V. Shilpi,
Surinder Pal Kaur and
C. N. Ramachandran*
Department of Chemistry, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India-247667. E-mail: ramcnfcy@iitr.ac.in
First published on 17th August 2015
Fused cages with maximum number of t1d bonds are modelled by combining two dodecahedral cages (DD + DD), two irregular-dodecahedral cages (IDD + IDD) and a dodecahedral cage with an irregular-dodecahedral (DD + IDD) cage and are studied using the dispersion corrected density functional method B97-D in conjunction with the cc-pVTZ basis set. The stabilization energy per water molecule for the most stable fused cages followed the order fused dodecahedral (FDD) > fused dodecahedral-irregular-dodecahedral (FDI) > fused irregular-dodecahedral (FII), and is higher than that of the corresponding single cages from which they are constituted, showing an enhanced interaction between water molecules in the fused cages.
It is a well-known fact that the structure and the stability of a water cage depend largely on the hydrogen-bond topology.4–16 Among the studies on this subject, the investigations by Kirov et al.15,17 are unique and need special mention. They proposed two models, namely, the strong–weak bond model (SWB) and the strong–weak-effective-hydrogen bond model (SWEB), to explain the most stable networks in polyhedral water clusters. According to the SWB model, a hydrogen bond is considered to be strong when the hydrogen atom of the donor molecule, which is not involved in the hydrogen bond under consideration, is trans with respect to the bisector of ∠HOH of the acceptor water molecule. This model, however, has the drawback that it considers only the interactions between the nearest-neighbors (n-n). In the SWEB model, this drawback is rectified by considering the effect of the interactions between the next-nearest-neighbors (n-n-n). According to the SWEB model, the hydrogen bond with one dangling O–H bond on the donor water molecule, which is trans with respect to the bisector of ∠HOH of the acceptor water molecule, is designated as a t1d type and is considered to be the strongest hydrogen bond.17
Recently, we used the SWEB model to study the isomers of different families of (H2O)20 clusters.18 These families include (i) edge-sharing pentagonal prisms, (ii) face-sharing pentagonal prisms, (iii) fused cubes, (iv) dodecahedrons and (v) irregular dodecahedrons. Being the building blocks of gas hydrates, the dodecahedral and irregular-dodecahedral water cages have attracted special attention and are well discussed in the literature.19–27
Although several studies have been carried out in the past on the dodecahedral and irregular-dodecahedral water cages, not much is known about their fused cages. Using semi-empirical quantum mechanical calculations (ZINDO), Arshad Khan studied the fused cages formed by the various combinations of dodecahedral, irregular-dodecahedral and icosahedral cages.28 To the best of our knowledge, the relative stabilities of the isomers of fused cages formed from the same or different types of single cages have not yet been investigated. Because of the different possible orientations of O–H bonds, a large number of isomers are possible for a water cage and hence the modeling of these cages is tedious.29–32 Because the number of such isomers increases with increase in the number of water molecules, the modeling of fused water cages becomes more challenging.
Keeping this in mind, in the present study, the concept of the SWEB model was extended for investigating the structure and the stability of fused cages formed from dodecahedral and irregular-dodecahedral water cages. Being building blocks, the modeling of these fused cages is important to obtain a molecular level understanding of the gas hydrates.
The stabilization energy (SE) was calculated using the supermolecular approach as
SE = Ecluster − nEwater |
Because the present study involves the clusters of different numbers of water molecules, the stabilization energy per water molecule (SEP) was calculated using the equation
To model the FDD cage, the most stable dodecahedral cage (DD) with seven t1d hydrogen bonds was used. There are three types of five-membered rings present in such a dodecahedral cage, each with zero, one and two t1d hydrogen bonds, as illustrated in Fig. 1 of the ESI.‡ The fusion of two such dodecahedral cages by sharing a pentagon with no t1d hydrogen bonds leads to the formation of a fused dodecahedral cage. On fusion, two t1d bonds of the shared ring are transformed to t0 bonds (trans without any dangling hydrogen), thereby giving a fused cage with 12 t1d bonds; this is the maximum number possible (7 + 7 − 2), as shown in Fig. 2 of the ESI.‡
The number of t1d bonds present in a fused cage (N) can be obtained from the expression N = x + y − n; where x and y are the t1d bonds present in the respective single cages and n is the number of t1d bonds converted to t0 bonds on fusion.
The most stable dodecahedral (DD) and irregular-dodecahedral (IDD) cages have 7 and 8 t1d hydrogen bonds, respectively. Fusion of the abovementioned water cages is possible by sharing a five-membered ring. The maximum number of t1d hydrogen bonds for the fused dodecahedral-irregular-dodecahedral cage can be obtained by sharing a five-membered ring with zero t1d hydrogen bonds, similar to the previous case. The maximum number of t1d hydrogen bonds possible for the fused dodecahedral-irregular-dodecahedral water cage (FDI) is 13.
As it is known that fusion is not energetically feasible between two irregular-dodecahedral water cages via five-membered rings,28 we considered the fusion of the abovementioned two cages by sharing a four-membered ring. The fusion of two irregular-dodecahedral (IDD) cages sharing a four-membered ring, which has zero t1d hydrogen bonds, gives rise to 14 t1d hydrogen bonds; it is the maximum possible number.
Fig. 1 depicts the most stable geometry for each of the abovementioned combinations. The stabilization energy (SE), the stabilization energy per water molecule (SEP), the number of t1d hydrogen bonds and the number of four-membered rings for these fused cages are listed in Table 1. The optimized geometries of the higher energy isomers of each type are given in the ESI.‡
Isomer | SE (kcal mol−1) | SEP (kcal mol−1) | Number of hydrogen bonds | Number of t1d hydrogen bonds | Number of four membered rings |
---|---|---|---|---|---|
FDD | −452.28 (−357.76), −264.17 | −12.92 (−10.22), −7.55 | 55 | 12 | 0 |
FDI | −446.98 (−353.04), −260.24 | −12.77 (−10.08), −7.43 | 55 | 13 | 3 |
FII | −452.74 (−357.88), −263.01 | −12.56 (−9.94), −7.31 | 56 | 14 | 5 |
The stabilization energy per water molecule for the dodecahedral and irregular-dodecahedral water cages is −6.99 and −6.93 kcal mol−1, respectively.18 The high value of stabilization energy per water molecule for the fused cages compared to that of the constituent single cages imply enhanced interactions between water molecules of the fused cages. These enhanced interactions can be considered as the driving force for the formation of fused cages.
The number of t1d hydrogen bonds in FDD, FDI and FII are 12, 13 and 14, respectively, which is in the reverse order of their SEP. As there is no correlation between the number of t1d hydrogen bonds and the value of SEP, it can be concluded that the relative stability of fused water cages cannot be explained on the basis of the SWEB model. However, the difference in SEP between the most stable cages of different types of fused cages can be correlated to the number of four-membered rings present in them. The fused cage FDD, which has the highest SEP, does not have any four-membered rings, whereas the fused cages FDI and FII possess three and five such rings, respectively. The presence of four-membered rings results in strain, thereby increasing the energy of the cage. Thus, the SEP of FII is lower, despite the fact that it has more t1d hydrogen bonds.
The relative stability of the isomers within the family of a fused water cage given in the ESI‡ can be correlated to the number of t1d hydrogen bonds present in them. It was found that within a family of fused cage, the stabilization energy decreases with a decrease in the number of t1d hydrogen bonds, similar to our observation for (H2O)20 clusters.18 For the isomers with the same number of t1d hydrogen bonds, the energy difference can be attributed to the difference in the hydrogen bond parameters (O–H bond distance, O–H⋯O distance and O–H⋯O angle). The bond parameters for the isomers with the same number of t1d hydrogen bonds for the FDD cages are also given in the ESI.‡
Footnotes |
† Dedicated to Professor Eli Ruckenstein on the occasion of his 90th birthday. |
‡ Electronic supplementary information (ESI) available: See DOI: 10.1039/c5ra13268a |
This journal is © The Royal Society of Chemistry 2015 |