Computerized simulation and fitting of singlet–triplet spectra of orthorhombic asymmetric tops: Theory and extensions to molecules with large multiplet splittings

Abstract

Motivated by our recent finding that the singlet-triplet bands of selenoformaldehyde involve an upper state with large zero field splittings, we have extended the theory and written a program for predicting and fitting such rotationally resolved spectra. Triplet state matrix elements for a case ͑A͒ basis have been developed, including corrections for centrifugal and spin-centrifugal distortion. The full Hamiltonian matrix has been symmetry adapted, simplifying the problem to four individual matrices of approximately equal size for molecules of orthorhombic symmetry. Diagonalization of these matrices yields triplet state energies that are in agreement with previous treatments using a basis in which the spin splittings are small relative to the rotational intervals. Methods have been developed for sorting the eigenvalues and assigning quantum labels regardless of the magnitude of the spin splittings. The calculation of the relative intensities of the rotational lines within a band has been programmed using transition moment matrix elements from the literature. The selection rules for various upper state symmetries have been developed in a form useful for the analysis of spectra. Band contour predictions of spectra for various coupling cases have been presented.

Contribution to the Analysis of the3A2←X1A1“Wulf” Transition of Ozone by High-Resolution Fourier Transform Spectrometry

“…It was generally negative, however. The general case (a) basis set program of Judge et al (22) was used to calculate the band contour. Its least-squares feature gave an identical set of rotational and spin parameters (to within the rms errors).…”

A new graphical version of STROTAB: The analysis and fitting of singlet–triplet spectra of asymmetric top molecules in the prolate or oblate limits

“…[2] shows that the rotational constants, spin-rotation constants as well as the spin-spin constants contribute to the splittings of the levels even for a non-rotating molecule. For example, the matrix element labeled as Z 00 = H ΣΣ pp (Σ = 0, p = 0) for a non-rotating molecule (J = 0; p = 0) is 2((X + Y )/2 − α + a 0 + a) and is the energy of the |z spin state.…”

“…The derivation of the selection rules for the oblate case under the two coupling situations follows exactly that outlined in the earlier theory paper, Ref. [2]. These tables should be applied carefully since there are subtle differences in both the selection rules and the allowed moments under the two representations.…”

“…In both tables, the symbols EPLUS, EMINUS, OPLUS and OMINUS refer to the symmetry adapted blocks formed from the product function of the spin and rotational wavefunctions formed under the case (a) basis set (in which P is a valid quantum number) (see Ref. [2]). Within these blocks, all eigenvalues can be labeled with all even (E) or all odd (O) K values and share the same direct product group theoretical representation (PLUS or MINUS).…”

“…The program was designed to be applicable to molecules which show either Hund's case (a), case (b) or case (ab) type splittings. The Hamiltonian upon which the computer code is based has been published elsewhere [2] and remains fundamentally unaltered in this new version. Up to 22 rotational, spin, centrifugal distortion and spin-centrifugal distortion constants are contained within the matrix elements of the Hamiltonian.…”