Electrostatic deflection of the water molecule: A fundamental asymmetric rotor

An inhomogeneous electric field is used to study the deflection of a supersonic beam of water molecules. The deflection profiles show strong broadening accompanied by a small net displacement towards higher electric fields. The profiles are in excellent agreement with a calculation of rotational Stark shifts. The molecular rotational temperature being the only adjustable parameter, beam deflection is found to offer an accurate and practical means of determining this quantity. A pair of especially strongly responding rotational sublevels, adding up to $\approx 25\%$ of the total beam intensity, are readily separated by deflection, making them potentially useful for further electrostatic manipulation.

Figure 1

Stark curves for the lowest states of ${\mathrm{H}}_2\mathrm{O}$. The states are represented by $J$, $\tau$, and $M$. The spin statistical weights for states with $\tau$ odd are three times as large than those for $\tau$ even.

Figure 2

Deviation probability distributions for the beam of ${\mathrm{H}}_2\mathrm{O}$ molecules, calculated from their Stark shifts and electronic polarizability. The parameters for this example are $v=1250\mathrm{m}∕\mathrm{s}$, $E=63.5\mathrm{kV}∕\mathrm{cm}$, $\partial E∕\partial z=300\mathrm{kV}∕{\mathrm{cm}}^2$, and $T_{\mathit{rot}}=30\mathrm{K}$ (a) or $T_{\mathit{rot}}=300\mathrm{K}$ (b).

Figure 3

(Color online) A comparison between the calculated average projection of the dipole moment of the water molecule in a thermal bath (Langevin function [15], solid lines) and isolated in a beam (Stark shift calculation, dashed lines) for two magnitudes of the external electric field. For $T_{\mathit{rot}}>100\mathrm{K}$, the difference is below 10%.

Figure 4

(Color online) Comparison of the experimental deflections of ${\mathrm{H}}_2\mathrm{O}$ molecules with the patterns derived from rotational Stark calculations. The supersonic beam was produced with the source reservoir temperature of $50°\mathrm{C}$, nozzle temperature of $65°\mathrm{C}$ (nozzle diameter $75\mu \mathrm{m}$), and helium carrier gas pressure of $670\text{Torr}$. The thin solid black lines are the experimental undeflected beam profiles. The solid thick red lines are the experimental profiles taken with six different voltages applied to the deflection plates. The blue stick patterns are the deviation probability distributions (as in Fig. 2) calculated for the beam at a rotational temperature of $84\mathrm{K}$, the best-fit value from Fig. 5. The dashed red lines show the expected deflection profiles obtained by convolving the theoretical deviation probability distributions with the undeflected peak profiles. Notice that in this experimental configuration the beam can be detected only within the mass spectrometer acceptance window, indicated by the vertical margins.

Figure 5

Goodness of fit of the deflection profiles as a function of ${\mathrm{H}}_2\mathrm{O}$ rotational temperature for the six experiments shown in Fig. 4; the best estimate is $T_{\mathit{rot}}=84\pm 8\mathrm{K}$.

Figure 6

(Color online) Experimental and theoretical profiles for heavy water $\left({\mathrm{D}}_2\mathrm{O}\right)$ molecules prepared with the source and nozzle at room temperature, without carrier gas. Lines are marked in the same way as in Fig. 4, and the best-fit rotational temperature is $167\mathrm{K}$.

Figure 7

(Color online) Detection of the intense low-field seeker sideband for ${\mathrm{H}}_2\mathrm{O}$, at a setting of $V=20\mathrm{kV}$, $E=63.5\mathrm{kV}∕\mathrm{cm}$, $\partial E∕\partial z=300\mathrm{kV}∕{\mathrm{cm}}^2$. The central profile, from Fig. 4, was extended by shifting the mass spectrometer off-axis, thereby detecting the predicted high-deflection “beamlet” shown as the solid thick black line. Its position and strength (11% of the total intensity) are reproduced without any adjustable parameters (dashed red curve). A companion high-field seeker sideband of similar magnitude (14%) will be present on the opposite side.