^{1,a)}, Nathan E. Schultz

^{1,b)}, Donald G. Truhlar

^{1,c)}and Doreen G. Leopold

^{1,d)}

### Abstract

Computational results are reported for the ground and low-lying excited electronic states of and and compared with the available spectroscopic data. In agreement with previous assignments, the six photodetachment transitions observed in the vibrationally resolved photoelectron spectrum of are assigned as arising from the ground and excited states of and accessing the ground and excited , , and states of (with labels for states in parentheses). Geometries and vibrational frequencies obtained by PBE0 hybrid density functional calculations using the basis set and energies calculated using coupled cluster theory with single and double excitations and a quasiperturbative treatment of connected triple excitations (CCSD(T)) with the aug-cc- {, T, Q} basis sets with exponential extrapolation to the complete basis set limit are in good agreement with experiment. Franck–Condon spectra calculated in the harmonic approximation, using either the Sharp–Rosenstock–Chen method which includes Duschinsky rotation or the parallel-mode Hutchisson method, also agree well with the observed spectra. Possible assignments for the higher-energy bands observed in the previously reported UVphotoelectron spectra are suggested. Descriptions of the photodetachment transition between the and ground states in terms of natural bond order (NBO) analyses and total electron density difference distributions are discussed. A reinterpretation of the vibrational structure in the resonant two-photon ionization spectrum of is proposed, which supports its original assignment as arising from the ground state, giving an bond dissociation energy,, of . With this reduction by from the currently recommended value, the present calculated dissociation energies of , , and are consistent with the experimental data.

We thank Dr. Michael Morse, Dr. Kent Ervin, and Dr. Susan Green for helpful discussions. This research was supported by the National Science Foundation under Grant No. CHE07-04974 (D.G.T), by the Research Corporation (D.G.L.), and by computer resources provided by the Minnesota Supercomputing Institute.

I. INTRODUCTION

II. COMPUTATIONAL METHODS

A. Electronic structure

B. Franck–Condon simulations

III. COMPUTATIONAL RESULTS

A. and electronic states

B. Photodetachment transitions

1. Transition X

2. Transition Y

3. Transition A

4. Transition B

5. Transition C

6. Transition D

7. UV photodetachment transitions

C. Natural bond order analysis

D. Dissociation energies

IV. DISCUSSION

A. dissociation energy and reinterpretation of the R2PI spectrum

B. Validity of Franck–Condon simulation methods

C. Ion-neutral total electron density difference distributions

V. SUMMARY AND CONCLUSIONS

SUPPORTING INFORMATION AVAILABLE

### Key Topics

- Ground states
- 80.0
- Excited states
- 54.0
- Photoelectron spectra
- 52.0
- Aluminium
- 42.0
- Dissociation energies
- 38.0

## Figures

Comparison of the observed photoelectron spectrum of anions prepared in the short liquid nitrogen cooled flow tube (solid line) with predicted spectra from PBE0 calculations (dashed lines and sticks) for (transition X), (transition Y), and (transition D). Franck–Condon factors are calculated by the SRC method. For each transition, the origin band position and intensity are chosen to match the observed spectrum. Assignments are given as , where for the symmetric stretch, for the bend, and for the asymmetric stretch, and and are the vibrational quantum numbers of mode in the initial and final states, respectively. For transition Y between states with equilibrium structures, the label also represents , and also represents and ; stick heights are summed for degenerate or nearly degenerate transitions. For overlapping transitions Y and D, which are expanded (four times) in the middle and upper spectra, the short dashed line shows the individual transitions (for Y in the middle and for D in the upper spectra) and the long dashed line (in the middle spectrum) shows their sum. Anion vibrational temperatures of are assumed and sticks are convoluted with Lorentzian line shapes with widths of 5, 10, and for transitions X, Y, and D, respectively, as in Paper I.

Comparison of the observed photoelectron spectrum of anions prepared in the short liquid nitrogen cooled flow tube (solid line) with predicted spectra from PBE0 calculations (dashed lines and sticks) for (transition X), (transition Y), and (transition D). Franck–Condon factors are calculated by the SRC method. For each transition, the origin band position and intensity are chosen to match the observed spectrum. Assignments are given as , where for the symmetric stretch, for the bend, and for the asymmetric stretch, and and are the vibrational quantum numbers of mode in the initial and final states, respectively. For transition Y between states with equilibrium structures, the label also represents , and also represents and ; stick heights are summed for degenerate or nearly degenerate transitions. For overlapping transitions Y and D, which are expanded (four times) in the middle and upper spectra, the short dashed line shows the individual transitions (for Y in the middle and for D in the upper spectra) and the long dashed line (in the middle spectrum) shows their sum. Anion vibrational temperatures of are assumed and sticks are convoluted with Lorentzian line shapes with widths of 5, 10, and for transitions X, Y, and D, respectively, as in Paper I.

Comparison of the observed spectra for anions prepared in the long liquid nitrogen cooled flow tube (solid line) with predicted spectra from PBE0 calculations (dashed lines and sticks) for transitions from the excited state of to the , , and states of for transitions A, B, and C, respectively. Notation as in Fig. 1; e.g., represents the transition from of to of in normal mode 2, the bend. Origin band positions and intensities are fit to the observed values. As in Paper I, the assumed vibrational temperatures are for the symmetric stretch and for the bend and asymmetric stretch , and transitions are convoluted with Lorentzian line shapes with widths of for A and B and for C. Top panel: Harmonic Franck–Condon factors calculated by the SRC method using displacements. Bottom panel: Harmonic Franck–Condon factors calculated in the parallel mode approximation using displacements for transitions A, B, and C (short dashed lines and sticks) or displacements for transition A (long dashed lines).

Comparison of the observed spectra for anions prepared in the long liquid nitrogen cooled flow tube (solid line) with predicted spectra from PBE0 calculations (dashed lines and sticks) for transitions from the excited state of to the , , and states of for transitions A, B, and C, respectively. Notation as in Fig. 1; e.g., represents the transition from of to of in normal mode 2, the bend. Origin band positions and intensities are fit to the observed values. As in Paper I, the assumed vibrational temperatures are for the symmetric stretch and for the bend and asymmetric stretch , and transitions are convoluted with Lorentzian line shapes with widths of for A and B and for C. Top panel: Harmonic Franck–Condon factors calculated by the SRC method using displacements. Bottom panel: Harmonic Franck–Condon factors calculated in the parallel mode approximation using displacements for transitions A, B, and C (short dashed lines and sticks) or displacements for transition A (long dashed lines).

As in Fig. 2, for transitions from the excited state of . Franck–Condon factors are calculated using the Duschinsky SRC method with displacements. For transition A, the intensity of the origin transition is 10% that in Fig. 2.

As in Fig. 2, for transitions from the excited state of . Franck–Condon factors are calculated using the Duschinsky SRC method with displacements. For transition A, the intensity of the origin transition is 10% that in Fig. 2.

Franck–Condon simulation of a transition from the ground state to a excited state, with parameters chosen to model the R2PI spectrum (Ref. 38). Frequencies are for the symmetric stretch and for the degenerate bend and asymmetric stretch in the ground state; for the excited state, and for and for and . As in Fig. 1, the label also represents the degenerate transition (and also represents ) and stick heights are summed for degenerate transitions. Franck–Condon factors are calculated for Morse potentials for (with ), and for harmonic potentials for and . A symmetric stretching displacement of and a ground state vibrational temperature of are assumed.

Franck–Condon simulation of a transition from the ground state to a excited state, with parameters chosen to model the R2PI spectrum (Ref. 38). Frequencies are for the symmetric stretch and for the degenerate bend and asymmetric stretch in the ground state; for the excited state, and for and for and . As in Fig. 1, the label also represents the degenerate transition (and also represents ) and stick heights are summed for degenerate transitions. Franck–Condon factors are calculated for Morse potentials for (with ), and for harmonic potentials for and . A symmetric stretching displacement of and a ground state vibrational temperature of are assumed.

(a) Square of the HOMO in the ground state showing contours in the molecular plane for isodensity values of 0.001, 0.002, 0.005, and . (b) Total electron density difference plot (anion minus neutral) for transition X (Sec. ???) between the and ground states, both calculated at the PBE0/MG3 level assuming the same geometry . Contours are shown in the molecular plane for the same isodensity magnitudes as in (a). Dark contours indicate decreased density in as compared with , and light contours show regions of increased density in . (c) As in (b), but showing (dark) and (light) isodensity surfaces with the molecule rotated by 45°.

(a) Square of the HOMO in the ground state showing contours in the molecular plane for isodensity values of 0.001, 0.002, 0.005, and . (b) Total electron density difference plot (anion minus neutral) for transition X (Sec. ???) between the and ground states, both calculated at the PBE0/MG3 level assuming the same geometry . Contours are shown in the molecular plane for the same isodensity magnitudes as in (a). Dark contours indicate decreased density in as compared with , and light contours show regions of increased density in . (c) As in (b), but showing (dark) and (light) isodensity surfaces with the molecule rotated by 45°.

## Tables

Summary of the computational results for and states of and .

Summary of the computational results for and states of and .

Comparison of computational to experimental results. [Experimental results (in italics) are from Paper 1 (Ref. 35, Table II) except as noted.]

Comparison of computational to experimental results. [Experimental results (in italics) are from Paper 1 (Ref. 35, Table II) except as noted.]

Comparison of calculated to experimental normal mode displacements.

Comparison of calculated to experimental normal mode displacements.

Comparison of calculated to experimental dissociation energies (eV). Calculated total energies in hartrees at the CCSD(T)/CBS//PBE0/MG3 level. EA, IE, and dissociation energy values include PBE0/MG3 zero point energies (eV) of 0.0169 , 0.0204 , 0.0097 , 0.0530 , 0.0536 and 0.0353 . Experimental values show the uncertainty in the last digit(s) in parentheses.

Comparison of calculated to experimental dissociation energies (eV). Calculated total energies in hartrees at the CCSD(T)/CBS//PBE0/MG3 level. EA, IE, and dissociation energy values include PBE0/MG3 zero point energies (eV) of 0.0169 , 0.0204 , 0.0097 , 0.0530 , 0.0536 and 0.0353 . Experimental values show the uncertainty in the last digit(s) in parentheses.

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