On the state selection of linear triatomic molecules by electrostatic hexapole fields.

Electrostatic hexapole state-selector is a versatile tool in experimental stereodynamics. The requirement of appropriate models to correctly predict the behavior of molecules in the hexapole motivated us to realize a treatment that predicts the Stark effect of linear triatomic molecules with rotational doublet states. Various perturbative approximations are conventionally adopted to obtain analytic Stark energy derivatives of a truncated Hamiltonian matrix, without utilizing numerical diagonalization of the full Hamiltonian matrix. By including both the low and high field effects, which were alternatively ignored in the analytical formulae of such approximate approaches, herein we demonstrate that the performance of hexapole state selector to linear triatomic molecules can be appropriately predicted via Van Vleck transformation. This method can provide analytic Stark energy derivatives that are acceptably in consistent with the ones obtained via numerical diagonalization of the full Hamiltonian matrix. Particularly, this work is suitable for v2 = 1 level of linear triatomic molecules, due to the following reasons: (1) the Stark energy derivative and the molecular orientation as a function of the electric field are expressed in analytical formulae, hence it is suitable for implementation without involving numerical diagonalization of the full Hamiltonian matrix; (2) a better prediction of the focusing curves with respect to conventional analytical treatments is provided, allowing a reliable determination of the selected state compositions and molecular orientation.