Photodetachment spectroscopy of the beryllium oxide anion, BeO⁻

The chemistry of beryllium is known to be significantly different from the behavior exhibited by the heavier group IIA elements.^1–13 In part, this is due to the high ionization energy (9.32 eV) and small radius of Be. As a consequence, the bonds formed by Be have appreciably more covalent character. Theoretical techniques have often been used to explore Be chemistry, conveniently circumventing the toxicity issues (see, for example, Ref. 1 and the references therein). At first glance, Be seems to be well suited for investigation using non-relativistic quantum chemical methods. It is a light element with just four electrons. However, calculations for Be-compounds often prove to be difficult, with the Be₂ dimer being a celebrated example.^14–23 Problems arise because the bonds involving Be can be dominated by electron correlation, such that they include significant contributions from doubly excited electron configurations.

Diatomic beryllium oxide (BeO) is a prototypical species for studies of Be bonding. It has been the subject of both spectroscopic and theoretical investigations.^24–38 Based on theoretical calculations, Frenking and co-workers^6,39–41 have noted that BeO is an extraordinarily strong Lewis acid, with the ability to attract He with a bond energy of 1500 cm⁻¹. This prediction has been supported by subsequent theoretical studies.^42,43 Similarly, electronic structure calculations indicate that the electron affinity of BeO is relatively large (2.1–2.2 eV).^44,45 The electron binding energy is high enough for the BeO⁻ anion to support both valence and dipole-bound electronically excited states. The latter are stabilized by the 6.26 D permanent dipole moment of BeO.⁴⁴ To date, there have been no published experimental studies of BeO⁻.

In the present work, we have used anion photodetachment spectroscopy to determine the electron affinity of BeO and molecular constants for the ground state of BeO⁻. This effort was motivated by interest in testing the previous theoretical predictions for BeO⁻ and to provide data for further testing and refinement of the quantum chemistry models used for anions. Looking beyond these immediate objectives, this will be the first step towards studies of larger Be_nO_m clusters by means of anion photodetachment techniques. Studies of such clusters can reveal the degree of covalency and some of the unique electrostatic binding capabilities of small beryllium oxide species. For example, theoretical calculations predict that (BeO)_n clusters can be used as a lightweight, reversible storage medium for H₂.^8,13,46 Hence, in addition to the fundamental science questions, the work on the oxide clusters relates to potential practical applications of these materials.

The data presented here were recorded using photoelectron velocity-map imaging spectroscopy. The details of the technique have been described extensively in other publications.^47–49 The imaging apparatus used in this study was modified from an existing setup described elsewhere.⁵⁰ Only the new additions to the current spectrometer are discussed in detail here.

Figure 1 shows a diagram of the apparatus used to study BeO⁻. Anions were produced in a laser ablation source⁵¹ using a beryllium rod target and the focused, frequency doubled output of a Nd:YAG laser (532 nm, ∼8 mJ). This source was coupled to a pulse valve that delivered 70%/30% Ne/He carrier gas seeded with 2.5% N₂O at a backing pressure of 55 psia. The anions produced by the ablation process were supersonically expanded into a differentially pumped vacuum chamber, where a Wiley-McLaren time of flight mass spectrometer (WM-TOFMS),⁵² in a perpendicular orientation with respect to the direction of the expansion, was housed. Fast rising, negative pulsed voltages were applied to the repeller and extractor of the WM-TOFMS by high voltage switches, accelerating the anions into a drift region to allow for mass separation before reaching the photodetachment region of the velocity-map imaging optics. The resolution of the mass spectrometer was m/$Δm$ = 690 at masses around 40 amu.

Along the flight-path of the anions from the WM-TOFMS, an Einzel lens and four sets of deflector plates were used to focus and guide the anions into the velocity-map imaging (VMI) optics. Additionally, a fifth set of deflector plates could be pulsed to act as a mass gate to only allow the anion of interest to enter the detachment region. One plate of each pair was grounded while the opposite plate was connected to a dual polarity voltage source.

Once inside the VMI optics, the mass selected anions were intercepted by the polarized, focused output of a Nd:YAG pumped dye laser or an excimer pump dye laser operating at a photon energy above the detachment threshold of the species of interest. Typical detachment laser pulse energies were in the range of 0.5–1.0 mJ, with a beam diameter of <2 mm. The dye laser linewidths were approximately 0.3 cm⁻¹ (FWHM). Wavelength calibrations of the lasers were established using the gas phase absorption spectrum of the B–X transition of room temperature I₂. The absolute energies of the I₂ lines were taken from the PGOPHER software package.⁵³ 

The velocity-map imaging electrodes were replicated from the original Eppink and Parker design⁴⁹ using 1/16 in. thick 304 stainless steel. The photoelectrons produced within the VMI lens were accelerated down a 66 cm long drift region, shielded from external electric and magnetic fields by layers of mu-metal, to the detector (Photonis USA, Inc., 75 mm Chevron stacked microchannel plates (MCPs) with a fiberoptic P47 phosphor screen). Images from the detector screen were recorded by a CCD camera (Physimetrics UI-2230SE-M-GL, 1024 × 768). The photodetached electrons were discriminated from all other charged particles by pulsing the voltage (gain) on the MCPs at the appropriate arrival time. Individual cycles of the experiment were recorded and summed over several hundred thousand laser pulses to produce an image. The final image was saved using the imaging collection software developed by Li et al.⁵⁴ The transformation of the image from velocity space to energy was done using the Maximum Entropy Velocity Legendre Reconstruction (MEVELER) technique.⁵⁵ The total emission of the screen from electron or anion impacts could also be monitored with a photomultiplier tube positioned off axis from the camera (not shown in Fig. 1). This mode of detection produced a TOF-MS spectrum and was extremely useful in the optimization of anion and photoelectron production. The repetition rate of the experiment was 10 Hz. All images were calibrated using the known transitions from the detachment of the sulfur anion, S⁻.^56–58 

The ground state electronic configurations of BeO and BeO⁻ are easily anticipated. BeO is a closed-shell ionic species with an experimentally verified $X1Σ+$ ground state. The unpaired electron of BeO⁻ resides in an orbital that is primarily of Be 2s character, giving rise to a $X2Σ+$ ground state. Electronic structure calculations were performed on both the anion and neutral beryllium oxide molecules. This was done to assist in the assignment of the spectra and to evaluate the suitability of the chosen electronic structure methods for the treatment of this prototypical small molecular anion. For both beryllium and oxygen, the aug-cc-pwCVXZ (X = T, Q, 5) basis sets were employed, denoted by awCVXZ herein. A second set of diffuse functions was added to these basis sets in order to better describe the diffuse nature of the BeO⁻ frontier orbitals. The exponents of the diffuse functions were determined from an even-tempered expansion of the two lowest exponent functions of the awCVXZ basis sets. The resulting basis sets are denoted d-awCVXZ in the following.

All calculations were performed with the MOLPRO suite of programs.⁵⁹ Potential energy curves (PECs) were calculated, pointwise, by means of the partially spin adapted coupled cluster method including single and double excitations and perturbative corrections for triple excitations (RCCSD(T)), and the complete active space self-consistent field followed by multireference configuration interaction (CASSCF+MRCI+Q) levels of theory. The PECs are shown in Fig. 2. In the RCCSD(T) calculations, all electrons were included in the correlation treatment. The active space in the complete active space self-consistent field (CASSCF) calculations consisted of the 2s and 2p orbitals of both Be and O, while the “core” orbitals, which are linear combinations of the 1s atoms orbitals, were constrained to be doubly occupied. Their wavefunctions were optimized in the CASSCF procedure to aid convergence. For both the anion and neutral BeO species, all electrons were included in the correlation treatment of the subsequent multireference configuration interaction with doubles (MRCID) calculation in an attempt to recover the core-valence correlation energy. The Davidson correction was applied in order to partially compensate for the size inconsistency of the MRCI calculations. Total RCCSD(T) and multireference configuration interaction with singles and doubles (MRCISD) interaction energies were extrapolated to estimate the complete basis set limit using the two point formula of Halkier et al.⁶⁰ (referred to as d-aV(Q,5)Z). The bound ro-vibrational levels of the resulting PECs were calculated using the LEVEL 8.0 program.⁶¹ The lowest vibrational energy levels were least squares fit to the standard Morse energy level expression, yielding effective values for $ωe$ and $ωexe$⁠. Predictions for the electron affinity were made with the inclusion of the zero point vibrational energies.

Initially, restricted Hartree–Fock RCCSD(T) (RHF-RCCSD(T)) calculations were carried out for the expected $Σ+2$ ground state of BeO⁻. Although the T₁ diagnostic, a commonly employed test of the degree of multi-reference character of the electronic wavefunction, had values of ∼0.022 at internuclear separations in the vicinity of the equilibrium bond length of the anion (1.3-1.5 Å), it increased to ∼0.04 at an internuclear separation of 1.8 Å. Additionally, the convergence of the RHF wavefunction became unstable at longer bond lengths. Values of the T₁ diagnostic lying above 0.044 suggest distinctly the multi-reference character. The T₁ diagnostic examines amplitudes of single excitation in the RCCSD procedure, based on a given self-consistent field (SCF) wavefunction. Large values of the T₁ diagnostic may be obtained when the reference wavefunction is a poor description of the electronic state of interest, and therefore large amplitude single electron excitations are apparent in the more representative RCCSD wavefunction (note that CCSD calculations using a spin unrestricted reference wavefunction are not supported by MOLPRO). As an alternative, initial wavefunctions obtained from a B3LYP (Becke, three-parameter, Lee-Yang-Parr exchange-correlation functional) calculation were used in subsequent RCCSD and RCCSD(T) calculations. These calculations displayed well-behaved convergence at internuclear separations of 1-50 Å, with values for the T₁ diagnostic below 0.04 being obtained at internuclear separation between 1.0 and 5 Å. This method is referred to as B3LYP-RCCSD(T) later in the section titled “Experimental results and discussion.”

The results from calculations for both BeO and BeO⁻ are presented in Table I. The predictions for BeO are in good agreement with previous theoretical calculations and reasonably close to the experimental data. The equilibrium bond length was within the experimental error range, while the harmonic vibrational frequency was slightly overestimated. Our calculations for BeO⁻ are also in agreement with earlier theoretical studies.^44,45 The additional electron, which primarily resides in the Be 2s orbital, causes the bond to lengthen and the vibrational frequency to decrease by approximately 100 cm⁻¹. Lastly, the vertical electron detachment energy is predicted to be in the range of 17 200–17 500 cm⁻¹ (2.13–2.17 eV).

Figure 3 shows photodetachment spectra for BeO⁻, obtained by analyses of velocity map images. All of the stronger features in the images yielded near isotropic electron angular distributions. The horizontal scale for these spectra, labeled as transition energy, is the photon energy minus the electron kinetic energy. The traces correspond to images recorded using photon energies of 18 110.48, 17 733.93, 16 744.75 cm⁻¹, and 16 359.34 cm⁻¹, respectively. Note that the intensities of the four spectra were scaled for presentation purposes. Comparisons of intensities for spectra recorded using different detachment energies are not meaningful. However, the relative intensities of features within a single spectrum are valid.

Traces A and C combined show three groups of features. The analysis of trace A, which was recorded with the highest energy photons, is the most straightforward. Based on the molecular constants given in Table I, the features in the 17 400–18 000 cm⁻¹ range are consistent with the $Δυ=0$⁠; 0–0, 1–1, 2–2, 3–3 sequence bands. Similarly, the bands in the 16 000-16 700 cm⁻¹ range (trace C) are the $Δυ$ = −1; 0–1, 1–2, 2–3, 3–4 transitions, while the bands in the 14 600–15 700 cm⁻¹ range are the $Δυ$ = −2; 0–2, 1–3, … 6–8 transitions. Clearly there was appreciable population of the excited vibrational states of the anion. Note that the $Δv$ = −2 features of traces C and D show more extended vibrational sequence structure than the $Δv$ = −1 and 0 features. Franck-Condon factor (FCF) calculations, based on the theoretical potential energy curves, account for this behavior. The 0–0 band is predicted to have the highest FCF for the $Δv$ = 0 group, while the FCF maximum for the $Δv$ = −2 was for the 3–5 band. Another interesting detail of the $Δv$ = −2 bands was the marked difference in the contours of traces C and D at energies near 15 125 cm⁻¹. The reason for this anomaly will be considered following the analysis that yields the electron affinity (EA) of BeO.

The intensity contours of the photodetachment bands were found to be significantly dependent on the excess energy imparted to the electron (with some random fluctuations caused by day-to-day variations in the laser ablation source). For example, traces A and B of Fig. 3 were recorded using energies that differed by 376.6 cm⁻¹. As the photon energy was lower for trace B, the slightly higher resolution was expected. However, the shift in the peak positions was not anticipated. Modeling of the rotational contours provided an explanation for this effect. With higher energy photodetachment, the band contours were dominated by detachment events where there was no change in the rotational angular momentum (i.e., $ΔN$ = 0, where N is the Hund’s case (b) quantum number for the angular momentum, exclusive of spin). When the photon energy was closer to the detachment threshold, transitions with $ΔN$ = −1, −2, and −3 became increasingly more important. Fig. 4 shows an expanded view of trace B, along with a rotational structure simulation described by the following equation:

where $ν0(v′,N′,v″,N″)$ is the threshold energy required to detach an electron from BeO⁻ in ro-vibration state $v″$⁠, $N″$ and produce the neutral molecule in state $v′$⁠, $N′$⁠. This energy is defined by the expression

where EA is the electron affinity of BeO and the ro-vibrational energies are given by

Each transition was assigned a Gaussian line shape

with a linewidth of $Δ𝑣$ (FWHM) and $Γ=Δ𝑣$/2ln2. $Pv″,N″$ is the ro-vibrational Boltzmann population distribution function for the anion ground state. $AΔN$ is an intensity scaling constant for transitions with like changes in the rotational angular momentum. Lastly, $σ(eKE)$ is a Wigner threshold law factor⁶² simplified here as $σ(eKE)=eKEl+1/2$⁠, where eKE is the kinetic energy of the ejected electron. σ was implemented in Eq. (1) to simulate the overall intensity profiles of the images. A value of l = 2 was found to best represent the intensity profiles based on experimentally reasonable values found for $AΔN$ and $Pv″,N″$⁠. We do not attribute the physical meaning to l and consider it to be no more than a convenient model parameter. However, l = 2 does have the effect that there will be almost no signal from photodetachment processes that are very close to threshold. Consequently, transitions where the electron kinetic energy can be increased by transferring rotational energy from the molecule (negative $ΔN$ processes) will become favored as the energy threshold for the $ΔN$ = 0 processes is approached.

The input data for the simulation consisted of the literature values for the molecular constants of BeO, and BeO⁻ rotational constants derived from our theoretical calculations (Table I). The vibrational term energies of BeO⁻, the electron binding energy, and the rotational temperature were treated as variable parameters. As indicated in Fig. 4, the sharpest features of trace B corresponded to the P- and Q-branch band heads, with a lower energy feature arising from the O-branch band head. The rotational temperature of this simulation was 750 K.

The contours of the $Δυ$ = −1 sequence bands, recorded using a detachment photon energy of 16 744.75 cm⁻¹, were consistent with predominantly $ΔN$ = 0 transitions, as were the $Δυ$ = −2 bands. However, the 0 – 1 band $ΔN$ = −2 feature is observed near 16 070 cm⁻¹. The intensity pattern for this $Δυ$ = −1 group was quite similar to that of the $Δυ$ = 0 sequence bands, as they appear in trace A. Note that the electron kinetic energies (energies above observed thresholds) probed in traces A and C were comparable. Likewise, when using photon energies close to threshold (traces B and D), the resulting images have similar rotational contours.

Simulations, like that shown in Fig. 4, were carried out for all four traces shown in Fig. 3. The most important fitting parameters were the anion vibrational term energies, the electron affinity of BeO, and the rotational temperature. These fits defined an electron affinity (detachment threshold) of 17 535 ± 15 cm⁻¹ (2.1741 ± 0.0019 eV) and the anion vibrational intervals listed in Table I. Rotational temperatures between 600 and 750 K gave reasonable simulations. The rotational constants from the ab initio calculations (Table I) were consistent with the observed spectrum and could not be further refined due to the limited resolution of the experimental data. It is believed that the calculated anion rotational constants are close to the true values based on the good agreement between the theory and experiment in the $ΔGν+1/2$ values and the electron affinity. Previous theoretical predictions from Jordan and Seeger⁴⁵ (2.162 eV) and Gutsev et al.⁴⁴ (2.15 eV) are also in agreement with the measured electron affinity.

Lastly, we return to the intensity anomaly exhibited near 15 125 cm⁻¹ within the $Δv$ = −2 group of trace D. The anomaly corresponds to the 2–4 band and it is most likely caused by the accidental excitation of the BeO⁻(v = 3) dipole bound state, which autodetaches to produce the BeO(v = 2) product. Using the above values for the EA and vibrational constants of BeO⁻, we find that 16 359 cm⁻¹ excitation from BeO⁻(v = 4) will terminate 180 ± 20 cm⁻¹ below BeO(v = 3). This energy interval is consistent with the theoretical estimate⁴⁴ of 199 cm⁻¹ for the binding energy of the electron in the first dipole bound state of BeO⁻. Similar intensity anomalies, caused by the excitation of dipole bound states, were reported by Dao and Mabbs⁶³ in their study of the photodetachment spectrum of AuF⁻.

The $X1Σ+−X2Σ+$ electronic transition of BeO⁻ was studied by means of photoelectron velocity-map imaging spectroscopy. The detachment threshold (electron affinity) and vibrational and rotational constants of BeO⁻ were determined for the first time. Ab initio electronic structure calculations were in good agreement with the experimental results. The electron detachment characteristics were found to be dependent on the electron kinetic energy. For near threshold detachment, channels involving multiple quanta changes in the rotational angular momenta had significant cross sections. These channels diminished as the detachment photon energy was increased, leaving $ΔN$ = 0 as the dominant channel.

We are most grateful to Professor Arthur Suits (University of Missouri) for providing advice on the optimization of our imaging system and for the software used to capture and analyze the images. We thank Joseph Czekner (Brown University) for his advice on troubleshooting our spectrometer and improving the quality of the images. We also thank the referee for bringing to our attention the possibility that excited states of BeO⁻ may be observed via intensity anomalies. This work was supported by the National Science Foundation under Grant Nos. CHE-1265586 and CHE-1565912.