Channel branching ratios in CH₂CN⁻ photodetachment: Rotational structure and vibrational energy redistribution in autodetachment

Autodetachment, the anion equivalent of autoionization, is the process whereby an excess electron is lost from a metastable excited anionic state of an atom or molecule. Broadly speaking, autodetachment can be characterized as rotational, vibrational, or electronic. The first two involve non-adiabatic transitions, requiring redistribution of the excess energy of the excited anion state from one of the nuclear modes of freedom to the electronic energy of the final neutral state and the departing electron,

Here ″ indicates the initial state of the anion, hν is the photon energy, the unprimed quantities refer to the excited anion state, and ′ refers to the final state of the neutral. The excess electron kinetic energy is denoted eKE, and in the limit that E_el < E_el′, autodetachment must occur through vibrational or rotational energy conversion unless there is a large change in geometry of the excited anion and final neutral state.¹ Thus, studies of anion autodetachment from excited anion states that are electronically stable with respect to the parent neutral ground state can yield much information about the coupling of the electronic and nuclear degrees of freedom.

In this paper, we highlight the possibility of using photoelectron action spectra to observe energy transfer between different vibrational modes accompanying a vibrational autodetachment process. The cyanomethylide anion, CH₂CN⁻, serves as our illustrative system. In addition to its possible importance in diffuse interstellar band spectra,^2,3 this molecule is appealing for several reasons. Its vibrational modes and their frequencies are well-characterized for both CH₂CN⁻ and CH₂CN, with a progression showing even numbered changes in the vibrational quantum number for the ν₅ umbrella mode being the main contributors.^4,5 The rotational constants of the parent and anion ground states are well known.^6,7 Additionally, several direct detachment transition vibrational origins have been measured with high accuracy in recent slow electron velocity map imaging (SEVI) experiments.⁸ However, the primary reason for choosing this species is the documented existence of a dipole-bound state just below the neutral ground state. Figure 1 shows calculated energies of the anion and neutral ground states at their respective equilibrium geometries (black horizontal lines). In addition, the figure shows the presence of two dipole-bound states, a triplet (orange) and singlet (blue), which lie 3 and 1 meV, respectively, below the supporting neutral at either geometry. Details of the calculations are given below.

Rotational and vibrational autodetachment tend to have longer lifetimes than electronic autodetachment and thus manifest as relatively narrow features in the photon energy dependence of the detachment cross section. Photoelectron spectroscopy is typically thought of as a technique that at best resolves vibrational transitions. However, with sufficiently narrow excitation linewidths, fully resolved rotational structure has been observed in measurements of the total detachment cross section for CH₂CN⁻ for photon energies between 11 800 and 13 650 cm⁻¹.^6,9,10 The energy dependence of the total detachment cross section represents an action spectrum in which structure is ascribed to excitation of various ro-vibrational levels of the (singlet) dipole-bound state. Between 11 800 and 12 600 cm⁻¹, absorption via the fundamental (0₀⁰) band to the dipole-bound state followed by electron loss via rotational-electronic energy transfer produces rotational states of the CH₂CN zero point vibrational level.⁶ Coupling of rotational and electronic degrees of freedom is the only mechanism for electron loss in this case, and consistent with this, autodetachment was only observed from higher J levels of the low K_a (<4) manifolds. At higher excitation energies (12 600-13 650 cm⁻¹), vibrationally excited levels of the dipole-bound state are accessed and vibrational autodetachment becomes viable. Rotational structure was still observed in the overall detachment cross section, but all J, K levels of the dipole-bound state autodetach.¹⁰ 

These previous measurements reveal the photon energy dependence of autodetachment but were insensitive to the internal energy disposal in the final neutral state and, therefore, any internal energy redistribution. Of course, in the case of excitation to the zero-point level, the final neutral state is unambiguous. Similarly, comparison of the results of Ref. 10 and later SEVI measurements⁸ allows us to the conclusion that vibrational autodetachment between 12 600 and 13 650 cm⁻¹ must occur from the ν₅, (v = 1) level of the singlet dipole-bound state (excited via a hot-band transition) to the zero point level of the neutral (vibrational mode descriptions are found in Table I). However, at higher excitation energies, more vibrational levels of the dipole-bound state become accessible and, consequently, more autodetachment channels become energetically feasible.

In this paper, we use a combination of photoelectron spectroscopic imaging detection and tunable photoexcitation to gain a better understanding of the states involved in the autodetachment process. The measurements presented in the current work extend the excitation energy to 15 400 cm⁻¹, accessing higher vibrational levels of the ν₅ mode as well as levels associated with the ν_3-6 and ν₉ modes and combinations thereof (Table I). Employing a detection scheme that affords at least partial vibrational resolution, we show that for the most part the expectations of the vibrational propensity rule¹ and normal mode approximation are observed. However, the results also reveal evidence that ν₃ mode levels autodetach to levels associated with different modes.

The results presented in this paper are vibrationally resolved (or partially resolved) photodetachment spectra of the CH₂CN⁻ ion recorded over a range of photon energies. The (anion photoelectron imaging) instrumentation has been described in detail elsewhere^11,12 and in the interests of brevity only relevant or new details are presented here.

CH₂CN⁻ ions are produced via expansion of an acetonitrile/O₂ mixture through a pulsed general valve (Series 9) nozzle. The gas mixture is formed by flowing O₂ (60 pounds per square inch gauge) over liquid acetonitrile (Sigma-Aldrich, Inc., 99.9% purity). Expansion into a vacuum chamber maintained at <6.0 × 10⁻⁶ Torr occurs through a pulsed electrostatic discharge.¹³ The discharge is produced using a pair of metal needles as electrodes, located 8 mm downstream from the nozzle orifice and held in place with Teflon insulators. The anode is pulsed up to 1.3 kV for 95-120 μs, timed to coincide with the gas pulse, while the cathode is kept at ground.

CH₂CN⁻ and a number of other ions are produced in the discharge. These are separated using a 2 m long time of flight (TOF) mass spectrometer arrangement incorporating Wiley-McLaren and einzel lens focusing elements. The ion TOF mass spectrum was recorded using a microchannel plate (MCP) detector coupled to a digital oscilloscope. The mass spectrum was calibrated using the peak corresponding to the O₂⁻ ion which in turn was verified using the electron binding energy and photoelectron angular distribution of the vibrational transitions in the X-X band.^14,15 CH₂CN⁻ photodetachment was achieved using the linearly polarized output of a pulsed nanosecond tunable laser (Cobra-Strech, Sirah Laser, pumped at 10 Hz by second harmonic of a Spectra Physics INDI-10 neodymium yttrium aluminum garnet laser). Photon-ion interaction within the lens of a perpendicular velocity mapped imaging arrangement^16,17 over a number of laser shots (>6000) results in collection of electron impacts to form a composite photoelectron image. The position sensitive imaging detector is comprised of a dual chevron type MCP and P20 phosphor screen (Burle, Inc.), and individual electron impacts are accumulated into the composite image using a charge coupled device (CCD) camera (IMPERX VGA). To account for spurious charged particle impacts and dark current in the CCD, a second image is subtracted. This background image is collected over the same number of laser shots with the laser pulse desynchronized from the ion of interest (and all other ions). The resulting background subtracted image represents a two dimensional (2D) projection of the 3D photoelectron density distribution resulting from the detachment event. The photoelectron velocity distribution is extracted from the 2D projection using the BASEX (basis set expansion) method.¹⁸ At least three composite images are recorded at each photon energy to ensure repeatability and to eliminate random fluctuations in intensity of the individual features in the spectra.

Electronic structure and photodetachment cross-section calculations were performed using Q-Chem^19,20 and the ezDyson code.²¹ We used coupled-cluster (CC) and equation-of-motion coupled-cluster (EOM-CC) methods to describe electronic states of the anion and the neutral.^22,23 The ground state of the closed-shell CH₂CN⁻ anion was computed using CCSD (coupled-cluster method with single and double excitations). The ground and excited states of the neutral radical were then described by EOM-IP-CCSD (EOM-CCSD for ionization potentials) using the closed-shell CCSD reference. The excited states of the anion were computed using EOM-EE-CCSD (EOM-CCSD for excitation energies) using the same closed-shell reference state.

In agreement with previous calculations,^3,24–26 the ground-state structure of the anion (optimized using CCSD/aug-cc-pVTZ) has C_s symmetry, whereas the equilibrium geometry of the ground-state neutral radical, computed by EOM-IP-CCSD/aug-cc-pVTZ, has C_2v symmetry, corresponding to a planar structure. Bond lengths and angles are given in Fig. 1, and the respective Cartesian coordinates are provided as supplementary material. The labels of electronic states follow the Mulliken convention.^27,28

At the anion equilibrium geometry, the computed vertical detachment energy (VDE) is 1.675 eV (EOM-IP-CCSD/aug-cc-pVTZ) and the dipole moment of the neutral X²A′ state is 3.608 D, which is sufficient to support a dipole-bound state. As pointed out in previous studies, electron correlation effects are important for dipole-bound states,^29–32 and, as evidenced by excellent agreement between the theoretical and experimental binding energies, EOM-EE-CCSD is capable of quantitative accuracy, provided an adequate basis set is used.³³ We augmented the aug-cc-pVTZ basis set with 9s,9p,3d sets of diffuse functions. As shown in Fig. 1, the calculations reveal two dipole-bound states, in agreement with previous studies.²⁶ These are a triplet (³A′) and a singlet (¹A′), which we calculate to be bound by 3 meV and 1 meV, respectively, in excellent agreement with the experimentally measured 5 meV.⁸ 

At the optimized geometry of the neutral (C_2v), the vertical electron affinity (VEA) is 1.506 eV (EOM-IP-CCSD/aug-cc-pVTZ). This structure has a (slightly) larger dipole moment of 3.666 D. EOM-EE-CCSD calculation using the aug-cc-pVTZ(+9s,9p,3d) basis set shows that the triplet (³B₁) and singlet (¹B₁) dipole-bound states still lie 3 and 1 meV below the neutral state. To analyze state characters, we used natural transition orbitals (NTOs) as implemented in the libwa code.^33,34 The leading NTO pair corresponding to the excitation to the singlet dipole-bound state is shown in Fig. 2. NTOs afford the most compact description of the electronic transition between correlated many-body states $Ψf,i$ as they represent the difference between the two wave functions. Using NTOs, one can express the expectation value of observables (such as the transition dipole moment) in terms of the matrix elements between hole and particle orbitals by summing over all NTO pairs,

where $ψKp,h$ represent a particular NTO (particle or hole), $μ$ is the dipole moment operator, and σ_K is the weight of the Kth NTO pair. For a pure, singly excited transition dominated by a single NTO pair, σ = 1. The dominant NTO pair for the X¹A → ¹B₁ transition is shown in Fig. 2. The weight of this NTO pair is σ = 0.87 making this essentially a one electron transition.

We also computed the oscillator strength for the dipole-allowed transition of the anion. At the equilibrium geometry of the anion, the oscillator strength of the X¹A₁ → ¹B₁ transition is 0.0018.

Photoelectron images were recorded in ≤2 cm⁻¹ photon energy increments over the range 13 460–15 384 cm⁻¹, with smaller intervals used in regions of interest. Spectra extracted from the images show several vibrational features that correspond to detachment from the CH₂CN⁻ ground state to the CH₂CN ground state.

Four representative photoelectron spectra are shown in Fig. 3. The spectra in the left-hand column are taken from the extremes of the photon energy range (E_hν = 13 460 and 15 380 cm⁻¹).

The spectra are plotted in the electron binding energy (eBE) domain, and the lowest energy feature, labeled A, corresponds to the vibronic origin band (0₀⁰ direct detachment transition) with an eBE at the center of 12 468 cm⁻¹.⁸ The eBE domain spectra of Fig. 3 are converted (unsmoothed) directly from velocity domain spectra extracted via the BASEX technique,¹⁸ calibrated for electron kinetic energy (eKE = E_hν – eBE) using the peak of feature A and scaled for intensity using the appropriate Jacobian transformation. The spectra of Fig. 3 are normalized to a maximum P(E) of 1 for convenience of viewing.

At 15 380 cm⁻¹, the highest photon energy used, four distinct features (A,C,D,E) stand out in the spectrum. These correspond to detachment via different vibrational levels of the CH₂CN ground electronic state. Assignments of these levels can be made according to low temperature SEVI measurements.⁸ Band origins are summarized in Table I, along with a description of the most relevant modes. The greatest change in geometry from the non-planar anion to the planar neutral occurs along the ν₅ umbrella mode coordinate,^4,6,9,10 but 5₀^v′ transitions to odd v′ of this b₁ mode are symmetry forbidden.⁴ Consequently, features C and E are predominantly associated with 5₀^v′ (v′ even) in the neutral ν₅ vibration. Minor contributions from the 3₀¹ (C), 3₀² (E), and 3₀¹5₀² (E) detachment bands are also convoluted into these features at the resolution of our detection scheme. Features B (in the 13 460 cm⁻¹ spectrum) and D (in the 15 380 cm⁻¹ spectrum) are associated with excitation to 1 and 3 quanta in the ν₅ mode, respectively. For most of the excitation energy range, the main contributors to features B and D are the direct detachment hot bands 5₁¹ and 5₁³. These arise as the inversion doubling associated with the anion umbrella mode separates the ν₅ (v″ = 1) and zero point levels of the anion by only 130 cm⁻¹.

As the right hand column of Fig. 3 shows, the relative intensities of spectral features B and D change greatly depending on the excitation energy. This is in contrast with the expectations of direct detachment. Figure 3 shows feature B dominating the spectral intensity at E_hν = 13 800 cm⁻¹ while it has a much smaller contribution in the 13 460 cm⁻¹ spectrum. Similarly, feature D shows a marked increase in intensity at 15 163 cm⁻¹ compared to 15 380 cm⁻¹. In fact, as will be shown later, the relative intensities of B and D undergo several rapid changes within the energy ranges 13 690–13 900 cm⁻¹ (B) and 15 100–15 350 cm⁻¹ (D).

While intensities for individual vibrational transitions cannot be extracted across the whole range of these measurements, the relative intensities of features A-E can be determined. Three factors complicate the analysis: partial spectral resolution, non-uniformity of transition widths in the energy domain, and non-uniformity of the widths of features A-E in the velocity domain due to the different spacing of the contributing transitions to each feature. In the energy domain, our instrumental resolution is not constant but conforms to ∆E/E ≈ 10%. However, the instrumental resolution is uniform in the velocity domain allowing the following, fitting based approach. A series of Gaussian functions of the same width (approximating the instrument response and rotational envelope) are used to represent the individual vibrational transitions and summed to recreate the whole, velocity domain spectrum. Only transitions with eBE lower than the photon energy are considered in each case; the centers of these transitions are fixed (for a given photon energy) using conservation of energy and the SEVI reported vibrational band center (Table I),⁸ and a single width is used for all transitions. This reduces the fitting parameters to an area for each Gaussian and a common width for all.

An example of the procedure is illustrated in Fig. 4. The sum (solid thicker red line) of the individual Gaussians (thinner solid lines) is fit to the velocity domain spectrum (filled circles) using the Levenberg-Marquardt algorithm. Regions corresponding to the spectral features of the energy domain spectrum of Fig. 3 are indicated with the corresponding letters A–E. It should be stressed that, to avoid over-interpretation, this procedure is not used to assess absolute contributions of the individual bands. Noise-induced intensity variations and local minima encountered by the fitting routine, particularly at higher electron kinetic energies do not allow for a reliable assessment of individual contributions to the grouped features. For example, in the spectrum of Fig. 4, the majority contribution to feature B appears to be from the 5₀¹ transition. However, the 5₀¹ and 5₁¹ transition centers differ by only 130 cm⁻¹ while at the kinetic energies associated with these transitions for 15 380 cm⁻¹ excitation the energy resolution is 280 cm⁻¹ and the fitting procedure does not reliably distinguish between the 5₀¹ and 5₁¹ transitions. In fact, in this case, the 5₁¹ transition is the more likely contributor when the symmetry of the transition is considered, but the fitting procedure converges on the 5₀¹ transition.⁸ Nevertheless, the relative intensity of feature B determined by summing over the individual contributions comprising this feature (whatever they may be) is far less sensitive to such artefacts.

Figure 5(a) shows σ_det, the calculated electronic contribution to the cross section for direct detachment (at the CCSD/aug-cc-pVTZ equilibrium geometry of the anion using Dyson orbitals computed by EOM-IP-CCSD).^35,36 Franck-Condon factors are not included in this calculation. The cross sections are presented in atomic units, and the abscissa represents the energy (E) relative to the origin of the detachment band. There is an initial onset followed by a more gradual rise in σ_det, behavior which reflects angular momentum threshold effects that are well known in photodetachment spectroscopy.³⁷ 

Branching ratios, $σi$ (where i represents A through E), for each spectral feature can be determined based on the summed areas of the fitting functions. $σi=∑kAk∑jAj$⁠. $∑kAk$ is the sum of the Gaussian areas contributing to feature i and $∑jAj$ is the sum of the areas under each of the fitting functions (i.e., the area under the whole vibronic detachment band). The results are shown in Fig. 6.

We expect that there should be a gradual increase in the electron cross section in the case of direct detachment, as preciously outlined in Fig. 5(a). We observe similar behavior in the branching ratios for feature C, Fig. 6 (blue line), which varies smoothly as the photon energy increases past the 5₀² detachment threshold, and for feature E, Fig. 6 (green line). The latter case shows a pronounced step as the threshold of the 3₀¹5₀² channel is crossed reflecting the opening of a second channel. Note that the onsets in these analyses are a little artificial as the fitting procedure ignores vibrational transitions at photon energies less than the eBEs given in Table I. In reality, the anion rotational population distribution allows electrons in low yield for these channels at lower photon energies. However, the key point is that the evolution of σ_C and σ_E is as expected for direct detachment to the continuum.

In contrast, there are strong deviations from direct detachment behavior in the branching ratios σ_B (Fig. 6, black) and σ_D (Fig. 6, red) at particular excitation energies. Sharp structure is observed in σ_B for excitation between 13 600 and 13 900 cm⁻¹, while σ_D shows sharp structure for excitation between 15 100 and 15 400 cm⁻¹.

The structure observed in σ_B and σ_D is due to the influence of a metastable anion state (a vibrational resonance) lying in the CH₂CN + e⁻ continuum. Autodetachment from excited vibrational levels of the singlet dipole-bound state (i.e., these levels act as autodetaching resonances) has been previously invoked to explain changes in the overall cross section at lower excitation energies. The question arises as to whether an absorption transition would have sufficient strength to excite an electron from the HOMO of the anion to the much more diffuse dipole-bound orbital. Experimentally, the enhancements in the overall photoelectron cross section previously observed^6,9,10 argue in favor of this mechanism. The computed oscillator strength for the X¹A₁ → ¹B₁ transition is small (0.0018) but not negligible. The magnitude can be rationalized by examining Fig. 2, which reveals noticeable spatial overlap between the dipole-bound (particle) and the hole NTOs of CH₂CN⁻; the hole NTO is very similar to HOMO. The issue is further addressed in Fig. 5(b) where the electronic absorption cross section (σ_abs) to the dipole-bound state is plotted against energy (E) relative to the threshold for detachment to the supporting neutral state. This value gives an upper bound for detachment via a vibrational autodetachment channel. Values are based on the molar extinction coefficient, which is in turn determined using the calculated oscillator strength and resonance width (the illustrated case is for 0.004 eV).³⁸ On resonance, for a width of 0.004 eV, the two cross sections are of a similar order of magnitude. Furthermore, the maximum value of σ_abs increases as the resonance width decreases, lending further support to the feasibility of absorption to the dipole-bound state, at least when the resonances are narrow.

As clearly seen in Fig. 2, the dipole-bound state can be described as a neutral molecule with an excess electron occupying a diffuse orbital.³⁹ The excess electron has little interaction with the core of the neutral molecule. Therefore, the potential energy surface is very similar to that of the neutral ground state but lying lower in energy and hence electronically stable with respect to electron loss. Electron loss from internal states of the dipole-bound anion with energy in excess of the neutral zero-point energy requires conversion of nuclear kinetic to electronic energy and the internal levels of the dipole-bound state act as narrow, autodetaching resonances.

Coupling of the nuclear and electronic degrees of freedom is required for the autodetachment process. In the following, the rotational-electronic energy transfer is ignored (this is not necessarily accurate, e.g., Ref. 6) and the relevant vibronic matrix elements, in the one electron approximation, are thus⁴⁰ 

The primed quantities refer to the neutral state and unprimed refer to the dipole-bound state. Q represents the normal mode coordinate for a particular vibration, χ(Q_k) is the vibrational wave function of the k-th normal mode of the dipole-bound state, while χ′(Q_m′) is the wave function of the m-th normal mode of the neutral. ψ is the dipole-bound orbital, ψ′ is the free electron wave function, and (upper case) J and K represent the rotational quantum numbers.

Due to the operation $dχQkdQj$⁠, these vibronic coupling matrix elements are only non-zero in the simple harmonic oscillator and normal mode limits when k = j = m and v′ = v − 1 (where v represents the vibrational quantum number of the m-th mode of the dipole-bound state and v′ is the vibrational quantum number of the k-th mode of the neutral). Anharmonicity renders v′ – v = Δv = −1, a propensity rather than selection rule for vibrational autodetachment. Similarly, coupling of the dipole-bound state vibrational modes will lead to deviations from the restrictions of a true normal mode description.

The measurements presented in the current work employ excitation energies up to 15 400 cm⁻¹. Within the range of these measurements, several vibrational levels of the dipole-bound state become accessible upon excitation from the anion zero point level. Just as in previous work at lower photon energies,^6,9,10 sharp structure is superimposed on an underlying direct detachment contribution (Fig. 6, σ_B and σ_D). This structure is due to excitation to ro-vibrational levels of the intermediate dipole-bound state followed by autodetachment. For these absorption bands, individual (ΔJ) P, Q, and R branch transitions are unresolved. However, the ^rQ_K and ^pQ_K (where the lower case superscript represents ΔK_a) branches stand out sharply. The alternating strong (odd K_a)/weak (even K_a) intensity ratios are consistent with the nuclear spin statistics for the two H atoms.

Direct detachment to the continuum produces a significant and non-constant background which can be accounted for by dividing σ_B (or σ_D) by σ_A and subtracting the constant, non-zero baseline this produces. The black, filled circles in Fig. 7 are the result of this procedure for σ_B which allows remaining structure to be modeled as perpendicular absorption bands of a prolate rotor. The light gray lines joining individual points are intended only as a guide to the eye.

The prolate rotor absorption bands are simulated using previously reported spectral parameters. The anion rotational constants are A″ = 9.294 31 cm⁻¹ and $B¯″$ = 0.333 02 cm⁻¹,⁶ where $B¯$ represents the mean of the reported B and C rotational constants. For the dipole-bound state vibrational levels, we choose to use the neutral ground state zero point level $B¯′$ rotational constant (0.3386 cm⁻¹) but reduce the neutral ground state zero point level A′ constant to 9 cm⁻¹ (from 9.506 cm⁻¹).⁷ This reduction is qualitatively consistent with a higher level of vibrational excitation and satisfactorily reproduces the Q branch separations. Rotational line strengths are determined using Hönl-London factors,⁴¹ multiplied by the appropriate degeneracy, spin statistical, and Boltzmann factors and then convoluted with a Gaussian of full width at reciprocal e of 1 cm⁻¹ to represent the resolution of the excitation laser.

The blue solid line in the top panel of Fig. 7 represents the simulated absorption spectrum to the ν₅, v = 2 level of the singlet dipole-bound state. The band origin was set using the SEVI reported values for the 5₀² direct detachment transition⁸ but shifted to line up the simulated and experimental ^pQ₃ and ^rQ₃ branches in the 5₀² band. These branches are chosen to overlay the simulated and experimental data since any asymmetry doubling (ignored in the simulation) due to deviations from prolate behavior is negligibly small. Effectively this shifts the simulation 36 cm⁻¹ to the red (compared to direct detachment). Physically this shift represents the effect of the dipole binding interaction and is in good agreement with the recently reported dipole binding energy of 39 cm⁻¹.⁸ In simulating the ro-vibrational spectrum, several temperatures for the anion ground state were assessed, with the best overall agreement at 150 K, illustrated in Fig. 7. As an aside, it is noted that 150 K is consistent with the direct detachment background contribution to σ_B (assuming this reflects the relative intensities of the 5₁¹ and 0₀⁰ direct detachment transitions) and therefore suggests that the discharge source used in these experiments thermally equilibrates the rotational and vibrational degrees of freedom.

Photoabsorption from the ground vibrational level of the anion to ν₅ (v = 2) of the singlet dipole-bound state is an electric dipole allowed vibronic band. Subsequent autodetachment to ν₅ (v′ = 1) (ro)vibrational levels is also consistent with the propensity rule¹ and normal mode expectations. The two-step process is energetically equivalent to the symmetry forbidden 5₀¹ direct detachment channel which is included in the energy range of spectral feature B. However, examination of the top panel of Fig. 7 shows that there is structure to higher excitation energy (>13 850 cm⁻¹) than accounted for by the 150 K simulation.

Increasing temperature would increase intensity in the K_a > 5 ^rQ sub-branches and consequently produce structure in the simulated 5₀² absorption band at energies >13 850 cm⁻¹. However, this would also result in an increase in the K_a > 5 ^pQ sub-branch intensities (energies <13 700 cm⁻¹). These latter branches are notably absent in the experimental data allowing the conclusion that transitions from K_a > 5 levels of the anion do not manifest as sharp structure in our autodetachment data. Experimentally observed structure at photon energies >13 850 cm⁻¹ must be due to excitation to a different vibrational band of the dipole-bound state.

Using the previously reported SEVI photodetachment results⁸ as a guide, the only other viable absorption band is 3₀¹ (solid green line, Fig. 7 center panel). The same procedure was employed to simulate the 3₀¹ absorption band to the dipole-bound state with the exceptions that the band origin was shifted relative to the 3₀¹ direct detachment band origin, and the line strengths were scaled to 25% of the corresponding 5₀² lines to reflect the different vibrational band intensities. We note that this is qualitatively consistent with the SEVI direct detachment band intensities. Summing the two simulations yields the solid red line (Fig. 7, lower panel) which successfully reproduces the pattern of the Q branches across the whole band.

We emphasize that the goal is not to determine accurate spectral constants of the dipole-bound state. Several approximations contribute to quantitative differences between the experimental and simulated data. A single linewidth was used while it might reasonably be expected that the spectra will broaden as the energy of the rotational (J,K_a) levels of the dipole-bound state increases.⁶ Use of a Gaussian line shape is incorrect; the peaks in σ should have asymmetric profiles due to competition between direct and autodetachment.^42,43 We made no attempt to accurately model the P and R branches (an average of the neutral zero point level C′ and B′ rotational constants was used),⁷ and we also ignored asymmetry doubling in the Q branches.⁹ Similarly, we reduced the A′ constant to 9 cm⁻¹ to obtain agreement with the Q branch structure but this should not be considered a rigorous determination of A′ for the higher vibrational levels. Nevertheless, the observed Q branch patterns clearly show that the sharp structure in σ_B encompasses excitation of two different autodetaching vibrational levels of the dipole-bound state.

The data represent an action spectrum for spectral feature B, and hence this behavior indicates coupling between ν₃ and other modes (a breakdown of the normal mode approximation) either in the dipole-bound state itself or as the result of inelastic “rescattering” of the autodetaching electron off the neutral core (the latter explanation has been invoked to explain non-mode specific autodetachment in photoexcitation of uracil and 2-hydroxypyrimidine anions).^44,45 Feature B in the direct detachment spectrum includes contributions from the 6₀¹, 5₁¹, 5₀¹, 9₀², and 6₀² bands (Table I). The two step excitation-autodetachment sequence v″ = 0 → ν (v = n) → ν (v′ = m) produces electrons with kinetic energies equivalent to those of ν₀^m direct detachment channels. Hence subsequent to 3₀¹ excitation, autodetachment to (at least) one of the ν₆ v′ = 1, 2, ν₉ v′ = 2, or ν₅ v′ = 1 vibrational levels of the neutral must occur. This is counter to the normal mode expectation and indicates energy transfer between ν₃ (the CH₂ scissors mode) and one or more of the other “normal” modes. It is tempting to speculate that autodetachment is to the ν₅ (v′ = 1) level via coupling of ν₃ and ν₅ modes since both involve C–H motions. However, without full vibrational resolution of the photoelectron spectrum, this cannot be demonstrated conclusively.

Application of a similar approach to the structure observed in σ_D between 15 100 and 15 375 cm⁻¹ (Fig. 8) reveals the contribution of three vibrational levels of the dipole-bound state. The simulations of Fig. 8 are based on the SEVI direct detachment band origins (shifted by 36 cm⁻¹) and a temperature of 150 K. The lower panel highlights the different rovibrational transition energies for the 5₀⁴(blue):5₀²3₀¹(green):3₀²(red) absorption bands.

The structure in σ_D reflects overlap of the three bands, and the complete absorption spectrum (purple) is shown in the upper panel of Fig. 8, scaling the bands in the ratios 0.54 (5₀⁴):0.27 (5₀²3₀¹):0.19 (3₀²) which is qualitatively consistent with the different intensities in the SEVI photoelectron spectrum of Ref. 8. Other than the above scaling, no attempt was made to fit the absorption spectrum to the data and the rotational constants were left unchanged from the simulations of Fig. 7, although better agreement in the line positions would be achieved by further reducing A′. Nevertheless, all three bands are necessary to account for the range of rotational branches seen in σ_D.

Since feature D in the direct detachment spectrum is comprised of the 5₀²6₀¹, 5₁³, 5₀³, and 3₀¹5₀¹ bands, the final states subsequent to autodetachment can only be ν₅ (v′ = 3) or the combination mode levels [ν₅ (v′ = 2), ν₆ (v′ = 1)] and/or [ν₃ (v′ = 1), ν₅ (v′ = 1)]. Absorption to the dipole-bound state via the 5₀⁴ band followed by autodetachment to ν₅ v′ = 3 and absorption to the dipole-bound state via the 5₀²3₀¹ band followed by autodetachment to [ν₃ (v′ = 1), ν₅ (v′ = 1)] are consistent with the propensity rule and normal mode approximations. However, autodetachment from the ν₃ v = 2 dipole-bound state level (prepared via 3₀²) must be accompanied by vibrational energy redistribution.

Autodetachment results showing rovibronic bands in the total detachment cross section of CH₂CN⁻ have been presented in Refs. 6, 9, and 10. The present study is performed at higher photon energies than the earlier work and shows the presence of similar structure. However, unlike the earlier work, comparison of photoelectron spectral intensities (rather than measurement of total electron yields) allows at least partial assignment of the autodetachment process to specific vibrational channels. With supporting calculations, these results show that excitation takes place to one of the two dipole-bound states (a dipole-allowed singlet) supported by neutral CH₂CN. Despite the diffuse nature of the dipole bound orbital, calculation of the electronic transition dipole moment demonstrates the feasibility of the one-photon transitions to the singlet dipole-bound state.

The ability to identify the dipole-bound state vibrational levels accessed in the absorption process and the final vibrational states accessed in the neutral as the result of autodetachment allows us to study the autodetachment process in much more detail than has been previously achieved for this system. Analysis of the rotational structure shows that the majority of the observed ro-vibrational transitions can be assigned to autodetachment consistent with the vibrational propensity rule¹ (∆v = −1) and normal mode expectation (that autodetachment will be between vibrational levels within the same mode). However, this analysis also shows that for excitations involving the ν₃ mode of the dipole-bound state the final vibrational level accessed in the neutral cannot belong to the ν₃ mode. This is clearly counter to the normal mode expectation and highlights inter-mode coupling.

At the present time, the vibrational specificity of this approach is limited by the resolution of the imaging arrangement (ΔE/E ≈ 10%). However, recent improvements in photoelectron imaging detection resolution(ΔE/E better than 0.5% has been reliably reported)^46,47 for electrons with appreciable kinetic energies promise the ability to fully resolve the vibrational features and therefore allow vibrational state specific studies of autodetachment.

See supplementary material for computational details (basis sets, etc.) and relevant Cartesian geometries.

This work has been supported by (Washington University in St. Louis) the National Science Foundation under No. CHE–1566157 and (University of Southern California) by the Army Research Office through Grant No. W911NF-16-1-0232 and the Alexander von Humboldt Foundation (Bessel Award to A.I.K.).