Combined Quantum Mechanical and Molecular Mechanical Methods

Chapter 12

Downloaded by NORTH CAROLINA STATE UNIV on December 27, 2017 | http://pubs.acs.org Publication Date: December 28, 1998 | doi: 10.1021/bk-1998-0712.ch012

RISM-SCF Study of Solvent Effect on Electronic Structure and Chemical Reaction in Solution: Temperature Dependence of pKw 1

1

1

Fumio Hirata , Hirofumi Sato , Seiichiro Ten-no , and Shigeki Kato

2

1

Division of Theoretical Study, Institute for Molecular Science, Okazaki, 444, Japan Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606, Japan 2

The RISM-SCF method, or a hybridized method of the electronic structure theory and statistical mechanics of liquids, is applied to the auto-ionization process in water putting special stress on its temperature dependence. It is found that changes in the solvation free energies with increasing temperature drive the chemical reaction toward neutral species while energies associated with solvent-induced reorganization of electronic structure make opposite contribution. The actual temperature dependence is dominated by the latter contribution, which gives rise to good agreement with experimental results. It is suggested that the observed temperature dependence of pKw is related to the great sensitivity of the electronic structure of OH on solvent effect. -

A chemical reaction is undoubtedly the most important issue in the theoretical chemistry, and the electronic structure is a key to solve the problem. As long as molecules in the gas phase are concerned, theories for the electronic structure have been enjoying its great success. However, when it comes to molecules in solution, the stage of theories is still an infant. Since it is anyway impossible to solve the Schrödinger equation for entire system including about 10 solvent molecules, a most promising approach so far is any type of hybrid between classical solvent and quantum solute. Roughly three types of hybrid approaches have been appeared depending on how to treat the solvent degrees of freedom: molecular simulations, continuum models, and the integral equations. The continuum models employ the electrostatic theory in order to evaluate the reaction field exerted on the solute from the continuum dielectric regarded as a solvent. A variety of different methodologies including Onsager's reaction field, Born's model and the image charge models have been implemented for the reaction field. An obvious advantage of the method is its handiness, while well-documented disadvantages are the lack of molecular picture of solvent and an artifact introduced at the boundary between solute and solvent. The integral equation method is free from such disadvantages, and gives a microscopic picture for the solvent effect on the electronic structure of molecule with a reasonable 23

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©1998 American Chemical Society Gao and Thompson; Combined Quantum Mechanical and Molecular Mechanical Methods ACS Symposium Series; American Chemical Society: Washington, DC, 1998.


189 amount of computation time. We have recently proposed a new method refereed to as RISM-SCF based on the integral equation theory of molecular liquids (RISM) (/),(2)and the ab initio electronic structure theory(3). The integral equation approach replaces the reaction field in the continuum models by a microscopic expression in terms of the site-site radial distribution functions between solute and solvent. The statistical solvent distribution around solute is determined by the electronic structure or the partial charges of solute, while the electronic structure of solute is influenced by the solvent distribution. Therefore, the Hartree-Fock equation and the RISM equation should be solved in a self-consistent manner. It is the self-consistent determination of the solute electronic structure and the solvent distribution around the solute that features the RISM-SCF procedure. It has been further extended to the electronic structure with multiconfigurations, which also enables us calculation of optimized geometry in solutions(4). The method has been successfully applied to a variety of chemical processes in solution including the coupled solvent and substitution effects on proton affinity and tautomerization reaction in organic solvents. (3-6) As an example of the applications, here, we report a study for autoionization of liquid water putting special stress on its temperature dependence. ( Sato, H. ; Hirata, F., /. Phys. Chem. in press) A water molecule has amphoteric character, which means it can act as both an acid and a base. The autoionization equilibrium process in water,

Η 0 + Η 0 ptf (273.15) T

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The difference of the electronic energies in vacuo, AE iec > makes a dominant contribution to determine the "absolute" value of p £ w . However, A E i c is essentially independent of Τ, and it contributes to temperature dependence of pKw in aqueous phase only through \/T in Eq. (17).


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Results and discussion Solvent Induced Molecular Polarization and Solvation Structure. Temperature dependence of effective charges on oxygen atoms qo, which represents a change in the electronic structure induced by solvent effect, is shown in Figure 1. The effective charges were determined in such a way that electrostatic potential produced by the charges fits best with those arising from the electronic cloud of the solute (3). Compared with the gas phase values, -0.766 ( water ) , -0.633 ( hydronium ion ), and -1.128 ( hydroxide ion ), charges in all the species are largely enhanced by the interaction with surrounding solvent molecules. The change in the electronic structure or the polarization is appreciably reduced as temperature increases. The behavior can be explained in terms of the increased molecular motion such as rotation. As the motions increase, the hydrogen-bond between the solute species and solvent molecules is weakened, and the polarizing effects becomes less and less. Consequently, the electronic structure is relaxed toward that in the isolated molecule as temperature increases. Among three species, the greatest relaxation of polarization is observed in the hydroxide ion, which can be understood in terms of the temperature dependence of the hydration structure of "solute" molecules. In Figure 2, we show three sets of pair correlation functions (PCF) between (a) solute oxygen and solvent hydrogen, and (b) solute hydrogen and solvent oxygen, at 293.15 K . It is readily seen that sharp peaks are found around 2.0 Â in a pair of the ionic species and atoms with opposite charges in water molecules. An oxygen atom in the hydroxide ion has a large negative charge and attracts hydrogen sites of solvent water acutely. In contrast, a hydrogen atom in the hydronium ion attracts oxygen sites of solvent, but in a moderate manner. Water has an intermediate character of these two ions. The highest peak in PCF between hydroxide Ο and water Η concerns the greatest effective charge of this ion shown in Figure 1. The results indicate that the electronic structure of the hydroxide ion is most sensitive to the electrostatic field of solvent and that it is most easily to be polarized. Shown in Figure 3 is alteration of PCF due to temperature change, Δχ g(T)=g(T)-g(273.15K). The oxygen site of hydronium ion has the least negative charge among the three species, and Aj g(T) is rather loose and broad. But, changes in the others are extremely sharp and large. Especially, a negative deviation around 2.0 À corresponds to change in height of the first peak in PCF, being indicative of a drastic change in hydrogen bonds as temperature increases. It should be noted that Δ τ g in hydroxide ion is about ten times greater than that in water. The positive deviation around 1.5 À is a consequence of the increased probability of

Gao and Thompson; Combined Quantum Mechanical and Molecular Mechanical Methods ACS Symposium Series; American Chemical Society: Washington, DC, 1998.

194

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T/[K] Figure 1. Temperature dependence of electronic structure represented by effective charge on oxygen site: (a) hydronium ion; (b) water; (c) hydroxide ion.



195

Figure 2. Pair correlation function ( PCF ) at room temperature ( 293.15K ): (a) solute oxygen and solvent hydrogen; (b) solute hydrogen and solvent oxygen.



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Δ χ pK δμ, and Δχ pK kin are related, respectively, to the corresponding free energy changes, AE i c> ΔδΕ ΐεο Δδμ, and AôEkin by Eq. (16). In order to facilitate the inspection, a sum of Δχ pK δμ and Δχ pK ac is also plotted in the figure. Those contributions are very large but they compensate each other, and the sum shows slight and positive dependence on temperature. It is important to note that the components in Δχ pK show different temperature dependence from corresponding terms in AG \(T) due to "Γ" which appears in the denominator in Eq. (17). It is readily seen from the figure that the temperature dependence of pK^ is determined by an interplay of several contributions with different physical origins. It is also clear that the temperature dependence is dominated by Δχ p K after the largest contributions compensated each other. As a consequence, the theoretical results for the temperature dependence of the ionic product show good agreement with experiments. To summarize, so-called solvation free energies, or δμ, contribute to a positive temperature dependence on Δχ p#\v> while the energies associated with reorganization of electronic structure give rise to the opposite temperature dependence. In other words, the solvation free energies contribute to make a water molecule less dissociative with increasing temperature, which is in accord with the intuitive consideration in terms of the reduced hydrogen-bonding. On the other hand, the electronic reorganization energy contributes to facilitate the dissociation as temperature increases. The latter dominates the temperature dependence of the ionic product. The temperature dependence is in turn largely determined by characteristics of the electronic structure of O H , because the temperature dependence of the electronic reorganization energy is dominated by that species. Improvements of the theoretical calculations, especially in descriptions of electronic structures, can be expected for ApKw. However, as long as the temperature dependence is concerned, the qualitative feature of our results seems to be insensitive w

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280

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Τ/Κ Figure 4. Temperature dependence of p K of water. Dashed line indicates the experimentally observed value, while all other solid lines are computed by RISM - SCF / MCSCF procedure. w


200 to such elaboration in the quantum description according to our preliminary calculations based on the second - order M0ller - Plesset perturbation. Acknowledgments The present study is supported by Grants-in-Aid for Scientific Research form the Japanese Ministry of Education, Science, Sports, and Culture.


References

(1) Chandler, D.; Andersen, H. C. J. Chem. Phys. 1972, 57, 1930 . (2) Hirata, F.; Rossky, P. J. Chem. Phys. Lett. 1981, 84, 329 . (3) Ten-no, S.; Hirata, F.; Kato, S. Chem. Phys. Lett. 1993, 214, 391: Ten-no, S.; Hirata F.; Kato, S. J. Chem. Phys. 1994, 100, 7443. (4) Sato, H.; Hirata, F.; Kato, S. J. Chem. Phys. 1996, 105, 1546. (5) Kawata, M.; Ten-no, S.; Kato, S.; Hirata, F. Chem. Phys. 1996, 203, 53. (6) Kawata, M.; Ten-no, S.; Kato, S.; Hirata, F. J. Phys. Chem. 1996, 100, 1111. (7) Pearson, R. G. J. Am. Chem. Soc. 1986, 108, 6109. (8) Dobos, D. Electrochemical data ; a handbook for electrochemists in industry and universities, elsevier scientific publishing Inc., Amsterdam, 1975. (9) Tuckerman, M.; Laasonen, K.; Sprik, M.; Parrinello, M. J. Phys. Chem. 1995, 99, 5749. (10) Chipot, C.; Gorb, L. G.; Rivail, J.-L. J. Phys. Chem. 1994, 98, 1601. (11) Tortonada, F. R.; Pascual - Ahuir, J.-L.; Silla, E.; Tuñön, I. J. Phys. Chem.. 1993, 97, 11087. (12) Emsley, J.; Lucas, J.; Overill, R. E. Chem. Phys. Lett. 1981, 84, 593. (13) Gao, J. Acc. Chem. Res. 1996, 29, 298. (14) Tanaka, Y.; Shiratori, Y.; Nakagawa, S. Chem. Phys. Lett. 1990, 169, 513. (15) Singer, S. J.; Chandler, D. Mol. Phys. 1985, 55, 621. (16) Maw, S.; Sato, H.; Ten-no, S.; Hirata, F. Chem. Phys. Lett. 1997, 276, 20. (17) Poirier, R.; Kari, R.; Csizmadia, I. G. Physical science data 24, Handbook of gaussian basis set, Elsevier: New York, 1985. (18) Berendsen, H. J. C.; Postma, J. P. M.; van Gunstern, E. F. J. Hermans, in Intermolecular Forces, ed. Pullman, B., Ed; Reidel, Dordrecht, 1981. (19) CRC Handbook of chemistry and physics, 68th ed.; CRC Press: Boca Raton, FL, 1987. (20) Chong, S.-H.; Hirata, F. J. Phys. Chem. Β 1997, 101, 3209.


Combined Quantum Mechanical and Molecular Mechanical Methods

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