Cooperative effects, strengths of hydrogen bonds, and intermolecular interactions in circular cis, trans-cyclotriazane clusters (n = 3-8)

Based on Becke's three parameter functional J. Chem. Phys. 98, 5648 (1993)] of density functional theory (DFT) with the correlation of Lee-Yang-Parr Phys. Rev. B 37, 785 (1988)] (DFT/B3LYP), the natural bond orbital (NBO) analysis, the Bader's theory of atoms in molecule (AIM), our calculations indicate that as cluster size (n) increases, the n-dependent cooperative changes in the lengths of the N...H H bonds (HBs) and N-H bonds, the N-H stretching frequencies and intensities, and the n(N)-->sigma*(N-H) charge transfers are observed to be pervasive in the circular cis, trans-cyclotriazane clusters (n = 3-8), which is very different from the linear cis, trans-cyclotriazane clusters reported in previous work. According to the NBO and AIM theories, the cooperativity of the intermolecular n(N)-->sigma*(N-H) interaction leads to the n-dependent N...H contractions. In this way, the stronger N...H bond is formed, as reflected in the increase in their rho(r(cp)) values. This increased electron density is translated into the improved capacity to concentrate electrons at the HB bond critical point (BCP), i.e., a higher potential energy V(r(cp)). On the other hand, stronger repulsion is also activated to counteract the contraction, which is reflected in the increased G(r(cp)) value that gives the tendency of the system to dilute electrons at the HB BCP. In terms of the three-body symmetry-adapted perturbation theory (three-body SAPT), the induction nonadditivity accounts for up to 97% of the nonadditive energy in the circular trimer. It can believed that the marked cooperativity of the n(N)-->sigma*(N-H) interactions is of nonadditive induction in nature. The N...H formation and nature of cooperativity in the circular clusters differ from those in the linear clusters that have been reported previously. According to the SAPT(DFT) method which is a combination of SAPT with the asymptotically corrected DFT, the cis, trans-cyclotriazane systems should contain remarkable dispersion interactions. However, the short-range dispersion cannot be reproduced thoroughly by DFT/B3LYP. A quantum cluster equilibrium model illustrates the neglected dispersion energies and the nonadditive energies can affect markedly the properties of the liquid consisting of the circular clusters.