Interaction radius of a molecule
The short answer: no, there is no such a general distance.

The long answer: atoms and molecules are not just hanging is the vacuum and waiting someone to grab them. They actually have rather high energy in translation, rotation and vibration modes and particles actually collide during a reaction some of these energies can be involved. The science that study these collisions is called reaction dynamics, and you can read e.g. Polanyi's Nobel lecture.You should note that:


It is a quantum event, so technically speaking it is not deterministic.
The orientation of the collision and the geometry of the potential energy surface along the reaction can be favourable, and rotation, vibration etc can help the reaction, or can prevent it.  
The details are also influenced by the medium (is it a reaction in gas or condensed phase, on surface?) and what kind of orbitals are involved in the reaction. About frontier orbitals and their roles you also can find lot of materials in textbooks, eg. any text that discusses the work of Fukui and Hoffmann.