where the sums go over the entire ECI vector of state I in the ECSF basis. This diagnostic will be equal to 1 if only a single ECSF contributes to the state (with C ΦI = 1). If L ECSFs contribute with equal absolute values of ECI coefficients, PR will be equal to L, whereas if the ECI coefficients of the ECSFs are not equal, PR will have a value between 1 and L. Hence, it provides an estimation of the number of contributing ECSFs to the ECI vector. Further, to track the characters of the states in the terms of different excitation ranks (GS, LE, DLE, ...), we define the E n diagnostics for excitation rank n as