A density-matrix adaptation of the Hückel method to weak covalent networks.

The coupled-monomers model is built as an adaptation of the Hückel MO theory based on a self-consistent density-matrix formalism. The distinguishing feature of the model is its reliance on variable bond and Coulomb integrals that depend on the elements of the density matrix: the bond orders and partial charges, respectively. Here the model is used to describe electron reactivity in weak covalent networks Xn±, where X is a closed-shell monomer. Viewing the electron as the simplest chemical reagent, the model provides insight into charge sharing and localisation in chains of such identical monomers. Data-driven modelling improves the results by training the model to experimental or ab initio data. Among key outcomes is the prediction that the charge in Xn± clusters tends to localise on a few (2-3) monomers. This is confirmed by the properties of several known cluster families, including Hen+, Arn+, (glyoxal)n-, and (biacetyl)n-. Since this prediction is obtained in a purely coherent covalent regime without any thermal excitation, it implies that charge localisation does not require non-covalent perturbations (such as solvation), decoherence, or free-energy effects. Instead, charge localisation is an intrinsic feature of weak covalent networks arising from their geometry relaxation and is ultimately attributed to the correlation between covalent bond orders and equilibrium bond integrals.

Microsolvation of Hot Ions: Spectroscopy and Statistical Mechanics of Phenide-Water Interactions.

Thermal excitation alters the spectroscopic signatures of solvated ions and affects their interactions with neighboring molecules. By analyzing the photoelectron spectra of microhydrated phenide (Ph-), the temperatures of the Ph-·H2O and Ph-·(H2O)2 clusters from a hot ion source were determined to be 560 and 520 K, respectively, vs 700 K for unsolvated Ph-. Compared to theory predictions for cold clusters, the high temperature of the environment significantly reduces the average hydration stabilization of the ions and the corresponding band shifts in their spectra. The results are discussed in terms of a statistical model that describes the energy content of the intermolecular (IM) degrees of freedom of the cluster, ⟨EIM⟩. We show that over the entire solvation energy range, the density of states associated with the IM modes of Ph-·H2O, of which there are only 6, is more than an order of magnitude greater than that associated with the 27 internal vibrations of the core anion. The results suggest that the observed cluster temperatures are not determined by the ion source but represent the intrinsic properties of the clusters. The energetics and statistical mechanics of microsolvation limit the excitation that the IM degrees of freedom can sustain without significant solvent evaporation on the timescale of the experiment. The limit is expressed as a characteristic solvation temperature (CST), which is the maximum canonical temperature of a stable cluster ensemble. Driven by evaporative cooling, the terminal cluster temperature from a hot ion source will always be close to the cluster's CST. Only if the source temperature is lower than CST will the observed cluster temperature be determined by the source conditions. An approximate rule is proposed for estimating the characteristic temperature of any cluster using the inflection point on the ⟨EIM⟩ vs T curve.

Photoelectron Spectra of Hot Polyatomic Ions: A Statistical Treatment of Phenide.

Many distinct vibrational states contribute to the congested photoelectron spectra of hot polyatomic anions. This often makes the complete Franck-Condon (FC) analysis both impractical and unnecessary. Although it is common to limit the FC calculations to a subset of the FC-active modes, such a limited approach is strictly applicable to the ground-state (cold) anions only. At high temperatures, all vibrational modes participate in thermal excitation, and the FC and thermal activities become intertwined. We report the photoelectron spectra of ∼700 K phenide (C6H5-) obtained at 355 nm (3.49 eV), 532 nm (2.33 eV), and 611 nm (2.03 eV) and describe several practical models that help interpret and analyze the results. Among them are the active-modes model, the active modes + dark bath and the active modes + bright bath models, and, finally, the energy-conservation model. The models combine the results of limited (and, therefore, feasible) FC calculations with statistical analysis and provide efficient means of determining the ion temperature from the broad and congested photoelectron spectra. The described capability can be applied to hot plasmas, the collisional excitation or cooling of ions, and evaporative cooling in cluster ions.

Dipole effects in the photoelectron angular distributions of the sulfur monoxide anion.

Photoelectron angular distributions (PADs) in SO- photodetachment using linearly polarized 355 nm (3.49 eV), 532 nm (2.33 eV), and 611 nm (2.03 eV) light were investigated via photoelectron imaging spectroscopy. The measurements at 532 and 611 nm access the X3Σ- and a1Δ electronic states of SO, whereas the measurements at 355 nm also access the b1Σ+ state. In aggregate, the photoelectron anisotropy parameter values follow the general trend with respect to electron kinetic energy (eKE) expected for π*-orbital photodetachment. The trend is similar to O2-, but the minimum of the SO- curve is shifted to smaller eKE. This shift is mainly attributed to the exit-channel interactions of the departing electron with the dipole moment of the neutral SO core, rather than the differing shapes of the SO- and O2- molecular orbitals. Of the several ab initio models considered, two approaches yield good agreement with the experiment: one representing the departing electron as a superposition of eigenfunctions of a point dipole-field Hamiltonian, and another describing the outgoing electron in terms of Coulomb waves originating from two separated charge centers, with a partial positive charge on the sulfur and an equal negative charge on the oxygen. These fundamentally related approaches support the conclusion that electron-dipole interactions in the exit channel of SO- photodetachment play an important role in shaping the PADs. While a similar conclusion was previously reached for photodetachment from σ orbitals of CN- (Hart, Lyle, Spellberg, Krylov, Mabbs, J. Phys. Chem. Lett., 2021, 12, 10086-10092), the present work includes the first extension of the dipole-field model to detachment from π* orbitals.

Velocity map imaging spectroscopy of C2H- and C2D-: A benchmark study of vibronic coupling interactions.

High-resolution velocity-map imaged photoelectron spectra of the ethynyl anions C2H- and C2D- are measured at photon wavelengths between 355 and 266 nm to investigate the complex interactions between the closely lying X̃2Σ+ and Ã2Π electronic states. An indicative kinetic energy resolution of 0.4%, together with the full angular dependence of the fast electrons, provides a detailed description of the vibronically coupled structure. It is demonstrated that a modest quadratic vibronic coupling model, parameterized by the quasidiabatic ansatz, is sufficient to accurately recreate all the observed vibronic interactions. Simulated spectra are shown to be in excellent agreement with the experimental data, verifying the proposed model and providing a framework that may be used to accurately simulate spectra of larger C2nH monohydride carbon chains. New spectral assignments are supported by experimental electron anisotropy measurements and Dyson orbital calculations.

Anion of Oxalyl Chloride: Structure and Spectroscopy.

The structure and spectroscopy of the anion of oxalyl chloride are investigated using photoelectron imaging experiments and ab initio modeling. The photoelectron images, spectra, and angular distributions are obtained at 355 and 532 nm wavelengths. The 355 nm spectrum consists of a band assigned to a transition from the ground state of the anion to the ground state of the neutral. Its onset at ∼1.8 eV corresponds to the adiabatic electron affinity (EA) of oxalyl chloride, in agreement with the coupled-cluster calculations predicting an EA of 1.797 eV. The observed vertical detachment energy, 2.33(4) eV, is also in agreement with the theory predictions. The 532 nm spectrum additionally reveals a sharp onset near the photon-energy limit. This feature is ascribed to autodetachment via a low-energy anionic resonance. The results are discussed in the context of the substitution series, which includes glyoxal, methylglyoxal (single methyl substitution), biacetyl (double methyl substitution), and oxalyl chloride (double chlorine substitution). The EAs and anion detachment energies follow the trend: biacetyl < methylglyoxal < glyoxal ≪ oxalyl chloride. The electron-donating character of the methyl group has a destabilizing effect on the substituted anions, reducing the EA from glyoxal to methylglyoxal to biacetyl. In contrast, the strong electron-withdrawing (inductive) power of Cl lends additional stabilization to the oxalyl chloride anion, resulting in a large (∼1 eV) increase in its detachment energy compared to glyoxal.

Weak covalent interactions and anionic charge-sharing polymerisation in cluster environments.

We discuss the formation of weak covalent bonds leading to anionic charge-sharing dimerisation or polymerisation in microscopic cluster environments. The covalent bonding between cluster building blocks is described in terms of coherent charge sharing, conceptualised using a coupled-monomers molecular-orbital model. The model assumes first-order separability of the inter- and intra-monomer bonding structures. Combined with a Hückel-style formalism adapted to weak covalent and solvation interactions, it offers insight into the competition between the two types of forces and illuminates the properties of the inter-monomer orbitals responsible for charge-sharing dimerisation and polymerisation. Under typical conditions, the cumulative effect of solvation obstructs the polymerisation, limiting the size of covalently bound core anions.

Diradical Interactions in Ring-Open Isoxazole.

Electron capture by the σ* LUMO of isoxazole triggers the dissociation of the O-N bond and the opening of the ring. Photodetachment of the resulting anion accesses a neutral structure, in which the O· and ·N bond fragments interact through the intact remainder of the molecular ring and via a 3 Å gap created by the bond dissociation. These through-bond and through-space interactions result in a dense manifold of diradical states, including (in the order of increasing energy) a triplet, an open-shell singlet, a closed-shell singlet, and another triplet state. We report photoelectron spectra that reflect partially resolved signatures of these states. Remarkably, the structure of the isoxazole diradical manifold is qualitatively different from that of the analogous system in oxazole. The distinct properties of the two manifolds are explained by using a coupled-fragments molecular-orbital model. Consistent with the past conclusions [Culberson et al. Phys. Chem. Chem. Phys. 2014, 16, 3964-3972], the lingering through-space interactions between the O· and ·C bond fragments in ring-open oxazole are responsible for the relative stabilization of the closed-shell singlet state, which correlates with the ground-state cyclic structure. In contrast, the placement of the N atom in the terminal position within the ring-open structure of isoxazole is the key factor leading to the near degeneracy of the π and σ* orbitals, favoring a triplet-state configuration.

Deprotonation of Isoxazole: A Photoelectron Imaging Study.

We report a photoelectron imaging study of gas-phase deprotonation of isoxazole in which spectroscopic data are compared to the results of electronic structure calculations for the anion products corresponding to each of three possible deprotonation sites. The observed photoelectron spectra are assigned to a mixture of the anion isomers. Deprotonation at the most acidic (C5) and the least acidic (C4) positions yields the respective C5- and C4-isoxazolide anions, while the reaction at the intermediate-acidity C3 site leads to a cleavage of the O-N bond and an opening of the ring in the anion. Following photodetachment, the ground states of neutral C5- and C4-isoxazolyl are assigned to be σ radicals (X2A'), while the ground-state neutral derived from the ring-open C3-anion is a π radical (X2A″). The relative intensities of the spectral bands exhibit sensitivity to the ion source conditions, giving evidence of competing and varying contributions of the dominant C5 and C3, as well as possible C4, deprotonation pathways.

The quest to uncover the nature of benzonitrile anion.

Anionic states of benzonitrile are investigated by high-level electronic structure methods. The calculations using equation-of-motion coupled-cluster theory for electron-attached states confirm earlier conclusions drawn from the photodetachment experiments wherein the ground state of the anion is the valence 2B1 state, while the dipole bound state lies adiabatically ∼0.1 eV above. Inclusion of triple excitations and zero-point vibrational energies is important for recovering relative state correct ordering. The computed Franck-Condon factors and photodetachment cross-sections further confirm that the observed photodetachment spectrum originates from the valence anion. The valence anion is electronically bound at its equilibrium geometry, but it is metastable at the equilibrium geometry of the neutral. The dipole-bound state, which is the only bound anionic state at the neutral equilibrium geometry, may serve as a gateway state for capturing the electron. Thus, the emerging mechanistic picture entails electron capture via a dipole bound state, followed by non-adiabatic relaxation forming valence anions.

Photoelectron Spectroscopy of Biacetyl and Its Cluster Anions.

Photoelectron spectroscopy of the biacetyl (dimethylglyoxal) anion reveals the properties of the ground singlet and lowest triplet electronic states of the neutral biacetyl (BA) molecule. Due to the broad and congested nature of the singlet transition, which peaks at a vertical detachment energy VDE = 1.12(5) eV, only an upper bound of the adiabatic electron affinity of BA could be determined: EA(BA) < 0.7 eV. A narrower and more structured triplet band peaking at VDE = 3.17(2) eV reveals the adiabatic electron binding energy of the triplet to be 3.05(2) eV. These results are in good agreement with ab initio (coupled-cluster) calculations. The lowest-energy structures of the anion, singlet, and triplet states of biacetyl are characterized by different orientations of the methyl groups within the molecular frame. In the ground singlet state of neutral BA, the methyl torsion is offset by ∼60° compared to that of the anion, while in the triplet the methyl orientation is similar to that of the anion. Photoelectron spectra of the cluster anions reveal that the intermolecular interactions in the homogeneously solvated (BA) n- clusters are significantly stronger than the interactions of BA- with N2O or even of BA- with H2O. To account for these observations, π-π bonded structures of the dimer and trimer anions of biacetyl are proposed based on density-functional theory calculations. The analysis of the proposed structures indicates that the negative charge in the (BA) n- cluster anions, at least in the dimer and the trimer, is significantly delocalized between all BA moieties present and there is a significant degree of covalent bonding within the cluster.

Electron affinity and excited states of methylglyoxal.

Using photoelectron imaging spectroscopy, we characterized the anion of methylglyoxal (X2A″ electronic state) and three lowest electronic states of the neutral methylglyoxal molecule: the closed-shell singlet ground state (X1A'), the lowest triplet state (a3A″), and the open-shell singlet state (A1A″). The adiabatic electron affinity (EA) of the ground state, EA(X1A') = 0.87(1) eV, spectroscopically determined for the first time, compares to 1.10(2) eV for unsubstituted glyoxal. The EAs (adiabatic attachment energies) of two excited states of methylglyoxal were also determined: EA(a3A″) = 3.27(2) eV and EA(A1A″) = 3.614(9) eV. The photodetachment of the anion to each of these two states produces the neutral species near the respective structural equilibria; hence, the a3A″ ← X2A″ and A1A″ ← X2A″ photodetachment transitions are dominated by intense peaks at their respective origins. The lowest-energy photodetachment transition, on the other hand, involves significant geometry relaxation in the X1A' state, which corresponds to a 60° internal rotation of the methyl group, compared to the anion structure. Accordingly, the X1A' ← X2A″ transition is characterized as a broad, congested band, whose vertical detachment energy, VDE = 1.20(4) eV, significantly exceeds the adiabatic EA. The experimental results are in excellent agreement with the ab initio predictions using several equation-of-motion methodologies, combined with coupled-cluster theory.

HOCCO versus OCCO: Comparative spectroscopy of the radical and diradical reactive intermediates.

We present a photoelectron imaging study of three glyoxal derivatives: the ethylenedione anion (OCCO(-)), ethynediolide (HOCCO(-)), and glyoxalide (OHCCO(-)). These anions provide access to the corresponding neutral reactive intermediates: the OCCO diradical and the HOCCO and OHCCO radicals. Contrasting the straightforward deprotonation pathway in the reaction of O(-) with glyoxal (OHCCHO), which is expected to yield glyoxalide (OHCCO(-)), OHCCO(-) is shown to be a minor product, with HOCCO(-) being the dominant observed isomer of the m/z = 57 anion. In the HOCCO/OHCCO anion photoelectron spectrum, we identify several electronic states of this radical system and determine the adiabatic electron affinity of HOCCO as 1.763(6) eV. This result is compared to the corresponding 1.936(8) eV value for ethylenedione (OCCO), reported in our recent study of this transient diradical [A. R. Dixon, T. Xue, and A. Sanov, Angew. Chem., Int. Ed. 54, 8764-8767 (2015)]. Based on the comparison of the HOCCO(-)/OHCCO(-) and OCCO(-) photoelectron spectra, we discuss the contrasting effects of the hydrogen connected to the carbon framework or the terminal oxygen in OCCO.

Benzonitrile: Electron affinity, excited states, and anion solvation.

We report a negative-ion photoelectron imaging study of benzonitrile and several of its hydrated, oxygenated, and homo-molecularly solvated cluster anions. The photodetachment from the unsolvated benzonitrile anion to the X̃(1)A1 state of the neutral peaks at 58 ± 5 meV. This value is assigned as the vertical detachment energy (VDE) of the valence anion and the upper bound of adiabatic electron affinity (EA) of benzonitrile. The EA of the lowest excited electronic state of benzonitrile, ã(3)A1, is determined as 3.41 ± 0.01 eV, corresponding to a 3.35 eV lower bound for the singlet-triplet splitting. The next excited state, the open-shell singlet Ã(1)A1, is found about an electron-volt above the triplet, with a VDE of 4.45 ± 0.01 eV. These results are in good agreement with ab initio calculations for neutral benzonitrile and its valence anion but do not preclude the existence of a dipole-bound state of similar energy and geometry. The step-wise and cumulative solvation energies of benzonitrile anions by several types of species were determined, including homo-molecular solvation by benzonitrile, hydration by 1-3 waters, oxygenation by 1-3 oxygen molecules, and mixed solvation by various combinations of O2, H2O, and benzonitrile. The plausible structures of the dimer anion of benzonitrile were examined using density functional theory and compared to the experimental observations. It is predicted that the dimer anion favors a stacked geometry capitalizing on the π-π interactions between the two partially charged benzonitrile moieties.

Aromatic Stabilization and Hybridization Trends in Photoelectron Imaging of Heterocyclic Radicals and Anions.

We examine the photoelectron spectra and laboratory-frame angular distributions in the photodetachment of furanide (C4H3O(-)), thiophenide (C4H3S(-)), and thiazolide (C3H2NS(-)) and compare the results to the previously reported studies of pyridinide (C5H4N(-)) and oxazolide (C3H2NO(-)). Using the mixed s-p model for the angular distributions, the results are interpreted in terms of the effective fractional p character of the highest-occupied molecular orbitals of these heterocyclic anions, revealing trends related to the aromaticity. We conclude that aromatic stabilization across a series of systems may be tracked using the photoelectron angular distributions. In addition, we report an improved (higher-precision) electron affinity (EA) for the thiophenyl radical, EA((•)C4H3S) = 2.089(8) eV. The EA of thiazolyl falls within the 2.5(1) eV range, but it is not clear if this determination corresponds to the 2- or 5-cyclic species or the 2-ring-open isomer. These results are analyzed in conjunction with the properties of other heterocyclic radicals (pyridinyl, furanyl, and oxazolyl) and interpreted in terms of the C-H bond dissociation energies (BDEs) of the corresponding closed-shell molecules. The BDEs of all five-membered-ring heterocyclics studied fall within the 116-120 kcal/mol range, contrasting the lower BDE = 110.4(2.0) kcal/mol of the more aromatic six-membered-ring pyridine. The observed aromaticity trends are consistent with the findings derived from the anion photoelectron angular distributions.

Spectroscopy of Ethylenedione.

The long sought-after, intrinsically short-lived molecule ethylenedione (OCCO) was observed and investigated by anion photoelectron spectroscopy. The adiabatic electron affinity of its quasi-bound (3)Σ(g)(-) state is 1.936(8) eV. The vibrational progression with a 417(15) cm(-1) frequency observed within the triplet band corresponds to a trans-bending mode. Several dissociative singlet states are also observed, corresponding to two components of the (1)Δg state and the (1)Σ(g)(+) state. The experimental results are in agreement with theoretical predictions and constitute the first spectroscopic observation and characterization of this elusive compound.

Photoelectron angular distributions for states of any mixed character: an experiment-friendly model for atomic, molecular, and cluster anions.

We present a model for laboratory-frame photoelectron angular distributions in direct photodetachment from (in principle) any molecular orbital using linearly polarized light. A transparent mathematical approach is used to generalize the Cooper-Zare central-potential model to anionic states of any mixed character. In the limit of atomic-anion photodetachment, the model reproduces the Cooper-Zare formula. In the case of an initial orbital described as a superposition of s and p-type functions, the model yields the previously obtained s-p mixing formula. The formalism is further advanced using the Hanstorp approximation, whereas the relative scaling of the partial-wave cross-sections is assumed to follow the Wigner threshold law. The resulting model describes the energy dependence of photoelectron anisotropy for any atomic, molecular, or cluster anions, usually without requiring a direct calculation of the transition dipole matrix elements. As a benchmark case, we apply the p-d variant of the model to the experimental results for NO(-) photodetachment and show that the observed anisotropy trend is described well using physically meaningful values of the model parameters. Overall, the presented formalism delivers insight into the photodetachment process and affords a new quantitative strategy for analyzing the photoelectron angular distributions and characterizing mixed-character molecular orbitals using photoelectron imaging spectroscopy of negative ions.

Low-lying electronic states of cyclopentadienone.

We report a combined experimental and theoretical study of the low-lying electronic states of cyclopentadienone (C5H4O). The cyclopentadienone anion (C5H4O(-)) was generated in the gas phase via reaction of atomic oxygen radical anions (O(-)) with cyclopentanone (C5H8O). Photoelectron imaging was used to gain access to the first three electronic states of C5H4O, including the X (1)A1 ground state and the (3)B2 and (3)A2 excited states. The first two state assignments are supported by the Franck-Condon simulations of the vibrational progressions observed in the X (1)A1 and (3)B2 bands in the photoelectron spectra. The adiabatic electron affinity of cyclopentadienone in the ground state is determined to be EA(X (1)A1) = 1.06 ± 0.01 eV, and the corresponding values for the first two excited states are EA((3)B2) = 2.56 ± 0.02 eV and EA((3)A2) = 3.45 ± 0.01 eV. These experimental determinations are in excellent agreement with the CCSD(T) theory predictions, lending further confidence to the above state assignments. On the basis of these results, the lowest singlet-triplet splitting (between the X (1)A1 and (3)B2 states) in cyclopentadienone is ΔES-T = 1.50 ± 0.02 eV.

Photochemistry of fumaronitrile radical anion and its clusters.

The photodetachment and photochemistry of the radical anion of fumaronitrile (trans-1,2-dicyanoethylene) and its clusters are investigated using photoelectron imaging and photofragment spectroscopy. We report the first direct spectroscopic determination of the adiabatic electron affinity (EA) of fumaronitrile (fn) in the gas phase, EA = 1.21 ± 0.02 eV. This is significantly smaller than one-half the EA of tetracyanoethylene (TCNE). The singlet-triplet splitting in fumaronitrile is determined to be ΔES-T ≤ 2.6 eV, consistent with the known properties. An autodetachment transition is observed at 392 and 355 nm and assigned to the (2)Bu anionic resonance in the vicinity of 3.3 eV. The results are in good agreement with the predictions of the CCSD(T) and EOM-XX-CCSD(dT) (XX = IP, EE) calculations. The H2O and Ar solvation energies of fn(-) are found to be similar to the corresponding values for the anion of TCNE. In contrast, a very large (0.94 eV) photodetachment band shift, relative to fn(-), is observed for (fn)2(-). In addition, while the photofragmentation of fn(-), fn(-)·Ar, and fn(-)(H2O)1,2 yielded only the CN(-) fragment ions, the dominant anionic photofragment of (fn)2(-) is the fn(-) monomer anion. The band shift, exceeding the combined effect of two water molecules, and the fragmentation pattern, inconsistent with an intact fn(-) chromophore, rule out an electrostatically solvated fn(-)·fn structure of (fn)2(-) and favor a covalently bound dimer anion. A C2 symmetry (fn)2(-) structure, involving a covalent bond between the two fn moieties, is proposed.