在此研究中 ,我們發展一套方法,藉著成功的預測相對的pKa值,進而得到所有二價三價金屬水合離子準確的絕對pKa值.此外,這套方法也可以幫助決定一些在生物上扮演很重要角色的金屬離子, 例如,Ca2+在水溶液中的CN,6-9實驗上都被發現,Zn2+ 在水溶液解離後, CN會從6變成5或4 ;藉由此套方法,我們可以決定Ca2+在水中主要的配位數 ,以及Zn2+水解後的配位數變化
　　　

We present a computational strategy to derive the absolute pK11 values of divalent and trivalent metal cations in aqueous solution from computed pK11 changes relative to the measured pK11 of a reference metal. We show that our strategy could yield accurate relative pK11 values, which, in turn, can help to determine key properties of biologically important metal cations in aqueous solution such as the dominant CN of Ca2+ and the CN of the deprotonated Zn2+ hexahydrate. The key factors governing the deprotonation of a metal-bound water molecule were identified.

Contents
1 Introduction 2
2 Methods 7
Systems Studied 7
PK11 Calculation 7
Geometry Optimization 8
Gas Phase Free Energy Calculations 9
Effective Solute Radii Optimization 12
3.Results And Discussions
Geometry Calibrations 13
Geometries of the Metal Hydrates 15
Geometries of the Deprotonated Metal Hydrates 18
Validating the Basis Set For Computing Gas Phase Deprotonation Energies 21
Correlation Between Geometrical Parameters and the Gas Phase Basicities 25
Effective Oxygen and Hydrogen Radii from Comparing Computed and
Experimental pK11 26
Testing the Computational Strategy by Predicting the pK11 values of Hg2+ , La3+
and Ga3+ 30
Verifying that Sc3+ , Y3+ and Cu2+ are not hexacoordinated 30
Predicting the dominating CN of Ca2+ 33
Predicting the Prederred CN of the deprotonated Zn2+ Complex 34
List of the Tables
Table 1. Effective Metal Radii from Experimental Hydration Free Energies (in kcal/mol) of Metal Cations. 11
Table 2. Calculated Average Metal-Oxygen (<M-O>) Distance±Standard Deviation (Å) in [M (H2O)n]2+/3+ Complexes Fully Optimized with Various Methods. 14
Table 3. Calculated Bond Distances (Å) and Angles (in degrees) in [M (H2O)n-1
(OH)]+/2+ Complexes Fully Optimized at the B3-LYP/ [SDD/6-31+G(d)] Level. 19
Table 4. Calculated Deprotonation Energies (DEe), Enthalpies (DHg), TDSg and Free Energies for [M (H2O)n]m+ ® [M (H2O)n-1 (OH)](m-1)+ + H+ (in kcal/mol). 24
Table 5. Comparison between Computed and Experimental DpK11 values of [M (H2O)n]2+/3+ Hydrates. 28
Table 6. Predicting the pK11 of Divalent and Trivalent Metal Hydrates 29

(1)Tainer, J. A.; Robers, V. A.; Cetzoff, E. D. Curr.Opionion Ciotechnol
1991, 582-590.
(2)Carver, J. A.; Bradbury, J. H. Biochemistry 1984, 23, 4890-4905.
(3)Lim, C.; Bashford, D.; Karplus, M. J.Phys.Chem 1991, 95, 5610-5620.
(4)Chang, C. M.; Wang, M. K. Journal of Molecular Strcuture 1997, 417,
237-240.
(5)Rustad, J. R.; David, A.; Dixon, K. M.; Rosso, A. R. J.Am.Chem.Soc 1999,
121, 3234-3235.
(6)Marcus, Y. Chem .Rev 1988, 88, 1475-1498.
(7)Yamaguchi, T.; Niihara, M.; Takamuku, T.; Wakita, H.; Kanno, H.
Chemical Physics Letters 1997, 274, 485-490.
(8)Lindqvist-Reis, P.; Lamble, K.; Pattanaik, S.; Persson, I.; Sandstrom, M. J.
Phys. Chem. B. 2000, 104, 402-408.
(9)Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery Jr., J. A.; Stratmann, R.
E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, M. C.;
Strain, K. N.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.;
Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson,
G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.;
Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B.
B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin,
R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.;
Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.;
Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.;
Pople, J. A. Gaussian 98, Revision A.5,; Gaussian, Inc.: Pittsburgh, 1998.
(10)Saebo, S.; Almlof, J. Chem. Phys. Lett. 1989, 154, 83.
(11)Frisch, M. J.; Head-Gordon, M.; Pople, J. A. Chem. Phys. Lett. 1990, 166,
275.
(12)Head-Gordon, M.; Pople, J. A.; J., F. M. Chem. Phys. Lett. 1988, 153,
503.
(13)Head-Gordon, M.; Head-Gordon, T. Chem. Phys. Lett. 1994, 220, 122.
(14)Becke, A. D. J. Chem. Phys 1993, 98, 5648-5652.
(15)Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. 1988, B37, 785.
(16)Perdew, J. P. Phys.Rev.B 1986, 33, 8822.
(17)Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864.
(18)Kohn, W.; Sham, L. J. Phys. Rev. 1965, 140, A1133.
(19)Slater, J. C. Quantum theory of molecules and solids. Vol. 4: The self-
consistent field for molecules and solids; McGraw-Hill: New York, 1974.
(20)Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200.
(21)Fuentealba, P.; Preuss, H.; Stoll, H.; Szentpaly, L. V. Chem. Phys. Lett.
1989, 89, 418.
(22)Szentpaly, L. V.; Fuentealba, P.; Preuss, H.; Stoll, H. Chem. Phys. Lett.
1982, 93, 555.
(23)Friedman, H. L.; Krishnan, C. V. In Water: A comprehensive treatise
1973, 3, 1-118.
(24)Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein,
M. L. J. Chem. Phys. 1983, 79, 926-923.
(25)Baes, C. F.; Mesmer, R. E. The Hydrolysis of Cations 1976.
(26)Rosso, K. M.; Rustad, J. R.; Gibbs, G. V. J. Phys. Chem. A 2002, 106,
8133-8138.
(27)Dean, J. A. Lange's handbook of Chemistry 1987.
(28)Brown, P. L.; Sylva, R. N.; Ellis, J. J.Cehm.Soc.,Dalton Trans. 1985, 723.
(29)Richens, D. T. 1997, 47-49.