MP2, density functional theory, and molecular mechanical calculations of C–H···π and hydrogen bond interactions in a cellulose-binding module–cellulose model system

Exploring non-covalent interactions, such as C–H···π stacking and classical hydrogen bonding (H-bonding), between carbohydrates and carbohydrate-binding modules (CBMs) is an important task in glycobiology. The present study focuses on intermolecular interactions, such as C–H⋯π (sugar–aromatic stacking) and H-bonds, between methyl β-d-glucopyranoside and l-tyrosine—a proxy model system for a cellulose–CBM complex. This work has made use of various types of quantum mechanics (QM) and molecular mechanics (MM) methods to determine which is the most accurate and computationally efficient. The calculated interaction potential energies ranged between −24 and −38 kJ/mol. The larger interaction energy is due to H-bonding between the phenyl hydroxyl of tyrosine and the O4 of the sugar. Density functional theory (DFT) methods, such as BHandHLYP and B3LYP, exaggerate the H-bond. Although one of the MM methods (viz. MM+) considered in this study does maintain the C–H⋯π stacking configuration, it underestimates the interaction energy due to the loss of the H-bond. When the O–H bond vector is in the vicinity of O4 (O–H⋯O4 ≈ 2 Å, e.g., in the case of MP2/6-31G(d)), the torsional energy drops to a minimum. For this configuration, natural bond orbital (NBO) analysis also supports the presence of this H-bond which arises due to orbital interaction between one lone pair of the sugar O4 and the σ∗(O–H) orbital of the phenyl group of tyrosine. The stabilization energy due to orbital delocalization of the H-bonded system is ∼13 kJ/mol. This H-bond interaction plays an important role in controlling the CH/π interaction geometry. Therefore, the C–H⋯π dispersive interaction is the secondary force, which supports the stabilization of the complex. The meta-hybrid DFT method, M05-2X, with the 6-311++G(d,p) basis set agrees well with the MP2 results and is less computationally expensive. However, the M05-2X method is strongly basis set dependent in describing this CH/π interaction. Computed IR spectra with the MP2/6-31G(d) method show blue shifts for C1–H, C3–H, and C5–H stretching frequencies due to the C–H⋯π interaction. However, the M05-2X/6-311++G(d,p) method shows a small red shift for the C1–H stretching region and blue shifts for the C2–H and C3–H stretches. For the aromatic tyrosine Cδ1–Cε1 and Cδ2–Cε2 bonds in the complex, the calculated IR spectra show red shifts of 12 cm−1 (MP2/6-31G(d)) and 5 cm−1 (M05-2X/6-311++G(d,p)). This study also reports the upfield shifts of computed 1H NMR chemical shifts due to the C–H⋯π interaction.