J. Phys. Chem. 1995,99, 12450-12455
12450
Examining the Cubic, Fused Cubic, and Cage Structures of and 21: Do Fused Cubic Structures Form?
(H20),
for n = 8, 9, 12, 16, 20,
Arshad Khan Chemistry Department, The Pennsylvania State University, DuBois, Pennsylvania 15801 Received: October 4, 1994; In Final Form: May 2, 1995@
The structures and stabilization energies (SE) of water clusters, (HzO),, with n = 8, 9, 12, 16, 20, and 21, were calculated by applying the intermediate neglect of differential overlap self-consistent field restricted Hartree-Fock method (INDO SCF RHF) after proper parametrization. These cluster structures include the neutral cubic forms for 8 and 9 mers, fused cubic 12, 16, 20, and 21 mers and cage structures for 16, 20, and 21 mers. In addition, the structure and SE values of the protonated fused cubic 20 and 21 mer clusters were calculated and compared with those of the cage structures. A closer examination of the fused cubic and the cage structures combined with the experimental evidence suggests that the fused structures are not likely to form. The present study also explains the observed magic numbers in experiments.
1. Introduction The structure and stability of different water clusters has been the subject of quite a few recent theoretical and experimental studies. While most of the experimental studies involve large (H20), clusters with n > 19,I-li the theoretical studies were mostly limited to smaller clusters with n values ranging from 2 to 7.I2-l8 Recently, several theoretical results were reported on o c t a m e r ~ ' ~ -and ~ ' larger clusters.z2-z8 In all these studies with n = 8 (octamer), the most stable structure was predicted to be a distorted cube. Among the larger clusters (up to 20 mer), several groups have predicted fused structure to be the most table.^^-^^ These groups applied the molecular dynamics (MD) method of calculation, assuming rigid monomers and certain potential energy function^.^^-^' The clathrate structure having a dodecahedral arrangement of 0 atoms in each of the neutral 20 mers,22,z3,27,28 and the protonated 20 and 21 merz7clusters has already been reported. The calculated structural featuresz7 on the protonated 20 and 21 mer clusters agree quite well with the experimental results of Castleman and co-workers." In these experiments, the neutral clusters were first made by expanding a gas mixture containing trimethylamine (TMA) and water molecules. The neutral clusters were then ionized and the resulting protonated clusters were detected. Since each TMA molecule binds a nonhydrogen-bonding H (NHB H) atom, the analysis of the products predicts the number of NHB H atoms in these protonated clusters and, hence, their structures. The protonated 20 and 21 mer clusters were observed to bind a maximum of 11 and 10 TMA molecules, respectively, and, hence, suggest the existence of 11 and 10 NHB H atoms in these clusters. On the basis of the number of NHB H atoms, the protonated 20 and 21 mer clusters were postulated to have the same basic dodecahedral arrangements of 0 atoms as the neutral 20 mer cluster. The optimized clathrate structures of (H20)20H+ and (HzO)ZIH+ indeed have 11 and 10 NHB H atoms, respectively, and can explain the experimental results with TMA molecules. Even though the clathrate structures can explain the experimental results, one cannot establish unambiguously the predominantly formed cluster type in the experiment solely on the basis of the above theoretical results. As mentioned earlier, a recent @
Abstract published in Advnnce ACS Absrrucrs, July 1, 1995.
theoretical study suggests that the neutral 20 mer fused cubic cluster is more stable than the 20 mer clathrate structure,23and, hence, one may expect the formation of fused cubic structures in the gas phase. This result prompted reexamination of the stability of both the fused cubic and clathrate structures. Even though the well characterized magic number peak in experiment is known to be due to the (Hz0)21H+(protonated 21 mer) cluster, no previous studies report the structure or stability of the neutral (H20)21 fused cubic or cage structure, which after protonation may form the dominant magic number cluster, (H20)21Hf. Furthermore, the previously reported results on the neutral fused cubic cluster^^^-^^ do not provide sufficient detailed structural information, such as HOH or OOH angles (H in between 0 atoms) for examining the likelihood of formation of these clusters. In this paper, detailed structural features and stabilization energy (SE) values (relative to separated constituent molecules) for neutral 8, 9, 12, 16, 20, and 21 mer clusters and protonated 20 and 21 mer clusters have been discussed and the question of fused cubic cluster formation has been critically examined.
2. Methods and Calculations We optimized the cluster structure and calculated the SE values by applying the INDO SCF RHF method after appropriate parametrization. The ZINDO series of programs (in Hyperchem package), developed by Zemer and c o - w o r k e r ~ , ~ ~ - ~ ~ were used for this purpose. The parametrization was necessary as the default ZINDO parameters severely underestimated the 0-0 distance in the dimer and overestimated its stabilization energy value by 2-fold. The new set of /3 s, p, and d parameters (defining resonance integral) for H and 0 atoms were 0.0, 0.0, 0.0, and 28.0, 28.0 and 0.0, respectively. These sets of parameters provided a dimer binding energy (relative to separated monomer molecules) of 5.2 kcal/mol, which result agrees quite well with the experimental value of 5.4 kcaUm01.~' The 0-0 distance in the dimer was 2.78 A and was underestimated by about 0.20 8,. On the basis of the test results of the neutral (this work) and the protonated dimer,z7we can say that the neutral structures require an 0-0 distance correction by +0.20 8, and the protonated clusters require no such c o r r e c t i ~ n . ~ ~ In addition, the nearest neighbor 0-H distance is overestimated by about 0.14 A, and, hence, a correction is applied to report
0022-365419512099-12450$09.00/0 0 1995 American Chemical Society
Examining Structures of (H20),
J. Phys. Chem., Vol. 99, No. 33, 1995 12451 6
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Figure 1. (H2O)s structure presented with eight oxygen atoms at the comers of a distorted cube. The H bonds are shown with dotted lines. There are four NHB H atoms shown with numbers 1-4.
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