Radii and Occupancy of the Shells of Expanded Clusters

The occupancy 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). The number of water molecules and interstitial cavities are given, together with the fraction 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 last column gives the percentage hydrogen bonding within the cluster (see Graph below).

**Shell content in the expanded cluster**
Shell	Radius nm	Water molecules	Cavities	n₁	n₂	n₃	n₄	% H–bonds
	0.00		1
1	0.39	20		0.00	0.00	1.00	0.00	75
	0.53		12
2	0.66	20		0.50	0.00	0.00	0.50	63
3	0.79	60		0.00	0.00	0.60	0.40	85
	0.98		12
4	1.06	60		0.38	0.00	0.00	0.63	72
5	1.15	60		0.00	0.00	0.55	0.45	86
6	1.23	60		0.00	0.00	0.43	0.57	89
	1.35		60
7	1.43	60		0.18	0.00	0.18	0.65	82
8	1.48	60		0.30	0.00	0.00	0.70	78
	1.50		12
9	1.52	60		0.00	0.13	0.26	0.61	87
10	1.57	30		0.00	0.18	0.12	0.69	88
11	1.62	60		0.00	0.16	0.11	0.73	89
12	1.74	60		0.00	0.10	0.20	0.70	90
	1.80	60	60
13	1.81	60		0.09	0.09	0.09	0.73	87
14	1.87	20		0.08	0.08	0.08	0.75	88
15	1.91	120		0.00	0.16	0.11	0.73	89
	2.02		12
16	2.05	60		0.00	0.14	0.09	0.77	91
17	2.06	60		0.06	0.13	0.02	0.78	88
18	2.08	120		0.06	0.06	0.14	0.74	89
	2.11		60
19	2.16	20		0.00	0.05	0.18	0.77	93
20	2.22	30		0.02	0.05	0.16	0.77	92
21	2.25	60		0.02	0.03	0.21	0.75	92
22	2.26	60		0.02	0.02	0.20	0.76	93
23	2.35	120		0.00	0.07	0.14	0.79	93
24	2.37	60		0.09	0.06	0.04	0.81	89
25	2.40	120		0.00	0.12	0.08	0.79	92
	2.46		60
26	2.49	20		0.00	0.00	0.23	0.77	94
27	2.49	60		0.04	0.00	0.18	0.78	93
28	2.51	120		0.00	0.00	0.20	0.80	95

Hydrogen bonding in expanded water clusters.