In order to compute a highly accurate statistical rate constant for the CO2 + O+ reaction, it is necessary to first calculate the potential energy of the system at many different geometric configurations. Quantum mechanical calculations are very time-consuming, making it difficult to obtain a sufficient number to allow for accurate interpolation. The number of quantum mechanical calculations required can be significantly reduced by using known relations in classical physics to calculate energy for configurations where the oxygen is relatively far from the CO2. A chi-squared fit to quantum mechanical points is obtained for these configurations, and the resulting parameters are used to generate an equation for the potential energy. This equation, combined with an interpolated set of quantum mechanical points to give the potential energy for configurations where the molecules are closer together, allows all configurations to be calculated accurately and efficiently.
Sawilowsky, Ellen F.
"Combining Quantum Mechanical Calculations And A χ^2 Fit In A Potential Energy Function For The CO_2 + O^+ Reaction,"
Journal of Modern Applied Statistical Methods: Vol. 1
, Article 49.
Available at: http://digitalcommons.wayne.edu/jmasm/vol1/iss2/49