^{1,a)}, Tsuyoshi Kato

^{1}and Kaoru Yamanouchi

^{1}

### Abstract

Ionization of acetylene (C_{2}H_{2}) induced by an intense laser field whose polarization direction is parallel to the molecular axis is investigated by time-dependent Hartree-Fock calculations. It is found that, in the ionization process, the probability of the ejection of an electron from the two highest occupied orbitals of σ symmetry increases drastically as the C–H distance is symmetrically increased. On the contrary, the ejection probability of an electron in the two degenerate π orbitals is much less influenced by the bond elongation. The laser-induced dynamics of the time-dependent orbitals are interpreted by projecting them onto time-independent orbitals, which are eigenfunctions of the time-independent Fock operator.

This work was supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan (Grant-in-Aid for Specially Promoted Research on Ultrafast Hydrogen Migration (Grant No. 19002006) and Grant-in-Aid for Global COE Program for Chemistry Innovation). E.L. gratefully acknowledges a Grant-in-Aid for Scientific Research (Grant No. 21-09238) from the Japan Society for the Promotion of Science.

I. INTRODUCTION

II. THEORETICAL MODEL

A. Ground state

III. RESULTS OF TIME-DEPENDENT CALCULATIONS

A. Time-dependent orbital densities

B. Comparison with the results of 1D calculations

IV. CONCLUSIONS

### Key Topics

- Ionization
- 30.0
- Orbital dynamics
- 18.0
- Ionization potentials
- 9.0
- Protons
- 5.0
- Carbon
- 4.0

## Figures

Stationary, spatial orbitals of the ground state acetylene molecule. The C–H internuclear distance is and the C–C distance is . Shown is the value of in units of [see Eq. (5) ]. Panels (a) and (b) depict the core orbitals 1σ_{ g } and 1σ_{ u }, panels (c)–(e) picture the 2σ_{ g }, 2σ_{ u }, and 3σ_{ g } orbitals, and (f) the 1π_{ u } orbital. Note that there are two degenerate 1π_{ u } orbitals which have the same function. The positions of the C atoms (•) and the H atoms (○) are indicated in each panel. Panel (g) depicts , the ground state orbital densities integrated over ρ and φ. Note that the 1σ_{ g } and 1σ_{ u } curves lie almost on top of each other.

Stationary, spatial orbitals of the ground state acetylene molecule. The C–H internuclear distance is and the C–C distance is . Shown is the value of in units of [see Eq. (5) ]. Panels (a) and (b) depict the core orbitals 1σ_{ g } and 1σ_{ u }, panels (c)–(e) picture the 2σ_{ g }, 2σ_{ u }, and 3σ_{ g } orbitals, and (f) the 1π_{ u } orbital. Note that there are two degenerate 1π_{ u } orbitals which have the same function. The positions of the C atoms (•) and the H atoms (○) are indicated in each panel. Panel (g) depicts , the ground state orbital densities integrated over ρ and φ. Note that the 1σ_{ g } and 1σ_{ u } curves lie almost on top of each other.

(a) The total energy of the electronic ground state as a function of . Filled circles: HF energies (shifted vertically by −1.48*E* _{ h }) of the present model, open triangles: HF energies calculated by GAMESS, and open squares: CASSCF energies calculated by GAMESS. (b) Ground state orbital energies ɛ_{ n } as a function of . The dashed lines represent the almost degenerate core orbitals. The dashed-dotted lines correspond to orbitals of π symmetry, while solid lines show σ orbitals. The occupied orbitals in the ground state are 1σ_{ g }, 1σ_{ u }, 2σ_{ g }, 2σ_{ u }, 3σ_{ g }, and 1π_{ u }. The line styles used for the occupied orbitals are the same as in Fig. 1(g) . is fixed at in both (a) and (b). The lowest unoccupied orbitals of each symmetry are the 3σ_{ u }, 4σ_{ g }, 1π_{ g }, and 2π_{ u }. On the scale of this plot, the 1π_{ g } and 2π_{ u } curves are almost overlapping. Note the break of the vertical axis.

(a) The total energy of the electronic ground state as a function of . Filled circles: HF energies (shifted vertically by −1.48*E* _{ h }) of the present model, open triangles: HF energies calculated by GAMESS, and open squares: CASSCF energies calculated by GAMESS. (b) Ground state orbital energies ɛ_{ n } as a function of . The dashed lines represent the almost degenerate core orbitals. The dashed-dotted lines correspond to orbitals of π symmetry, while solid lines show σ orbitals. The occupied orbitals in the ground state are 1σ_{ g }, 1σ_{ u }, 2σ_{ g }, 2σ_{ u }, 3σ_{ g }, and 1π_{ u }. The line styles used for the occupied orbitals are the same as in Fig. 1(g) . is fixed at in both (a) and (b). The lowest unoccupied orbitals of each symmetry are the 3σ_{ u }, 4σ_{ g }, 1π_{ g }, and 2π_{ u }. On the scale of this plot, the 1π_{ g } and 2π_{ u } curves are almost overlapping. Note the break of the vertical axis.

Electron ejection probability as a function of at (a) , (b) , and (c) . The different curves refer to the three different orbitals 2σ_{ u } (⧫), 3σ_{ g } (■), 1π_{ u } (▲), and the average ejection probability (•).

Electron ejection probability as a function of at (a) , (b) , and (c) . The different curves refer to the three different orbitals 2σ_{ u } (⧫), 3σ_{ g } (■), 1π_{ u } (▲), and the average ejection probability (•).

Projections at C–H internuclear distance for (a) *m* = 3σ_{ g } and (b) *m* = 2σ_{ u }. The thick gray line in the background shows the temporal behavior of the laser field (not to scale). The peak value of the laser field is .

Projections at C–H internuclear distance for (a) *m* = 3σ_{ g } and (b) *m* = 2σ_{ u }. The thick gray line in the background shows the temporal behavior of the laser field (not to scale). The peak value of the laser field is .

Time evolution of *b* _{ n }(*z*, *t*) (in units of 1/*a* _{0}), at C–H internuclear distance . (a) Total density *b*(*z*, *t*) on logarithmic color scale, (b) , (c) , and (d) on linear color scale. (e) shows the laser field, which has .

Time evolution of *b* _{ n }(*z*, *t*) (in units of 1/*a* _{0}), at C–H internuclear distance . (a) Total density *b*(*z*, *t*) on logarithmic color scale, (b) , (c) , and (d) on linear color scale. (e) shows the laser field, which has .

Time evolution of *b* _{ n }(*z*, *t*) (in units of 1/*a* _{0}), at C–H internuclear distance . (a) Total density *b*(*z*, *t*) on logarithmic color scale, (b) , (c) , and (d) on linear color scale. (e) shows the laser field, which has .

*b* _{ n }(*z*, *t*) (in units of 1/*a* _{0}), at C–H internuclear distance . (a) Total density *b*(*z*, *t*) on logarithmic color scale, (b) , (c) , and (d) on linear color scale. (e) shows the laser field, which has .

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