Radii and Occupancy of the Shells of Expanded Clusters

The occupancies of the shells of expanded clusters are shown below. The radii are given from the center of a modeled super-cluster (thirteen complete but overlapping icosahedra; 6½ ˣ 280 =1820 water molecules) to the center of the outermost oxygen atoms. The number of water molecules and interstitial cavities are given, together with the percentage of singly (n₁), doubly (n₂), trebly (n₃), and tetra (n₄) hydrogen-bonded water molecules, assuming that no outer water molecules are further hydrogen-bonded. On this basis, the second to last column gives the percentage hydrogen bonding (100% = each water molecule has a share in four hydrogen bonds) within the cluster (see Graph below). The number of

H–bonds/H₂O give an indication of the enthalpic stability/H₂O of the cluster, with the entropic stability inversely indicated by the number of water molecules present. The larger clusters, therefore, become relatively more stable at lower temperatures and higher enthalpic stability per H₂O molecule.

**Shell content in the expanded cluster**
Shell	Radius nm	Water molecules	Cavities	% n₁	% n₂	% n₃	% n₄	% H-bonds	H-bonds /H₂O
	0.00		1
1	0.38	20		0	0	100	0	75.0	1.50
	0.54		12
2	0.66	20		50	0	0	50	62.5	1.25
3	0.80	60		0	0	60	40	85.0	1.70
	0.97		12
4	1.07	60		38	0	0	63	71.9	1.44
5	1.14	60		0	0	55	45	86.4	1.73
6	1.23	60		0	0	43	57	89.3	1.79
	1.35		60
7	1.43	60		18	0	18	65	82.4	1.65
8	1.48	60		30	0	0	70	77.5	1.55
9	1.51	60		0	13	26	61	87.0	1.74
	1.51		12
10	1.59	30		0	18	12	69	87.8	1.76
11	1.63	60		0	16	11	73	89.1	1.78
12	1.75	60		0	10	20	70	90.2	1.80
13	1.78	60		9	9	9	73	86.6	1.73
	1.81		60
14	1.82	60		8	8	8	75	87.7	1.75
15	1.87	20		0	16	11	73	89.3	1.79
16	1.91	120		0	14	9	77	90.8	1.82
17	2.06	60		6	13	2	78	88.2	1.76
18	2.07	60		6	6	14	74	88.9	1.78
19	2.10	120		0	5	13	82	94.1	1.88
	2.12		12
20	2.17	20		2	5	11	82	93.4	1.87
	2.17		60
21	2.19	30		2	3	16	80	93.5	1.87
22	2.23	60		2	2	15	81	93.9	1.88
23	2.27	60		0	7	14	79	93.0	1.86
24	2.33	60		4	4	13	78	91.0	1.82
25	2.35	120		0	12	12	75	90.8	1.82
26	2.41	120		0	0	23	77	94.3	1.89
	2.43		12
27	2.47	120		0	7	11	82	93.8	1.88
28	2.47	60		0	0	20	80	94.9	1.90
	2.47		60
	2.54		20
29	2.66	60		0	0	20	80	95.1	1.90
	2.94		12

Hydrogen bonding in expanded water clusters.