Free Energetics of NaI Contact and Solvent-Separated Ion Pairs in Water Clusters

Journal of Physical Chemistry A

Volumn 104, Issue 19, 2000, Pages 4533-4548

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

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

^b UNIVERSITY OF COLORADO   (United States)

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008137770     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp993641t     Document Type: Article

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123. In the NEMO model of ref 60, individual contributions (electrostatic, polarization, dispersion, etc.) to the solvent-solvent binding energy are arbitrarily obtained from ab initio data and used as the basis for parameterization.
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130. Another approach for introducing polarization effects in molecular systems is the electronegativity equalization [Mortier, W. J.; Ghosh, S. K.; Shankar, S. J. Am. Chem. Soc. 1986, 108, 4315. York, D. M. Int. J. Quantum Chem., Quantum Chem. Symp. 1995, 29, 385 ] or charge equilibration method of Rappé et al. [Rappé, A. K.; Goddard, W. A. J. Phys. Chem. 1991, 95, 3358], which can be derived from density functional theory [Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules. Clarendon Press: New York, 1989]. Briefly, in this method, the atomic charges are solved by minimizing the total electrostatic energy of the molecular system (or equivalently equating the atomic chemical potentials), and the atomic energy is usually assumed to be a parameterized quadratic form of the atomic charges. The charge equilibration method has had success describing the charge distributions of large molecules at their ground state equilibrium geometry, and fluctuating charge water models employing this technique have been proposed, such as the TIP4P-FQ model of Berne and co-workers [Rick, S. W.; Stuart, S. J.; Berne, B. J. J. Chem. Phys. 1994, 101, 6141. Rick, S. W.; Stuart, S. J.; Bader, J. S.; Berne, B. J. J. Mol. Liq. 1995, 65/66, 31] , which reproduces various properties of liquid water quite well. However, we were unable to reproduce both the energetics and (ab initio) charge distribution of ion-water clusters or ion pair-water clusters, whether we employed the TIP4P-FQ and OPLS parameters, the original parameters of Rappé et al., or a combination of both sets. Another set of more adequate parameters could be derived, but they did not seem to be appropriate for describing the ion pair-water cluster charge distribution over a wide range of NaI internuclear separations. Thus, it appears that the quadratic expression in the atomic charges assumed for the atomic energy may not be a very good representation of the polarization energy for the complex molecular systems studied here, and the method does not seem readily applicable to chemical systems that react or dissociate. The Rappé group is presently developing extensions of the charge equilibration method to reacting systems (A. K. Rappé, private communication).
131. Another approach for introducing polarization effects in molecular systems is the electronegativity equalization [Mortier, W. J.; Ghosh, S. K.; Shankar, S. J. Am. Chem. Soc. 1986, 108, 4315. York, D. M. Int. J. Quantum Chem., Quantum Chem. Symp. 1995, 29, 385 ] or charge equilibration method of Rappé et al. [Rappé, A. K.; Goddard, W. A. J. Phys. Chem. 1991, 95, 3358], which can be derived from density functional theory [Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules. Clarendon Press: New York, 1989]. Briefly, in this method, the atomic charges are solved by minimizing the total electrostatic energy of the molecular system (or equivalently equating the atomic chemical potentials), and the atomic energy is usually assumed to be a parameterized quadratic form of the atomic charges. The charge equilibration method has had success describing the charge distributions of large molecules at their ground state equilibrium geometry, and fluctuating charge water models employing this technique have been proposed, such as the TIP4P-FQ model of Berne and co-workers [Rick, S. W.; Stuart, S. J.; Berne, B. J. J. Chem. Phys. 1994, 101, 6141. Rick, S. W.; Stuart, S. J.; Bader, J. S.; Berne, B. J. J. Mol. Liq. 1995, 65/66, 31] , which reproduces various properties of liquid water quite well. However, we were unable to reproduce both the energetics and (ab initio) charge distribution of ion-water clusters or ion pair-water clusters, whether we employed the TIP4P-FQ and OPLS parameters, the original parameters of Rappé et al., or a combination of both sets. Another set of more adequate parameters could be derived, but they did not seem to be appropriate for describing the ion pair-water cluster charge distribution over a wide range of NaI internuclear separations. Thus, it appears that the quadratic expression in the atomic charges assumed for the atomic energy may not be a very good representation of the polarization energy for the complex molecular systems studied here, and the method does not seem readily applicable to chemical systems that react or dissociate. The Rappé group is presently developing extensions of the charge equilibration method to reacting systems (A. K. Rappé, private communication).
132. Another approach for introducing polarization effects in molecular systems is the electronegativity equalization [Mortier, W. J.; Ghosh, S. K.; Shankar, S. J. Am. Chem. Soc. 1986, 108, 4315. York, D. M. Int. J. Quantum Chem., Quantum Chem. Symp. 1995, 29, 385 ] or charge equilibration method of Rappé et al. [Rappé, A. K.; Goddard, W. A. J. Phys. Chem. 1991, 95, 3358], which can be derived from density functional theory [Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules. Clarendon Press: New York, 1989]. Briefly, in this method, the atomic charges are solved by minimizing the total electrostatic energy of the molecular system (or equivalently equating the atomic chemical potentials), and the atomic energy is usually assumed to be a parameterized quadratic form of the atomic charges. The charge equilibration method has had success describing the charge distributions of large molecules at their ground state equilibrium geometry, and fluctuating charge water models employing this technique have been proposed, such as the TIP4P-FQ model of Berne and co-workers [Rick, S. W.; Stuart, S. J.; Berne, B. J. J. Chem. Phys. 1994, 101, 6141. Rick, S. W.; Stuart, S. J.; Bader, J. S.; Berne, B. J. J. Mol. Liq. 1995, 65/66, 31] , which reproduces various properties of liquid water quite well. However, we were unable to reproduce both the energetics and (ab initio) charge distribution of ion-water clusters or ion pair-water clusters, whether we employed the TIP4P-FQ and OPLS parameters, the original parameters of Rappé et al., or a combination of both sets. Another set of more adequate parameters could be derived, but they did not seem to be appropriate for describing the ion pair-water cluster charge distribution over a wide range of NaI internuclear separations. Thus, it appears that the quadratic expression in the atomic charges assumed for the atomic energy may not be a very good representation of the polarization energy for the complex molecular systems studied here, and the method does not seem readily applicable to chemical systems that react or dissociate. The Rappé group is presently developing extensions of the charge equilibration method to reacting systems (A. K. Rappé, private communication).
133. Another approach for introducing polarization effects in molecular systems is the electronegativity equalization [Mortier, W. J.; Ghosh, S. K.; Shankar, S. J. Am. Chem. Soc. 1986, 108, 4315. York, D. M. Int. J. Quantum Chem., Quantum Chem. Symp. 1995, 29, 385 ] or charge equilibration method of Rappé et al. [Rappé, A. K.; Goddard, W. A. J. Phys. Chem. 1991, 95, 3358], which can be derived from density functional theory [Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules. Clarendon Press: New York, 1989]. Briefly, in this method, the atomic charges are solved by minimizing the total electrostatic energy of the molecular system (or equivalently equating the atomic chemical potentials), and the atomic energy is usually assumed to be a parameterized quadratic form of the atomic charges. The charge equilibration method has had success describing the charge distributions of large molecules at their ground state equilibrium geometry, and fluctuating charge water models employing this technique have been proposed, such as the TIP4P-FQ model of Berne and co-workers [Rick, S. W.; Stuart, S. J.; Berne, B. J. J. Chem. Phys. 1994, 101, 6141. Rick, S. W.; Stuart, S. J.; Bader, J. S.; Berne, B. J. J. Mol. Liq. 1995, 65/66, 31] , which reproduces various properties of liquid water quite well. However, we were unable to reproduce both the energetics and (ab initio) charge distribution of ion-water clusters or ion pair-water clusters, whether we employed the TIP4P-FQ and OPLS parameters, the original parameters of Rappé et al., or a combination of both sets. Another set of more adequate parameters could be derived, but they did not seem to be appropriate for describing the ion pair-water cluster charge distribution over a wide range of NaI internuclear separations. Thus, it appears that the quadratic expression in the atomic charges assumed for the atomic energy may not be a very good representation of the polarization energy for the complex molecular systems studied here, and the method does not seem readily applicable to chemical systems that react or dissociate. The Rappé group is presently developing extensions of the charge equilibration method to reacting systems (A. K. Rappé, private communication).
134. Another approach for introducing polarization effects in molecular systems is the electronegativity equalization [Mortier, W. J.; Ghosh, S. K.; Shankar, S. J. Am. Chem. Soc. 1986, 108, 4315. York, D. M. Int. J. Quantum Chem., Quantum Chem. Symp. 1995, 29, 385 ] or charge equilibration method of Rappé et al. [Rappé, A. K.; Goddard, W. A. J. Phys. Chem. 1991, 95, 3358], which can be derived from density functional theory [Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules. Clarendon Press: New York, 1989]. Briefly, in this method, the atomic charges are solved by minimizing the total electrostatic energy of the molecular system (or equivalently equating the atomic chemical potentials), and the atomic energy is usually assumed to be a parameterized quadratic form of the atomic charges. The charge equilibration method has had success describing the charge distributions of large molecules at their ground state equilibrium geometry, and fluctuating charge water models employing this technique have been proposed, such as the TIP4P-FQ model of Berne and co-workers [Rick, S. W.; Stuart, S. J.; Berne, B. J. J. Chem. Phys. 1994, 101, 6141. Rick, S. W.; Stuart, S. J.; Bader, J. S.; Berne, B. J. J. Mol. Liq. 1995, 65/66, 31] , which reproduces various properties of liquid water quite well. However, we were unable to reproduce both the energetics and (ab initio) charge distribution of ion-water clusters or ion pair-water clusters, whether we employed the TIP4P-FQ and OPLS parameters, the original parameters of Rappé et al., or a combination of both sets. Another set of more adequate parameters could be derived, but they did not seem to be appropriate for describing the ion pair-water cluster charge distribution over a wide range of NaI internuclear separations. Thus, it appears that the quadratic expression in the atomic charges assumed for the atomic energy may not be a very good representation of the polarization energy for the complex molecular systems studied here, and the method does not seem readily applicable to chemical systems that react or dissociate. The Rappé group is presently developing extensions of the charge equilibration method to reacting systems (A. K. Rappé, private communication).
135. Another approach for introducing polarization effects in molecular systems is the electronegativity equalization [Mortier, W. J.; Ghosh, S. K.; Shankar, S. J. Am. Chem. Soc. 1986, 108, 4315. York, D. M. Int. J. Quantum Chem., Quantum Chem. Symp. 1995, 29, 385 ] or charge equilibration method of Rappé et al. [Rappé, A. K.; Goddard, W. A. J. Phys. Chem. 1991, 95, 3358], which can be derived from density functional theory [Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules. Clarendon Press: New York, 1989]. Briefly, in this method, the atomic charges are solved by minimizing the total electrostatic energy of the molecular system (or equivalently equating the atomic chemical potentials), and the atomic energy is usually assumed to be a parameterized quadratic form of the atomic charges. The charge equilibration method has had success describing the charge distributions of large molecules at their ground state equilibrium geometry, and fluctuating charge water models employing this technique have been proposed, such as the TIP4P-FQ model of Berne and co-workers [Rick, S. W.; Stuart, S. J.; Berne, B. J. J. Chem. Phys. 1994, 101, 6141. Rick, S. W.; Stuart, S. J.; Bader, J. S.; Berne, B. J. J. Mol. Liq. 1995, 65/66, 31] , which reproduces various properties of liquid water quite well. However, we were unable to reproduce both the energetics and (ab initio) charge distribution of ion-water clusters or ion pair-water clusters, whether we employed the TIP4P-FQ and OPLS parameters, the original parameters of Rappé et al., or a combination of both sets. Another set of more adequate parameters could be derived, but they did not seem to be appropriate for describing the ion pair-water cluster charge distribution over a wide range of NaI internuclear separations. Thus, it appears that the quadratic expression in the atomic charges assumed for the atomic energy may not be a very good representation of the polarization energy for the complex molecular systems studied here, and the method does not seem readily applicable to chemical systems that react or dissociate. The Rappé group is presently developing extensions of the charge equilibration method to reacting systems (A. K. Rappé, private communication).
136. Another approach for introducing polarization effects in molecular systems is the electronegativity equalization [Mortier, W. J.; Ghosh, S. K.; Shankar, S. J. Am. Chem. Soc. 1986, 108, 4315. York, D. M. Int. J. Quantum Chem., Quantum Chem. Symp. 1995, 29, 385 ] or charge equilibration method of Rappé et al. [Rappé, A. K.; Goddard, W. A. J. Phys. Chem. 1991, 95, 3358], which can be derived from density functional theory [Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules. Clarendon Press: New York, 1989]. Briefly, in this method, the atomic charges are solved by minimizing the total electrostatic energy of the molecular system (or equivalently equating the atomic chemical potentials), and the atomic energy is usually assumed to be a parameterized quadratic form of the atomic charges. The charge equilibration method has had success describing the charge distributions of large molecules at their ground state equilibrium geometry, and fluctuating charge water models employing this technique have been proposed, such as the TIP4P-FQ model of Berne and co-workers [Rick, S. W.; Stuart, S. J.; Berne, B. J. J. Chem. Phys. 1994, 101, 6141. Rick, S. W.; Stuart, S. J.; Bader, J. S.; Berne, B. J. J. Mol. Liq. 1995, 65/66, 31] , which reproduces various properties of liquid water quite well. However, we were unable to reproduce both the energetics and (ab initio) charge distribution of ion-water clusters or ion pair-water clusters, whether we employed the TIP4P-FQ and OPLS parameters, the original parameters of Rappé et al., or a combination of both sets. Another set of more adequate parameters could be derived, but they did not seem to be appropriate for describing the ion pair-water cluster charge distribution over a wide range of NaI internuclear separations. Thus, it appears that the quadratic expression in the atomic charges assumed for the atomic energy may not be a very good representation of the polarization energy for the complex molecular systems studied here, and the method does not seem readily applicable to chemical systems that react or dissociate. The Rappé group is presently developing extensions of the charge equilibration method to reacting systems (A. K. Rappé, private communication).
137. Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. J.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput. Chem. 1993, 14, 1347.
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157. - solvated in separate clusters, with W(r) defined to be zero in this situation, thereby defined as an asymptotic reference free energy.
158. The convergence referred to is "local", in that contributions from more than a few kT units above the SSIP minimum are negligible, so long as one restricts the integration to the neighborhood of the SSIP well.
159. The CIP cluster diameter is simply estimated as the largest intermolecular O-H distance in the cluster structure, and the average cluster dimension is found by averaging over a few thousands cluster configurations. Since the upper bound of the SSIP integral is in practice always smaller than the CIP cluster diameter, the SSIP population integral obviously does not include configurations corresponding to "free" ions solvated in separate clusters.
160. Simulations of NaI in liquid water, with the same model potentials as employed here, are underway to make a more quantitative comparison between clusters and bulk solution results. Peslherbe, G. H.; Koch, D., unpublished results.
161. The polarization of the water molecule does not depend on its local environment and is only represented in an average way with the TIP4P model. The dipole moment of the TIP4P water is close to that of liquid water.
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174. The method actually proves exact for point charges.
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176. -3 convergence and (b) the approximation in eq 13 is most similar to that made in the numerical model calculations to which it is compared in Figure 6.
177. The evaporative ensemble model has been discussed and/or reviewed in: Klots, C. E. Nature 1987, 327, 222. Klots, C. E. Int. J. Mass Spectrom. Ion Processes 1990, 100, 457, Klots, C. E. Z. Phys. D 1991, 20, 105. Klots, C. E. Z. Phys. D 1991, 21, 335. Klots, C. E. J. Chem. Phys. 1993, 98, 1110.
178. The evaporative ensemble model has been discussed and/or reviewed in: Klots, C. E. Nature 1987, 327, 222. Klots, C. E. Int. J. Mass Spectrom. Ion Processes 1990, 100, 457, Klots, C. E. Z. Phys. D 1991, 20, 105. Klots, C. E. Z. Phys. D 1991, 21, 335. Klots, C. E. J. Chem. Phys. 1993, 98, 1110.
179. The evaporative ensemble model has been discussed and/or reviewed in: Klots, C. E. Nature 1987, 327, 222. Klots, C. E. Int. J. Mass Spectrom. Ion Processes 1990, 100, 457, Klots, C. E. Z. Phys. D 1991, 20, 105. Klots, C. E. Z. Phys. D 1991, 21, 335. Klots, C. E. J. Chem. Phys. 1993, 98, 1110.
180. The evaporative ensemble model has been discussed and/or reviewed in: Klots, C. E. Nature 1987, 327, 222. Klots, C. E. Int. J. Mass Spectrom. Ion Processes 1990, 100, 457, Klots, C. E. Z. Phys. D 1991, 20, 105. Klots, C. E. Z. Phys. D 1991, 21, 335. Klots, C. E. J. Chem. Phys. 1993, 98, 1110.
181. The evaporative ensemble model has been discussed and/or reviewed in: Klots, C. E. Nature 1987, 327, 222. Klots, C. E. Int. J. Mass Spectrom. Ion Processes 1990, 100, 457, Klots, C. E. Z. Phys. D 1991, 20, 105. Klots, C. E. Z. Phys. D 1991, 21, 335. Klots, C. E. J. Chem. Phys. 1993, 98, 1110.
182. n cluster thermodynamics is being studied in greater detail using quantum Monte Carlo simulations. Peslherbe, G. H.; Faivre, D. unpublished results.
183. In contrast to the MP2 calculations discussed in section II.B.3, which are nonvariational but presumably yield reliable relative energies, CI(S) calculations are not size-consistent; this means that this level of theory is certainly insufficient to describe the NaI ground and first electronically excited state energy curves over the whole range of NaI internuclear separations. Using a not very large basis set like the modified 6-31+G** decreases the size-consistency error (and the small correlation space in CI(S) calculations presumably decreases the basis-set-superposition-error), but also results in a poorer description of the wave function in general. CI calculations can be made size-consistent at the expense of including up to quadrupole excitations, but reliable CI calculations require very large basis sets in any event [see. e.g., ref 71]. It should also be noted that a rigorous treatment of the NaI system should include spin-orbit coupling [see refs 36 and 56], which splits the energy levels of atomic iodine by as much as 0.96 eV [see Moore, C. E. Atomic Energy Lewis; U.S. GPO: Washington, 1958], and certainly must be significant for NaI as well.
184. Note that a more refined treatment such as a multireference CI is more justified for model SSIPs than for CIPs, since the NaI wave function at large internuclear separations is best represented as a combination of ionic and covalent references, especially close to the avoided crossing region. As a result, the present CI(S) results may be more reliable for model CIPs than for SSIPs.
185. Note that the increase in the state energy gap of the ion pair clusters is consistent with the ion pair solvation energies (i.e., the cluster binding energies) calculated with the MP2 level of theory and listed in Table 2.
186. We anticipate that the blue shifting evident in Table 5 for increasing number of solvent molecules would cease with several solvent shells.
187. It is important to note that the results quoted for 6 Åseparations are at separations for which a SSIP is only stable for larger clusters (cf. Table 3); there are no stable SSIP species at this separation for the clusters in Table 5. This however does not compromise the point of Table 5, which is to indicate trends in energy gap, transition dipole moment and oscillator strength for the ion pair upon addition of water solvent molecules.
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189. Liang, C.; Newton, M. D. J. Phys. Chem. 1993, 97, 3199. Cave, R. J.; Newton, M. D.; Kumar, K.; Zimmt, M. B. J. Phys. Chem. 1995, 99, 17501.
190. This aspect was first clarified in discussions of C. Jouvet (Orsay) and J.T.H.
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194. Fawcett, W. R.; Tikanen, A. C. J. Mol. Liq. 1997, 73-74, 373.
195. Peslherbe, G. H.; Nguyen, T. N., work in progress.
196. Peslherbe, G. H.; Harpham, M. R.; Ladanyi, B. M.; Hynes, J. T., work in progress.
197. Peslherbe, G. H., unpublished results.
198. n (n = 12) may exist preferentially as CIPs at room temperature. In light of our present findings for water, these clusters might thus have optically accessible excited states and could be involved in the cluster photodissociation experiments unless some alternative CTTS mechanism is involved. These issues deserve further investigation.