A b i n i t i o evaluation of the fine structure and radiative lifetime of the 3A2(n→π*) state of formaldehyde

Abstract

The spin–orbit contribution to the zero-field splitting (ZFS) in the CH2O 3A2(n→π*) state is evaluated using the full Breit–Pauli Hamiltonian. All calculations are carried out at the planar ground state geometry using a double-zeta plus polarization basis of contracted Gaussian-lobe functions augmented with diffuse s and p functions. Configuration–interaction wavefunctions, constructed using the 3A2 canonical orbitals, are used to describe the 3A2 state and all states coupling to it via the spin–orbit Hamiltonian. The excitation energies and oscillator strengths obtained from these wavefunctions are in good agreement with other theoretical calculations and with experiment. Of the 12 states considered in the second-order perturbation theory treatment of the spin–orbit interaction, the 1A1 ground and the nearby 3A1(π→π*) states were the most important. Rydberg states were observed to have very small spin–orbit matrix elements and consequently to have little effect on the ZFS. The spin–orbit contributions to the ZFS parameters D and E were −0.224 and 0.009 cm−1, respectively, which when added to the spin–spin contribution obtained in an earlier paper [S. R. Langhoff, S. T. Elbert, E. R. Davidson, Int. J. Quantum Chem. 7, 999 (1973)] give total values of D=0.314 cm−1 and E=0.04 cm−1. These results are larger than the best experimental results of D=0.141 cm−1 and E=0.02 cm−1, determined by Birss et al. [F. W. Birss, R. Y. Dong, and D. A. Ramsay, Chem. Phys. Lett. 18, 11 (1973)] from a rotational analysis of the 0+←0 bands of the 3A2←1A1 transition. An extensive calculation was also undertaken to assess the degree of convergence in the second-order perturbation theory treatment. The contribution of the lowest 100 singlet and triplet states of A1, B1, and B2 symmetry were considered where each state was described by a 100-term CI wavefunction. This calculation gives a spin–orbit contribution to D of −0.221 cm−1 essentially identical to the previous result providing evidence that the second-order treatment has indeed converged. The radiative lifetimes of the three sublevels of the triplet state were determined using the same representations for the manifold of electronic states. In the high temperature limit, the radiative lifetime was determined to be between 0.02 and 0.06 sec, somewhat longer than the estimated experimental value of 0.01 sec. The mutual perturbation of the 1A1 ground and 3A2 states and the perturbation of the 3A2 state by the 1A1(π→π*) state were determined to be most important in determining the lifetime. These results ensure that the emitted light is polarized primarily along the carbon–oxygen bond in agreement with experiment. A critical examination of the quantitative validity of the numerical results is presented to assess the reliability of the theoretically determined lifetimes.