Theor Chem Account (2008) 121:135–146 DOI 10.1007/s00214-008-0456-1 REGULAR ARTICLE Theoretical study of N–H··· O hydrogen bonding properties and cooperativity effects in linear acetamide clusters Mehdi D. Esrafili · Hadi Behzadi · Nasser L. Hadipour Received: 13 February 2008 / Accepted: 7 May 2008 / Published online: 31 May 2008 © Springer-Verlag 2008 Abstract We investigated geometry, energy, ν N–H harmonic frequencies, 14 N nuclear quadrupole coupling tensors, and n O → σ ∗ N–H charge transfer properties of (acetamide) n clus- ters, with n = 1-7, by means of second-order Møller-Plesset perturbation theory (MP2) and DFT method. Dependency of dimer stabilization energies and equilibrium geometries on various levels of theory was examined. B3LYP/6-311++G** calculations revealed that for acetamide clusters, the aver- age hydrogen-bonding energy per monomer increases from -26.85 kJ mol -1 in dimer to -35.12 kJ mol -1 in heptamer; i.e., 31% cooperativity enhancement. The n-dependent trend of ν N–H and 14 N nuclear quadrupole coupling values were reasonably correlated with cooperative effects in r N–H bond distance. It was also found that intermolecular n O → σ ∗ N–H charge transfer plays a key role in cooperative changes of geometry, binding energy, ν N–H harmonic frequencies, and 14 N electric field gradient tensors of acetamide clusters. There is a good linear correlation between 14 N quadrupole coupling constants, C Q ( 14 N), and the strength of Fock matrix elements ( F ij ). Regarding the n O → σ ∗ N–H interaction, the capability of the acetamide clusters for electron localiza- tion, at the N–H··· O bond critical point, depends on the cluster size and thereby leads to cooperative changes in the N–H··· O length and strength, N–H stretching frequencies, and 14 N quadrupole coupling tensors. M. D. Esrafili · H. Behzadi · N. L. Hadipour (B ) Department of Chemistry, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran e-mail: hadipour@modares.ac.ir; nas.hadipour@gmail.com N. L. Hadipour Institute of Chemistry, Academia Sinica, Nankang, Taipei 11529, Taiwan, ROC Keywords Hydrogen-bonding cooperativity · DFT · 14 N quadrupole coupling tensors · Acetamide · NBO · AIM 1 Introduction One particularly relevant aspect in the hydrogen bonding theory is hydrogen-bond cooperativity, which is typically described as nonadditive enhancement of a hydrogen bond through formation of another hydrogen bond with either a proton donor or proton acceptor [1–8]. In other words, due to the nonadditive character of the polarization effects involved in hydrogen bonding, H-bonding, structure and electronic properties of the aggregates are mostly dependent on number of monomers in the cluster. On the other hand, it is expected that for clusters larger than a size limit n, the importance of these effects be noticeably reduced. Considerable attention has been given to cooperative effects of hydrogen-bonding chains in molecular clusters. For example, Weinhold et al. [9, 10] employed reasonably high levels of ab initio theory to investigate cooperative aspects of C–H··· N H-bonding in (HCN) n=1-7 clusters. Their results indicated that cooperative effects are robust and pervasive in (HCN) n clusters, extend- ing to virtually every aspect of energetic, structural, dielectric and vibrational properties. The ab initio study performed by Parra and coworkers [11, 12] revealed existence of signifi- cant cooperative effects in a linear network of three-centered bifurcated A 1 HA 2 hydrogen bond. They also indicated that cooperative effects play a significant role in stabilization of ring-like network containing bifurcated H 1 ··· A ··· H 2 H-bonding interaction, where the two proton-donors are located in the same molecules. On the basis of density func- tional theory studies, Ludwig et al. [3, 4] found strong cooper- ative effects in linear clusters of trans- N -methylamide using quantum cluster equilibrium (QCE) methodology and 123