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The sign preference of hydrogen bonded aqueous ionic clusters
The importance of a clear and insight understanding of ioninduced nucleation phenomena for a number of issues related to the Earth climate, air quality, public health and various technologies is well established [
Initial generated structures were treated initially by semiempirical PM3 method and then by PW91PW91/631+G*. Finally, the most stable (within ∼4 kcal/mole from the lowest energy isomer) structures obtained at PW91PW91/631+G* level have been optimized at PW91PW91/6311++G(3df.3pd) level. PW91PW91/6311++G(3df,3pd) has been used to obtain both equilibrium geometries and thermochemical properties from computed vibrational spectrums. The PW91PW91 density functional has been used in the combination with the largest Pople basis set 6311++G(3df,3pd) that provides quite small basis set superposition error (BSSE). In order to ensure the quality of the obtained DFT results, additional MP2/6311++G(3df,3pd) calculations, both harmonic and anharmonic, have been carried out.
The interest to stepwise Gibbs free energy changes as standalone quantities is related directly to very high sensitivity of nucleation rates to the thermochemistry of initial cluster growth steps.
The difference in the cluster structure has direct impact on the stepwise Gibbs free energy changes associated with the addition of water molecules to the ionic clusters.
As seen from
It is important to note that the sign preference of
Ongoing discussion [
Another important indication of the reasonable performance of the harmonic approximation implemented in the frame of DFT PW91PW91/6311++G(3df,3pd) method has been obtained from the comparison of Zero Point Energies (ZPE) computed using the harmonic and anharmonic approximation. As seen from
The present study leads us to the following conclusions:
The effect of ion sign on the formation free energies of aqueous ionic clusters of identical chemical composition is very strong. For example, the difference in the stepwise Gibbs free energy changes Δ
The harmonic approximation implemented in the framework of the DFT works well in the case of aqueous ionic clusters. Both DFT and ab initio MP2 studies show that the effect of vibrational anharmonicity is mild, and is unlikely a source of large uncertainties in computed free energies.
Support of this work by the U.S. National Science Foundation under grant 0618124 is gratefully acknowledged.
Structures and geometric properties of most stable isomers of
Comparison of experimental and theoretical values of the stepwise Gibbs free energy change Δ
Ratio of anharmonic ZPE to harmonic ZPE.
Experimental and theoretical frequencies of
F^{−}(H_{2}O)

F^{−}(H_{2}O)_{2}
 

PW91^{H}  PW91^{A}  MP2^{H}  MP2^{A}  Exp 
Exp 
PW91^{H}  PW91^{A}  Exp  
1  3768  3556  3952  3770  3690  3687  3776  3578  3700 
2  1844  1783  2069  953  
3  1623  1609  1715  1625  1650  2717  2375  2520  
4  1157  1178  1242  1260  1083–1250  2506  2236  2435  
5  569  598  595  586  
6  436  401  412  441 
[
[
Experimental and theoretical frequencies of
Cl^{−}(H2O)

Cl^{−}(H_{2}O)_{2}
 

PW91^{H}  PW91^{H}  MP2^{H}  MP2^{A}  Exp.  PW91^{H}  PW91^{A}  exp.1  exp.2  
1  3770  3567  3952  3764  3698 

2  3069  2740  3376  3161  3285 
3618  3431  3700 
3686 
3  1626  1612  1678  1743  1650 
3418  3092  3317 
3375 
4  763  782  794  795  745 
3037  2720  3245 
3130 
5  394  352  387  366  
6  215  204  200  196  210 
[
[
[
Experimental and theoretical frequencies of
PW91^{H}  PW91^{A}  MP2^{H}  MP2^{A}  Exp  

1  3769  3575  3948  3759  3689 
2  3223  2871  3506  3257  3270 
3  1619  1578  1669  1633  1642 
4  668  675  699  690  664 
5  323  345  328  310  
6  161  159  158  155  158 
[
Ratio of anharmonic ZPE to harmonic ZPE.
Cl^{−}(H_{2}O)  0.979  Cl^{−}(H_{2}O) MP2  0.985 
Cl^{−}(H2O)_{2}  0.979  
Br^{−}(H_{2}O)  0.982  Br^{−}(H_{2}O) MP2  0.983 
Br^{−}(H_{2}O)_{2}  0.985  
F^{−}(H_{2}O)  0.949  F^{−}(H_{2}O) MP2  0.966 
F^{−}(H_{2}O)_{2}  0.945  
Cl^{+}(H_{2}O)  0.984  Cl^{+}(H_{2}O)MP2  0.981 
Cl^{+}(H_{2}O)_{2}  0.977  
Br^{+}(H_{2}O)  0.981  Br^{+}(H_{2}O)MP2  0.984 
Br^{+}(H_{2}O)_{2}  0.985  
F^{+}(H_{2}O)  0.980  F^{+}(H_{2}O) MP2  0.981 
F+(H_{2}O)_{2}  0.979 