3.2 Cooperative nature of H-bond in CHD clusters:
As there are two distinct types of clusters possible, the discussion on the cooperativity in CHD clusters has been divided into two parts; the first one focusing on linear clusters and the second one centered on cyclic clusters. As discussed previously, only the all trans linear conformers has been considered for this comparison and the dimer through hexamer are represented as LD, LTr, LTe, LP and LH, respectively. The molecular geometries of the above mentioned linear clusters optimized at ωB97X-D/6-311++G** level of theory is shown in Figure 2. Similarly, for cyclic variant only the ones having all free carbonyl pointing in the same direction have been considered for the discussion and they are represented as CD, CTr, CTe, CP and CH in the same order. The molecular geometries of these 5 cyclic clusters optimized at ωB97X-D/6-311++G** level of theory is shown in Figure 3.
As multiple H-bonds are involved between two monomers, there doesn’t exist any well-defined correlation between H-bond lengths with cluster size that could be used as an indicator for estimating the extent of cooperativity. Therefore, we have used C=O bond length and binding energy to estimate overall cooperative and anti-cooperative nature of cluster. Further, to estimate how strength of one H-bond influences the others, effect of multiple H-bonds formed between two particular monomeric moieties influencing each other with increasing cluster size has also been studied.
Cooperativity in linear clusters:
In case of the linear clusters, binding energies of LD, LTr, LTe, LP and LH were found to be -8.8, -16.2, -24.0, -31.7, and -39.0 kcal mol-1, respectively, given in Table 2. Also binding energy per interaction was calculated by dividing the total binding energy by the number of bonded carbonyls. It was found that binding energy per interaction decreases gradually from LD (-4.4 kcal mol-1) to LTr (-4.1 kcal mol-1), LTe (-4.0 kcal mol-1), LP (-4.0 kcal mol-1) and LH (-3.9 kcal mol-1) as can be seen from Figure 4. Therefore, the linear clusters show overall anti-cooperative behavior as binding energy per interaction decreases monotonically with increase in cluster size.
The above values clearly show that, on average, H-bonding interaction becomes weaker with increasing size in linear clusters. However, it would be more interesting to see how the interaction energy of a particular cluster gets modified upon addition of one or more monomeric units to the cluster. For example, the existing 4 H-bonds in LD get affected when another CHD molecule gets attached to form LTr. Now if the binding energy of LD is calculated in its conformation inside LTr, this will provide the exact change in binding energy LD experiences when a CHD molecule is added to it. Now, when two CHD molecules are added to LD, there are two possibilities, both of them could be added to the same side or to either sides. When binding energy LD is calculated in similar manner for LTr, it will give us an idea of how addition of two monomeric moieties influence the interaction in LD. Similar calculations have been carried out for LD within LP and LH, for LTr within LTe, LP and LH, for LTe within LP and LH and finally for LP within LH. For easier comparison the obtained results have been normalized by considering binding energies per interaction as defined above (Table 3) and plotted as bar diagram (Figure 5). It was found that the binding energy of a certain size of cluster decreases monotonically with increasing addition of CHD monomer to that cluster and finally reaches an asymptotic limit near the upper limit. For example, the value for LD (4.4 kcal mol-1) reduces to 4.3 kcal mol-1 in LTr and 4.1 kcal mol-1 in LTe and remains at the same value in LH. The other clusters also show similar trends. This result unambiguously shows that addition of one or more CHD molecules to an existing linear cluster results in weakening of the existing H-bonds originally holding the cluster. This is a clear manifestation of anti-cooperative behavior of C-H—O H-bonds in linear CHD clusters.
The anti-cooperative behavior is also evident from the C=O bond length of the H-bonded carbonyl groups. C=O bond length of H-bonded carbonyl group is known to be sensitive to H-bond strength; stronger H-bond results in longer C=O bond63,64Average C=O bond length of H-bonded carbonyl groups for the LD, LTr, LTe, LP and LH were found to be 1.2104, 1.2095, 1.2094, 1.2093 and 1.2093 Å, respectively (Figure 4). Thus, it is evident that the decrease in average C=O bond length with increasing cluster size is due to the weakening of H-bonds as a result of anti-cooperative effect. Therefore, both binding energy per interaction and average C=O bond length show that C-H—O H-bond is anti-cooperative in the linear clusters.
In linear clusters, every H-boned carbonyl group forms two H-bonds, i.e. HB1 and HB2 as defined beforehand. Consequently, it would be interesting to see how each of these two types of H-bonds individually modulate and also how they influence each other, both as a function of cluster size. For this purpose we have plotted the H-bond length of both HB1 and HB2 against the number of H-bonded carbonyl groups, as each carbonyl group forms one each of HB1 and HB2 (Figure 6). The numbering of H-bonded carbonyl groups in Figure 2 is done from one end of the cluster to the other end. As two carbonyl groups remain free in every cluster, irrespective of its size, the total number of H-bonded carbonyl groups would be 2N-2 for a cluster formed by N CHD molecules. It is evident from Figure 6 that neither HB1 nor HB2 show any monotonic variation in their length with cluster size. Nevertheless, there are systematic modulations of HB1 and HB2, both individual as well as mutual, in each of the clusters. In each of the clusters, the two terminal HB1s are the shortest and shows a zigzag pattern as one moves from one end to the other. HB2 also shows a similar zigzag pattern, but in completely opposite manner, i.e. it increases when HB1 decreases and vice versa. Therefore, it could be said that these two types of H-bonds show an anti-cooperative behavior between themselves; strengthening of one is always accompanied by weakening of the other.
In order to corroborate the above findings, we carried out NBO analysis to examine the delocalization energies associated with the charge transfer from lone pairs of acceptor oxygen atom to the anti-bonding orbital of donor C-H bond. Besides, AIM analysis was performed to estimate electron density and it’s Laplacian at the bond critical points for HB1 and HB2. When these obtained values given in Table S1 were plotted against H-bond lengths (Figure S6), delocalization energy along with electron density and its Laplacian for both HB1 and HB2 were found to decrease monotonically with diminishing strength (i.e. lengthening) of both H-bonds.