Composite NIPES, VMI, and SEVI spectra over the range of energies studied in this work. The color scheme, which is used throughout this paper, is: NIPES in black, VMI in dark blue, and SEVI in cyan. The state label does not denote the origin transition for this state.
Frontier molecular orbitals of propadienylidene anion. These calculations used the ANO1 basis (see text) and were carried out using restricted open-shell Hartree-Fock theory at the anion geometry. The view is from 45° above the molecular plane, with the methylene group closest and the linear CCC framework extending away from the eye, and is shown schematically in the lower left-hand side of the figure. The electron configuration shown is that for the anion.
Energy level diagram for the electronic states of propadienylidene. All energies are based on those determined in this research, except for that of the state, which is taken from Refs. 18 and 72. The (italicized) energy for the state is estimated by adjusting the measured position of its ν2 level by the vibrational frequency, as estimated from the calculations. Note the marked difference in singlet–triplet splittings of the excited states, which are represented by the dotted lines. The ground state is obtained by removal of the 2b 1 electron from the anion (see Fig. 2); excited A 2, B 1, and A 1 states are obtained by removal of the 2b 2, 7a 1, and 1b 1 electrons, respectively.
Photoelectron spectra of H2CCC− from eBE = 14 000 to 17 000 cm−1. The upper black trace is the 364-nm NIPES spectrum; the lower cyan trace is the SEVI data, obtained with a photon energy of 17 790 cm−1. The red sticks along the baseline are from a Franck-Condon simulation, based on the corresponding diagonal block of the effective Hamiltonian used here. The eigenvalues of the model Hamiltonian have been shifted so that the origin feature coincides with that seen experimentally.
Photoelectron spectra of H2CCC− from eBE = 17 000 to 21 000 cm−1. The upper black trace is the 364-nm NIPES spectrum, and the red sticks from the Franck-Condon calculation are shown. The shift of the model Hamiltonian eigenvalues is as described in Fig. 4. The large number of prominent states in the stick spectrum are various combinations of the Franck-Condon active ν2, ν3, and ν4 modes, together with even quantum levels involving ν5 and ν6.
Photoelectron spectra of H2CCC− from eBE = 24 500 to 26 050 cm−1. The upper black trace is the NIPES spectrum; the lower cyan trace is the SEVI spectrum, obtained with a photon energy of 26 450 cm−1. Green and red sticks shown along the baseline are vibronic levels with b 1 and a 2 vibronic symmetries, respectively, as obtained from the model Hamiltonian assuming equal photodetachment cross sections for the and electronic states. Nominal vibrational quantum numbers are also given, and all states in this range can be assigned as vibrational levels of the state. The simulation has been shifted so that the origin feature coincides with that seen in the SEVI experiment.
Photoelectron spectra of H2CCC− from eBE = 25 800 to 29 000 cm−1. The cyan trace is the SEVI data obtained at photon energies of 27 550 cm−1 and 31 740 cm−1, with the boundary between the two clearly demarcated. The lower blue trace is the VMI spectrum obtained with a photon energy of 32 260 cm−1 (4.0 eV). The stick spectrum, obtained from the model Hamiltonian, is shown along the baseline, with red sticks indicating levels with a 2 vibronic symmetry and green indicating b 1 vibronic symmetry. The dominant lower energy peak in the spectrum is the ν4 band of the state which is also seen in the preceding figure; the position of the apparent origin is indicated with an arrow. The shift applied to the calculated spectrum is the same as that used in Figure 4. The red trace is obtained from the model Hamiltonian spectrum, with each peak in the stick spectrum convoluted with a Gaussian with FWHM 40 cm−1.
Photoelectron VMI spectrum of H2CCC− from eBE =34 500 to 38 000 cm−1 obtained with a photon energy of 37 940 cm−1. Along the baseline is a stick spectrum obtained from the model Hamiltonian in the Franck-Condon approximation. Note the resonance between ν2 and 2ν4 that results in the polyad structure of the spectrum.
Simulated photoelectron spectrum of H2CCC− to the and states of H2CCC, as calculated from the purely ab initio Hamiltonian (the relative energies of the two neutral states are unadjusted). Red sticks correspond to vibronic levels of a 2 symmetry, while the green sticks indicate b 1 vibronic levels. Due to the strong vibronic coupling that mixes these two states, only the origin has a “clean” assignment; general assignments of the various features are given in the figure. The energy range shown extends just beyond what roughly corresponds to the 3ν2 vibrational level in the state, which exhibits very little activity. At higher energies, no significant features are present. The simulated spectrum has been shifted so that the origin is coincident with the T 0 feature measured by SEVI.
Experimental VMI photoelectron spectrum of H2CCC− in the region of eBE = 27 500 to 33 200 cm−1, obtained at a photon energy of 33 590 cm−1. The stick spectrum (same color scheme as in Fig. 6) from the simulation is also shown, where the vertical gap between the and states has been shifted by −800 cm−1 (0.1 eV) due to the higher-order correlation effects that principally affect the state (see text). Apart from moving the vibronic features associated with the state to lower energy, note that shifting the gap has a profound effect on the intensity profile (see Fig. 9 for the unadjusted spectrum) in the vicinity of origin.
Cartesian coordinates (in bohr) of the state of the propadienylidene anion, along with Cartesian representations (unit length) of the totally symmetric reduced normal coordinates. The approximate descriptions (and positive phase conventions) for the normal coordinates, which can be inferred from the data below, are: q 1 C1H symmetric stretch (compression); q 2 C2C3 stretch (compression); q 3 HC1H scissor (closing); q 4 C1C2 stretch (expansion). The atomic numbering follows Fig. 2.
Linear and quadratic parameters (in cm−1) for quasidiabatic Hamiltonian, expressed in the reduced normal coordinate representation of the state of the propadienylidene anion. See Eqs. (4) and (5) for definitions of all parameters.
Cubic and quartic parameters (in cm−1) for the quasidiabatic Hamiltonian, expressed in the reduced normal coordinate representation of the state of the propadienylidene anion. See Eqs. (4) and (5) for definitions of the various parameters.
Parameters associated with adiabatic potential energy surfaces of H2CCC. All values for the singlet states are obtained with the CCSDT treatment of electron correlation, with EOMEE-CCSDT used for the excited states. For triplet states and the anion, the CCSD(T) treatment of correlation is used. The ANO1 basis set and the frozen-core approximation were adopted in all calculations. Bond lengths in Ångstroms, angles in degrees; harmonic frequencies and energies are in cm−1. Normal coordinates are in dimensionless units.
Assigned vibrational levels in the ground electronic state of propadienylidene. All energies are in units of cm−1.
Observed features and assignments for the ground vibronic state and selected excited state levels of H2CCC in the photoelectron spectrum of H2CCC−. All energies in cm−1, with reported uncertainties of ∼ 1σ. While the various experimental results are consistent within the indicated uncertainty, the recommended values are shown in boldface. Energies in the upper row are the electron binding energies (relative to the ground state of the anion); italicized values in the row below are relative to the ground vibronic level of the neutral.
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