Orientation of Asymmetric Top Molecules in a Uniform Electric Field:  Calculations for Species without Symmetry Axes

Abstract

Calculations of orientation effects of polar molecules in a uniform electric field are presented for the most general scenario, an asymmetric top molecule with a permanent dipole not parallel to a principal axis. In addition to details of the calculation procedure, including matrix elements of the Hamiltonian, three different treatments of the population distribution of the Stark levels in an electric field are discussed. The adiabatic approach assumes the noncrossing rule for all energy levels as the orientation field increases, the nonadiabatic approach searches for the level with the most similar wave function under field-free conditions to find the population of the Stark level in the field, and the thermal calculation assumes thermal distribution for all of the Stark levels. Among these, the thermal calculation results in the highest degree of orientation, and in high fields, it shows the best agreement with available experimental data in terms of polarization ratios (the ratios of overall excitation probabilities under two perpendicular polarization directions of the laser). By use of cytosine at a rotational temperature of 5 K and adenine at 2 K as model compounds, the thermal calculation suggests that in a field of 50 kV/cm, more than 30% of the molecules should be confined within a 45° cone surrounding the direction of the orientation field, and that if a transition dipole is perpendicular to the permanent dipole, the excitation probability can be enhanced by 50% when the polarization direction of the laser is perpendicular, rather than parallel, to the orientation field. The adiabatic and nonadiabatic calculations yield similar distribution functions of the permanent dipole, both predicting weaker orientation than that of the thermal calculation. According to comparisons of spectroscopic details between the calculations and experiment using the π* ← n transition in pyrimidine, however, all three calculations agree with the experimental spectra. Further experimental evidence with higher quality spectra is needed for a conclusive statement. Orientation using a uniform electric field is particularly suitable for studies of large systems with small rotational constants: the orientation effect is proven to be determined by the size of the permanent dipole, essentially independent of the orientation of the permanent dipole in the molecular frame. For small molecules, however, this type or orientation is unfavorable, and the resulting orientation is sensitive to the molecular parameters, such as the rotational constants, and the size and direction of the permanent dipole in the molecular frame.

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

“…Because of the additional K mixing, a second-order perturbation approach is intractable, and one has to resort to numerical diagonalization 37,38 or molecular dynamics simulations. 39 There are suggestions that because of the nascent chaotic character of asymmetric top motion [40][41][42] and/or because of the general action of avoided crossings in the coupled Stark ͑Zeeman͒-rotational level diagram, 12 the statistical Langevin-Debye behavior will be restored.…”

“…For several asymmetric tops the adiabatic-entry orientation was calculated exactly and found to be close to the Langevin-Debye equation. 37,38 Curiously, this is the case even for the water molecule ͑where the Stark-split rotational energy levels are well ordered and well separated͒ already at relatively low rotational temperatures. 43 …”

Infrared Spectroscopy of (HCl)m(H2O)n Clusters in Helium Nanodroplets: Definitive Assignments in the HCl Stretch Region

“…This dipole distribution function, P(cos θ), is computed according to the procedures of Kong and Bulthuis. 52 Here, θ is defined as the angle between µ p and the Stark field axis. Calculations of P(cos θ) assume the ab initio dipole moment components and rotational constants (divided by 3 to account for the helium solvent) for a specific cluster and a rotational temperature of 0.37 K. Projecting µ t onto the polarization axis of the OPO (either parallel to or perpendicular to the Stark field axis) and averaging over θ gives the relative intensity due to cluster orientation at a given field strength, 53 where R is the VTMA:…”

Alternating gradient focusing and deceleration of polar molecules

“…2(c) are caused by avoided crossings. Details on the calculation of the Stark shifted energy levels in an asymmetric top molecule can be found elsewhere [35]. Table I gives the relevant properties for Stark deceleration for a selection of polar molecules.…”