A velocity-map imaging study of methyl non-resonant multiphoton ionization from the photodissociation of CH₃I in the A-band

Abstract

Chemical reaction dynamics and, particularly, photodissociation in the gas phase are generally studied using pump–probe schemes where a first laser pulse induces the process under study and a second one detects the produced fragments. Providing an efficient detection of ro-vibrationally state-selected photofragments, the resonance enhanced multiphoton ionization (REMPI) technique is, without question, the most popular approach used for the probe step, while non-resonant multiphoton ionization (NRMPI) detection of the products is scarce. The main goal of this work is to test the sensitivity of the NRMPI technique to fragment vibrational distributions arising from molecular photodissociation processes. We revisit the well-known process of methyl iodide photodissociation in the A-band at around 280 nm, using the velocity-map imaging technique in conjunction with NRMPI of the methyl fragment. The detection wavelength, carefully selected to avoid any REMPI transition, was scanned between 325 and 335 nm seeking correlations between the different observables—the product vibrational, translational and angular distributions—and the excitation wavelength of the probe laser pulse. The experimental results have been discussed on the base of quantum dynamics calculations of photofragment vibrational populations carried out on available ab initio potential-energy surfaces using a four-dimensional model.

This article is part of the themed issue ‘Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces’.

1. Introduction

The development of the ion imaging technique, firstly by Chandler & Houston [1] and, later, the improved velocity-map imaging (VMI) version by Eppink & Parker [2], has permitted important progress on the study of the dynamics of chemical reactions. Correlated direct measurement of both translational energy and angular distributions of the products allows getting a better insight on the dynamics that takes place. Moreover, the VMI technique in conjunction with pump–probe schemes has become an irreplaceable approach to study photodissociation dynamics of small polyatomic molecules [3,4]. In particular, the resonance enhanced multiphoton ionization (REMPI) technique provides highly resolved translational energy distributions (TEDs) of ro-vibrationally state-selected photofragments. By contrast, experimental studies on dissociation dynamics using non-resonant multiphoton ionization (NRMPI) detection are quite scarce and generally employ 800 nm MPI in femtosecond pump–probe schemes [5] or the so-called ‘universal detection’, which employs VUV radiation (at 118 nm or 121 nm) to ionize all the produced fragments with a single photon [6–16]. Femtosecond multiphoton excitation involves several (approx. 6–7) 800 nm photons to reach the ionization threshold of most three or four-atom photofragments. In opposition to nanosecond excitation, multiphoton absorption using femtosecond laser pulses is rather simply achieved, which makes femtosecond MPI a common technique in many fields. The extraction of information from MPI-induced dissociation processes is, however, considerably complex, particularly the information relative to photofragment polarization. On the other hand, the universal detection technique employs a single VUV photon at energy several electronvolts above fragment ionization thresholds, to provide non-state selective product detection. With ionization thresholds around 10 eV, alkyl radicals and halogen atoms, make the VUV detection particularly suitable for the study of the photodissociation of alkyl halides. In particular, Xu & Pratt [13,15] have used extensively the VUV detection technique in the photodissociation of methyl iodide in the second absorption band, namely the B-band, associated with the excitation to the (²E_3/2) 6 s Rydberg state, and it has been recently employed to determine the I(²P_3/2) and I*(²P_1/2) branching ratio for different vibronic levels of the Rydberg state [15]. One-photon detection experiments are easily interpreted, but lack the capabilities that multiphoton resonant schemes provide. On the non-resonant MPI fragment detection, Kitsopoulos and co-workers published a study on the methyl bromide photodissociation dynamics in the first continuum in which the produced methyl fragments were detected using non-resonant MPI [17]. Later, a second study on methyl iodide excitation using femtosecond, picosecond and nanosecond lasers showed the possibility of detecting methyl fragments from the CH₃I dissociation by non-resonant MPI exclusively in the case of nanosecond lasers [18].

The main goal of this work is to study the sensitivity of the NRMPI detection to the observables of a photodissociation process, in particular to the fragment translational energy and angular distributions. For such purpose, we have selected a well-known reaction: the photodissociation of the methyl iodide molecule in the first absorption band at wavelengths around 280 nm. Spectroscopically, the CH₃I absorption spectrum [19] presents a first continuous unstructured band, called the A-band, lying from 350 to 220 nm with a maximum at 261 nm and corresponding to the σ* ← n transition. Three excited electronic states contribute to this band: the ³Q₀ state (in Mulliken's notation), the major contribution especially between 240 and 280 nm, and the ¹Q₁ and ³Q₁ states, contributing at the blue-edge and the red-edge of the band, respectively. The photodissociation in the centre of the absorption band has been extensively studied originally by time-of-flight mass spectrometry [20] and imaging techniques [21]. Later on, the study was extended to the red [4,22,23] and blue edges [24] using imaging techniques in conjunction with (2 + 1) REMPI detection of the CH₃ and I(²P_3/2) and I*(²P_1/2) photofragments at different excitation wavelengths. Two channels were identified corresponding to the formation of the CH₃( A₂′′) radical in correlation with the I*(²P_1/2) and I(²P_3/2) atoms. For wavelengths between 240 and 280 nm, the quantum yield of I*(²P_1/2) in correlation with CH₃(A₂′′, ν = 0) and CH₃(A₂′′, all ν) was estimated to be around 0.9 and 0.7, respectively. In agreement with ab initio calculations [25], the formation of CH₃(A₂′′) + I*(²P_1/2) in the centre of the band was assigned to direct dissociation through the ³Q₀ state, while the production of CH₃(A₂′′) + I(²P_3/2) is due to non-adiabatic crossing between the repulsive ³Q₀ state and the ¹Q₁. This non-adiabatic crossing is presumed to be allowed by torsion of the C–I bond [26,27]. Li et al. [28] reported a high-resolution translational spectroscopy study and demonstrated a favoured vibrational excitation in the ν₁ and ν₂ modes for the I(²P_3/2) channel.

In this work, we revisit the photodissociation of methyl iodide in the A-band around 280 nm using the VMI technique in conjunction with NRMPI detection of the methyl fragment. The detection wavelength, carefully selected to avoid any (2 + 1) REMPI transition, was scanned between 325 and 335 nm seeking for correlations between the different observables—the product vibrational, translational and angular distributions—and the selected wavelength of the probe pulse. The experimental results have been discussed on the base of photofragment vibrational-state distributions obtained by quantum dynamics calculations carried out on available ab initio potential-energy surfaces using a four-dimensional model.

The paper is organized as follows: in §2, the experimental set-up and the theoretical approach are presented. In §3, the most relevant experimental results are presented while §4 summarizes the theoretical results obtained and a comparative discussion is presented. Section 5 is dedicated to presenting the most important conclusions of the work.

2. Methods

(a). Experimental

The main characteristics of the experimental set-up have been described in detail previously [23,24]. The whole experiment runs at a repetition rate of 10 Hz. A molecular beam is created by expanding a gas mixture of CH₃I in He (10%, 1 atm backing pressure) into a vacuum using a pulsed nozzle (General Valve Series 9, 0.5 mm orifice). The gas pulse passes through a skimmer (Beam Dynamics, Standard Model 2, 0.5 mm diameter orifice) and reaches the ionization chamber where the molecular beam is intersected at right angles, in the middle of the electrical plates of a time-of-flight (TOF) mass spectrometer, by the excitation and the probe laser pulses, which are focused (f = 25 cm) and counter propagated to each other.

The second harmonic of a Nd : YAG (Quanta Ray Pro 190) pumped dye laser (Sirah Cobra-Stretch) is used directly in order to set the excitation wavelength between 280 and 287 nm (≈2.5 mJ). The CH₃ fragments produced are detected 10 ns later via multiphoton ionization at wavelengths between 326 and 335 nm (≈3.5 mJ) using a Nd : YAG (Quanta Ray Pro 230) pumped frequency doubled dye laser (Sirah Cobra-Stretch). The detection wavelengths were carefully selected in order to ensure an NRMPI taking into account the different (2 + 1) REMPI lines in the region including all the vibrational overtones and hot bands. In the experiments shown here, images were recorded using a parallel polarization configuration with respect to the detector plane of both the photolysis and detection lasers. However, images were also recorded (not shown) using a perpendicular polarization set-up of both lasers in order to check the detector response as well as the possible rotational angular momentum alignment of the fragment. The images are recorded using our VMI apparatus in the single-field configuration [29,30]. The generated ions are accelerated by an electric potential of 5 kV applied to the repeller plate and pass through a field-free TOF region (45 cm) before hitting the impedance matched microchannel plates (MCPs, Chevron configuration, 40 mm diameter). The MCPs can be gated with a high voltage pulse to allow only the ions of interest to be detected. The resulting electron avalanche strikes a phosphor screen (P47), thereby creating the ion image, which is recorded by a CCD camera (SONY 1024 × 768 pixel) controlled using National Instruments (NI) LabView 7.1 and IMAQ VISION software. The final image is obtained as the sum of around 20 000–100 000 laser shots, depending on the quality of the signal. The velocity-map images are quadrant symmetrized and Abel inverted using the pBasex method [31], prior to extracting the translational energy and angular distributions. We note that for all the images measured, the two-colour signal represents five times the probe signal while the pump signal is almost inexistent.

Independent velocity-radius calibration of the apparatus is done by measuring resonantly multiphoton ionized CH₃(ν = 0) fragments produced after the photodissociation of CH₃I at 333.45 nm (one colour pump–probe experiment) at different repeller potentials, taking advantage of the well-known kinetic energy release of the I(²P_3/2) yielding channel at this photolysis wavelength [23].

(b). Theoretical

A polyatomic molecule like CH₃I is an ideal prototype in order to develop theoretical models of photodissociation processes [32,33]. In the present case, the model used to represent the CH₃I system considers four degrees of freedom (R, r, α, θ), where the dissociation coordinate R is the distance between I and the CH₃ centre-of-mass, r is the symmetric C–H bond distance representing the CH₃ symmetric stretch mode (ν₁), α is the umbrella bending angle of the CH₃ group (ν₂) and θ is the in-plane H₃–C–I bending angle (ν₆) between the C–I axis and the axis perpendicular to the plane containing the three hydrogen atoms. Wave packet simulations considering five degrees of freedom, namely the current four modes plus the out-of-plane bending mode, have shown that this last mode plays a small role in the CH₃I photodissociation dynamics and can be ignored [34], and this is why it is neglected in the present model. Furthermore, full-dimensional, nine-dimensional calculations carried out using the multiconfiguration time-dependent Hartree (MCTDH) scheme have been reported [35], and it was shown that the five-dimensional and nine-dimensional descriptions led to rather similar results. It is expected, therefore, that the four modes considered in the current model are able to describe reliably the main features of the CH₃I non-adiabatic photodissociation dynamics in the A-band. It is also noted that the present model allows one to represent the dynamics of the CH₃ symmetric stretch mode ν₁, and to simulate the CH₃ fragment vibrational distributions associated with excitations of this mode, which are measured experimentally.

At the 281 nm excitation wavelength used in this work the intensity of the ³Q₁ ← A₁ transition is very small, as shown by the experimental data. Thus, in the model the ³Q₁ ← A₁ transition is neglected, and only the ³Q₀ ← A₁ and ¹Q₁ ← A₁ transitions are considered. A detailed description of the representation of the potential-energy surfaces of the different electronic states involved in the photodissociation process and of the transition dipole moment functions for the ³Q₀ ← A₁ and ¹Q₁ ← A₁ transitions has been given elsewhere [23,25,27,36–39]. Photodissociation of CH₃I at 281 nm has been simulated by means of a wave packet method. The Hamiltonian, the wave packet method, and the procedure applied to obtain the product fragment distributions have been described in detail previously [36].

3. Experimental results

(a). CH₃ translational energy distributions

Figure 1 presents a series of pBasex inverted velocity-map images for the CH₃ fragment recorded at different excitation wavelengths (280, 281, 286.5 and 287.3 nm), using NRMPI at 335 nm and a parallel polarization configuration of the lasers employed for photolysis and probe. For all excitation wavelengths, three high-recoiled anisotropic rings are observed, which can be ascribed to the photodissociation of the methyl iodide in the A-band. The intense feature in the centre of the images is assigned to multiphoton dissociative ionization of the parent methyl iodide. Methyl TEDs, obtained from angular integration of the images depicted in figure 1, are shown in figure 2. The vertical bars appearing in the TEDs for the excitation wavelengths of 281 and 287.3 nm indicate the maximum available translational energy for the CH₃(A₂′′) + I*(²P_1/2) and CH₃(A₂′′) + I(²P_3/2) channels, respectively, given by

3.1

where hν is the energy of the excitation photon, D₀ = 2.41 eV is the dissociation energy of CH₃I [22], E_SO(I) = 0.943 eV is the spin-orbit splitting for I(²P) [22], E_i(CH₃I) is the internal energy of the methyl iodide in the molecular beam, which is negligible under molecular beam conditions, and m_I and m_CH3I are the masses for I and CH₃I, respectively. The combs show the position of the maximum translational energy considering the formation of methyl fragment vibrationally excited in the ν₁ and ν₂ modes.

Figure 1.

Inverted (pBasex) velocity map ion images for the CH₃ fragment produced in the methyl iodide photodissociation at different photolysis wavelengths (280, 281, 286.5, 287.3 nm) using non-resonant multiphoton ionization at 335 nm. The contribution from the photolysis and probe lasers alone has been carefully subtracted.

Figure 2.

Methyl translational energy distributions obtained through angular integration of the pBasex inverted images shown in figure 1. Vertical bars indicate the maximum available energy for the CH₃(A₂′′) + I*(²P_1/2) and CH₃(A₂′′) + I(²P_3/2) channels. The combs show the available energy for the different vibrational levels in the ν₁ and ν₂ modes of the methyl fragment. All distributions are normalized to have the same intensity in the peak corresponding to the CH₃ (A₂′′) + I*(²P_1/2) channel. (Online version in colour.)

For the excitation wavelength of 287.3 nm, the intense peak centred at about 0.84 eV is assigned to the CH₃(A₂′′, ν₁ = 0, ν₂ = 0) + I*(²P_1/2) channel. In agreement with previous experimental work [22] and the computed potential surfaces by Alekseyev et al. [25,38], one-photon absorption at 287.3 nm populates the ³Q₀ repulsive state, leading directly to the formation of methyl radical in correlation with the iodine atom in the spin-orbit excited state. The two other structures observed at 1.3 and 1.6 eV correspond to the CH₃(A₂′′, ν₁ = 1, ν₂ = 0) + I(²P_3/2) and CH₃(A₂′′, ν₁ = 0, ν₂ = 1) + I(²P_3/2) channels, respectively. Finally, the shoulder observed at 1.50 eV can be assigned to CH₃(A₂′′, ν₁ = 0, ν₂ = 2–3) + I(²P_3/2).

A CH₃ TED quite similar to those depicted in figure 2 was reported previously by Eppink & Parker [4] for a one-photon experiment at a wavelength of 286.81 nm, using non-resonant MPI detection. The observed structures were then tentatively assigned to the ν₄ mode activity. The results presented in this work are, however, in better agreement with vibrational excitation in the ν₁ and ν₂ modes exclusively. The I* : I branching ratio measured considering all vibrational levels is 0.80 : 0.20, similar to those already reported by Eppink & Parker [4] from iodine (2 + 1) REMPI detection as a function of the excitation wavelength.

The three described structures are recovered in the methyl TEDs for 286.5, 281 and 280 nm excitation wavelengths depicted in figure 2 with minor differences in the relative intensities, in agreement with the dissociation mechanism associated with the continuous structureless A-band [4,22,23]. An approximate estimation of the ratio between the different vibrational channels can be obtained, therefore, through the averaged relative intensities of the four TEDs depicted in figure 2. Thus, the CH₃(A₂′′, ν₁ = 0, ν₂ = 0) + I*(²P_1/2) channel accounts for 80% of the total signal, while the CH₃(A₂′′, ν₁ = 1, ν₂ = 0) + I(²P_3/2) and CH₃(A₂′′, ν₁ = 0, ν₂ = 1) + I(²P_3/2) channels account for 10% of the total signal, each one of them. The shoulder associated with the formation of methyl vibrationally excited in ν₂ = 2–3 vanishes when the excitation wavelength decreases.

A series of pBasex inverted images corresponding to methyl fragments recorded at an excitation wavelength of 281 nm and at different detection wavelengths are depicted in figure 3. A parallel polarization configuration of both lasers is employed again. The probe wavelengths were carefully selected to ensure a non-resonant MPI detection of the methyl fragment. The three high-recoiled anisotropic rings observed in figure 1 are recovered for all detection wavelengths, although their relative intensity depends strongly on the probe wavelength.

Figure 3.

Inverted (pBasex) velocity map ion images for the CH₃ fragment produced in the methyl iodide photodissociation at 281 nm using non-resonant multiphoton ionization, NRMPI, at several probe wavelengths (326.8, 330, 331 and 335 nm). The individual contribution from the photolysis and probe lasers has been carefully subtracted.

The methyl translational distributions obtained by angular integration of the images in figure 3 are represented in figure 4. As the apparatus is not calibrated for total intensities, the vertical axis has been normalized to the CH₃(A₂′′, ν₁ = 0, ν₂ = 0) + I*(²P_1/2) signal in order to establish a vertical reference. As in figure 2, the vertical bars indicate the maximum available translational energy for the CH₃(A₂′′) + I*(²P_1/2) and CH₃(A₂′′) + I(²P_3/2) channels (given by equation (3.1)) for different vibrational states in the ν₁ and ν₂ modes. In order to identify the different methyl vibrational states contributing, the TED profiles have been fitted to a series of Gaussian functions, with the position and amplitude of each Gaussian as fitting parameters, which are represented in figure 4 as coloured thin curves.

Figure 4.

Methyl translational energy distributions obtained through angular integration of the pBasex inverted images shown in figure 3. The solid vertical bars indicate the maximum available energy for the CH₃(A₂′′, ν = 0) + I*(²P_1/2), CH₃(A₂′′, ν₁ = 1, ν₂ = 0) + I(²P_3/2) and CH₃(A₂′′, ν = 0) + I(²P_3/2) channels, while the dashed ones show the position of different vibrational levels in the ν₁ and ν₂ modes of the methyl fragment. All distributions are normalized to have the same intensity in the peak corresponding to the CH₃(A₂′′) + I*(²P_1/2) channel. Cyan, magenta, orange, brown and dark blue curves represent the result of Gaussian fits of the peaks associated with ν₂ = 0, ν₂ = 1, ν₂ = 2, ν₂ = 3, ν₂ = 4, respectively, for the CH₃(ν₁ = 0, ν₂) + I*(²P_1/2), CH₃(ν₁ = 1, ν₂) + I(²P_3/2) and CH₃(ν₁ = 0, ν₂) + I(²P_3/2) channels.

A strong dependence of the methyl fragment vibrational-state detection by NRMPI on the probe wavelength is spotted. The three peaks corresponding to the rings observed in the images shift towards smaller translational energy values as the probe wavelength decreases from 335 nm to 326.8 nm, which indicates that higher vibrational states of the methyl fragment are more efficiently detected by NRMPI as the probe wavelength gets shorter. For all probe wavelengths, the three broad peaks reflect a vibrational distribution in the ν₂ mode. According to the vibrational combs, at least, two or three different ν₂ vibrational levels are populated for all CH₃(A₂′′, ν₁ = 0, ν₂) + I*(²P_1/2), CH₃(A₂′′, ν₁ = 1, ν₂) + I(²P_3/2) and CH₃(A₂′′, ν₁ = 0, ν₂) + I(²P_3/2) channels. Moreover, at 326.8 nm, the detection of CH₃(A₂′′, ν₁ = 0, ν₂) in correlation with I(²P_3/2) is strongly enhanced by the probe, while at 330 nm the CH₃(A₂′′, ν₁ = 1, ν₂) in correlation with I(²P_3/2) remarkably increases.

In every case, as the probe wavelength decreases, higher ν₂ levels for a given ν₁ are detected. At 335 and 331 nm, the distribution peaks at ν₂ = 0 and ν₂ = 1, for the I*(²P_1/2) and I(²P_3/2) channels, respectively, while at 330 nm, the maxima correspond to ν₂ = 1 and ν₂ = 2 for the same channels. At detection wavelength 326.8 nm, the CH₃(A₂′′, ν₁ = 0, ν₂) + I(²P_3/2) channel is preferentially produced in correlation with ν₂ = 3 methyl radicals, whereas for the CH₃(A₂′′, ν₁ = 1, ν₂) + I(²P_3/2) channel, the most populated vibrational state is ν₂ = 2. As commented on before, NRMPI detection is presumed to involve simultaneous ionization of all ro-vibrational states and thus, to impede a selective detection of vibrational states. However, the TEDs reported here clearly demonstrate the possible selection of a favoured ro-vibrational population depending on the detection wavelength.

In our recent work on the photodissociation of methyl iodide at 193 nm, we show that non-resonant contributions could, in some cases, overcome the resonant signal. When the probe laser was tuned to the CH₃(ν₂ = 1) resonance, for instance, the main contribution in the translational energy distribution had to be surprisingly assigned to non-resonant MPI signal of CH₃(ν₂ = 0). A small shoulder assigned to REMPI detection of CH₃(ν₂ = 1) and minor contributions from MPI of CH₃(ν₁ = 1,ν₂ = 0,1) were clearly observed at lower translational energies. Our results reproduced those obtained by Pratt and co-workers using VUV universal detection [13]. MPI excitation has, however, an unexpected advantage over the VUV detection related to the Franck–Condon factors. As Pratt and co-workers state, the vibrational frequency of the ν₂ umbrella mode in the ion is nearly double than that in the neutral. This fact implies that the Franck–Condon envelope spreads over a broad range of vibrational levels in the ion, and that the range will increase as the vibrational excitation in the neutral is increased. Because the VUV photon energy is only approx. 5170 cm⁻¹ above the ionization threshold for CH₃, as the vibrational excitation is increased, an increasing fraction of the Franck–Condon envelope will become energetically inaccessible, which will reduce in turn the total photoionization cross-section. MPI excitation provides, in principle, as much energy above the ionization threshold as needed—either through the photon energy or through the number of photons—and, therefore, selection of favoured ro-vibrational states should not be limited by energetic arguments.

(b). CH₃ angular distributions

Radial integration of a selected range of pixels on the images depicted in figure 3 leads to the angular distribution for each channel observed in the TEDs. According to Mo & Suzuki [40] and Coroiu et al. [41], product signal distributions in pump–probe processes can be expressed as the product of the photofragment angular recoil distribution (I_rec) and the detection efficiency (I_det)

3.2

where θ represents the angle between the photolysis laser polarization and the fragment recoil velocity. The fragment distribution for a one-photon transition [42] is given by

3.3

where P₂(cosθ) is the second order Legendre polynomial and −1 ≤ β ≤ 2 is the translational anisotropy parameter. The detection efficiency depends on the polarization of the photofragment with respect to the polarization of the probe laser [40]

3.4

where the ρ^(k)_0,RF are the components with q = 0 of rank-k multipole moments of the density matrix describing the populations and coherences of the magnetic sublevels with angular momentum quantum number J_i and projection quantum numbers m. The projections are defined with respect to the recoil velocity vector (recoil frame, RF). For a probe transition induced by linearly polarized light, the index k takes values of 2n, with n ranging from cero to the number of photons of the resonant step. are normalized line-strength factors for the two-photon transition between levels with angular momentum quantum numbers J_i (initial state) and J_f (final state) (i.e.  = P_k(J_f, J_i)/P₀(J_f, J_i)) and P_k(cos θ) are the Legendre polynomials. Equation (3.4) has a limitation, being valid as far as the initial state does not coincide with the final state, i.e. J_i≠ J_f. As

3.5

we finally get

3.6

As it was pointed out before, equation (3.4) presents some limitations. The expressions reported in reference [40] for the line-strength factors are incompatible with the concomitance of linearly polarized light and ΔJ = 0 transitions. For a two-photon dipole transition from an initial i state to a final f state, the virtual states accessed by the first photon are not unique and the intensity must be calculated taking into account all possible paths with different magnetic quantum numbers. As Mo and Suzuki showed, however, the fact that the relative ratios between the geometrical factors in two-photon transitions are invariant to the character of the virtual states, simplifies considerably the problem and, therefore, the intricate expression for the P_k(J_f, J_i) developed by Zare and co-workers (KSZ) [43]. In the early years of the photofragment polarization analysis, KSZ had already underlined that the radial integrals of the transition dipole moments (between the initial and virtual states, and between the virtual and final states), which are unknown, can be usually included in the detection constant [43]. The exception to KSZ's and Mo and Suzuki's studies are the ΔJ = 0 transitions excited with linearly polarized light. In those cases, the branching ratio between the different intermediate states of the two-photon processes must be known. Detection of the methyl radical constitutes a good example of this case. The most efficient way of detecting CH₃ fragments produced in a photodissociation process is a (2 + 1) REMPI scheme through the Q branch. Being a Σ ← Σ transition, ΔJ = 0 and the line-strength factors must be calculated numerically [44]. It is important to clarify that, even though equation (3.4) might not be applicable, the phenomenological equation (3.6) has no restrictions. The limitations involve only our capability of getting disentangled information from the β_i parameters.

Equation (3.6) constitutes the starting point in the analysis of the product angular distribution for most experimental works. From the fit of the recorded angular distributions to equation (3.6), the β_i coefficient expansion is obtained. The β_i parameters comprise the information related to the dissociation dynamics and the photofragment polarization. For linear polarized light, the sum extends to 2n + 2, where n is the number of photons involved in the resonant step of the detection scheme employed. For a (2 + m) REMPI detection scheme, three coefficients, β₂, β₄ and β₆, are needed to fit the experimental data; when a (1 + m) REMPI scheme is used, the parameters are reduced to β₂ and β₄.

The experiments presented in this work have been carried out using NRMPI, which, according to the previous discussion, should be insensitive to the fragment polarization. In other words, a single β_i parameter should be needed to fit the experimental angular distributions, which necessarily would coincide with the dissociation anisotropy, β. Furthermore, the β_i parameter should be invariant for those sets of images taken at the same photolysis wavelength.

Figure 5 shows the angular distributions for the three main structures obtained for an excitation and detection wavelengths of 281 nm and 326.8 nm, respectively (top panel of figure 4). The red lines represent the fit of the experimental data to equation (3.6). Clearly, although strongly anisotropic, the experimental angular distributions cannot be described by a single anisotropy parameter. Two or three β_i are necessary, highlighting an important polarization alignment manifested by the non-resonant MPI probe laser. The obtained β_i anisotropy parameters for all detection wavelengths used in figure 5 and for the three main dissociation channels are summarized in figure 6. The β₂-values are around 2 for all cases in agreement with previous experimental work reported, for instance, by Eppink & Parker [4,22]. At an excitation wavelength of 281 nm and using a (2 + 1) REMPI detection of the methyl fragment, they determined β ≈ 1.95 and β = 1.7 for the CH₃(A₂′′, ν = 0) + I*(²P_1/2) and CH₃(A₂′′, ν = 0) + I(²P_3/2) channels, respectively. These values are consistent with the established dissociation mechanism, namely an initial parallel transition ³Q₀ ← A₁, followed by a non-adiabatic crossing towards the ¹Q₁ state leading to I(²P_3/2) formation. The β₄ and β₆ values depend on the dissociation channel and on the detection wavelength. For CH₃(A₂′′, ν₁ = 0, ν₂) + I*(²P_1/2), these values are close to zero for all probe wavelengths, λ_probe, and only a non-zero, negative β₄ value is obtained at 326.8 nm. On the contrary, for CH₃(A₂′′, ν₁ = 1, ν₂) + I(²P_3/2), for all probe wavelengths, the angular distributions are characterized by β₄ values around 0.25, except at 330 nm. Finally, for the CH₃(A₂′′, ν₁ = 0, ν₂) + I(²P_3/2) channel, the angular distributions reflect positive β₄ and β₆ values, ranging between 0.05 and 0.25 and between 0 and 0.6, respectively, depending on λ_probe. As the anisotropy value does not depend of the probe step, the variation of the β₂, β₄ and β₆ parameters indicates a CH₃ photofragment polarization effect-alignment, because linear polarized light has been used.

Figure 5.

Angular distributions obtained through radial integration of the pBasex inverted velocity map image in figure 3 corresponding to the methyl fragment from the photodissociation of methyl iodide at 281 nm and detected by non-resonant MPI at 326.8 nm, for the three main channels. Open circles: experimental points. Solid line: fit to equation (3.2). (Online version in colour.)

Figure 6.

β_i anisotropy parameters obtained from the fit to equation (3.2) of the angular distributions associated with the images shown in figure 3, corresponding to the methyl fragment from the photodissociation of methyl iodide at 281 nm and detected by non-resonant MPI at 326.8, 330, 330 and 335 nm, for the three main channels. Black squares: β₂; red circles: β₄; blue triangles: β₆.

Figures 5 and 6 prove that fragment polarization effects can be observed using NRMPI detection. In REMPI transitions, a virtual intermediate state is degenerate with a real atomic or molecular level, increasing the probability of absorption of another photon, because real states are much longer-lived than virtual states. Except for that, virtual states do not differ essentially from resonant real states. In fact, non-resonant detection constitutes a generalization of the exceptions excluded by Mo and Suzuki in their treatment. For a non-resonant two-photon dipole transition as a previous step in an ionization process, the virtual states accessed by both photons are not unique and the intensity must be calculated taking into account all possible paths with different magnetic quantum numbers. The mathematical approach for the photofragment polarization analysis should be based, therefore, on the work of KSZ. To be able to extract useful information from the β_i parameters, however, any treatment which considers the multiple pathways with different magnetic numbers that can take the neutral photofragment above the ionization continuum, is needed.

Figure 6 shows a dependence of the photofragment polarization on the probe wavelength and, therefore, according to the discussion carried out in the previous section, with the CH₃ vibrational state. The effect might seem be feeble, but it must be remarked that the irradiation geometry used is not particularly sensitive to polarization effects. The Z (pump) X (probe) configuration, where X is the direction perpendicular to the laser propagation axis (Y) and Z is parallel to the molecular beam, suppresses the information relevant to the dissociation anisotropy and, therefore, reflects primarily the photofragment polarization. Such crossed configuration is not Abel-invertible and, hence, impractical in a velocity mapping experiment. Slice imaging experiments overcome such inconvenience and it has been proven to constitute a powerful tool to study photofragment vector correlations [44].

4. Theoretical results

Theoretical umbrella mode (ν₂) vibrational populations of the CH₃(ν₁ = 0) fragment obtained for the I*(²P_1/2) and I(²P_3/2) dissociation channels are displayed in figure 7a,b, respectively. The CH₃(ν₁ = 1) fragment ν₂ vibrational populations corresponding to the I(²P_3/2) channel are shown in figure 7c. As can be seen, the ν₂ vibrational distribution of the I*(²P_1/2) channel is significantly colder than the two distributions of CH₃(ν₁) with ν₁ = 0,1 of the I(²P_3/2) channel, in the same line of previous results for excitation at 267 nm [36]. In the present case with excitation at 281 nm, the vibrational distributions display a higher excitation (hotter distributions), reaching higher ν₂ levels, when compared with excitation at 267 nm [36]. The two distributions associated with the I(²P_3/2) channel are very similar, being somewhat hotter that associated with CH₃(ν₁ = 0). Interestingly, all the vibrational distributions in figure 7 exhibit a degree of vibrational excitation of the methyl fragment in agreement with that found experimentally. Indeed, as shown in figure 4, the present experiments reveal ν₂ vibrational excitation up to ν₂ = 2 for the I*(²P_1/2) channel and up to ν₂ = 4 for the I(²P_3/2) channel, in agreement with the present theoretical calculations.

Figure 7.

Calculated vibrational distributions for the CH₃(ν₂) fragment produced through the (a) CH₃(ν₁ = 0, ν₂) + I*(²P_1/2), (b) CH₃(ν₁ = 0, ν₂) + I (²P_3/2), and (c) CH₃(ν₁ = 1, ν₂) + I*(²P_1/2) dissociation channels. (Online version in colour.)

The excitation increase in the ν₂ mode found experimentally for the detected CH₃ fragment as the probe photon energy is increased (figure 4) can be readily explained in terms of Franck–Condon factors between the vibrational states of the CH₃ fragment and the ion, which is the species actually detected. In order to estimate these Franck–Condon factors, the vibrational states of both CH₃ and have been calculated using a one-dimensional (1D) model to represent the CH₃ umbrella mode by a stretching coordinate q associated with the perpendicular distance between the C atom and the plane containing the three H atoms.

The CH₃ 1D potential curve, , is taken from [27], by fixing the three C–H distances at their equilibrium value of 2.05266 a.u. The parameters k₂₂ = 0.012559 a.u. and k₁ = 0.388582 a.u. of [27] have been modified to the values k₂₂ = 0.010869 a.u. and k₁ = 0.342835 a.u. in the present CH₃ potential function. Regarding the potential, the functional form

4.1

with K₁ = 0.0924779 a.u. and K₂ = 0.0099969 a.u. has been used [45]. By solving the 1D Schrödinger equation

4.2

where is the kinetic energy operator and i = CH₃, , the vibrational eigenenergies and eigenfunctions are obtained. The energies and the Franck–Condon factors are collected in table 1. The Franck–Condon factors are also plotted in figure 8.

Table 1.

Computed Franck–Condon factors for the photoionization of the methyl radical as a function of the ν₂ and vibrational excitation in the umbrella mode of the CH₃ and , respectively. The energy position (E_ν2 and E_ν′2 in cm⁻¹) of the ν₂ and vibrational levels is also indicated.

	ν2		0	1	2	3
ν'2	E’ν2 (cm−1)	Eν2 (cm−1)	278.3617	887.14062	1584.52745	2347.99762
0	713.204		0.91254	1.3392 × 10−16	0.08052	1.90862 × 10−17
1	2143.58951		6.15467 × 10−17	0.79781	2.23191 × 10−16	0.17809
2	3581.86883		0.07842	3.46115 × 10−17	0.60972	2.73054 × 10−16
3	5027.92196		1.47823 × 10−17	0.17327	1.05136 × 10−17	0.42484
4	6481.63348		0.0082	2.37365 × 10−17	0.25194	2.29828 × 10−19
5	7942.89234		2.43354 × 10−18	0.02572	2.75405 × 10−17	0.30437
6	9411.59157		7.73826 × 10−4	5.89947 × 10−18	0.05034	2.65342 × 10−17
7	10887.62806		3.07841 × 10−19	0.00292	1.00888 × 10−17	0.07891

Figure 8.

Franck–Condon (FC) factors calculated for the photoionization of the methyl radical as a function of the ν₂ and vibrational excitation in the umbrella mode of the CH₃ and , respectively. (Online version in colour.)

Both table 1 and figure 8 show clearly that for a given vibrational state, the maximum Franck–Condon factor occurs with the vibrational state for which . The value of the factor drops quickly as the value of gets away (either increasing or decreasing) from  = ν₂. Thus, detection of ν₂ excited vibrational states of the CH₃ fragment implies probing similarly excited vibrational states of with the probe laser. Moreover, the energy levels shown in table 1 indicate that due to the different anharmonicity of the interaction potential of CH₃ and in the ν₂ mode, the energy separation grows faster for than for CH₃. As a result, the probe transition ( = ν₂) ← CH₃(ν₂) requires an increasing amount of energy (shorter wavelength) as ν₂ increases, as found experimentally.

In order to obtain a better visualization, figure 9 shows a schematic representation of the potential-energy curves computed for the methyl radical and methyl ion in their respective ground states as a function of the α umbrella bending angle of the CH₃ group. The computed wave functions for different ν₂ levels of CH₃() and of () are also represented, taking into account the position in energy of these vibrational levels resulting from the calculations. The ionization energy was selected such as the absorption of three photons at 335 nm from the CH₃(ν₂ = 0) permits to populate exclusively the ( = 0). Vertical arrows represent the three-photon absorption from different ν₂ levels. In figure 9a, we show the case for a probe laser set at 335 nm. The cyan arrow represents the absorption from the ν₂ = 0 to the  = 0. As can be observed, the absorption of three photons from the ν₂ = 1 (magenta arrow) would allow to only populate the  = 0. However, the overlap between both wave functions is almost inexistent. Similarly, for the methyl radical produced in ν₂ = 2 (orange arrow), three photons at 335 nm would have led to methyl ions in the  = 0 or 1, but the overlap between the wave functions is again almost zero. On the contrary, for shorter wavelengths as for 326.8 nm (figure 9b), the excitation energy corresponding to the three photon-absorption allows one to populate the  = 0 (cyan), 1 (magenta), 2 (orange) and 3 (brown) from the methyl radical produced in the ν₂ = 0, 1, 2 and 3, respectively. The observed overlap between the wave functions lead preferentially to  = ν₂ in agreement with figure 8 and the experimental results. Therefore, the computed vibrational distributions as well as the Franck–Condon factors permit indeed to clarify the increasing ν₂ vibrational-state detection as the probe photon energy increases in the NRMPI of the methyl fragment.

Figure 9.

Schematic representation of the computed potential-energy curves and associated vibrational wave functions for the different vibrational levels in the ν₂ mode for the methyl radical and methyl cation in their respective ground states. The arrows represent the absorption of three photons of the probe laser at 335 nm (a) and at 326.8 nm (b) from the produced CH₃ in the ν₂ = 0 (cyan), ν₂ = 1 (magenta), ν₂ = 2 (orange) and ν₂ = 3 (brown) vibrational states. (Online version in colour.)

5. Conclusion

The well-known photodissociation of methyl iodide in the A-band at about 280 nm using the VMI technique is revisited in conjunction with NRMPI of the methyl fragment in order to elucidate the sensitivity of the NRMPI to the photofragment vibrational distribution arising from a molecular photodissociation process. The detection laser wavelength, carefully selected to avoid any REMPI transition for the methyl fragment, was scanned between 325 and 335 nm in order to look for evidence of a direct effect in the distribution of vibrational states detected, the TEDs as well as in the angular distributions of the observed channels. The experimental results have been compared with quantum dynamics calculations of fragment vibrational populations carried out on available ab initio potential-energy surfaces using a four-dimensional model. A high sensitivity in the vibrational state of the detected methyl fragment has been observed characterized by an increasing excitation in the ν₂ mode for increasing probe photon energy, which is found in agreement with calculated Franck–Condon factors for the NRMPI of methyl using a one-dimensional model. The analysis of the CH₃ angular distributions proves that NRMPI detection is sensitive to photofragment polarization. In particular, a dependence of the CH₃ alignment on the vibrational state has been found.

Competing interests

We declare we have no competing interests.

Funding

This work was funded by the Ministerio de Economía y Competitividad, MINECO (Spain), grants nos CTQ2012-37404-C02-01 and CTQ2015-65033-P, and COST Action program, grant nos CM1401 and CM1405. S.M.P. acknowledges financial support from Campus de Excelencia Internacional Moncloa and LASING S. A. D.V.C. acknowledges a contract from MINECO under the Fondo de Garantía Juvenil.