^{1}and A. J. C. Varandas

^{1,a)}

### Abstract

A quantum dynamics study is performed to examine the complex nuclear motion underlying the first photoelectron band of methane. The broad and highly overlapping structures of the latter are found to originate from transitions to the ground electronic state,, of the methane radical cation. *Ab initio* calculations have also been carried out to establish the potential energy surfaces for the triply degenerate electronic manifold of . A suitable diabatic vibronic Hamiltonian has been devised and the nonadiabatic effects due to Jahn-Teller conical intersections on the vibronic dynamics investigated in detail. The theoretical results show fair accord with experiment.

This work has the support of Fundação para a Ciência e a Tecnologia, Portugal, under Contract Nos. PTDC/QUI-QUI/099744/2008 and PTDC/AAC-AMB/099737/2008.

I. INTRODUCTION

II. EQUILIBRIUM STRUCTURE AND NORMAL MODES OF VIBRATION OF METHANE IN ITS ELECTRONIC GROUND STATE

III. THE VIBRONIC HAMILTONIAN AND DYNAMICAL OBSERVABLES

IV. ADIABATIC POTENTIAL ENERGY SURFACES

V. VIBRONIC ENERGY LEVELS

VI. SUMMARY AND OUTLOOK

### Key Topics

- Manifolds
- 15.0
- Ab initio calculations
- 12.0
- Eigenvalues
- 9.0
- Jahn Teller effect
- 8.0
- Photoelectron spectra
- 8.0

## Figures

Adiabatic potential energies of the electronic state of along the dimensionless normal coordinate for the totally symmetric vibrational mode ν_{1}. The present vibronic model is shown by the solid line and the computed *ab initio* data by the solid dots.

Adiabatic potential energies of the electronic state of along the dimensionless normal coordinate for the totally symmetric vibrational mode ν_{1}. The present vibronic model is shown by the solid line and the computed *ab initio* data by the solid dots.

Same as in Fig. 1 along the ε component of ν_{2} (*e*) vibrational mode.

Same as in Fig. 1 along the ε component of ν_{2} (*e*) vibrational mode.

Same as in Fig. 1 along the θ component of ν_{2} (*e*) vibrational mode.

Same as in Fig. 1 along the θ component of ν_{2} (*e*) vibrational mode.

Same as in Fig. 1 along the ξ component of ν_{3} (*t* _{2}) vibrational mode.

Same as in Fig. 1 along the ξ component of ν_{3} (*t* _{2}) vibrational mode.

Same as in Fig. 1 along the ξ component of ν_{4} (*t* _{2}) vibrational mode.

Same as in Fig. 1 along the ξ component of ν_{4} (*t* _{2}) vibrational mode.

Vibrational energy levels of the electronic manifold of : (a) partial spectrum computed with the totally symmetric *a* _{1} vibrational mode ν_{1}, (b) partial spectrum computed with the JT active doubly degenerate *e* vibrational mode ν_{2}, and (c) partial spectrum computed with two JT active triply degenerate *t* _{2} vibrational modes ν_{3} and ν_{4}. The intensity (in arbitrary units) is plotted as a function of the energy of the final vibronic state. The zero of energy correspond to the equilibrium minimum of the electronic ground state of CH_{4}. The theoretical stick spectrum in each panel is convoluted with a Lorentzian function of 40 meV FWHM to generate the spectral envelope.

Vibrational energy levels of the electronic manifold of : (a) partial spectrum computed with the totally symmetric *a* _{1} vibrational mode ν_{1}, (b) partial spectrum computed with the JT active doubly degenerate *e* vibrational mode ν_{2}, and (c) partial spectrum computed with two JT active triply degenerate *t* _{2} vibrational modes ν_{3} and ν_{4}. The intensity (in arbitrary units) is plotted as a function of the energy of the final vibronic state. The zero of energy correspond to the equilibrium minimum of the electronic ground state of CH_{4}. The theoretical stick spectrum in each panel is convoluted with a Lorentzian function of 40 meV FWHM to generate the spectral envelope.

Vibronic band of the electronic state of . The intensity (in arbitrary units) is plotted along the energy (relative to minimum of the state of CH_{4}) of the final vibronic states.

Vibronic band of the electronic state of . The intensity (in arbitrary units) is plotted along the energy (relative to minimum of the state of CH_{4}) of the final vibronic states.

## Tables

Description of the vibrational modes of the electronic ground state of CH_{4}. The theoretical frequencies are harmonic, whereas the experimental ones are fundamental. All values are in eV.

Description of the vibrational modes of the electronic ground state of CH_{4}. The theoretical frequencies are harmonic, whereas the experimental ones are fundamental. All values are in eV.

*Ab initio* calculated linear and quadratic coupling constants for the electronic state of . The vertical ionization energy of this electronic state is also given in the table. All data are given in eV.

*Ab initio* calculated linear and quadratic coupling constants for the electronic state of . The vertical ionization energy of this electronic state is also given in the table. All data are given in eV.

Normal mode combinations, sizes of the primitive and the single particle basis used in the WP propagation within the MCTDH framework in the coupled electronic manifold using the complete vibronic Hamiltonian of Eqs. (2)–(5). First column denotes the vibrational degrees of freedom (DOF) which are combined to particles. Second column gives the number of primitive basis functions for each DOF. Third column gives the number of single particle functions (SPFs) for each JT splitted electronic state.

Normal mode combinations, sizes of the primitive and the single particle basis used in the WP propagation within the MCTDH framework in the coupled electronic manifold using the complete vibronic Hamiltonian of Eqs. (2)–(5). First column denotes the vibrational degrees of freedom (DOF) which are combined to particles. Second column gives the number of primitive basis functions for each DOF. Third column gives the number of single particle functions (SPFs) for each JT splitted electronic state.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content