A. The collision theory outlined above does not account for orientation of the collision, front to back and along the line-of-centers. That is, molecules need to collide in the correct orientation for reaction to occur. Figure PRS.3A-4 shows molecules colliding whose centers are off set by a distance b.
Figure PRS.3A-4 Grazing collisions
B. Collision theory does not explain activation barriers. Activation barriers occur because bonds need to be stretched or distorted in order to react and these processes require energy. Molecules must overcome electron-electron repulsion in order to come close together† C. The collision theory does explain the observed temperature dependence given by Arrhenius Equation  D. Collision theory assumes all A molecules have the same relative velocity, the average one.
 (1)
However there is a distribution of velocities f(U,T). One distribution most used is the Maxwell-Boltzmann distribution.
III. Modifications of Collision Theory
We are now going to account for the fact that we have (1) a distribution of relative velocities UR and (2) that not all collisions result in a reaction, only those collisions with an energy EA or greater. The goal is to arrive at
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