Calculations of the rotational lines and their strength for the Swan band of C₂ molecules: A study on the degenerate four wave mixing spectrum

Kaminski et al. (1997) assigned the DFWM rotational energy level for the (0,0) Swan band of a C₂ molecule using molecular constants for Brown et al.'s effective Hamiltonian (1979). This Hamiltonian formalism diagonalizes upper and lower-state Hamiltonian matrices of the transition using a basis set of the Hund's case (a) representation, and it is very useful for empirical fitting of the data. The Hamiltonian formalism proposed by Zare et al. (1973), also uses a basis set of Hund's case (a) and the second-order perturbations are based on a unique perturbing model, in which the submatrix connecting the electronic states of interest to a single perturbing state is diagonalized. This formalism is better for understanding the physically meaningful values of the molecular parameters rather than the empirical fitting. However, the molecular constants that must be used in any particular effective molecular Hamiltonian are more or less unique to that Hamiltonian. For our calculation, we chose Σ⁺ as the unique perturber of the a-state and Σ/sup -/ as perturber for the d-state, simply because we could associate real states with those choices. The molecular constant for the Zare Hamiltonian is obtained from a conversion of molecular constants of Prasad et al. (1994). Since centrifugal distortion terms are not included here, the difference of the rotational lines between theory and experiment is increased as rotational quanta J is increased. When the centrifugal distortion terms are included by a nonlinear least-square fit method, the difference for the high J quanta is improved. The molecular constants obtained by both a conversion method and nonlinear least-square fit method are given. The accuracy of the assigned rotational lines of the DFWM spectrum for the (0,0) Swan band of C₂ molecule is checked with experimental data.