Accurate Electron Affinity of Iron and Fine Structures of Negative Iron ions

Ionization potential (IP) is defined as the amount of energy required to remove the most loosely bound electron of an atom, while electron affinity (EA) is defined as the amount of energy released when an electron is attached to a neutral atom. Both IP and EA are critical for understanding chemical properties of an element. In contrast to accurate IPs and structures of neutral atoms, EAs and structures of negative ions are relatively unexplored, especially for the transition metal anions. Here, we report the accurate EA value of Fe and fine structures of Fe− using the slow electron velocity imaging method. These measurements yield a very accurate EA value of Fe, 1235.93(28) cm−1 or 153.236(34) meV. The fine structures of Fe− were also successfully resolved. The present work provides a reliable benchmark for theoretical calculations, and also paves the way for improving the EA measurements of other transition metal atoms to the sub cm−1 accuracy.

onset of p-wave detachment at threshold 39 . As shown later, the ability to resolve the congested photodetachment channels is crucial to measure the fine structures of Fe − . Similar to the case of Fe, the uncertainties of EA values for many other transition metals also remain 10 meV [40][41][42] . The experiment method we demonstrated in this study can serve as a powerful approach to improve the EA measurement and fine structure for other transition metal elements.
In this study, the accurate EA value of Fe and the fine structures of Fe − were obtained using the slow electron velocity imaging (SEVI) method. SEVI has a super energy resolution for slow electrons [43][44][45][46] . Recently, an energy resolution 1.2 cm −1 for E k = 5.2 cm −1 has been reported by Wang and coworkers 45 . The conversion factor between cm −1 and eV is 1 eV = 8065.544 005(50) cm −1 , recommended by CODATA 47 . Since the neutral Fe atomic energy levels are well known, this gives a freedom to choose the final neutral state of photodetachment. This flexibility is crucial for current Fe study and other elements with a low EA value 48 . To avoid using a tunable laser in far infrared region, the Fe( 3 F 4 ) ← Fe − ( 4 F 9/2 ) channel, threshold photodetachment wavelength λ ≈ 745 nm, is chosen for conducting the Fe EA measurement. With our newly constructed SEVI apparatus, this study successfully resolved all fine structures of Fe − and significantly improved the EA accuracy of Fe.

Results
Photoelectron Spectroscopy. The descriptions of our spectrometer have been reported in previous work 49 . The Fe − ion beam was produced by a laser ablation ion source assisted with sodium vapor. The photoelectron spectra were obtained for Fe − at various detachment laser wavelengths. Figure 1 presents the spectrum at a photon energy hν = 13414.38 cm −1 . There are six sharp peaks labelled with letters (a-f). The photoelectron imaging shown in the inset clearly shows expected parallel transitions due to the p-wave detachment. The related transitions of each peak are shown in Fig. 2. The vertical spikes in Fig. 1 are the theoretical simulation according to the assigned transitions. These intensity simulations were derived by assuming the ion temperature of 800 K 6 and further rescaled according to the Wigner threshold law σ ∝ E k 3/2 for p-wave detachment. Here σ is the cross section of photodetachment. The excellent agreement between experimental results and simulations confirmed the validity of current assignment. Based on the assignment, transition d [Fe( 3 F 4 ) ← Fe − ( 4 F 9/2 )] is the only photodetachment channel originated from the ground state Fe − ( 4 F 9/2 ), so it was selected as the target channel for the accurate EA measurement.  Electron Affinity and Fine Structures. In order to obtain high accurate EA of Fe, the photoelectron imaging system for the transition d was carefully calibrated. After inverse-Abel transformation 50 , the hitting positions of photoelectrons on the phosphor screen form a ring for each individual transition. The radius r of the ring is proportional to the velocity of photoelectrons. The radius can be obtained by summing the intensity over all angles, and then finding the peak center via a Gaussian profile fitting. A series of photoelectron spectra were measured with the photon energy scanned from 13227 cm −1 to 13247 cm −1 with a step 5 cm −1 . The measured radius square (r 2 ) of transition d versus the photon energy hν was plotted in Fig. 3. The energy calibration parameters of the linear relation between hν and r 2 were determined by linear fitting. The binding energy of transition d and its uncertainty can be also derived from this procedure. Figure 4 shows the measured binding energy versus the photoelectron kinetic energy. The mean binding energy is 13212.17 cm −1 with an uncertainty 0.27 cm −1 . The neutral Fe ( 3 F 4 ) state is 11976.239 cm −1 above the iron neutral ground state ( 5 D 4 ). Therefore, EA(Fe) is determined as 1235.93 ± 0.28 cm −1 . The uncertainty 0.28 cm −1 has included the 0.06 cm −1 laser linewidth. The fine structure of Fe − ( 4 F) were derived from the observed transitions. The splitting of Fe − ( 4 F 7/2 ) ← Fe − ( 4 F 9/2 ), Fe − ( 4 F 5/2 ) ← Fe − ( 4 F 9/2 ), Fe − ( 4 F 3/2 ) ← Fe − ( 4 F 9/2 ) was determined as 520.9(11), 901.0(14), 1160.8(15) cm −1 by the standard spectroscopic method, the covariance algebra, respectively 51,52 .  The measured binding energies of transitions and fine structures of Fe − are summarized in Tables 1-3. The measured fine structures of Fe − are in comparison with the calculated ones using the spin-orbit coupling multi-reference configuration interaction method. The calculated values are slightly higher than the experimental results. The measured EAs were also compared with the theoretical predictions in Tables 1-3. The small value of EA of iron is a particular challenge to theory. Some methods even predicted a negative binding energy.
The energy gaps between different neutral Fe states can also be extracted from the six transitions. It is worth comparing them with the standard atomic data 53 . The interval between peaks d and e is 585.4 cm −1 , in an excellent agreement with the energy difference 584.695 cm −1 between 3 F 3 and 3 F 4 states of neutral Fe. Similarly, we have an energy interval 408.3 cm −1 between peaks b and f versus 407.620 cm −1 between Fe( 3 F 2 ) and Fe( 3 F 3 ). These accurate data can be considered as the fingerprints of anionic states for the unambiguous assignment.

Discussion
In conclusion, the EA value of Fe was determined as 1235.93(28) cm −1 or 153.236(34) meV using the slow electron velocity imaging method. The accuracy of EA of Fe was improved by a factor more than 80 compared with previous reported 151(3) meV 7 . The fine structures of Fe − were successfully resolved. The Fe − 4 F 7/2 , 4 F 5/2 , 4 F 3/2 are 520.9(11) cm −1 , 901.0(14) cm −1 , and 1160.8(15) cm −1 above the ground state 4 F 9/2 , respectively.    During past 40 years, the measurement accuracy of the electron affinity (EA) of main group elements has been steadily improved to 0.01-0.05 meV. However, the uncertainties of EA values of many transition elements still remain 10 meV [40][41][42] . The experimental EA values for most of the f-block lanthanides and actinides are not available yet [54][55][56][57] . The super energy resolution of SEVI method combined with the sodium vapor assisting laser ablation ion source makes it possible to improve the EA measurement accuracy to sub cm −1 for nearly all transition metal atoms.

Methods
The experiment was conducted using a slow electron velocity imaging apparatus equipped a laser ablation ion source. The Fe − ion beam was produced by a laser ablation ion source. Sodium vapor was introduced to enhance Fe − yield by an inline oven. The 56 Fe − ions were selected by a Wiley-McLaren type time-of-flight mass spectrometer. Then, the selected ions were perpendicularly crossed by the detachment laser beam in the interaction zone. The photodetachment laser is from a Spectra-physics dye laser system (400-920 nm, line width 0.06 cm −1 at 625 nm) pumped by a Quanta-Ray Pro 290 Nd:YAG laser (20 Hz, 1000 mJ/pulse at 1064 nm). The photon energy (hν) was further measured by a HighFinesse WS6-600 wavelength meter with an accuracy of 0.02 cm −1 . The detached photoelectrons were projected onto a phosphor screen behind a set of micro-channel plates and recorded by a CCD camera. Each photoelectron imaging was an accumulated result of 200,000 laser shots. The photoelectron spectrum was then generated by an inverse Abel transformation of the raw photoelectron imaging. The obtained energy resolution is 3.1 cm −1 for E k = 25 cm −1 at an imaging voltage − 150 V. It should be noted that the energy resolution Δ E k depends on the kinetic energy E k , roughly Δ E k ∝ E k 1/2 . The fine structures of Fe − were calculated using the spin-orbit coupling multireference configuration interaction method with the TZP-DKH basis set. The TZP-DKH basis set was obtained from the basis set exchange website https://bse.pnl.gov. The calculations were carried out using the Molpro package.