Orientation of dipole molecules and clusters upon adiabatic entry into an external field

Abstract

The induced polarization of a beam of polar clusters or molecules passing through an electric or magnetic field region differs from the textbook Langevin-Debye susceptibility. This distinction, which is important for the interpretation of deflection and focusing experiments, arises because instead of acquiring thermal equilibrium in the field region, the beam ensemble typically enters the field adiabatically, i.e., with a previously fixed distribution of rotational states. We discuss the orientation of rigid symmetric top systems with a body-fixed electric or magnetic dipole moment. The analytical expression for their "adiabatic-entry" orientation is elucidated and compared with exact numerical results for a range of parameters. The differences between the polarization of thermodynamic and "adiabatic-entry" ensembles of prolate and oblate tops, and of symmetric top and linear rotators, are illustrated and identified.

Beam broadening of polar molecules and clusters in deflection experiments

“…(Note, however, that due to inversion symmetry a spherical rigid rotor cannot have a finite electric dipole moment but may have a magnetic moment, since the former is a polar vector and the latter is an axial vector.) It has been shown in earlier work 22,18 that the orientation for adiabatic entry is quite distinct from the well-known Langevin-Debye expression for in-field equilibrium. The latter corresponds to the universal form…”

“…3,27 For a numerical evaluation, the energies and eigenfunctions of a dipolar rotor in the presence of a field can be calculated to high accuracy by diagonalizing the truncated Hamiltonian matrix. 18,28 For symmetric top molecules the electric field mixes only J states, hence for each K and M (the states are doubly degenerate in M) one diagonalizes a matrix that includes all parent J states populated at the given rotational temperature and a sufficient number of additional J states to ensure convergence. (For asymmetric tops, which are not considered here, the calculation would be complicated by the fact that not only J, but also K no longer remains a good quantum number.)…”

“…How reliable are the analytical and perturbative treatments, and how strongly do inferences from deflection data depend on the various parameters: the rotational temperature, the symmetry, the dipole moment, and the strength of the deflecting field? Analogously to our earlier examination of average particle orientation, 18 here we consider these questions as they relate to beam broadening. In this aspect, the paper can be viewed as complementary to the aforementioned work by Heiles et al 17 To set the stage, recall that the average deflection of the beam, associated with a permanent dipole moment, is given by 3,19 ( )…”

“…The shape parameter κ depends on the ratio of rotational constants: 23 κ=(C−A)/C for a prolate top (with B=C<A and therefore κ<0), and κ=(A−C)/A for an oblate top (with B=A>C and 0<κ<0.5); z(κ) is a function written out in Ref. [18]. For small deviations from a spherical rotor, i.e., for small κ, one finds ( )…”

Dependences of Q-branch integrated intensity of linear-molecule pendular spectra on electric-field strength and rotational temperature and its potential applications

“…Since a new concept on pendular states of molecules in strong electric field was first proposed in 19911 and the pendular-state spectra of (HCN) 3 in strong electric fields were first reported in 199223, theoretical45678 and experimental91011121314 investigations on the pendular-state properties and their spectrum structures of cold polar molecules have made a great progress. These studies show that such a novel pendular-state spectrum can be used to precisely measure molecular electric dipole moment1516 and its change17, to study some new complexes, such as, NH 3 CN complex18 and CH 3 ---H 2 O radical complex19, and so on.…”