The effect of parent rotational state on fragment anisotropy and application to formaldehyde

A quantum mechanical model for the fragment anisotropy parameter in the limit of a long dissociation lifetime with respect to parent rotation is derived. For excitation with light plane polarized along the Z axis, the anisotropy parameter can be expressed as β=A〈P2(cos θ′t)〉 +B〈sin2 θt cos 2φ′t〉, where A and B are functions of the excitation branch employed and the rotational level of the excited parent, and (θt,φ′t) are the Euler angles of the final fragment recoil direction in the molecular frame, where the z axis is along the parent excitation transition dipole moment. For low J values, classically derived expressions for the anisotropy parameter of fragments produced from the photodissociation of a Boltzmann distribution of rotating parent molecules are shown to not be valid for H2 fragments produced from the photodissociation of H2CO excited to single rovibronic levels. This formula is applied to the measured anisotropies of the H2 (v=1,J=0) fragments produced from the fragmentation of H2CO excited to several different rotational levels of the 2141 band in S1.