# Charge Transfer and Electron Production in Proton Collisions with Uracil: A Classical and Semiclassical Study

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

_{2}[18]. The application of the method involves the calculation of the energies of several electronic states of the supermolecule along each trajectory.

## 2. Results and Discussion

#### 2.1. Semiclassical Results

#### 2.2. CTMC Results

## 3. Materials and Methods

#### 3.1. Semiclassical Method

#### 3.2. CTMC Method

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

U | Uracil |

CT | Charge transfer |

EP | Electron production |

CTMC | classical-trajectory Monte Carlo |

MO | Molecular orbital |

CASSCF | Complete active space self consistent-field |

PEC | Potential energy curve |

IPM | Independent particle model |

EC | Entrance channel |

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**Figure 1.**Potential energy curves along the trajectory t2d with impact parameter $b=7$ ${a}_{0}$. The states are labeled according to the electronic state of ${\mathrm{U}}^{+}$ when the projectile is at an asymptotic distance. The energy curve of the entrance channel, corresponding to ${\mathrm{H}}^{+}$+uracil(X A′), is shown with a black solid line. The CT channels are shown with dashed lines.

**Figure 2.**Projectile trajectories characterized by the set {$\widehat{\mathit{b}}$, $\widehat{\mathit{v}}$}. Taking into account the planar geometry of the molecule, the 24 trajectories of a 6-point Cotes formula are reduced to the 16 trajectories represented in the figure. The trajectories are classified in families attending to whether $\widehat{\mathit{v}}$ is perpendicular (t1), contained in (t2) or parallel to (t3) the molecular plane, and subfamilies t1x, t2x, and t3x that share the same unitary vectors ($\widehat{\mathit{v}},\widehat{\mathit{b}}$).

**Figure 3.**Total single charge transfer cross section in collisions of protons with uracil molecules as functions of the collision energy. Broken lines correspond to the averages of the subfamilies within a family, Equations (3)–(5), labeled in the figure; the solid line is the average of the three families and corresponds to the orientation average of Equation (6).

**Figure 4.**Branching-ratio for production of uracil cations by CT in collisions of protons with uracil molecules. Broken lines correspond to ions in A${}^{\u2033}$ state, while solid ones are those in a A${}^{\prime}$ state.

**Figure 5.**Natural orbitals of the uracil cation obtained with the CASSCF calculations when the projectile is at asymptotic distances along the t2d trajectory. The labels underneath each orbital refer to the sequence number of the orbital within its symmetry in the Cs point group, and the bracket contains the ${\mathrm{U}}^{+}$ electronic state of the uracil cation (see Table 1).

**Figure 6.**Electron production cross sections from individual MO of uracil after collision with protons, given by their ionization energy ${I}_{k}$. The different symbols correspond to different collision energies specified in the figure with numbers in keV. The lines are the fitted Equation (7).

**Figure 7.**Same as in Figure 6, but for the single charge transfer process.

**Figure 8.**Total cross sections for electron production in proton–uracil collisions as functions of the collision energy. The present CTMC results (solid lines marked with 21 MO and 10 MO) are compared with those of previous calculations Paredes et al. [9], Lüdde et al. [11], Lekadir et al. [12], Sarkadi [13], and the experimental results of Itoh et al. [3] and Chowdhury et al. [4],as indicated in the figure. An estimation of the Auger contribution to ionization is added with a gray shade.

**Table 1.**Electronic states of ${\mathrm{U}}^{+}$ with specification of the main electronic configuration (see molecular orbitals in Figure 5) and the electronic energies (in eV) referred to its ground state.

Electronic State | Dominant Configuration | Energy (eV) |
---|---|---|

1A${}^{\u2033}$ | ${\left(23{a}^{\prime}\right)}^{2}{\left(2{a}^{\u2033}\right)}^{2}{\left(3{a}^{\u2033}\right)}^{2}{\left(4{a}^{\u2033}\right)}^{2}{\left(24{a}^{\prime}\right)}^{2}{\left(5{a}^{\u2033}\right)}^{1}$ | 0.0 |

1A${}^{\prime}$ | ${\left(23{a}^{\prime}\right)}^{2}{\left(2{a}^{\u2033}\right)}^{2}{\left(3{a}^{\u2033}\right)}^{2}{\left(4{a}^{\u2033}\right)}^{2}{\left(24{a}^{\prime}\right)}^{1}{\left(5{a}^{\u2033}\right)}^{2}$ | 0.75 |

2A${}^{\u2033}$ | ${\left(23{a}^{\prime}\right)}^{2}{\left(2{a}^{\u2033}\right)}^{2}{\left(3{a}^{\u2033}\right)}^{2}{\left(4{a}^{\u2033}\right)}^{1}{\left(24{a}^{\prime}\right)}^{2}{\left(5{a}^{\u2033}\right)}^{2}$ | 1.40 |

2A${}^{\prime}$ | ${\left(23{a}^{\prime}\right)}^{1}{\left(2{a}^{\u2033}\right)}^{2}{\left(3{a}^{\u2033}\right)}^{2}{\left(4{a}^{\u2033}\right)}^{2}{\left(24{a}^{\prime}\right)}^{2}{\left(5{a}^{\u2033}\right)}^{2}$ | 2.95 |

3A${}^{\u2033}$ | ${\left(23{a}^{\prime}\right)}^{2}{\left(2{a}^{\u2033}\right)}^{2}{\left(3{a}^{\u2033}\right)}^{1}{\left(4{a}^{\u2033}\right)}^{2}{\left(24{a}^{\prime}\right)}^{2}{\left(5{a}^{\u2033}\right)}^{2}$ | 4.28 |

4A${}^{\u2033}$ | ${\left(23{a}^{\prime}\right)}^{2}{\left(2{a}^{\u2033}\right)}^{1}{\left(3{a}^{\u2033}\right)}^{2}{\left(4{a}^{\u2033}\right)}^{2}{\left(24{a}^{\prime}\right)}^{2}{\left(5{a}^{\u2033}\right)}^{2}$ | 4.47 |

3A${}^{\prime}$ | ${\left(23{a}^{\prime}\right)}^{2}{\left(2{a}^{\u2033}\right)}^{2}{\left(3{a}^{\u2033}\right)}^{2}{\left(4{a}^{\u2033}\right)}^{2}{\left(24{a}^{\prime}\right)}^{1}{\left(5{a}^{\u2033}\right)}^{1}{\left(6{a}^{\u2033}\right)}^{1}$ | 4.91 |

4A${}^{\prime}$ | ${\left(23{a}^{\prime}\right)}^{2}{\left(2{a}^{\u2033}\right)}^{2}{\left(3{a}^{\u2033}\right)}^{2}{\left(4{a}^{\u2033}\right)}^{2}{\left(24{a}^{\prime}\right)}^{1}{\left(5{a}^{\u2033}\right)}^{1}{\left(6{a}^{\u2033}\right)}^{1}$ | 6.22 |

**Table 2.**Molecular orbital ionization energies (in Hartree) of uracil at the Hartree–Fock level, ${I}_{k}$. A${}^{\prime}$ MO from 20 to 24 and all A${}^{\u2033}$ are used in the CTMC calculations, while A${}^{\prime}$ orbitals from 9 to 19 are only used to compute the final CTMC cross sections.

MO (A${}^{\prime}$) | ${\mathit{I}}_{\mathit{k}}$ | MO (A${}^{\u2033}$) | ${\mathit{I}}_{\mathit{k}}$ |
---|---|---|---|

24 | $0.4563$ | 5 | $0.3752$ |

23 | $0.4910$ | 4 | $0.4432$ |

22 | $0.6097$ | 3 | $0.5321$ |

21 | $0.6236$ | 2 | $0.5776$ |

20 | $0.6613$ | 1 | $0.6759$ |

19 | 0.6860 | ||

18 | 0.7224 | ||

17 | 0.7742 | ||

16 | 0.8153 | ||

15 | 0.9109 | ||

14 | 0.9416 | ||

13 | 1.0954 | ||

12 | 1.2528 | ||

11 | 1.3211 | ||

10 | 1.4068 | ||

9 | 1.4442 |

**Table 3.**Parameters of Equation (7) for the fit of the electron production and charge transfer at a given collision energy as a function of the ionization potential of the first 10 MOs (20–24 A${}^{\prime}$ and 1–5 A${}^{\u2033}$, see Table 2) of uracil.

Electron Production | Charge Transfer | |||
---|---|---|---|---|

E (keV) | a | b | a | b |

20 | $0.8298$ | $2.0$ | $3.557$ | $0.790$ |

30 | $1.1820$ | $2.0$ | $3.145$ | $0.138$ |

50 | $1.5294$ | $1.5$ | $1.385$ | $-0.305$ |

100 | $1.3643$ | $1.0$ | $0.266$ | $-0.772$ |

225 | $0.6584$ | $1.0$ | $0.030$ | $-1.815$ |

500 | $0.2993$ | $1.0$ | ||

1000 | $0.1571$ | $1.0$ | ||

2000 | $0.0769$ | $1.0$ | ||

2500 | $0.0615$ | $1.0$ |

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**MDPI and ACS Style**

Illescas, C.; Méndez, L.; Bernedo, S.; Rabadán, I.
Charge Transfer and Electron Production in Proton Collisions with Uracil: A Classical and Semiclassical Study. *Int. J. Mol. Sci.* **2023**, *24*, 2172.
https://doi.org/10.3390/ijms24032172

**AMA Style**

Illescas C, Méndez L, Bernedo S, Rabadán I.
Charge Transfer and Electron Production in Proton Collisions with Uracil: A Classical and Semiclassical Study. *International Journal of Molecular Sciences*. 2023; 24(3):2172.
https://doi.org/10.3390/ijms24032172

**Chicago/Turabian Style**

Illescas, Clara, Luis Méndez, Santiago Bernedo, and Ismanuel Rabadán.
2023. "Charge Transfer and Electron Production in Proton Collisions with Uracil: A Classical and Semiclassical Study" *International Journal of Molecular Sciences* 24, no. 3: 2172.
https://doi.org/10.3390/ijms24032172