University of Birmingham Measurement of the orientation of buffer-gas-cooled, electrostatically-guided ammonia molecules

The extent to which the spatial orientation of internally and translationally cold ammonia molecules can be controlled as molecules pass out of a quadrupole guide and through diﬀerent electric ﬁeld regions is examined. Ammonia molecules are collisionally cooled in a buﬀer gas cell, and are subsequently guided by a three-bend electrostatic quadrupole into a detection chamber. The orientation of ammonia molecules is probed using (2+1) resonance-enhanced multiphoton ionisation (REMPI), with the laser polarisation axis aligned both parallel and perpendicular to the time-of-ﬂight axis. Even with the presence of a near-zero ﬁeld region, the ammonia REMPI spectra indicate some retention of orientation. Monte Carlo simulations propagating the time-dependent Schr¨odinger equation in a full basis set including the hyperﬁne interaction enable the orientation of ammonia molecules to be calculated – with respect to both the local ﬁeld direction and a space-ﬁxed axis – as the molecules pass through diﬀerent electric ﬁeld regions. The simulations indicate that the orientation of ∼ 95% of ammonia molecules in J K = 1 1 could be achieved with the application of a small bias voltage (17 V) to the mesh separating the quadrupole and detection regions. Following the recent combination of the buﬀer gas cell and quadrupole guide apparatus with a linear Paul ion trap, this result could enable one to examine the inﬂuence of molecular orientation on ion-molecule reaction dynamics and kinetics.


Introduction
A prevailing goal in the study of reaction dynamics is to develop a complete understanding of the reaction process. Studying chemical reactions under cold conditions can provide control over the internal quantum state population distribution, which typically collapses down into the lowest few levels in small molecules at temperatures ≤1 K. The long-range intermolecular forces experienced by slow-moving molecules can also affect the orientation of reactants during the collision process -and thus influence the properties of the resulting products [1,2]. Over the past half century, the development of methodologies to control the spatial orientation of reactants has seen the investigation of steric effects [3] as well as the direct measurement of "molecular-frame" photofragment distributions [4,5].
Spatially orienting molecules can allow one to control the outcome of reactive collisions. This was demonstrated in 1976, with the introduction of molecular beam scattering experiments: CH 3 I molecules were state-selected using a hexapole and aligned with a static field, before reacting with K atoms. The production of KI showed a strong dependence on whether the methyl group was oriented towards or away from the K atom [6]. Orientation effects have been demonstrated under ultracold conditions with KRb molecules held in an optical lattice trap. The 2KRb → K 2 + Rb 2 reaction was suppressed when the dipoles of the KRb molecules were aligned, such that only unfavourable "side-by-side" collisions could occur; the reactive "head-to-tail" collisions were prevented and the reaction rate constant was significantly reduced from that recorded with no orientation of the reactants [7]. Recently, the total electronic angular mo-2 mentum of O( 3 P 2 ), Ne( 3 P 2 ) and He( 3 S 1 ) beams emerging from a bent magnetic guide have been found to exhibit a substantial degree of orientation to the quantisation axis -in spite of the absence of additional uniform magnetic fields after the guide [8]. A combination of weak fringe fields emanating from the guide, stray magnetic fields, and the way that the species are transmitted through the bent guide has been proposed as the cause of the observed orientation.
Electric fields serve to shift and split the energy levels of polar molecules, in addition to orienting the dipole moment of the species. The orientation of dipoles can be considered from a classical or a quantum mechanical perspective.
Classically, molecules tend to adopt the most stable (i.e. lowest energy) configuration, which sees the dipole moment orient parallel to the local electric field, although the rotational kinetic energy may be sufficient to overcome the orientational force. Quantum mechanically, the orientation of the dipole is governed by the change in the rotational wave function induced by the field [9]. The electric fields in a quadrupole (or hexapole) guide enable one to state-select molecules and to orient them in the local electric field, which is not uniform in direction within the quadrupole. Typically, molecules exiting the guide enter a homogeneous field region provided by parallel electrodes. This post-quadrupole applied field adiabatically reorients the molecules from the inhomogeneous field in the quadrupole to a fixed laboratory axis, as molecules follow the direction of the local field [6]. Thus symmetric top molecules can be state-selected and oriented in the laboratory frame through the combination of a quadrupole guide and static electric fields. However, if the transmission into the homogeneous field region involves passage through a near-zero-field zone, non-adiabatic transitions could lead to loss of orientation.
In this paper, we probe the orientation of cold ammonia molecules after they exit a quadrupole guide and enter a reaction chamber, designed ultimately for the study of cold ion-molecule collisions. (2+1) resonance-enhanced multiphoton ionisation (REMPI) spectroscopy is employed, with the laser polarisation axis aligned both parallel and perpendicular to the time-of-flight (ToF) axis to determine the molecular orientation. The extent to which ammonia molecules can be oriented in the experimental apparatus in this work, and the conditions necessary to achieve orientation, is examined using Monte Carlo simulations.
The ultimate goal is to gain control over all ion-molecule reaction parameters.
While there is significant scrambling of the orientation of ammonia molecules as they pass through the different electric field regions, amendments to the experimental apparatus present conditions for preserving the orientation of polar symmetric top molecules. This presents the exciting prospect of controlling the translational energy, rotational population distribution and orientation of polar reactants as they undergo reactive collisions with cold ions confined in a linear Paul trap.

Experimental apparatus
The experimental apparatus, based on the design of Sommer et al. [10], has been described in reference [11], hence only a brief description is provided here. Ammonia molecules, either NH 3 or ND 3 , are injected into a quadrupole guide after being collisionally cooled by helium buffer gas. A 20 × 40 × 40 mm (length × height × width) buffer-gas cell is attached to the second stage of a two-stage pulse-tube cryocooler. The buffer gas line thermalises with each of the nested temperature stages, and helium enters the cell at 6 K. The molecular line is thermally insulated from the cryogenic environment, with a small heating block ensuring that ammonia molecules enter the cell at 210 K. Ammonia molecules are cooled by collisions with helium buffer gas atoms in the cell, and pass out of the cell through an exit aperture. A 2 m-long three-bend electrostatic quadrupole then guides internally and translationally cold ammonia molecules (in low-field seeking states) through two differentially pumped regions and into a reaction chamber (see figure 1 of reference [11]). Previous work [11] has shown that a low rotational temperature, ca. 10 K, is maintained at the exit of the quadrupole guide. The transmission of the different J K states through the quadrupole guide is discussed in detail in reference [11]. 4 The quadrupole is assembled from hand-polished stainless steel rods with a circular cross section and 2 mm diameter. Voltages of ±5 kV are applied to the quadrupole electrodes, achieving maximal field strengths of up to 90 kV cm −1 at the electrode surfaces. After exiting the guide, molecules pass through a grounded Ni mesh covering an area with a 20 mm diameter. The ammonia molecules subsequently pass through a repeller electrode (inner diameter 25 mm) and are intersected by a REMPI laser between the repeller and extractor plates (see figure 1). The resulting ions are accelerated into a flight tube and onto microchannel plates (MCPs) for detection.

Orientation of molecules
Electric (magnetic) fields are commonly used to orient molecules that have a permanent electric dipole moment (magnetic moment). For a symmetric top molecule, the interaction energy between a permanent dipole, µ, and an external electric field, E, can be expressed in scalar terms as −µE cosθ , where cosθ = KM/J(J + 1) and θ is the angle between the dipole and the field axis [12]. J is the total angular momentum quantum number excluding nuclear spin, K is the projection of J onto the molecular axis, and M is the projection of J onto the external field axis. Hence orientation effects are molecule and state dependent.
The magnitude of the electric field in the quadrupole guide, which near the axis 5 varies linearly with distance from the axis and is approximately independent of azimuthal angle, is more than sufficient to influence the orientation of ammonia molecules (except very close to the axis).
Between the quadrupole guide and the point of ionisation -specifically, at the entrance to the mesh -the quantisation axis is rapidly rotated from the inhomogeneous electric field in the quadrupole (perpendicular to the quadrupole axis) to the homogeneous field between the repeller and extractor plates (parallel to the quadrupole axis). The extent to which ammonia molecules remain oriented to the field as they pass through these regions is dependent on the properties of the electric fields. Polar molecules typically follow the field adiabatically, and the adiabatic eigenstates can be quantized with respect to the axis of the electric field vector. The probability of a nonadiabatic transition occurring as molecules pass through different electric fields is dependent on a number of factors. Nonadiabatic transitions can occur when a molecule is not able to follow the changes in the electric field direction, such as when the frequency at which an electric field is rotated is comparable to the splitting between neighbouring M states, or when the molecule passes rapidly through a zero-field crossing, as described in Landau-Zener theory. Such situations are generally avoided inside the quadrupole guide, as the rate of rotation of the field is orders of magnitude slower than the minimum splitting between states (1.9 × 10 9 rad s −1 in ND 3 , at a field of 2 kV cm −1 ) [13]. However, in situations where the magnitude of the electric field is minimal, there is a near-degeneracy in states differing only in their orientation with respect to the electric field. At zero field, the ammonia energy levels are no longer split by the Stark effect -although the manifold is not entirely degenerate, owing to the presence of inversion and hyperfine splittings.
To maintain their orientation to the local field, molecules must follow the field adiabatically. It has been demonstrated that nonadiabatic transitions can be largely suppressed in an ensemble of trapped ammonia molecules through the use of an electrostatic trap with a non-zero field minimum at the trap centre [14]. This study also notes that nonadiabatic transitions are minimised when only the magnitude of the field -and not the direction -changes rapidly [14]. 6 Hence the longer the molecules spend in near-zero field regions, and the higher the rate at which the field direction changes, the greater the probability of a nonadiabatic transition occurring and thus a loss of orientation to the local field.
To probe the orientation of ammonia molecules, (2+1) REMPI spectra are recorded using linearly polarised light. The polarisation of the REMPI laser can be controlled such that it is parallel or perpendicular to the ToF axis, using

Quantum state populations
(2+1) REMPI spectra are recorded by exciting theB(v 2 = 5) ←X(v 2 = 0) transition in ND 3 and NH 3 . As can be seen in figure 2, there are clear differences in the intensities of many of the transitions when comparing spectra recorded with parallel and perpendicular linearly polarised light. These consistent and significant differences in intensity arise due to the preferential orientation of ammonia molecules to the local field at the point of spectroscopic probing. The laser polarisation axis is the only parameter that is changed between the two spectra, and no other known factor is believed to affect the intensities in this manner. If the M -state distribution was entirely isotropic then there would be no differences in peak intensities between the parallel and perpendicular polarisations. Numerous repeat scans have been recorded over a shorter spectral range; the 63008 − 63028 cm −1 (two-photon energy) region of the ND 3 REMPI spectrum is chosen for examination as it exhibits several isolated transitions and the peak intensities display a strong dependence on the laser polarisation direction. ND 3 also has a greater transmission efficiency through the electrostatic guide, yielding spectra with an enhanced signal-to-noise ratio when compared to NH 3 [15], hence the analysis focuses on ND 3 .
Here, k is the rank of the interaction and p the component; for this work we only require k = 2, and ignore any quantum number dependence of the ionisation step. T k p (E) describes the laser field and T k p (µ) is the transition moment operator, whose matrix elements give rise to the quantum number dependence of the transition intensity -which includes a dependence on M . This M dependence 8 is independent of molecule type, and is simply given by a 3-j symbol involving M and the total angular momentum, J.
While typically unimportant (providing the distribution of population over M states is uniform), the M dependence must be specifically included here.
The selection rule on M is determined by p (as M − M = p), and for rank 2 transitions three values of p must be included: −2, 0 and +2. The relative weightings must also be considered, and these can be found by considering the Cartesian forms of the second rank electric field tensor formed by coupling the first rank electric field vector with itself if only one component of the field is non-zero. If only E z = 0 (described as a parallel transition), then If only E x = 0 (described as a perpendicular transition), then (Note that E y has a different sign for p = ±2, but is otherwise identical to E x .) An important difference here is that two different values of |p| must be included for perpendicular polarisation, in contrast to the one photon case where only one is required. This more general case, including the relative weightings shown above, has been added to version 10 of the PGOPHER program for the calculation of the polarisation dependent, M -dependent REMPI intensities -in fact, in a more general form using the formula for coupling tensor operators to allow for arbitrary rank.  The agreement of the independently measured "perpendicular" and "parallel" population distribution is well within the stated uncertainty in all instances.
However, a clear difference is evident and consistently reproducible when comparing the experimental M K-state populations with the statistical distribution, providing further evidence that the residual orientation observed in the spectra is a real effect.  (7) 0.14 (7)

Simulations
The electric fields that the ammonia molecules experience as they pass through the quadrupole guide and into the ionisation region are modelled using SIMION [19], and are depicted in  of an external electric field) to be calculated using a tensor coupling scheme [21,22]. The time-dependent Schrödinger equation is solved in a co-ordinate system that rotates with the field direction, as this is more efficient than considering a rotating field in a fixed co-ordinate system, as demonstrated by Wall et. al [13]. This is achieved through the use of a rotation operator, with the time evolution of the Schrödinger equation in the rotating frame subsequently expressed in a basis set of the instantaneous eigenvectors. As set out by Wall et. al [13], such an approach enables the effect of the rotation of the electric field and changes in the field magnitude to be evaluated. As the rate of rotation of the field experienced by a molecule as it moves through the apparatus is generally very low compared to the rotational frequency of the molecule or the Stark frequency differences of the M states, the field rotation does not induce population changes except when the field is very low, i.e. the states follow the field direction adiabatically. However, as discussed below, the region near the entry to the mesh is an exception in that the field rotates relatively rapidly in a near-zero field situation. After passing through the mesh, molecules in the 1 1 state experience complete loss of orientation; i.e. a statistical population distribution is seen at a distance of 7.15 mm after the guide exit. It is interesting to observe that the transfer of population from the |1, −1 state to either the |1, 0 state or the |1, 1 state occurs at the same rate. One might expect, due to the inversion splitting and thus lack of total degeneracy at zero field, that population would be transferred to the |1, 0 state in preference to the |1, 1 state. This is, in fact, the behaviour observed if an artificially large inversion splitting is implemented.
Employing the inversion splitting reported for NH 3 , 0.792 cm −1 [25], sees the majority of molecules oriented to the local field: the population in |1, −1 is ∼74% at the point of ionisation, with 23% in the |1, 0 state and 3% in |1, 1 . added complexity of additional M K states. Within the J K = 2 2 manifold, population appears to initially decay fastest from the |J, M K = |2, −2 state, but after a short distance the loss rate from this state reduces significantly.
The change in population of a given low-field seeking state is unlikely to be

Maintaining orientation through the detection region
The orientation of molecules as they exit a hexapole guide and enter a region of uniform field has been previously studied, with fields as low as 3 V cm −1 sufficient to orient CH 3 I molecules to the external field axis [12,26].  . While the mesh itself is not depicted, the effect of the mesh can be seen in the change in the field lines at 0 µm. Note that the colour scale has again been altered from those adopted for figures 4 and 6, to highlight the difference that a 17 V bias applied to the mesh makes to the fields in this region.
These simulations are in agreement with the significant orientation effects  [26]. While the field rotation occurs just as rapidly with the removal of the near-zero field region, at a higher field the splitting between states is larger, hence nonadiabatic transitions are suppressed. An alternative approach could see the mesh holder -currently made of stainless steel -replaced with an insulating material. The mesh itself has a width of only 0.1 mm; replacing the 1.00 mm-width mesh holder with an insulating material will significantly reduce the length of the near-zero field region along the z axis. As a result, molecules will spend less time in near-zero fields, reducing the probability of nonadiabatic transitions in this region and thus curtailing the loss of orientation to the local field -although losses due to the rapid rotation of the field between the quadrupole and the mesh will still occur. Simulations indicate that replacing the mesh holder with an insulating material will result in the orientation of 70% of ammonia molecules at the detection region, as depicted in figure 11.

Conclusion
Ammonia molecules exiting an electrostatic quadrupole guide and passing through a grounded mesh into a reaction chamber exhibit some orientation to the local electric field. It is, however, easy to lose orientation when molecules pass through near-zero field regions; fields need to be designed to preserve the To preserve the orientation of molecules as they enter the ion trap, one would need to prevent the radiofrequency trapping fields from inducing nonadiabatic transitions. This could be achieved through the use of digital trapping waveforms (also termed square-wave or pulsed waveforms), whereby a rectangular waveform of period T and pulse width τ is employed. The digital waveform is zero when τ T /2 < |t| ≤ (1 − τ )T /2 and (1 + τ )T /2 < |t| ≤ (2 − τ )T /2. This "off time" can be extended by switching off the trapping fields for a short time, allowing the oriented molecules to be admitted to the trapping region without adverse fields being present, although there are still challenges associated with molecules entering the trap at zero field. If a compromise can be achieved between shielding the ion trap from external fields and maintaining the orientation of the ammonia molecules as they pass through the region, this will enable the examination of ion-molecule reactions with unprecedented control over the reaction parameters.