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Vibronic coupling in the excited cationic states of ethylene: Simulation of the photoelectron spectrum between 12 and
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10.1063/1.1924594
/content/aip/journal/jcp/122/20/10.1063/1.1924594
http://aip.metastore.ingenta.com/content/aip/journal/jcp/122/20/10.1063/1.1924594

Figures

Image of FIG. 1.
FIG. 1.

Approximate plots of the four highest occupied molecular orbitals of ethylene. The letter label of the ionized state corresponding to the particular orbital is indicated in brackets next to the symmetry label.

Image of FIG. 2.
FIG. 2.

Potential-energy surfaces of the four lowest ionized states of ethylene obtained by diagonalizing the potential-energy matrix [Eq. (1)] of the vibronic model Hamiltonian as a function of the symmetric normal-mode coordinates.

Image of FIG. 3.
FIG. 3.

Simulated spectra of the state. (a) Vertical FC calculation using the adiabatic potential-energy surfaces obtained from the potential-energy matrix of the vibronic model. (b) Diagonalization of the linear vibronic model Hamiltonian. (c) Diagonalization of the vibronic model Hamiltonian with all coupling constants.

Image of FIG. 4.
FIG. 4.

Simulated spectra of the state using a vibronic model that has only the symmetric mode coupling constants. (a) Only linear coupling constants included in the model. (b) and (c) Respectively, vertical FC calculation and traditional adiabatic FC calculation using the adiabatic potential-energy surfaces obtained from the model. (d) Diagonalization of the vibronic model Hamiltonian.

Image of FIG. 5.
FIG. 5.

Simulated spectra of the state by diagonalizing the vibronic model Hamiltonian with vibrational basis sets which have quanta in one coupling mode besides the symmetric modes. The coupling modes that are included in the different spectra are (a) torsion and (b) rock .

Image of FIG. 6.
FIG. 6.

Comparison of the simulated spectrum of the state from a vibronic model Hamiltonian (top panel) with the corresponding experimental spectrum (Ref. 12) (bottom panel).

Image of FIG. 7.
FIG. 7.

Potential-energy surfaces of the second and third ionized states obtained from the potential-energy matrix [Eq. (1)] plotted as a function of a symmetric mode (C–C stretch) and a coupling mode ( rock ). In the bottom panel, a contour plot of the lower surface is shown.

Image of FIG. 8.
FIG. 8.

Simulated spectra of the state. (a) Vertical FC calculation using the adiabatic potential-energy surfaces obtained from the potential-energy matrix of the vibronic model. (b) and (c) Diagonalization of the vibronic model Hamiltonian with all coupling constants. Spectrum plotted using two different abscissa ranges.

Image of FIG. 9.
FIG. 9.

Simulated spectra of the state by diagonalizing a vibronic model Hamiltonian that has only the symmetric mode coupling constants.

Image of FIG. 10.
FIG. 10.

Simulated spectra of the state by diagonalizing the vibronic model Hamiltonian with vibrational basis sets which have quanta in one coupling mode besides the symmetric modes. The coupling modes that are included in the different spectra are (a) stretch , (b) rock , (c) stretch , and (d) rock .

Image of FIG. 11.
FIG. 11.

Simulated spectra of the state. (a) Vertical FC calculation using the adiabatic potential-energy surfaces obtained from the potential-energy matrix of the vibronic model. (b) Diagonalization of the vibronic model Hamiltonian with all coupling constants.

Image of FIG. 12.
FIG. 12.

Simulated spectra of the state by diagonalizing the vibronic model Hamiltonian with vibrational basis sets which have quanta in (a) only the symmetric modes, (b) the symmetric modes plus the stretch coupling mode, and (c) the symmetric modes plus the rock coupling mode.

Image of FIG. 13.
FIG. 13.

Comparison of the simulated spectrum of the and states from a vibronic model Hamiltonian (top panel) with the corresponding experimental spectrum (Ref. 12) (bottom panel).

Tables

Generic image for table
Table I.

Vibrational normal modes and vibrational frequencies of ethylene.

Generic image for table
Table II.

Vertical ionization potentials (eV) using IP-EOM-CCSD.

Generic image for table
Table III.

Linear coupling constants (eV). The number in parentheses corresponds to the normal mode .

Generic image for table
Table IV.

Quadratic coupling constants (eV). In the model . The numbers in parentheses correspond to the normal modes and .

Generic image for table
Table V.

Cubic coupling constants (eV). The number in parentheses corresponds to the normal mode .

Generic image for table
Table VI.

Quartic coupling constants (eV). In the model . The numbers in parentheses correspond to the normal mode .

Generic image for table
Table VII.

Numerical details of vibronic model Hamiltonian diagonalization for calculating the spectrum of the state.

Generic image for table
Table VIII.

Details of vibronic model Hamiltonian diagonalization for calculating the spectrum of the and states.

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/content/aip/journal/jcp/122/20/10.1063/1.1924594
2005-05-27
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Vibronic coupling in the excited cationic states of ethylene: Simulation of the photoelectron spectrum between 12 and 18eV
http://aip.metastore.ingenta.com/content/aip/journal/jcp/122/20/10.1063/1.1924594
10.1063/1.1924594
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