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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!!