## 4 Discussion
However, the experimental result exhibits a much lower value, due to the fact that the chemical bond binding impacts the CE process of low-charge parent ions. As a result, a dissociation process taking place in the PE curves, as opposed to the CP curve, ought to make sense. In the pink rectangle area in Figure 3a,b, the PE curve coincides with the green line, which is in line with the experimental results. Thus, the starting point of multi-electron ionization is determined to be at \(\rm R_{e}\). Using the potential energy of the parent ions IBr\({}^{\rm x+}\) (x = 2-7), we calculated the critical distance, \(\rm R_{ij}\). The relationship between the KER, \(\rm E_{ij}\), and the potential energy V are described as follows [25; 46]:  
\[\rm E_{n,m}^{exp}\ =V_{n,m}(R_{n,m})\ -V(\infty), \tag{3}\]  
where we define the V at infinity as zero. However, Equation (3) does not account for the accumulated kinetic energy recoveries from earlier stages. Consequently, it is necessary to include the accumulated KER:  
\[\rm E_{n,m}^{exp}\ V_{n,m}(R_{n,m})\ +E_{n,m}^{acc}, \tag{4}\]  
The accumulated KER can be written as follows:  
\[\rm E_{n,m}^{exp}\ -\ E_{ij}^{exp}\ =\ V_{n,m}(R_{n,m})\ +E_{n,m}^{acc}\ -\ V_{ij}(R_{ij})\ -\ E_{ij}^{acc}, \tag{5}\]  
The energy increment accumulated between (i, j) and (n, m) can be expressed as follows:  
\[\rm\Delta E\ =\ E_{n,m}^{acc}\ -\ E_{ij}^{acc}\ =\ V_{ij,j}(R_{ij})\ -\ V_{ij}(R_{n,m}), \tag{6}\]  
Substituting Equation (6) into Equation (5), we arrived at:  
\[\rm E_{n,m}^{exp}\ -\ E_{ij}^{exp}\ =\ V_{n,m}(R_{n,m})\ -\ V_{ij}(R_{n,m}), \tag{7}\]  
Chemical bonding interactions between two atoms are significant at shorter nuclear distances, but they become negligible when the distance exceeds 3 A. At this point, the Coulomb  
Figure 3: PE curves illustrating the IBr\({}^{2+}\) ion’s ground and excited states in the (**a**) singlet and (**b**) triplet states, respectively. The CP curve represents the relationship between Coulomb repulsion energy and nuclear distance. The pink rectangles show the \(\pm\)0.05 Å region around the Re and the green line represents the measured KER of the channel (1, 1). repulsive force of two positive charges dominates the interaction process. \(\rm V_{n,m}(R_{n,m})\) can be expressed as Equation (2), and Equation (7) can be expressed to Equation (8). \[\rm E_{n,m}^{exp}\ -\ E_{ij}^{exp}\ =\ 14.4\ \rm nm/R_{n,m}\ -\ 14.4 ij/R_{n,m}\ =\ 14.4(nm-ij)/R_{n,m} \tag{8}\]  
Once both \(\rm V_{n,m}(R_{n,m})\) and \(\rm R_{n,m}\) are known, it becomes feasible to estimate the time needed to progress from one ionization stage to the next [25, 47], as expressed by Equation (9). \[\rm T_{ij\to n,m}=\int_{R_{ij}}^{R_{n,m}}\frac{dr}{\sqrt{\frac{4}{m}[V_{ij}(R_{ ij})-V_{ij}(r)]}}, \tag{9}\]  
By substituting the measured KER values into Equations (8) and (9), we can obtain all possible critical distances and the corresponding travel times for each channel of one-electron sequential ionization, as shown in Table 2.  
Based on the experimental results, we can invert the one-electron sequential ionization process. Table 2 lists all the possible ionization paths. Based on the different Coulomb explosion channels, we can classify the above ionization paths into five categories, as shown in (a)-(e). It is noted that most of the \(\rm R_{n,m+1}\) or \(\rm R_{n+1,m}\) are larger than \(\rm R_{n,m}\), which is in line with the \"ladder-path\" model's prediction, but there are some ionization processes that are not reasonable. Taking process (a) as an example, \(\rm IBr^{5+}\) ionized to \(\rm IBr^{6+}\) at \(\rm R_{2,3}=5.49\) A, while \(\rm IBr^{6+}\) further ionized to \(\rm IBr^{7+}\) at \(\rm R_{3,3}=5.35\) A. The calculation result shows that \(\rm R_{n+1,m}<R_{n,m}\), which contradicts common sense. Naturally, it is also impossible to calculate the travel time according to Equation (9). The other processes (b)-(e) again fail to explain the existence of the experimental result of the channel (4, 3). Other experimental results, such as (3, 1) and (4, 2), present the same dilemma.