not require the use of periodic boundary conditions, the exact implementation of which remains to date controversial [Aqvist, J.; Hansson, T. J. Phys. Chem. B 1998, 102, 3837. Hummer, G.; Pratt, L. R.; Garcia, A. E.; Garde, S.; Berne, B. J.; Rick, S. W. J. Phys. Chem. B 1998, 102, 3841. Ashbaugh, H. S.; Sakane, S.; Wood, R. H. J. Phys. Chem. B 1998, 102, 3844].
83. Peslherbe, G. H.; Ladanyi, B. M.; Hynes, J. T. Structure and Free Energetics of NaI in Water Clusters. A Theoretical Study. Manuscript in preparation.