The origin of the linear relationship between the reaction energy of the CH2/NH/O exo and endo additions to armchair (n, n) single-walled carbon nanotubes (SWNTs) and the inverse tube diameter (1/d) measuring sidewall curvature was elucidated using density functional theory and density functional tight binding methods for finite-size SWNT models with n) 3, 4,..., 13. A nearly perfect linear relationship between Delta E and 1/d all through exohedral ( positive curvature) and endohedral ( negative curvature) additions is due to cancellation between the quadratic contributions of the SWNT deformation energy and the interaction energy (INT) between the deformed SWNT and CH2/NH/O adducts. Energy decomposition analysis shows that the quadratic contributions in electrostatic, exchange, and orbital terms mostly cancel each other, making INT weakly quadratic, and that the linear 1/d dependence of INT, and therefore of Delta E, is a reflection of the 1/d dependence of the back-donative orbital interaction of b(1) symmetry from the occupied CH2/NH/O p pi orbital to the vacant C=C pi* LUMO of the SWNT. We also discuss the origin of the two isomers ( open and three-membered ring) of the exohedral addition product and explain the behavior of their associated minima on the C-C potential energy surfaces with changing d.