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.