Theoretical Evaluation of Strain, Bent Bonds, and Bonding Behavior of Strained Organic Molecules

Abstract

A new approach is presented to evaluate the molecular strain and bonding behavior in strained organic molecules on the basis of the electrostatic theorem of Hellmann−Feynman through the force concept instead of energetics. Taking advantage of the physical simplicity, visuality, and quantification of this model, chemically meaningful definitions of equivalent point charge, overlap force angle, strain force, binding force, tension energy, and the bond force angle have been proposed to measure the molecular strain, bent bonds, and bonding behavior of strained organic molecules at the HF/6-31G* level of theory. The overlap force angles are consistent with the experiment and other ab initio molecular orbital calculations. Results reveal that the overlap force angle, strain force, tension energy, and bond force angle can be used to account for the relative stabilities of small propellanes. The magnitude of binding force suggests the existence of central bonds in small propellanes. The bond force angles in most strained organic molecules seem to prefer the tetrahedral angle 109.5°, while those in three-membered rings prefer the angle 120° over the angle 109.5°, though the geometrical angles can largely range from 60° to 132°. This indicates that, in most cases, the atomic orbitals have to be overlapped in the manner of the ideal or nearly ideal tetrahedral hybrid in order to relax the molecular strain. The largely shifted overlapping charge outside rings and bond force angles of nearly 120° for HCH, HCC, and CCC and the resultant increased s character of C−H bond for three-membered rings can rationalize the C−C bond's higher reactivity than the C−C bonds of other rings. In general, the departure (Δβ) of the bond force angle from the tetrahedral angle provides a measure of the degree of relaxation of the charge density from the geometrical constraints imposed by the nuclear framework and may be used as a way of assessing the molecular strain, reactivity, and stability for strained organic molecules.