The NCO free radical is an important molecule to study because its linear conformation allows us to create a simple effective Hamiltonian describing the most prominent contributing factors, but still allows us room to take into account the abundance of smaller interactions taking place on the molecular level. Among the most important factors yielded by examining NCO is the Renner-Teller effect. Our computational study is part of an ongoing project to simultaneously analyze the lowest energy vibronic quantum states of NCO, using existing, high-resolution spectroscopic data. These vibronic states are grouped into "unique" states, which are obtained by specific vector combinations of the electronic and vibrational angular momenta, and the more complicated "non-unique"states, for which there are two different vecotr sums that yield the same overall vibronic angular momentum. Presently, the unique v2=0 2-Pi, v2=1 2-Delta, and v2=2 2-Phi vibronic states and non-unique v2=1 2-SigmaΣstate

have been analyzed and fit to experimental data with high precision. This study now aims to develop the computer code for analyzing data from the non-unique v2=2 2-Pi, v3 = 1-0 band of NCO. The non-unique states are split by a combination of spin-orbit and Renner-Teller coupling, and this requires a more general labeling scheme for the eigenstates of the Hamiltonian matrix than has previously been implemented. Additional terms in the effective Hamiltonian may also have to be derived by perturbation theory in order to fit the data to the experimental precision, and the program will then be applicable to a variety of free radical systems.