Collisions are very important in determining the abundances of the di erent species that existin our world. Atoms, molecules, ions, electrons and even photons, have their concentrationsdictated by the collisions they undergo. In this work, three types of collisions are studied.The photodissociation, collision with photons, of cyanogen (CN) is studied in chapter 1.Cross sections were computed for the 2 +(4) X 2 +, 2 +(5) X 2 +, 2 (4) X 2 +,and 2 (5) X 2 + electronic transitions. Partial and LTE cross sections were evaluatedfor all rovibrational levels (v00N00) of the ground electronic state of CN, X 2 +, and over alarge wavelength range of astrophysical interest. The results will allow for the calculationof reliable CN photodissociation rates for astrophysical environments with varying radiationand dust properties. The rotational quenching of CO2 by collisions with He is the subjectof Chapters 3 and 4. CO2 was treated as a rigid rotor in the ground state. If CO2 is initiallyin the rotational state speci ed by the rotational quantum number jo, cross sections fortransitions to all possible lowerj rotational states, for a wide range of relative collisionenergy, were calculated. In Chapter 4, the emphasis is on rotational quenching of CO2by collisions with He in the ultracold regime. Complex scattering lengths and elastic andinelastic rotational quenching cross sections have been computed for carbon dioxide, withrotational excitation j as high as 200, due to ultracold 4He collisions. It is predicted that theratio of the elastic to inelastic cross section, or gure-of-merit, is su ciently large that highlyrotationally excited CO2 could be a viable candidate for cooling and trapping. In chapter 5,new potential energy curves were used to calculate the cross section for excitation transferfrom the He(23S) atoms to the He(11S) gas, the di usion of He(23S) atoms in He(11S) gas,and the total elastic cross sections for the collision of He(11S) and He(23S) atoms. Theresults were compared to published results and a good agreement is observed. The elasticcross sections for the collision of He(11S) and He(33S) were calculated for the first time.