Phenanthrene: establishing lower and upper bounds to the binding energy of a very weakly bound anion

Quite a few molecules do not form stable anions that survive the time needed for their detection; their electron affinities (EA) are either very small or negative. How does one measure the EA if the anion cannot be observed? Or, at least, can one establish lower and upper bounds to their EA? We propose two approaches that provide lower and upper bounds. We choose the phenanthrene (Ph) molecule whose EA is controversial. Through competition between helium evaporation and electron detachment in HenPh− clusters, formed in helium nanodroplets, we estimate the lower bound of the vertical detachment energy (VDE) of Ph− as about −3 meV. In the second step, Ph is complexed with calcium whose electron affinity is just 24.55 meV. When CaPh− ions are collided with a thermal gas of argon, one observes Ca− product ions but no Ph−, suggesting that the EA of Ph is below that of Ca.


Fig. S1
Sections of a negative ion mass spectrum of HNDs doped with phenanthrene. Panels a, b, c show the regions where Ph -, Ph 2and Ph 3complexed with a few He atoms appear. The x-axis is chosen such that members of the homologous He n Ph mion series (m = 1, 2, 3) with identical n are horizontally aligned. Ph 2and Ph 3are observed, but Phis not.
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Fig. S2
Mass spectra of ions produced by collisions of (H 2 O) 3 Phand Ph 2with argon atoms at 5 eV ion energy (in the lab system) (panels a and b, respectively).

Fig. S3
Mass spectra of ions produced by collision of CaPhwith argon atoms at E = 5 eV ion energy (in the lab system) at two different argon pressures (panels a and b). The main product ion is Ca -. A contamination of the parent ion mass peak at 218 u by H 2 OCa 5gives rise to a weak series of H 2 OCa nproduct ions. He 8 Phand He 9 Pharise from a contamination by He 10 Ph -, and H 2 OPhfrom a contamination by He(H 2 O) 2 Ph -. Vertical bars indicate the expected position of ions; question marks flag ion peaks that are not positively identified.

Fig. S4
Panel a: Negative ion mass spectrum of HNDs doped with Ca but no Ph. Panels b and c: CID spectra of mass 218 u anions (mostly H 2 OCa 5ions) with argon atoms at 2 and 10 eV, respectively. The main dissociation channels are loss of H 2 O, H 2 , and one or two Ca, but Cais not detected.

Fig. S5
Electron affinities, EA, and binding energies, E bind , (both in meV) for phenanthrene complexed with He n , n = 1-3, and He.H 2 . Binding energies are given for both neutral ("n") and anionic ("a") form. Energies are given as calculated at the ωB97XD/aug-cc-pVDZ level; B3LYP-D3/aug-cc-pVDZ results are shown in parenthesis. Optimized structures of neutral molecules at the B3LYP-D3/aug-cc-pVDZ level are displayed.

Fig. S7
Structure of Ph 2shown in top and side view as optimized at the B3LYP/aug-cc-pVDZ and ωB97XD/aug-cc-pVDZ levels.

Table S1
Benchmark of electron affinities (in meV) calculated using various DFT functionals. Both results for aug-cc-pVDZ ("augcc-pVDZ") and for optimization using aug-cc-pVDZ and single-point recalculation using aug-cc-pVTZ ("aug-cc-pVTZ//aug-cc-pVDZ") are given. In the latter case, the zero-point energy correction calculated using the aug-cc-pVDZ basis set was employed.