Restricted internal rotation of amino acid esters. Quantitative evaluation of rigidity of a molecule in terms of internal rotation entropy

As a model of molecular recognition of a flexible guest through multi-point recognition, the two-point fixation of the NH₂ group and the C=O group of amino acid esters to porphyrin host was investigated from thermodynamic point of view. The negative entropy change owing to restriction of internal rotation around the C_α-C(carbonyl) bond of guest as driven by the two-point fixation was calculated from the following steps: (1) ab initio molecular orbital calculations at the 3-21G level to generate a potential energy surface for internal rotation along the C_α-C(carbonyl) bond and the C_α-C_β bond, and (2) a calculation of partition function of the system based on classical statistical mechanics. The entropy loss due to the restriction of a rotation around the C_α-C(carbonyl) bond was 5.0 cal·K^-1·mol^-1 for alanine methyl ester and 1.9 cal·K^-1·mol^-1 for valine methyl ester, indicating that valine methyl ester is more rigid with respect to the C_α-C(carbonyl) rotation. This entropy loss was found to originate from the correlated rotation of the C_α-C(carbonyl) bond and the C_α-C_β bond.