Open Access Article

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Dequan Wang*^{a},
Deguo Wang^{b},
Liwei Fu^{a},
Jianyu Wang^{c},
Guang Shi*^{d},
Yanchun Li*^{a} and
Xuri Huang^{a}
^{a}Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, People’s Republic of China. E-mail: dequan_wang@jlu.edu.cn
^{b}Department of Assets Logistic Management, Jilin University, Changchun, People’s Republic of China
^{c}State Key Laboratory of Inorganic Synthesis & Preparative Chemistry, Jilin University, Changchun, People’s Republic of China
^{d}Hematology and Oncology Department, The Second Hospital, Jilin University, Changchun, People’s Republic of China

Received
22nd November 2018
, Accepted 3rd January 2019

First published on 15th January 2019

The accuracy of three-dimensional adiabatic potential energies for F_{3}^{−} ions is reduced with higher level ab initio methods. The accurate numerically fitted method, the 3D-spline method, was performed to obtain an accurate adiabatic potential energy surface for the ground state of F_{3}^{−} ions. A linear minimum geometry was found in the present work, and the corresponding parameters were in excellent agreement with those of the optimized structure and those reported in previous work. By comparing the lowest potential energies for different attacking angles one can see that the favorite reaction pathway for the title reaction is F^{−} + F_{2}(v,j) → F_{3}^{−}(C_{∞}) → F^{−} + F_{2}(v′,j′).

Since quantum chemical calculations can produce sufficiently reliable data for this system, a careful look at the potential energy surfaces (PESs) can help us guess the likely reaction mechanism. Despite several investigations of the F^{−} + F_{2} reaction kinetics, an accurate understanding of the reaction mechanism of this system is still quite limited. For the precise dynamical simulation of this system, high-quality electronic structure PESs over a broad range of molecular configurations are the first requisite step.

Up to now, no accurate PES data are presently available for the reaction of F^{−} colliding with F_{2}. To obtain more perfect dynamic study results for this system, a three dimensional PES is constructed in the present work.

In the current study, we carried out high level ab initio calculations for the ground state of a global PES for F_{3}^{−}. Our main goal is to produce a highly accurate potential energy surface for the title reaction system with Jacobi coordinates over a broad range of molecular configurations, so that we can perform further dynamical studies. The outline of the present work is as follows: the second section will introduce the computational methods, the global PES will be presented in the third section and the conclusions and discussions will be shown in the fourth section.

As with our previous works,^{12,13} Jacobi coordinates (R, r, θ) were used to characterize this three-body system, in which R indicates the distance of the fluorine anion (F^{−}) from the center of mass of the two fluorine atoms, r is the distance of the two fluorine atoms, and θ represents the angle between the two vectors R and r. The singlet state of the F_{3}^{−} configurations was sampled over a broad range, i.e. r distances from 0.4 Å to 5.0 Å, R from 0.0 Å to 20.0 Å, and θ from 0.0° to 90.0°.

The scan grids of r, R and θ were set with different steps according to their ranges. The grid details for these ranges are as follows: the angle grid was 10°, for r from r = 0.4 Å to r = 3.0 Å, Δr = 0.1 Å including r = 1.73 Å, 1.74 Å, and 1.75 Å; for r from r = 3.2 Å to r = 5.0 Å, Δr = 0.2 Å; for R from R = 0.0 Å to R = 4.4 Å, ΔR = 0.2 Å, and includes the R = 0.1 Å point; for R from R = 4.8 Å to R = 12.0 Å, ΔR = 0.4 Å; for R from R = 12.5 Å to R = 15.0 Å, ΔR = 0.5 Å; the other grids are fixed in 1.0 Å. The 21200 geometries were chosen to generate the ab initio energy points in this region. The large number of points warrant the quality of the following fitted PES. The three dimensional (3D) B-spline method was used in this work.

From Fig. 1 one can see that the equilibrium distance of F_{2} is 1.413 Å, which is in good agreement with the real value of 1.412 Å;^{6} the electronic energy for the vibrational state v = 0 and the rotational state j = 0 of this equilibrium structure is 0.061 eV. With an increase in r(F–F), the energy increased to a transition state then separated to the two F atoms. The diatomic atom distance and potential energy for the transition state point were 2.21 Å and 1.314 eV, respectively.

For the title reaction, the three atoms are identical and the potential energy surface for the reaction entrance (F^{−} attacking F_{2} reaction pathway) and exit (the new F^{−} separating from F_{2} reaction pathway) should be the same. After analyzing the reaction entrance, the whole reaction potential energy surface was clearly shown. In the following two sections, the reaction entrances for the one-dimensional (1D) and two-dimensional (2D) potential energy surface will be discussed.

Fig. 2 Potential energy surface as a function of distance R (in Å) with different angles and r values. |

Fig. 3 shows the F_{3}^{−} potential energy surface for θ = 0°. Fig. 3 shows that when the F^{−} ion is far away from the F_{2} molecule (3.5 Å < R, and 1.1 Å < r < 1.8 Å), the potential energy is nearly consistent with the change in R value; when R < 3.5, with a decrease in R value, the r value is increased and the minimum geometry is then formed; when R is reduced to 2.6 Å, and r extends to 1.73 Å, the F_{3}^{−} molecule reaches its global minimum area. The bond distances of the minimum structure are 1.730 Å and 1.735 Å in our fitted PES, which are in good agreement with the optimized values (1.745 Å and 1.746 Å) with the b3lyp/6-311++g** calculation level using the Gaussian program.^{11} The potential energy of the global minimum is −1.02 eV, which is consistent with the results of Artau et al.^{5} (from −0.911 eV to −1.127 eV).

The potential energy surface for θ = 30° is shown in Fig. 4. By shortening the R distance, the potential energy becomes lower and lower; when the R values reach 2.7 Å, and the r value stretches to 1.78 Å, the system arrives at its minimum energy (−0.445 eV). This minimum is not really the minimum of the structure, if it is optimized the linear minimum geometry will be achieved.

Fig. 4 2D and contour plot of the potential energy surface (in eV) as a function of the distances R and r (in Å) at a fixed θ = 30°. |

For θ = 60° and 90°, the characteristics of these two PESs are similar to each other (see Fig. 5 and 6). For every fixed r value, the potential energy slightly changed with the transformation of the R values. From these two figures, one can see that a slight minimum may have existed, and its energies were higher than −0.2 eV. We tried to optimize these geometries many times to find them with the Gaussian program, but we failed in the end.

Fig. 5 2D and contour plot of the potential energy surface (in eV) as a function of the distances R and r (in Å) at θ = 60°. |

Fig. 6 2D and contour plot of the potential energy surface (in eV) as a function of the distances R (in Å) and r at θ = 90°. |

From analyzing the globle PESs, the F_{3}^{−} system could overcome the reaction barrier (nearly 3.2 eV) to reach it's three atom area. The r value of this reaction barrier is nearly equal to 2.2 Å. This characteristic is different from the HCC,^{12} LiHH,^{13} and OCC^{14} systems which were investigated in our previous studies.

To easily understand the relationship of the PES with different angles, the lowest potential energy surface is plotted in Fig. 7. From Fig. 7, we can find that the potential energies become lower and lower with decrease the attacking angles; the lowest energy corresponds to the linear geometry, and the potential energies changed from 90° to 0° do not have any reaction barrier. From this PES, we can predict the reaction mechanics. No matter which angle the F^{−} ion attacks the F_{2} molecule from, the reaction should form the linear F_{3}^{−} ion first, then separate to the new F^{−} ion and F_{2} products. The accurate trajectory method can be used to confirm the mechanism of this reaction, and we will continue this work in the near future using the present fitted adiabatic PES.

Fig. 7 2D and contour plot for the lowest potential energy surface (in eV) as a function of distance R (in Å) and θ (in degree) at a fixed r = 1.73 Å. |

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