The Bell-Evans model which predicts the linear dependence of the most probable intermolecular bond rupture force on the logarithm of stretching force loading rate is usually used to discuss the dynamic force spectroscopy experiment data. This model is consistent with the Kramers' theory of the bond dissociation rate only if one presupposes an independence of the pre-exponential factors in the Kramers relation on the acting force and a linear decrease of the dissociation barrier height on this same force, and for this to be true rather special shape of the interaction landscape is required. Here, we present a first order correction to this model (first terms of corresponding Taylor expansions are taken into account), discuss its implication for the interpretation of dynamic force spectroscopy experiment data and compare our model with the Monte Carlo simulation of a specially designed single molecule dynamic force spectroscopy experiment. In addition to the most probable bond rupture force, an average rupture force values are also calculated. All approximations made and the range of applicability of the obtained results are carefully described and compared with those for some other models in the field. (C) 2013 AIP Publishing LLC.