Multi-Electron Ionization and Coulomb Explosion of the IBr Molecule in the Near-Infrared Femtosecond Laser Field

Abstract

The DC-sliced ion velocity map imaging approach was used to analyze the multi-electron ionization and subsequent Coulomb explosion of an IBr molecule exposed to a near-infrared femtosecond laser field. The existence of the molecular ions up to IBr⁷⁺ was observed in the experiment, and a series of Coulomb explosion channels are assigned. According to the “ladder-path” ionization model, the multi-electron ionization paths of IBr molecules are determined. We find that the charge transfer process does not occur during ionization, and the presence of higher charge states can be explained by considering the higher-order ionization process.

1. Introduction

Ionization is one of the most fundamental physical processes in the interaction between intense lasers and matter. The ionization process governs many other physical processes, including high harmonic generation, photoelectron holographic imaging, molecular dissociation, electron correlation, etc. [1,2,3,4,5,6,7,8,9]. With the development of femtosecond and attosecond laser pulses, scientists now have better knowledge of ionization [10,11,12,13,14,15,16,17,18]. The Keldysh parameter value can be utilized to identify the ionization process under various laser conditions [19,20]. When the Keldysh parameter exceeds one, an electron can absorb multiple photons simultaneously and overcome the ionization potential. When the Keldysh parameter is far less than one, the laser field instead significantly suppresses the Coulomb potential, and electrons escape through tunneling across the potential energy surface.

Recently, there has been significant interest in multi-electron ionization in a strong laser field. To understand the dynamic processes involved, a variety of theoretical models have been developed. The femtosecond laser field may swiftly remove many electrons with minimum change to the molecule structure. Next, the Coulomb repulsive force affects the charged molecular ions’ dissociation, according to the multi-electron dissociative ionization (MEDI) model [21]. In the post-dissociative ionization (PDI) model, reaction products may undergo a second ionization process after dissociation [22]. Conversely, the two-step model proposes that molecule electron loss and, at equilibrium and critical distances, Coulomb explosions (CE) occur twice [23]. Bandrauk et al. put forward a model of charge resonance enhanced ionization (CREI), wherein they showcased the charge resonant states, highlighting a strong correlation with the laser field at a given distance R_c [24]. Based on this model, all charged molecular ions exhibit an identical energy defect ratio. However, Gibson et al. proposed a sequential ionization process for CREI, whereby the electrons are stripped one by one in a laser pulse and nuclear stretching cannot be averted [25]. The energy collected in the previous ionization step is also included in the kinetic energy (KE) that accumulates from each channel. As a result, rather than having a constant value, the R_c value should fluctuate when the charge states change [26]. Thus, it is important to investigate what causes these dissociation processes, as well as how kinetic energy accumulates in the molecules before dissociation.

Most studies are mostly focused on homo-nuclear halogen molecules, such as H₂, N₂ and I₂ [26,27,28,29,30,31]. The study of the dissociation and ionization process for heteronuclear halogen molecules has been relatively underreported. As a classical heteronuclear halogen molecule, IBr has mostly been studied for the coherent control of the photo-dissociation process [32,33,34,35]. However, we are interested in the intense field dynamic process of IBr. In this paper, we explore the ultrafast dynamics processes of multi-electron ionization and the Coulomb explosion (CE) of IBr in the near-infrared femtosecond laser field. Our results show that high-charged molecular ions are formed when electron ionization is enhanced by increasing nuclear separation. Furthermore, the charge transfer process does not occur in the process and higher-order ionization processes need be considered to achieve higher charge states. This work can provide an understanding of the complex field-induced multi-electron dynamics of heteronuclear diatomic molecules.

2. Experiment and Theory Calculation

An in-house DC-sliced velocity imaging system was utilized to carry out the experiment. The system has been further detailed elsewhere [36,37]. In brief, a biconvex lens focuses femtosecond laser pulses into the reaction chamber at a repetition rate of 1 kHz, a center wavelength of 800 nm, and a pulse duration of 70 fs. The polarization vector of the laser is perpendicular to the direction of ion flight, and the laser intensity in the focal volume is estimated to be 40 to 300 TW/cm², which was calibrated by measuring the yield ratio of Ar²⁺/Ar⁺ [38]. After being seeded with helium in a 1:10 ratio, the gaseous iodine bromide sample is expelled into the reaction chamber (~5.0 × 10⁻⁹ mbar) using a pulsed valve (General Valve, Parker, Cleveland, OH, USA) that repeats at a rate of 100 Hz for 130 µs. The supersonic molecular beam interacts at a right angle with the linearly polarized femtosecond pulse in the middle of the extraction and repeller plates. As the fragment ion clouds pass through the velocity mapping lens, they are stretched and detected using micro-channel plates (MCPs) coupled with the P47 phosphor screen. An oscilloscope (LeCroy Wave Pro) is coupled to a photomultiplier tube (Hamamatsu H7732-11), which records the related time-of-flight (TOF) mass spectra in one dimension. An intensified charge-coupled device camera (ICCD, PI-MAXII) with a time resolution of 5 ns is used to capture the two-dimensional images. Utilizing a digital delay/pulse generator (DG645, Stanford Instruments, Sunnyvale, CA, USA), timing sequencing control is performed.

To enhance the comprehension of the ultrafast dynamic processes involved in the IBr molecule, we conducted various theoretical calculations by using the Gaussian 09 software [39]. The molecular structure was optimized using the B3LYP/aug-cc-pVTZ level [40,41]. The potential energy curves of ionic IBr²⁺ were calculated at the EOM-CCSD level of theory using a def2TZVP basis set [42,43].

3. Results

Figure 1a–c show the TOF mass spectra of an IBr molecule exposed to an 800 nm femtosecond laser pulse with a pulse duration of 70 femtoseconds (FWHM). The laser intensities are (a) 40 TW/cm², (b) 90 TW/cm², and (c) 300 TW/cm², respectively. In our work, dissociative ionization dominates the dissociation and ionization process due to the femtosecond laser field. A series of ions, Br^m+ (m = 1–3) and Iⁿ⁺ (n = 1–4), are observed, implying that the parent molecule ions are highly unstable and easily break down into fragment ions. At a low laser intensity, the ions Br⁺, I⁺, and I²⁺ are the main products. As the laser intensity increases, the generation of multipe-charged ions Br^m+ (m = 2–3) and Iⁿ⁺ (n = 3–4) shows the involvement of Coulomb explosion processes (CE) in this experiment. In addition, the raw DC-sliced ion images (512 × 512 pixel) and the normalized velocity distributions of the ions Iⁿ⁺ (n = 1–4) and Br^m+ (m = 1–3) are shown in Figure 2.

4. Discussion

As shown in the polycyclic structure of Figure 2a–g, it is clear that fragment ions with the same charge state come from different reaction channels. The corresponding KER values have been extracted and labeled in Figure 2a’–g’. It can be seen that all these ion kinetic energy distributions have both high and low kinetic energy components. Generally, the multiphoton dissociative ionization (MPDI) process would produce fragment ions with low KER (<0.5 eV), while the Coulomb explosion (CE) process would produce fragment ions with high KER [44]. Here, we concentrate on these channels in the CE processes.

KER(A^P+)/KER(B^q+) = M(B^q+)/M(A^P+),

(1)

KER_total = 14.4pq/r,

(2)

In the classical two-body CE model, two fragmented ions should satisfy momentum conservation, as explained by Equation (1), where A^p+ and B^q+ represent the two fragment ions, p/q denote the charge states, and M stand for the mass of the fragment ions. Equation (2) represents the total KER of a CE channel, where r indicates the internuclear distance when the CE starts. Based on the equations given above, the possible CE channels are listed in

Table 1. The possible CE channels for the molecular ions IBr^x+ (x = 2–7).

(n, m)	CE Channels	KER_In+ (eV)	KER_Bm+ (eV)	KER_total (eV)	Rc (Å)
(1, 1)	IBr2+→I+ + Br+	1.58	2.20	3.78	3.81
(1, 2)	IBr3+→I+ + Br2+	3.25	4.32	7.57	3.80
(2, 1)	IBr3+→I2+ + Br+	2.72	4.47	7.19	4.01
(2, 2)	IBr4+→I2+ + Br2+	5.40	8.12	13.52	4.26
(2, 3)	IBr5+→I2+ + Br3+	7.21	12.24	19.45	4.44
(3, 1)	IBr4+→I3+ + Br+	4.26	6.39	10.65	4.06
(3, 2)	IBr5+→I3+ + Br2+	7.49	11.43	18.92	4.57
(3, 3)	IBr6+→I3+ + Br3+	10.28	17.04	27.32	4.74
(4, 2)	IBr6+→I4+ + Br2+	9.88	15.07	24.95	4.62
(4, 3)	IBr7+→I4+ + Br3+	14.29	21.10	35.39	4.88

.

The channel (n, m) represents the predicted CE process, IBr^(n+m)+→Iⁿ⁺ + Br^m+. The energy collected in the previous ionization step is included in the KER that accumulates from each channel, as seen by the R_c changing with the charge states in Table 1. It is generally believed that the time for the double ionization to occur is more than a dozen fs. On this time scale, the molecular structure (e.g., the distance between nuclei) does not change. Therefore, the starting point of multi-electron ionization or the site where the third electron is ionized should still be at the equilibrium internuclear distance (R_e = 2.47 Å). Next, some theoretical calculations are performed to verify the above assumptions.

Figure 3 shows the dissociation potential energy (PE) curves of the ground electronic state and excited states of IBr²⁺ ion where the PE curves of the ionic IBr²⁺ are calculated at the def2TZVP/EOM-CCSD level and the pink rectangles show the ±0.05 Å region around the R_e. The charge-repulsive (CP) curves, as described by Equation (2), are also included. Similar to the relationship shown in ref. [45], the PE curve and CP curve will overlap when the nuclei are spread far apart enough. Here, we have defined E(∞) = 0 eV, so that the green line (3.78 eV) represents the measured KER of the channel (1, 1). If IBr²⁺ were to experience a succeeding Coulomb explosion at R_e, the channel would be expected to release a total kinetic energy of 5.83 eV. 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 R_e.

Using the potential energy of the parent ions IBr^x+ (x = 2–7), we calculated the critical distance, R_i,j. The relationship between the KER, E_i,j, and the potential energy V are described as follows [25,46]:

$${\mathrm{E}}_{\mathrm{n},\mathrm{m}}^{\exp }={\mathrm{V}}_{\mathrm{n},\mathrm{m}}({\mathrm{R}}_{\mathrm{n},\mathrm{m}})-\mathrm{V}(\infty ),$$

(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:

$${\mathrm{E}}_{\mathrm{n},\mathrm{m}}^{\exp }{\mathrm{V}}_{\mathrm{n},\mathrm{m}}({\mathrm{R}}_{\mathrm{n},\mathrm{m}})+{\mathrm{E}}_{\mathrm{n},\mathrm{m}}^{\mathrm{acc}},$$

(4)

The accumulated KER can be written as follows:

$${\mathrm{E}}_{\mathrm{n},\mathrm{m}}^{\exp }-{\mathrm{E}}_{\mathrm{i},\mathrm{j}}^{\exp }={\mathrm{V}}_{\mathrm{n},\mathrm{m}}({\mathrm{R}}_{\mathrm{n},\mathrm{m}})+{\mathrm{E}}_{\mathrm{n},\mathrm{m}}^{\mathrm{acc}}-{\mathrm{V}}_{\mathrm{i},\mathrm{j}}({\mathrm{R}}_{\mathrm{i},\mathrm{j}})-{\mathrm{E}}_{\mathrm{i},\mathrm{j}}^{\mathrm{acc}},$$

(5)

The energy increment accumulated between (i, j) and (n, m) can be expressed as follows:

$$\Delta \mathrm{E}={\mathrm{E}}_{\mathrm{n},\mathrm{m}}^{\mathrm{acc}}-{\mathrm{E}}_{\mathrm{i},\mathrm{j}}^{\mathrm{acc}}={\mathrm{V}}_{\mathrm{i},\mathrm{j}}({\mathrm{R}}_{\mathrm{i},\mathrm{j}})-{\mathrm{V}}_{\mathrm{i},\mathrm{j}}({\mathrm{R}}_{\mathrm{n},\mathrm{m}}),$$

(6)

Substituting Equation (6) into Equation (5), we arrived at:

$${\mathrm{E}}_{\mathrm{n},\mathrm{m}}^{\exp }-{\mathrm{E}}_{\mathrm{i},\mathrm{j}}^{\exp }={\mathrm{V}}_{\mathrm{n},\mathrm{m}}({\mathrm{R}}_{\mathrm{n},\mathrm{m}})-{\mathrm{V}}_{\mathrm{i},\mathrm{j}}({\mathrm{R}}_{\mathrm{n},\mathrm{m}}),$$

(7)

Chemical bonding interactions between two atoms are significant at shorter nuclear distances, but they become negligible when the distance exceeds 3 Å. At this point, the Coulomb repulsive force of two positive charges dominates the interaction process. V_n,m(R_n,m) can be expressed as Equation (2), and Equation (7) can be expressed to Equation (8).

$${\mathrm{E}}_{\mathrm{n},\mathrm{m}}^{\exp }-{\mathrm{E}}_{\mathrm{i},\mathrm{j}}^{\exp }=14.4\mathrm{nm}/{\mathrm{R}}_{\mathrm{n},\mathrm{m}}-14.4\mathrm{ij}/{\mathrm{R}}_{\mathrm{n},\mathrm{m}}=14.4(\mathrm{nm}-\mathrm{ij})/{\mathrm{R}}_{\mathrm{n},\mathrm{m}}$$

(8)

Once both V_n,m(R_n,m) and 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).

$${\mathrm{T}}_{\mathrm{i},\mathrm{j}\to \mathrm{n},\mathrm{m}}={\displaystyle {\int }_{{\mathrm{R}}_{\mathrm{i},\mathrm{j}}}^{{\mathrm{R}}_{\mathrm{n},\mathrm{m}}}\frac{\mathrm{d}\mathrm{r}}{\sqrt{\frac{4}{\mathrm{m}}[{\mathrm{V}}_{\mathrm{i},\mathrm{j}}({\mathrm{R}}_{\mathrm{i},\mathrm{j}})-{\mathrm{V}}_{\mathrm{i},\mathrm{j}}(\mathrm{r})]}}},$$

(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. The critical distance R_i,j and the travel time, T_i,j→n,m, for each channel of one-electron sequential ionization.

Process	Channel	Ri,j (Å)	Tij→nm (fs)
(a)	(1, 1)→(1, 2)	3.80	17.55
	(1, 2)→(2, 2)	4.84	16.25
	(2, 2)→(2, 3)	4.86	7.28
	(2, 3)→(3, 3)	5.49	9.13
	(3, 3)→(4, 3)	5.35	/
(b)	(1, 1)→(1, 2)	3.80	17.55
	(1, 2)→(2, 2)	4.84	16.25
	(2, 2)→(3, 2)	5.33	11.73
	(3, 2)→(3, 3)	5.14	/
(c)	(1, 1)→(2, 1)	4.22	20.55
	(2, 1)→(2, 2)	4.55	9.86
	(2, 2)→(2, 3)	4.86	7.28
	(2, 3)→(3, 3)	5.49	9.13
	(3, 3)→(4, 3)	5.35	/
(d)	(1, 1)→(2, 1)	4.22	20.55
	(2, 1)→(2, 2)	4.55	9.86
	(2, 2)→(3, 2)	5.33	11.73
	(3, 2)→(3, 3)	5.14	/
(e)	(1, 1)→(2, 1)	4.22	20.55
	(2, 1)→(3, 1)	4.16	/

.

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 R_n,m+1 or R_n+1,m are larger than 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, IBr⁵⁺ ionized to IBr⁶⁺ at R_2,3 = 5.49 Å, while IBr⁶⁺ further ionized to IBr⁷⁺ at R_3,3 = 5.35 Å. The calculation result shows that 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. Hence, we have considered two possible situations to explain the generation of these unreachable charge states; one involves the charge transfer (CT) process shown in Figure 4, while the other is the occurrence of the higher-order ionization process.

First, we consider the effects of the existence of a CT process on the one-electron sequential ionization process. Here, the CT process is defined as A^+qB^+q↔A^+q−1B^+q+1, as Ref. [48] mentioned. Here, the tunneling ionization process is not taken into account while performing the computation using the over-the-barrier (OBI) model. This makes sense because there is not much time for tunneling because the pulses are so short. The outer electrons are thought to move in the double-well potential U:

$$\mathrm{U}=-\frac{{\mathrm{Q}}_1/2}{|\mathrm{x}+\mathrm{R}/2|}-\frac{{\mathrm{Q}}_2/2}{|\mathrm{x}-\mathrm{R}/2|}-\mathsf{\epsilon }\mathrm{x},$$

(10)

where Q₁ and Q₂ represent the atomic core charges, x represents the axial position, R represents the internuclear separation, and ε is the laser E-field. The outer electron’s energy level, E_L, can be approximated by

$${\mathrm{E}}_{\mathrm{L}}=-\frac{(-{\mathrm{E}}_1-{\mathrm{Q}}_2/\mathrm{R})+(-{\mathrm{E}}_2-{\mathrm{Q}}_1/\mathrm{R})}{2},$$

(11)

where E₁ and E₂ are the known ionization potentials of the atomic ions.

Figure 5 illustrates the procedure for calculating the charge transfer. The R is tiny in Figure 5a, and the center barrier is much lower than the E_L (the laser electric field introduces a considerable Stark shift, E = ε·R/2). As a result, CT may occur effortlessly. At the intermediate R shown in Figure 5b, both the central barrier and E_L increase. Because the central barrier increases faster than E_L, the probability of CT decreases. When the probability of the charge transfer is zero, we can define the distance between the cores as R_cr. In Figure 5c, the R is beyond R_cr and the E_L is already lower than the central barrier, so that the CT process does not occur. Within the experimental conditions, the R_cr of each CT channel can be calculated and is labeled in

Table 3. Calculated R_cr under various laser intensities.

Channels	Ri,j (Å)	50 TW/cm2	100 TW/cm2	150 TW/cm2	200 TW/cm2	250 TW/cm2	300 TW/cm2
(1, 1)→(1, 2)↔(2, 1)	3.80	3.43	3.19	2.94	2.82	2.82	2.70
(1, 1)→(2, 1)↔(1, 2)	4.22	3.68	3.31	3.19	3.06	2.94	2.82
(1, 2)→(2, 2)↔(3, 1) *	4.84	3.68	3.68	3.68	3.68	3.68	3.68
(2, 1)→(2, 2)↔(3, 1) *	4.55	3.68	3.68	3.68	3.68	3.68	3.68
(2, 2)→(3, 2)↔(2, 3)	5.33	4.17	3.92	3.67	3.55	3.43	3.43
(2, 2)→(2, 3)↔(3, 2)	4.86	3.80	3.55	3.43	3.31	3.31	3.18
(2, 3)→(3, 3)↔(4, 2) *	5.49	3.80	3.80	3.80	3.80	3.80	3.80

* Stark shift (εR/2) is not applied to the same charged states IBr^(n+m)+ (n = m).

.

In Table 3, the first column represents the possible CT channels during the ionization process. The single arrow indicates the ionization process, and the double arrow represents the CT process. The second column represents the stretched value of the nuclear spacing when ionization occurs. The remaining columns indicate the R_cr calculated at various laser intensities. It is demonstrated that when the laser intensity rises, the R_cr decreases and the chance of CT rises. We are worried about whether each channel ionization and CT procedure can happen in order. Taking (1, 1)→(2, 1)↔(1, 2) as an example, the ionization process occurs when the internuclear distance R_(1,1) is 4.22 Å. But for the CT process, the maximum value of R_cr is 3.68 Å within the experimental conditions. This means that when the stretched length of the internuclear distance exceeds 3.68 Å, the CT process is prohibited from occurring. Therefore, once the charge state (2, 1) has been formed, it has no chance to undergo further charge transfer and form the charge state (1, 2). Other channels are similar. Hence, it is not reasonable for the ionization process to occur first and then for the charge transfer process to take place.

Second, we consider the effects of the existence of the next higher process, i.e., ionization with two electrons. This is important because in the atom, the ionization rate of two electrons is usually low. However, in molecules, the ionization rate of two electrons appears to exceed the ionization rate of one electron under certain conditions. Based on the experimentally obtained channels,

Table 4. The calculated R_i,j and the travel time, T_i,j→n,m, for each channel of one- and two-electron sequential ionization.

Process	Channel	Ri,j (Å)	Tij→nm (fs)
(f)	(1, 1)→(1, 2)	3.80	17.55
	(1, 2)→(2, 2)	4.84	16.25
	(2, 2)→(2, 3)	4.86	7.28
	(2, 3)→(4, 3)	5.42	8.59
(g)	(1, 1)→(1, 2)	3.80	17.55
	(1, 2)→(2, 2)	4.84	16.25
	(2, 2)→(4, 2)	5.04	9.21
	(4, 2)→(4, 3)	5.52	8.47
(h)	(1, 1)→(3, 1)	4.19	20.34
	(3, 1)→(3, 2)	5.22	14.62
	(3, 2)→(4, 3)	5.25	2.10
(i)	(1, 1)→(3, 1)	4.19	20.34
	(3, 1)→(3, 3)	5.18	14.32
	(3, 3)→(4, 3)	5.35	4.49
(j)	(1, 1)→(3, 1)	4.19	20.34
	(3, 1)→(4, 2)	5.03	13.16
	(4, 2)→(4, 3)	5.52	8.47

considers all possible situations for the sequential ionization paths with one and two electrons. Based on the different CE channels, we also classify the above ionization paths into five categories, as shown in (f)–(j). In contrast to the one-electron sequential ionization process in Table 2, the two-electron sequential ionization process is distinguished by bolding. Taking process (f) as an example, the ionization path is (1, 1)→(1, 2)→(2, 2)→(2, 3) → (4, 3). The first three steps are single ionization processes, and the last step is a double ionization process. As predicted by the “ladder-path” model, this configuration fully guarantees that the internuclear distance at the subsequent ionization phase is always higher than the internuclear distance at the preceding step. The travel times of each ionization path are 17.55, 16.25, 7.28, and 8.59 fs, respectively. Considering that the ionization from (0, 1) to (1, 1) also takes some time, it is reasonable to expect that the entire ionization process is completed within a laser pulse of 70 fs (FMHM). At this point, we can reproduce a complete picture of all these configurations in Figure 6, where the allowed processes are shown by a solid arrow and the internuclear distance is marked when ionization takes place. With the stretching process of the molecular ions IBr²⁺ under the effect of Coulomb repulsion, enhanced ionization processes occur to form a highly charged parent ion. This observation presents more proof that ionization is predominantly controlled by states with intense coupling to the laser field. These states are strongly pushed by the laser field, leading to double ionization.

5. Conclusions

Using the DC-sliced ion velocity imaging technique, we present a collaborative experimental and theoretical investigation into the multi-electron ionization and subsequent Coulomb explosion of IBr molecules in the near-infrared femtosecond laser field. We found that the stretching of the molecular core distance could enhance the ionization to form highly charged parent ions, involving ionization with one and two electrons based on the “ladder-path” model. The results show that the higher charge states can couple strongly to the laser field. Furthermore, the charge transfer process does not occur in the experiment. This work can provide an understanding of the complex field-induced multi-electron dynamics of heteronuclear diatomic molecules.