^{1,a)}and Kaoru Ohno

^{1}

### Abstract

Carrying out a semiclassical molecular dynamics simulation of a system by using the time-dependent local density approximation of the time-dependent density functional theory, we find that one-by-one electron and hole transfer takes place from to when an electron is excited in . Probability of the transfer is low when the molecules are fixed, but it increases when the molecules are freely relaxed or has of initial velocity.

The authors acknowledge the use of the Hitachi SR8000 supercomputer at the Computer Centre of Hokkaido University. This work has been partly supported by the Grant-in-Aid for scientific research (B) (Grant No. 17310067) from Japan Society for the Promotion of Science.

I. INTRODUCTION

II. METHODOLOGY

III. RESULTS AND DISCUSSION

A. The excited electron transfer from to

B. The hole transfer from to

IV. CONCLUSION

### Key Topics

- Energy transfer
- 16.0
- Eigenvalues
- 10.0
- Electron transfer
- 9.0
- Wave functions
- 9.0
- Band gap
- 5.0

## Figures

The amplitude of the wave function at the ground state. The cubes are the unit cell. The numbers indicate levels. For each level, the two points on the left and the five points on the right show and , respectively. Gray and black areas represent the positive and negative values of the wave function.

The amplitude of the wave function at the ground state. The cubes are the unit cell. The numbers indicate levels. For each level, the two points on the left and the five points on the right show and , respectively. Gray and black areas represent the positive and negative values of the wave function.

Illustration of an electron transfer from to . Black and white circles mean electrons and holes, respectively. First of all, the electron is excited from the (threefold degenerate) 5th to 7th levels (HOMO of ) to the 12th level (LUMO of ) in the side (solid line with an arrow). Then, the electron transfers from the 12th level of the side to the 11th level of the side (dashed line with an arrow), and the hole transfers from the 7th level of the side to the 8th level of the side (dotted line with an arrow). We investigate whether these transfers occur simultaneously or separately one by one.

Illustration of an electron transfer from to . Black and white circles mean electrons and holes, respectively. First of all, the electron is excited from the (threefold degenerate) 5th to 7th levels (HOMO of ) to the 12th level (LUMO of ) in the side (solid line with an arrow). Then, the electron transfers from the 12th level of the side to the 11th level of the side (dashed line with an arrow), and the hole transfers from the 7th level of the side to the 8th level of the side (dotted line with an arrow). We investigate whether these transfers occur simultaneously or separately one by one.

The time evolution of the coefficients of the eigenstates at the 11th and 12th levels in the wave packet (of the 12th level), after an electron is excited from the (threefold degenerate) 5th to 7th levels to the 12th level. The upper lines show the absolute squared coefficient of the eigenstate at the 12th level , while the lower lines show the absolute squared coefficient of the eigenstate at the 11th level . The solid, dashed, and dotted lines represent, respectively, the cases (i) where atomic nuclei are fixed, (ii) where atomic nuclei are freely relaxed, and (iii) where has of initial velocity. For the cases (ii) and (iii), it is found that two eigenstates (at the 11th and 12th levels) are mixed as the time goes by.

The time evolution of the coefficients of the eigenstates at the 11th and 12th levels in the wave packet (of the 12th level), after an electron is excited from the (threefold degenerate) 5th to 7th levels to the 12th level. The upper lines show the absolute squared coefficient of the eigenstate at the 12th level , while the lower lines show the absolute squared coefficient of the eigenstate at the 11th level . The solid, dashed, and dotted lines represent, respectively, the cases (i) where atomic nuclei are fixed, (ii) where atomic nuclei are freely relaxed, and (iii) where has of initial velocity. For the cases (ii) and (iii), it is found that two eigenstates (at the 11th and 12th levels) are mixed as the time goes by.

The time evolution of the energy eigenvalues (solid lines) and the energy expectation values (dashed lines) of (a) the 12th level and (b) the 11th level when the atomic nuclei are fixed.

The time evolution of the energy eigenvalues (solid lines) and the energy expectation values (dashed lines) of (a) the 12th level and (b) the 11th level when the atomic nuclei are fixed.

The time evolution of the energy eigenvalues (solid lines) and the energy expectation values (dashed lines) of (a) the 12th level and (b) the 11th level when the atomic nuclei are freely relaxed.

The time evolution of the energy eigenvalues (solid lines) and the energy expectation values (dashed lines) of (a) the 12th level and (b) the 11th level when the atomic nuclei are freely relaxed.

The time evolution of the energy eigenvalues (solid lines) and the energy expectation values (dashed lines) of (a) the 12th level and (b) the 11th level when has of initial velocity.

The time evolution of the energy eigenvalues (solid lines) and the energy expectation values (dashed lines) of (a) the 12th level and (b) the 11th level when has of initial velocity.

The time evolution of the coefficients of the eigenstates at the seventh and the eighth levels in the wave packet (of the seventh level), after the excited electron is transferred from to . The upper lines show the absolute squared coefficient of the eigenstate at the seventh level , while the lower lines show the absolute squared coefficient of the eigenstate at the eight level . The solid, dashed, and dotted lines represent, respectively, the cases (i) where atomic nuclei are fixed, (ii) where atomic nuclei are freely relaxed, and (iii) where has of initial velocity. For the cases (ii) and (iii), it is found that two eigenstates (at the seventh and eighth levels) are mixed as the time goes by.

The time evolution of the coefficients of the eigenstates at the seventh and the eighth levels in the wave packet (of the seventh level), after the excited electron is transferred from to . The upper lines show the absolute squared coefficient of the eigenstate at the seventh level , while the lower lines show the absolute squared coefficient of the eigenstate at the eight level . The solid, dashed, and dotted lines represent, respectively, the cases (i) where atomic nuclei are fixed, (ii) where atomic nuclei are freely relaxed, and (iii) where has of initial velocity. For the cases (ii) and (iii), it is found that two eigenstates (at the seventh and eighth levels) are mixed as the time goes by.

The time evolution of the energy eigenvalues (solid lines) and the energy expectation values (dashed lines) of (a) the seventh level and (b) the eighth level when the atomic nuclei are fixed.

The time evolution of the energy eigenvalues (solid lines) and the energy expectation values (dashed lines) of (a) the seventh level and (b) the eighth level when the atomic nuclei are fixed.

The time evolution of the energy eigenvalues (solid lines) and the energy expectation values (dashed lines) of (a) the seventh level and (b) the eighth level when the atomic nuclei are freely relaxed.

The time evolution of the energy eigenvalues (solid lines) and the energy expectation values (dashed lines) of (a) the seventh level and (b) the eighth level when the atomic nuclei are freely relaxed.

The time evolution of the energy eigenvalues (solid lines) and the energy expectation values (dashed lines) of (a) the seventh level and (b) the eighth level when has of initial velocity.

The time evolution of the energy eigenvalues (solid lines) and the energy expectation values (dashed lines) of (a) the seventh level and (b) the eighth level when has of initial velocity.

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