Deconvolution of spectral data using a doorway-coupling model Hamiltonian

The doorway-mediated mechanism for dynamical processes represents the first step beyond statistical dynamics toward an explicit mechanism. A bright state-->doorway state-->dark bath doorway-coupling model Hamiltonian characterizes the small molecule limit behavior of the doorway state in mediating the interaction with other dark states in the large molecule limit. Established methods of spectral deconvolution are extended to determine the parameters of a doorway-coupling model Hamiltonian from the energies and intensities of eigenstates in a high-resolution spectrum. The most important parameters of the Hamiltonian, including the doorway state energy and bright~doorway matrix element, may be computed directly from moments of the spectral intensity distribution. We demonstrate that these parameters can be recovered accurately even when some eigenstates are unresolved. The deconvolution procedure is applied to the spectrum of the 3nu(3) K(a)=1 vibrational level of S(1) acetylene, where a single, local, T(3) doorway level mediates coupling to the T(1,2) manifold. Previous studies of this S(1)~T(3) perturbation are discussed in light of the doorway state energies and matrix elements obtained by inversion of the spectral data.