Stoyanov and Reed1 have reported the IR spectrum of strong acid in water, trying to identify the true nature of the hydrated proton. In other words, what is n in the formula H(H2O)n+? The key to addressing this problem is to carefully measure the IR spectrum and then remove the signals due to (a) water associated with (or perturbed by) the anion and (b) bulk water. Simply subtracting out bulk water overcorrects because some waters are associated with the proton. By properly scaling the bulk water peak, they identify n as six. Deconvolution of the spectrum of H(H2O)6+ gives peaks at 3134 ±12, 2816 ± 40, 1746 ± 11, 1202 ± 4 and 654 ± 12 cm-1.

They suggest that the hydrated proton has structure 3, which is distinguished from previous proposals of H(H2O)4+ 2 and H(H2O)2+ 1.

Somewhat surprising is that these authors did not compute the structures of these ions and their IR spectrum. So just to motivate further work I have computed the spectrum of the three ions at PBE1PBE/6-311++G(2df,p)//PBE1PBE/6-31+G(d,p) (Figure 1) and their uncorrected IR frequencies within the range 500-3000 cm-1 (and intensities greater than 50) are listed in Table 1.

1

2

3

Figure 1. PBE1PBE/6-31+G(d,p) structures of 1 and 3 and PBE1PBE/6-311++G(2df,p) of 2.

Table 1. Computed frequencies (cm-1) and intensities of 1-3.

 1 

 2 

 3 

 ν 
1082
1490
1535
1786

 I 
2377
302
122
1554

 ν 
1024
1199
1634
2864
2994

 I 
66
313
75
3180
151

 ν 
857
887
938
1091
1465
1620
1640
1643
1647
1780

 I 
709
63
137
3310
237
117
80
154
44
1002

The comparison between experiment and computation leaves something to be desired and more careful computation is clearly warranted. In addition, these types of complexes are likely to be dynamic, and so multiple different configurations and conformations will need to be sampled. So, again to promote contributions to this problem, I offer three other configurations of H(H2O)6+, shown in Figure 2. Their computed IR frequencies are listed in Table 2. Any additional interested takers?

3b
-0.48 (0.60)

3c
3.41 (4.80)

3d
-1.33 (1.33)

Figure 2. PBE1PBE/6-31+G(d,p) structures of 3b-3d along with their relative (to 3) electronic energy (kcal mol-1 and electronic energy with ZPE (in parenthesis).

Table 2. Computed frequencies and intensities of 3b-3d.

  3b  

  3c  

  3d  

 ν 
546
834
845
959
1123
1258
1632
1638
2550
2703

 I 
52
136
153
86
60
232
90
69
4347
1791

 ν 
503
584
605
618
693
882
1247
1582
1645
1706
2013
2267

 I 
154
307
53
148
117
171
199
582
115
238
3235
2100

 ν 
603
731
800
928
952
1283
1637
1818
2684
2841

 I 
89
166
162
101
92
283
224
170
1877
2808

References

(1) Stoyanov, E. S.; Stoyanova, I. V.; Reed, C. A., "The Structure of the Hydrogen Ion (Haq+) in Water," J. Am. Chem. Soc., 2010, 132, 1484-1485, DOI: 10.1021/ja9101826