In this paper we first use ab initio simulations to study the strains induced by charging an armchair (5,5) carbon nanotube (CNT) segment. The observed behavior is far from a monotonic expansion that one might have expected from a classical point of view. Subsequently a new method is proposed to predict the nonelectrostatic part of the electromechanical actuation response of the nanotube based on the spatial distribution of its molecular orbitals. Locally bonding and locally antibonding molecular orbitals are defined for the CNT segment structure based on analogy with bonding and antibonding orbitals in diatomic molecules. The nonmonotonic overall actuation is explained based on the above proposition and the general alignment of the expanding and contracting bonds with respect to the axis or circumference of the CNT segment. Using the well-known concept of bond order, the actuation of this complex system of many atoms is predicted with close quantitative agreement with the ab initio simulations.