Spin Splittings and Rotational Structure of Nonlinear Molecules in Doublet and Triplet Electronic States

Abstract

Matrix elements are presented for the Hamiltonian of a nonlinear, nonrigid polyatomic molecule in a multiplet electronic state. Their use is only appropriate for electronic and vibrational spectra since hyperfine interactions involving nuclear spins and nuclear quadrupole moments are not considered. For the most general case, nine parameters are required to take full account of spin—rotation interactions, and five are required for spin—spin interactions. For molecules of orthorhombic symmetry only three spin—rotation parameters and two spin—spin parameters are nonzero. For nonlinear molecules in doublet and triplet electronic states, explicit formulas are presented for (a) the rotational term values of symmetric rotors and (b) spin splittings of asymmetric rotors possessing orthorhombic symmetry. All these formulas reduce to well‐known expressions for diatomic molecules in ²Σ and ³Σ states when K‐dependent terms are ignored. Application of the above formulas to the results of Dressler and Ramsay on the ²B₁ ground states of NH₂ and ND₂ permits the determination of the spin—rotation parameters of these molecules. All five spin parameters of formaldehyde in its lowest ³A₂ state are given together with curves of spin splittings in the lower K levels. The spin parameters of HCHO, NH₂, and ND₂ are compared with those of NO₂ and ClO₂ found by recent microwave studies. For a triplet state of an orthorhombic molecule, the spin—spin constants determined by band spectroscopy are simply related to the spin constants D and E determined from zero field splittings in electron spin resonance spectroscopy. The surprisingly small value of D=0.42 cm^—1 for the lowest triplet state of formaldehyde is briefly discussed in terms of a breakdown of the orbital approximation for this prototype ``n—π^* state.''