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Solvation Free Energy of Metal Ions: Experiments and Calculation
Chun-Shan Zuo
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Reaction in Chemistry
A(gas) + B(gas) C(gas)
A(sol) + B(sol) C(sol)
rG(gas)
rG(sol)
(Model system)
(Real system)
G(sol,A) G(sol,B) G(sol,C)
rG(sol)=rG
(sol)+G(sol,i)
Backgrounds
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Example for solvation free enregies in reaction
the relative electronic energy (E, in point line), Gibbs energy in gas phase (Ggas, in bold dashed) Gibbs energy in water solution from the optimized geometries both in gas phase (Gsol, in normal line) in condensed phase (Gsol, thick continuous lines)
Ardura et al., J. Phys. Chem. B 2005, 109, 23618-23623
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A(gas) A(sol)
G*(solv)=-RT ln{[A(sol)]/[A(gas)]}
Single species in gas phase and in solution
sol(A)=sol(A)+RT ln[A(sol)]
gas(A)=gas(A)+RT ln[A(gas)]
sol(A) - gas(A)=0
sol(A) -
gas(A)=G*(solv)(A)
sol(A)=gas(A)+G*
(solv)(A)+RT ln[A(sol)]
As chemical potential can be defined:
And
Then
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positive negative ion
i on OH- F- Cl - Br - I -
H+ -1535. 3 -1533. 4 -1408. 7 -1382. 0 -1344. 6Li + (-960. 2) -958. 1 -833. 8 -807. 0 -769. 5Na+ (-854. 6) -852. 6 -728. 0 -701. 2 -663. 9K+ (-782. 8) -780. 8 -656. 2 -629. 4 -592. 1Rb+ (-760. 1) -758. 2 -633. 6 -606. 8 -569. 4
Hf¡ã[H+(aq)] = Hf¡ã[H
+(g)]+ Haq¡ã[H+]
Haq¡ã,con[A+(aq)] = Haq¡ã[A+(g)]- Haq¡ã[H+(aq)]
Haq¡ã,con[B-(aq)] = Haq¡ã[B-(g)]+ Haq¡ã[H+(aq)]
Solvation Free Energy of Ion Pair in Aqueous
For hydration enthalpy should be calculated as:
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i on n=1 2 3 4 5 6
Li + -142. 3 -250. 2 -336. 8 -405. 4 -463. 6 -514. 2H3O
+ -144. 0 -230. 5 -302. 0 -356. 8 -407. 0 -454. 3
Na+ -104. 6 -187. 4 -251. 8 -307. 0 -355. 1 -399. 9K+ -75. 7 -143. 1 -198. 3 -247. 7 -292. 5 -334. 3Rb+ -66. 9 -123. 8 -174. 8 -221. 7 -265. 6OH- -109. 6 -188. 3 -257. 7 -317. 1 -376. 1F- -97. 5 -172. 4 -233. 1 -290. 4 -344. 0 -389. 6Cl - -60. 2 -113. 8 -162. 8 -208. 4 -248. 1 -284. 9Br - -54. 4 -104. 6 -152. 3 -198. 3 -243. 4 -286. 5I - -43. 9 -84. 6 -123. 5 -162. 0 -199. 7H2O 0. 0 -15. 7 -29. 1 -45. 7 (-66. 4)b (-88. 7)b
Water Clustered-Ion Solvation Free Energy
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Solvation enthalpy for proton in aqueous
Tissandier, et al, JPCA, 1998,102,7787
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Absolute Hydration Enthalpy and Free Energy
Tissandier, et al, JPCA, 1998,102,7787
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Explicit model in solvation free energy
-96.4kcal/mol -102.4 -104.6 -104.3
Zhan et al., J. Phys. Chem. A 2004, 108, 2020-2029
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Implicit model.. UAHF Radii(IEF-PCM).
Barone, Cossi, and Tomasi, J. Chem. Phys. 1997,107, 3210-3221
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Hydration free energies with different Radii.
Barone, Cossi, and Tomasi, J. Chem. Phys. 1997,107, 3210-3221
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Gibbs energy of solvation of A- and BH+ ions
Pliego Jr et al., PCCP, 2002, 4, 1622-1627
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Modification on atomic radii
Elvis S. Böes, et al., Chem. Phys. 2006, 331, 142-158
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Relationship between cation and constants
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y = -0. 0016x + 0. 9494
0. 9
0. 92
0. 94
0. 96
0. 98
1
-35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35G(kcal / mol )
r (An
gstr
om)
Ionic radii determination (for Be2+)
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SCAR vs Exp
y = 0.9689x + 14.579
R2 = 0.9999
-1200
-1000
-800
-600
-400
-200
0
-1200 -1000 -800 -600 -400 -200 0
Exp
SC
AR
UAHF vs. Exp
y = 0.7688x - 5.5759
R2 = 0.986
-1000
-800
-600
-400
-200
0
-1200 -1000 -800 -600 -400 -200 0
exp
UA
HF
Computational results and experiments
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MPy BPy MBPy
N
N
N N
N Mn+
Mn+
N N
Mn+
MPhen
r(M-N)
r(M-N) r(M-N)
rGU = 3. 929rG
expt - 13. 849
R2 = 0. 455
-80. 0
-70. 0
-60. 0
-50. 0
-40. 0
-30. 0
-20. 0
-10. 0-11. 0-9. 0-7. 0-5. 0-3. 0-1. 0
rG
expt
rG
U
rGmod = 1. 597rGexpt + 5. 129
R2 = 0. 726
-17. 0
-12. 0
-7. 0
-2. 0
3. 0
8. 0-11. 0-9. 0-7. 0-5. 0-3. 0-1. 0
rG
expt
rG
mod
Association constants for pyridines
Zuo, C.-S.; Olaf, W.; Wu, Y.-D. J. Phys. Chem. A 2009, 113, 12028–12034
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Association constants for pyridines
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A B C D E
Ions rGexptl rGgas rGU rGSMD rGSCAR
AgI -4.6 -47.1 -15.4 -5.8 -4.6
Mg2+*b -4.7 -156.9 -34.4 -28.5 3.3
Ca2+*b -1.9 -114.6 -18.0 1.4 0.5
Sr2+b -1.2 -95.5 -12.4 3.8 1.3
Ba2+b -1.0 -81.8 -3.0 10.6 0.3
MnII(5/2) -4.9 -153.5 -30.2 -0.9 -1.4
FeII(2) -5.9 -173.3 -54.5 -29.2 -3.4
CoII(3/2) -7.1 -193.4 -57.8 -20.0 -11.1
NiII(2) -8.4 -198.8 -59.1 -91.6 -5.6
CuII -11.7 -222.6 -130.7 -23.9 -13.0
ZnII -7.5 -197.0 -51.2 -14.5 -6.4
PdII(2) -12.4 -192.7 -51.3 -20.2 -8.8
HgII -14.0 -176.2 -21.2 -19.1 -15.0
PbII(s1) -7.4 -114.9 -60.4 -20.2 -7.4
SD 29.9 23.0 2.8
MUE 36.2 15.2 2.4
Association constants for amino acids
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rG
m = 1. 799rGexpt - 0. 2179
R2 = 0. 7257
rG
U = -0. 0371rGexpt - 56. 282
R2 = 1E-05
rG
S = 2. 6709rGexpt - 8. 7105
R2 = 0. 2636
-140. 0
-120. 0
-100. 0
-80. 0
-60. 0
-40. 0
-20. 0
0. 0
20. 0
40. 0
-12. 0 -10. 0 -8. 0 -6. 0 -4. 0 -2. 0 0. 0
rG
comp.
rG
expt .
Association constants for cation-anion
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Association constants for cation-anion
23Angew. Chem. Int. Ed. 2007, 46, 8295-8298
Estimate in cation- interaction
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J. Med. Chem., 1999, 42, 4474
JACS., 1984, 106, 8240JACS., 1999, 121, 8405
Eur. J. Org. Chem. 2000, 2967
Estimate in cation- interaction
-9.9
-19.3
-20.4
-12.0
-12.6
-12.5
-28.9
-22.9
-13.9
-14.5
25Chem. Comm. 2007, 2240
2.452
2.472
2.446
Molecule design
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Acknowledgement
Thanks for person list below:
Prof. Wu Yun-Dong Prof. Olaf Wiest
Ren Lin-Lin Zhou Xiao-Yan
Zhang Jun-Qi Wang Xin-Gang
Liu Lei-Lei
This research was supported by the Science Foundation of Henan Province(094300510101 and 102300410152)
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Thanks for attention!!