Conformations and rotational barriers of 2,2′-bi-1H-imidazole Semiempirical, ab initio, and density functional theory calculations

Abstract

Conformations and rotational barriers of 2,2′-bi-1H-imidazole (1) have been investigated by using semiempirical, ab initio, and density functional theory (DFT) calculations. All theoretical methods employed in this study agree that the trans conformation of 1 is the global minimum, and the cis conformation is a transition state. Although semiempirical methods have located only these two stationary points, ab initio and DFT calculations have found additional local minima at a slightly skewed cis conformation. The torsional angle between two imidazole ring planes at these local minima is calculated to be 26.3° at HF/3-21G, 45.9° at HF/6-31G*, and 37.8° at B3LYP/6-31G*. Our best estimate for the overall rotational barrier of 1 through the cis conformation is 11.8 kcal mol ^-1 , which is obtained from B3LYP/6-31G* calculations with the correction of zero-point vibrational energy. Estimations of this barrier by semiempirical methods are significantly lower than 8.6 kcal mol ^-1 by AM1, and 10.6 kcal mol ^-1 by PM3, while the overall rotational barriers predicted by the SCF methods (15.6 and 13.6 kcal mol ^-1 at the HF/3-21G and HF/6-31G* levels, respectively) are considerably higher than the B3LYP/6-31G* result. In order to better understand the origins of the rotational barrier, we have attempted to analyze (1) changes of the electrostatic potential maps and the V _min (r) values, (2) Fourier expansion terms for rotational potential energy functions, and (3) the bond length change during internal rotation. Based on these analyses, electrostatic interaction and π-conjugation appear to play an important role in forming the shape of the rotational barrier.