High-Resolution Photoelectron Spectroscopy of the Ground and First Excited Electronic States of MgXe⁺

Abstract

We report on the characterization of the X⁺²Σ⁺ ground and the A⁺²Π_Ω (Ω = 1/2, 3/2) and B⁺²Σ⁺ electronically excited states of MgXe⁺. Rotationally cold MgXe in the a ³Π₀(v″ = 0) metastable electronic state was generated in a laser-ablation supersonic-beam source. Following single-photon excitation from the metastable state, the vibrational structure of the X⁺ state of MgXe⁺ was measured by pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopy, and the adiabatic ionization energy of the X⁺ ← a ionizing transition was determined to be E_I/(hc) = 37,468.3(6) cm^–1. Spectra of the A⁺ ← X⁺ and B⁺ ← X⁺ transitions were recorded by using the method of isolated-core Rydberg-dissociation spectroscopy. The observation of the Mg⁺(3p) ²P_1/2 + Xe ¹S₀ dissociation limit enabled the determination of the dissociation energies of the X⁺ [D₀(X⁺) = 2970(7) cm^–1] and A⁺ states [D₀(A_1/2⁺) = 9781(7) cm^–1 and D₀(A_3/2⁺) = 9603(7) cm^–1]. We compare these results with those of earlier experimental studies and ab initio quantum-chemical calculations.

1. Introduction

Diatomic molecules ARg consisting of an alkaline-earth metal atom (A) and a rare gas atom (Rg) are weakly bound van der Waals molecules.¹⁻⁴ Both the neutral molecule ARg and the singly charged ARg⁺ are excellent model systems for studying the long-range nature of bonding interactions.⁵⁻⁸ In the neutral molecule, the strongest interactions are dispersion interactions, whereas in the singly charged molecule, the charge–induced-dipole interaction dominates (see Discussion in ref (9)).

ARg molecules are also interesting candidates for studying the Rydberg states of singly charged cations and doubly charged molecules.^6,10,11 Rydberg states of singly charged molecules are indeed challenging to study because their doubly charged ion cores are unstable or metastable in most molecules, making these states short-lived and their spectra diffuse. Additionally, the term values of the Rydberg states of molecular cations are large, requiring excitation with either VUV radiation or multiple photons. Consequently, only limited experimental information is available about these systems. In contrast, the ground electronic state of the doubly charged species ARg²⁺ is, in many cases, thermodynamically stable, and their Rydberg states are accessible by resonant multiphoton excitation.¹¹⁻¹³

We recently started systematic investigations of MgRg, MgRg⁺, and MgRg²⁺ as representative systems of the ARg family building up on the pioneering work of Duncan and co-workers^4,14 and Breckenridge and co-workers.¹⁻³ By varying the rare-gas atom, the influence of atomic properties, such as the polarizability volume, on the binding energies can be studied (see Figure 6 of ref (9)). The ionization energy E_I(Rg) of the rare-gas atom determines the stability of the ground electronic state of the doubly charged molecule MgRg²⁺ and of the Rydberg states converging to the doubly charged ion-core states. When the neutral rare gas exhibits a larger ionization energy than that of Mg⁺ [i.e., E_I(Rg) > E_I(Mg⁺)], a thermodynamically stable doubly charged molecule is formed. When E_I(Mg⁺) is larger than or comparable to E_I(Rg), then the doubly charged molecule can exhibit an unstable or even metastable ground state.¹² By varying Rg in the sequence He, Ne, Ar, Kr, Xe, and Rn, all cases can be studied from thermodynamically stable (MgHe²⁺, MgNe²⁺, and MgAr²⁺) to thermodynamically unstable (MgXe²⁺ and MgRn²⁺).

The present paper reports on a study of the electronic structure of the X⁺²Σ⁺, A⁺²Π_Ω, and B⁺²Σ⁺ states of MgXe⁺ (hereafter called X⁺, A⁺_Ω, and B⁺ states, respectively) by high-resolution photoelectron and photodissociation spectroscopy. The corresponding Born–Oppenheimer potential-energy functions are presented in Figure 1, which also shows the electronically excited states of MgXe⁺ near the Mg⁺(3d) + Xe ¹S₀ dissociation asymptotes, which may play a role in the detection of the electronic transitions (see below). The A⁺_Ω and B⁺ states correlate asymptotically to the Mg⁺(3p) ²P_1/2,3/2 + Xe ¹S₀ threshold and form the 3p complex of MgXe⁺. At large internuclear separation, these states can be regarded as the lowest members of the Rydberg series converging to low electronic states of the doubly charged MgXe²⁺. The first state in Mg–Rg⁺ molecules with a potential-energy function similar to the potential-energy function of the ground state of the doubly charged ion is the 3dδ state,¹⁵ corresponding to Mulliken’s rule of the absence of a precursor orbital of the corresponding symmetry in the ion core.¹⁶

Figure 1.

Excitation scheme used to study the X⁺²Σ⁺ ground state and the A⁺²Π_Ω and B⁺²Σ⁺ excited states of MgXe⁺. The potential-energy function of the X⁺ state (black) has been derived from the experimental data presented in this work (see Section 3.1 for details). The potential-energy functions for the electronically excited states are only presented schematically for illustration purposes. The lower and upper insets show the enlarged X⁺ and B⁺ states, respectively, with the addition of the wave functions of the measured X⁺-state vibrational levels in the lower inset. The red shaded area indicates the range of vibrational levels of the B⁺ state, which can predissociate into the Mg⁺(3p) ²P_1/2 + Xe ¹S₀ continuum. The blue and orange arrows indicate possible excitation mechanisms for the observation of the X⁺ ← a and the B⁺ ← X⁺ transitions by pulsed-field ionization of the Mg(n) fragment, as discussed in Section 3.2.

The ground X ¹Σ⁺ and metastable a ³Π₀ states, as well as other low-lying electronically excited states of MgXe, were investigated in detail by Breckenridge and co-workers.^3,17−19 The adiabatic ionization energy of the metastable a ³Π₀ state of MgXe was determined using two-color photoionization spectroscopy.²⁰ The lowest two vibrational levels of the X⁺ state and the vibrational and spin–orbit structure of the A⁺_Ω state of MgXe⁺ were characterized experimentally using photodissociation spectroscopy by Pilgrim et al.⁴ Ab initio calculations of the ground and several low-lying electronically excited states of MgXe⁺ were also reported.^6,21

Our investigations extend these previous studies of the X⁺ and the A⁺_Ω states of MgXe⁺, in particular through the determination of the dissociation energies of the a, X⁺, and the A⁺_Ω states, which are the focus of this work. The experimental determination of the dissociation energies of the molecules represents a challenge. The observation of the onset of a dissociation continuum is the most direct way, pioneered in H₂ by Herzberg and Jungen.²² In the case of metal-containing diatomic molecules, it was extensively used by Morse and co-workers (see refs (23–25) and references therein for recent examples). Here, we exploit the observation of the onset of the spin–orbit interaction-induced predissociation of the B⁺ state of MgXe⁺ to determine the position of the Mg⁺(3p) ²P_1/2 + Xe ¹S₀ threshold, from which the other dissociation thresholds can be derived using thermochemical cycles. We used a similar strategy in our previous studies of MgAr⁺²⁶ and MgKr⁺.²⁷ The photoexcitation sequence is depicted in Figure 1.

Starting from metastable MgXe in the a ³Π₀ state produced in a laser-ablation source, the X⁺ ground state of MgXe⁺ was studied by photoelectron spectroscopy. The A⁺ and B⁺ states were then investigated by photodissociation spectroscopy following the preparation of the MgXe⁺ ground state in selected vibrational levels.

2. Experimental Setup and Procedure

The experimental setup and procedure have been described in refs (9 and 27) with only minor adjustments made for the measurements reported in this study. A similar procedure was also used in studies of the electronic structure of other metal-containing molecular ions.²⁸⁻³² In summary, the experimental setup consists of a laser-ablation source of Mg in a pulsed supersonic expansion of a He/Xe gas mixture (10:1), generating a rotationally cold molecular beam containing MgXe in the a ³Π₀ metastable state. Various isotopomers are formed according to the abundances of the natural isotopes of Mg (²⁴Mg: 79.0%; ²⁵Mg: 10.0%; and ²⁶Mg: 11.0%) and Xe (¹²⁸Xe: 1.9%, ¹²⁹Xe: 26.4%; ¹³⁰Xe: 4.1%; ¹³¹Xe: 21.2%; ¹³²Xe: 26.9%; ¹³⁴Xe: 10.4%; and ¹³⁶Xe: 8.9%).³³ After passing a skimmer with a 3 mm diameter orifice located ∼26 cm downstream from the nozzle, the molecular beam enters the photoexcitation/photoionization region consisting of a resistively coupled cylindrical electrode stack within a double-layer magnetic shield, where it is crossed at right angles by one or two lasers. Pulsed electric fields are applied across the electrode stack and used to extract the electrons or ions generated by photoionization perpendicular to the propagation axes of the molecular beam and excitation lasers. The electric fields are also used to field-ionize high Rydberg states of MgXe when pulsed-field-ionization zero-kinetic-energy photoelectron (PFI-ZEKE PE) spectra³⁴ are recorded. The electrons or ions are detected at the end of a time-of-flight mass spectrometer on a microchannel-plate (MCP) detector.

MgXe molecules in the metastable a ³Π₀ state were photoexcited in the vicinity of the X⁺²Σ⁺ ← a ³Π₀ ionizing transition (see Figure 1) with the output of a Nd:YAG-pumped pulsed dye laser after frequency tripling with two successive β-barium-borate (BBO) crystals (pulse energy: 0.2 mJ, line width: 0.15 cm^–1). To subsequently excite the MgXe⁺ ion core to the A⁺²Π_Ω and B⁺²Σ⁺ states, a second Nd:YAG-pumped pulsed dye laser was used, which was frequency doubled or tripled with one and two BBO crystals, respectively. The fundamental wavenumbers of the lasers were calibrated by using a commercial wavemeter with a specified accuracy of 0.02 cm^–1.

PFI-ZEKE PE spectroscopy was used to record spectra of the MgXe⁺ X⁺²Σ⁺ ← MgXe a ³Π₀ ionizing transition and characterize the X⁺ state of MgXe⁺. To record overview spectra, a sequence of three pulsed electric fields [typically (+0.17, −0.69, −1.72) V/cm] was employed, and the electron signals generated by the second and third pulses were monitored as a function of the laser wavenumber. Individual vibrational bands were recorded at higher resolution with a multipulse electric-field sequence [e.g., (+0.09, −0.09, −0.17, −0.26, −0.34, −0.43) V/cm]. All spectra were corrected for the field-induced shifts of the ionization thresholds, which were determined from the PFI-ZEKE-PE spectra of the Mg⁺(3s) ← Mg(3s3p) ionizing transition, recorded with the identical pulse sequences, by comparing the position of the observed lines with the well-known ionization energy of Mg.³⁵ The absolute vibrational assignment of the X⁺ and A⁺_Ω states was obtained by analyzing the isotopic shifts observed in excited vibrational levels, as explained in Section 3.1. The isotopic shifts were confirmed by the analysis of mass-analyzed threshold-ionization (MATI) spectroscopy of individual isotopomers (not shown).

Spectra of the A⁺²Π_Ω ← X⁺²Σ⁺ and the B⁺²Σ⁺ ← X⁺²Σ⁺ transitions were recorded using the method of isolated-core Rydberg-dissociation (ICRD) spectroscopy.³⁶ A first laser excites metastable MgXe molecules to high-lying Rydberg states (n > 150) located just below a specific vibrational level of the X⁺ ionic ground state. In a good approximation, the Rydberg electron does not interact with the ion core, which can, therefore, be regarded as isolated. After a short time delay of ∼10 ns, a second laser excites the X⁺ ion core to either the A⁺_Ω or the B⁺ state. The resulting core-excited Rydberg states can dissociate through various mechanisms into Mg(3l) [nl′] and Xe(5p⁶) ¹S₀ fragments (see discussion in Section 3.2). The Rydberg electron remains attached to the Mg⁺ fragment during the dissociation and is ionized subsequently by a delayed pulsed-electric-field sequence [(−1.38, 172) V/cm]. The −1.38 V/cm prepulse spatially separates the Mg⁺ ions generated by field-ionization from prompt Mg⁺ ions, which can then be distinguished by their flight times to the MCP detector at the end of the time-of-flight spectrometer. The ICRD spectra are recorded by monitoring the Mg⁺ ions generated by field-ionization as a function of the wavenumber of the second laser.

3. Experimental Results and Analysis

3.1. X⁺²Σ⁺ Ground State of MgXe⁺

3.1.1. Photoionization and PFI-ZEKE-PE Spectra

The photoionization spectrum of ²⁴Mg¹³²Xe in the vicinity of the X⁺²Σ⁺(v⁺) ← a ³Π₀(v″ = 0) ionizing transition of MgXe is compared with the PFI-ZEKE-PE spectrum of a natural sample of MgXe in Figure 2. The photoionization spectrum exhibits a sharp onset at the position corresponding to the adiabatic ionization energy of the a ³Π₀ metastable state of ²⁴Mg¹³²Xe [E_I(v⁺ = 0)/(hc) = 37,468.3(6) cm^–1, see below]. After a strong autoionization resonance at the position of the v⁺ = 0 ionization threshold, the ion signal decreases. The PFI-ZEKE-PE spectrum exhibits a regular vibrational progression of the X⁺ ground state of MgXe⁺. Vibrational bands with v⁺ ≥ 3 show a weak double-peak structure on the low-frequency side of the main peak, which we attribute to the ²⁵MgXe and ²⁶MgXe isotopomers. The isotopic shifts depend on the reduced mass and primarily reflect the contributions from the Mg isotopes because the shifts induced by the different Xe isotopes are not observable at the resolution of our measurements. The isotopic shifts were used to determine the absolute vibrational assignment. As an illustration, the inset of Figure 2 compares the isotopic shifts determined experimentally ( in blue and in red) with the isotopic shifts calculated assuming that the lowest observed line corresponds to a transition to v⁺ = 0 (dotted line) and v⁺ = 1 (solid line). The absolute vibrational numbering of the X⁺ levels of MgXe⁺ determined in this way is displayed along the assignment bar above the calculated spectrum in Figure 2c.

Figure 2.

(a) Photoionization spectrum of ²⁴Mg¹³²Xe in the vicinity of the MgXe⁺ X⁺²Σ⁺ ←MgXe a ³Π₀ ionization threshold. (b) Measured and (c) calculated overview PFI-ZEKE-PE spectra of the X⁺²Σ⁺(v⁺) ←a ³Π₀(v″ = 0) ionizing transition of MgXe. The inset shows the measured isotopic shifts of the vibrational levels of ^25,26Mg¹³²Xe⁺ (red and blue dots) determined from the PFI-ZEKE-PE spectrum. The dotted and solid lines display the isotopic shifts calculated assuming that the lowest observed level corresponds to v⁺ = 0 and v⁺ = 1, respectively.

The vibrational bands are not rotationally resolved because of the small rotational constant and the overlap of the vibrational bands of different isotopomers containing the same Mg isotope but different Xe isotopes. To determine the band origin of all lines, a rotational-contour analysis was performed, taking into account the contributions of all isotopomers. To model these spectra, we assumed Hund’s angular-momentum coupling case (a) for the a ³Π₀ state and Hund’s case (b) for the X⁺²Σ⁺ state. The rotational energies were calculated according to standard expressions for pure Hund’s cases without centrifugal distortion. The rotational constant for the a ³Π_0^+/– state was taken from ref (3) as well as the ³Π_0⁺/³Π_0^– splitting of 1.46 cm^–1 (the 0^– component lies below the 0⁺ one³). The rotational constants of the X⁺ state of ²⁴Mg¹³²Xe⁺ were obtained from the potential-energy function derived in this work (see Section 3.1.2). The vibrational and rotational constants of the other isotopomers were calculated using the appropriate mass-scaling laws.³⁷ Rotational line intensities were calculated using the orbital ionization model derived in ref (38) assuming a thermal distribution of the rotational levels in the initial state (T_rot = 7 K). The calculated spectra of all of the isotopomers were scaled according to their relative abundances and summed. The fitted band origins E_I(v⁺)/(hc) of ²⁴Mg¹³²Xe, corrected for the field-induced shifts, are summarized in Table 1, which also lists the term values T(v⁺) relative to the X⁺(0) level. Vibrational constants were derived for the X⁺ ground state of ²⁴Mg¹³²Xe⁺ from the observed vibrational term values in a least-squares fit [ω_e = 136.9(3) cm^–1 and ω_ex_e = 1.69(3) cm^–1].

Table 1. Observed Positions E_I(v⁺)/(hc) of the Vibrational Levels of the X⁺²Σ⁺ Ground State of ²⁴Mg¹³²Xe⁺ Given with Respect to the Ground Vibrational Level of the Metastable a ³Π₀ State of MgXe^a.

v+	EI(v+)/(hc)	T(v+)	ΔTcalc(v+)	Bcalc(v+)
0	37,468.3(6)	0.0b	0.0	0.091
1	37,602.3(7)	134.0(9)	0.3	0.090
2	37,732.1(7)	263.8(9)	–0.2	0.088
	37,723.0(1.2) (26MgXe)
3	37,858.9(7)	390.6(9)	–0.2	0.087
	37,852.3(1.5) (25MgXe)
	37,845.4(1.2) (26MgXe)
4	37,982.2(6)	513.9(8)	–0.3	0.086
	37,973.5(1.2) (25MgXe)
	37,965.0(1.2) (26MgXe)
5	38,101.9(7)	633.6(9)	–0.5	0.084
	38,091.7(1.2) (25MgXe)
	38,081.6(1.2) (26MgXe)
6	38,218.6(6)	750.3(8)	–0.3	0.083
	38,206.5(1.2) (25MgXe)
	38,194.9(1.2) (26MgXe)
7	38,331.7(6)	863.4(8)	–0.3	0.082
	38,318.0(1.2) (25MgXe)
	38,305.0(1.2) (26MgXe)
8	38,442.1(1.0)	973.8(1.0)	0.4	0.080
	38,426.9(1.5) (25MgXe)
	38,412.2(1.5) (26MgXe)
9	38,548.4(1.0)	1080.1(1.2)	0.4	0.079

^aTerm values T(v⁺) are given along with their deviations ΔT_calc(v⁺) from the values calculated from the potential-energy function presented in Section 3.1, as well as rotational constants B_calc(v⁺), also determined from the potential-energy function. All values are in cm^–1.

^bReference value.

Figure 2c shows the calculated PFI-ZEKE-PE spectrum of the X⁺²Σ⁺ ← a ³Π₀ ionizing transition. The band origins and line intensities are obtained from the potential-energy function of the X⁺ state derived from the experimental vibrational term values in a least-squares fit (see Section 3.1.2 for details). The calculated and measured band origins are compared in the third column of Table 1 and are in excellent agreement. The agreement between the calculated and experimental line intensities is also good, although the calculated intensities for the low-v⁺ levels are systematically underestimated. This is particularly the case for the transition to the v⁺ = 0 level, which is much stronger in the experimental spectrum than in the calculated one. As in our analysis of the X⁺ ← a photoionizing transition of MgAr⁺³⁹ and MgKr⁺,²⁷ we attribute this intensity anomaly to channel interactions, through which transitions to low vibrational levels of MgXe⁺ with small Franck–Condon factors gain intensity by the coupling to Rydberg series converging to higher-lying vibrational levels of the ion. The photoionization spectrum supports this interpretation because a strong autoionization resonance is observed in Figure 2a at the position of the v⁺ = 0 band of the PFI-ZEKE-PE spectrum.

3.1.2. Potential-Energy Function of the X⁺²Σ⁺ State of MgXe⁺

The potential-energy function of the X⁺²Σ⁺ state of MgXe⁺ was determined from the vibrational structure of the PFI-ZEKE-PE spectrum in a least-squares fit. We calculated the vibrational term values by numerically solving the Schrödinger equation for the nuclear motion using a potential-energy function of the form⁴⁰

1

following the same procedure as in our studies of MgAr⁺,^15,39 MgKr⁺,²⁷ and MgNe⁺.⁹ The potential-energy function in eq 1 comprises an attractive and a repulsive short-range interaction term and a long-range interaction term u_LR(R). The parameters A and C are related to the well depth D_e and the equilibrium internuclear distance R_e through

2

and

3

respectively. The long-range term u_LR(R) accounts for the dominant electrostatic interactions between Mg⁺(3s) and Xe and is expressed in atomic units as

4

where α_Xe is the static electric polarizability volume of xenon and accounts for the charge–induced-quadrupole and the dispersion interactions. The polarizability volume of Xe (α_Xe = 27.78 a₀³)⁴¹ and the C₆ coefficient (C₆ = 193.53 a₀⁶)^5,42 were kept fixed. The switch functions

5

ensure a smooth change from the short-range to the long-range part of the potential.⁴³ In the fit, we kept the value of R_e fixed to the value calculated ab initio by Gardner et al.⁶ (R_e = 5.70 a₀). Additionally, we used an experimental value for D₀ based on the observation of the Mg⁺(3p) ²P_1/2 + Xe ¹S₀ dissociation threshold of the A_1/2⁺ state in combination with a thermochemical cycle, as discussed in Section 3.2. Within the approximation of an anharmonic oscillator, D_e was calculated from D₀ using the vibrational constants ω_e and ω_ex_e derived in this work (see above) so that D_e could be kept fixed in the fitting procedure.

Consequently, only two parameters were fitted: b and ρ. The parameters determining the X⁺²Σ⁺ potential-energy function are summarized in Table 2, and the differences between the calculated and observed term values are listed in the fourth column of Table 1. The potential-energy function is displayed in the lower inset of Figure 1 along with the wave functions of all experimentally observed vibrational levels of ²⁴Mg¹³²Xe⁺. The rotational constants, listed in the last column of Table 1, were calculated with

6

and used in the analysis of the rotational contours of the X⁺ vibrational bands. The Franck–Condon factors of the X⁺²Σ⁺(v⁺) ← a ³Π₀(v″ = 0) transitions depicted in Figure 2c correspond to the potential-energy function for the X⁺ state derived in this work and a simple Morse potential for the a ³Π₀ state with parameters from ref (3).

Table 2. Parameters Describing the Potential-Energy Function of the X⁺²Σ⁺ State of MgXe, Obtained in a Least-Squares Fit to the Vibrational Term Values Determined Experimentally.

Re	De	b	ρ	αXe	C6
5.70 a0a	0.0138 Ehb	0.79 a0–1	0.43 a0–1	27.78 a03a	193.53 a06Eha

^aValue not varied in the least-squares fit and taken from ref (6) (R_e) and refs (5, 41, and 42) (α_Xe and C₆), see text for details.

^bValue not varied in the least-squares fit and fixed to the value derived from the analysis of the 3p complex as explained in the text.

3.2. A⁺²Π_Ω and B⁺²Σ⁺ States of MgXe⁺

The A⁺²Π_Ω (Ω = 1/2, 3/2) and B⁺²Σ⁺ states of MgXe⁺ were characterized using ICRD spectroscopy. To measure the A⁺_Ω state, the wavenumber of the first laser was set to excite high-lying Rydberg states just below the v⁺ = 0 threshold of the X⁺ state of MgXe⁺. The second laser was used to record the A⁺_Ω(v⁺)← X⁺(0) transition of MgXe⁺. Core-excited molecules in the A⁺_Ω and the B⁺ states can dissociate into Mg⁺ and Xe ¹S₀ either following fluorescence to the repulsive wall of the X⁺ state, by the absorption of a second photon to the repulsive wall of a higher-lying electronic state, or through spin–orbit-induced predissociation (see Figure 1).

Figure 3 shows the overview spectrum of the A⁺²Π_Ω ← X⁺²Σ⁺ transition, obtained by monitoring the ²⁴Mg⁺ signal resulting from the field-ionization of Mg[nl′] fragments as a function of the wavenumber of the second laser . The spectrum consists of vibrational progressions corresponding to the two spin–orbit components Ω = 1/2 and 3/2 of the A⁺_Ω state, which appear as closely spaced pairs of lines with vibrational quantum numbers v⁺ for the Ω = 3/2 component and v⁺ + 1 for the Ω = 1/2 component. The origins of all vibrational bands were determined in an analysis of the rotational contours and are summarized in Table 3. The contours were modeled using standard expressions for a ²Π – ²Σ⁺ transition,^44,45 assuming Hund’s case (b) for the X⁺ state and Hund’s case (a) for the A⁺ state. Initial values of the rotational constants were estimated by scaling the rotational constants of the A⁺_Ω state of MgAr⁺²⁶ and MgKr⁺²⁷ and adjusted for each band to find the best agreement between the calculated and experimental contours. The overlap of the rotational structures of the different isotopomers made the fitting procedure challenging and resulted in large uncertainties for the rotational constants (the last column of Table 3). Our experimentally determined vibrational band origins are in good agreement with the measurements by Pilgrim et al.⁴ up to a global frequency shift of 34 cm^–1. For high vibrational levels v⁺_Ω ≥ 9, the isotopic shifts resulting from the different Xe isotopes become large enough to be observed and appear as a splitting of the lines, which can be attributed to ²⁴Mg¹³²Xe⁺ and ²⁴Mg¹²⁹Xe⁺. Inset (a) of Figure 3 depicts as an illustration the spectrum showing the partially resolved rotational/isotopic band structures of the transitions to the A⁺_1/2(10) (red) and A⁺_3/2(9) (blue) levels. The absolute vibrational assignments, given above the experimental spectrum in Figure 3, were determined from these isotopic shifts and confirmed the previous assignments by Pilgrim et al.⁴ based on the isotopic shifts of the different Mg isotopomers. Inset (b) in Figure 3 displays how the spin–orbit splittings of the A⁺_1/2,3/2 states vary with the vibrational quantum number v⁺. These splittings are much larger than the values expected from the atomic limit cm^–1, corresponding to the Mg⁺(3p) (²P_3/2 – ²P_1/2) spin–orbit splitting. In the A⁺ state, the spin–orbit splitting decreases linearly with increasing v⁺, from 269.8 cm^–1 at v⁺ = 0 to below 230 cm^–1 at v⁺ = 13. Matsika and Pitzer²¹ have predicted a spin–orbit splitting of 277.6 cm^–1 at the equilibrium geometry of the A⁺ state, in good agreement with the present results, and attributed the large value to a gain of Xe (n + 1)pπ character of the valence orbital at short distances.

Figure 3.

ICRD spectrum of the A⁺_Ω(v⁺) ← X⁺(0) band system of ²⁴MgXe⁺ obtained by monitoring the ²⁴Mg⁺ ions generated by field ionization of the high-n Rydberg states of ²⁴Mg. Inset (a) shows the rotational contour of the overlapping A⁺_1/2(10) ← X⁺(0) and A⁺_3/2(9) ← X⁺(0) bands (black line) and the fitted profiles in red and blue, respectively, which reveal a distinct substructure from the different Xe isotopes, as discussed in the text. Inset (b) displays the variation of the spin–orbit splitting of the A⁺_1/2,3/2 states with the vibrational quantum number v⁺.

Table 3. Observed Absolute Term Values E(v⁺)/(hc) of the Vibrational Levels of the A⁺²Π_Ω States of ²⁴Mg¹³²Xe⁺ and Their Vibrational Term Values T(v⁺) with Respect to the A⁺²Π_1/2(v⁺ = 0) State and Rotational Constants [B_exp(v⁺)]^a.

v+	Ω	E(v+)/(hc)	T(v+)	Bexp(v+)
0	1/2	28,858.6(1.5)b	0.0c
	3/2	29,128.2(1.5)b	269.6b
3	3/2	29,875.7(8)	1017.1(9)	0.146(5)
4	1/2	29,863.1(8)	1004.5(9)	0.143(5)
	3/2	30,118.8(8)	1260.2(9)	0.144(5)
5	1/2	30,106.8(8)	1248.2(9)	0.147(10)
	3/2	30,358.1(1.5)	1499.5(1.6)	0.144(10)
6	1/2	30,347.0(1.5)	1488.4(1.6)	0.142(10)
	3/2	30,595.4(8)	1736.8(8)	0.143(10)
7	1/2	30,584.0(8)	1725.4(9)	0.141(10)
	3/2	30,829.5(1.0)	1970.9(1.1)	0.142(10)
8	1/2	30,818.3(8)	1959.7(9)	0.140(10)
	3/2	31,060.1(8)	2201.5(9)	0.142(10)
9	1/2	31,049.7(6)	2191.1(8)	0.139(5)
24Mg129Xe	1/2	31,053.6(5)
	3/2	31,288.0(5)	2429.4(7)	0.139(5)
24Mg129Xe	3/2	31,291.9(5)
10	1/2	31,277.7(5)	2419.1(7)	0.138(5)
24Mg129Xe	1/2	31,281.9(5)
	3/2	31,512.7(5)	2654.1(7)	0.130(10)
24Mg129Xe	3/2	31,517.0(5)
11	1/2	31,502.5(5)	2643.9(7)	0.130(10)
24Mg129Xe	1/2	31,507.1(5)
	3/2	31,734.2(5)	2875.6(7)	0.128(10)
24Mg129Xe	3/2	31,738.8(5)
12	1/2	31,724.1(5)	2865.5(7)	0.127(10)
24Mg129Xe	1/2	31,729.0(5)
	3/2	31,952.6(8)	3094.0(7)	0.127(10)
24Mg129Xe	3/2	31,957.5(8)
13	1/2	31,942.8(1.0)	3084.2(7)	0.125(10)
24Mg129Xe	1/2	31,978.0(1.0)
	3/2	32,168.4(8)	3309.8(9)	0.125(10)
24Mg129Xe	1/2	32,173.6(8)
14	1/2	32,159.1(1.2)	3300.5(1.2)	0.124(10)
24Mg129Xe	1/2	32,164.7(1.2)

^aAll values are given in cm^–1. The numbers in parentheses represent one standard deviation.

^bNot experimentally observed but extrapolated with the vibrational constants given in Table 4.

^cReference value.

Figure 4 displays the ICRD spectrum of ²⁴MgXe⁺ in the region of the B⁺²Σ⁺(v⁺) ← X⁺²Σ⁺(7) transitions. The spectrum, which was recorded following the selective preparation of MgXe⁺ in the X⁺(7) level by MATI, can be divided into three different regions. In the first region (i) below 37,770 cm^–1, only a few weak lines corresponding to the X⁺²Σ⁺(v⁺) ← a ³Π₀ transition are observed (marked in blue above the spectrum). These transitions depend only on the second laser and thus do not correspond to transitions from the X⁺(7) state of ²⁴MgXe⁺. Instead, they are attributed to transitions from the a ³Π₀ state of MgXe to vibrationally excited levels of the X⁺ state, as indicated along the top assignment bar in Figure 4. The second region (ii) between 37,770 and 37,860 cm^–1 consists of a progression of sharp lines which turn into a continuum. The spacing between the lowest observed lines is ∼13 cm^–1 and decreases toward higher wavenumbers. The same progression of lines in region (ii) also appears in spectra recorded from the X⁺(8) state but is shifted in wavenumber by the difference ΔT_7,8 in the term values (not shown). This observation proves that they correspond to transitions of MgXe⁺, and their assignment is discussed below. The third region (iii) is dominated by a very intense line, which we can attribute to the X⁺²Σ⁺(5) ← a ³Π₀ transition. The weak line at 38,040 cm^–1 and marked by an asterisk was also observed in the PFI-ZEKE-PE spectra of MgKr⁺²⁷ but could not be assigned. It is neither an atomic Mg line nor a transition in a MgKr_n cluster, as explained in ref (27). The three weak lines between 37,890 and 37,940 cm^–1 (marked in magenta) are reproducible but not part of the B⁺ series. They have so far not been assigned.

Figure 4.

ICRD spectrum of the B⁺(v⁺) ←X⁺(7) band system of ²⁴MgXe⁺ obtained by monitoring the ²⁴Mg⁺ ions generated by field ionization of the high-n Rydberg states of Mg. The vertical bars indicate the positions of the Mg⁺²P_1/2,3/2 + Xe dissociation thresholds, and the red shaded areas correspond to their uncertainties. The blue assignment bar shows the positions of the X⁺²Σ⁺(v⁺) ← a ³Π₀ transitions induced by only the second laser. The line marked with an asterisk and the progression marked in magenta could not be assigned.

Table 4. Molecular Constants of the a ³Π₀ State of MgXe and of the X⁺²Σ⁺ and A⁺²Π_Ω⁺ (Ω = 1/2 and 3/2) States of MgXe^+a.

	T0	ωe	ωexe	D0+	ref
a 3Π0	–37,468.3(6)			618(7)	this work
X+2Σ+	0.0	136.9(3)	1.69(3)	2970(7)	this work
		134.8	1.66	2905.8	(6)
				2848(150)	(19)
				3359(1650)	(46)
				4182	(4)
A+2Π1/2	28,858.6(1.5)b	259.1(3)	1.55(3)	9781(7)	this work
	28,825	258	1.49	11,026	(4)
A+2Π3/2	29,128.2(1.5)b	255.2(3)	1.53(3)	9603(7)	this work
	29,093	254.6	1.5		(4)

^aThe term values T₀ of the ground vibrational levels of the different electronic states are given with respect to the ground vibrational level of the X⁺ state of MgXe⁺. All values are in cm^–1.

^bNot directly observed but derived from the calculated term value of the lowest experimentally observed vibrational level.

The specific pattern observed in region (ii) of Figure 4, i.e., a sharp onset followed by a progression of closely spaced lines going over into a continuum, has been observed before in the spectra of MgAr⁺ and MgKr⁺ and can be attributed to transitions to the B⁺ state. The 3p complex, consisting of the two spin–orbit components of the A⁺²Π_Ω states and the B⁺²Σ⁺ state, has two close-lying dissociation thresholds corresponding to Mg⁺²P_1/2,3/2 + Rg (see Figure 1). The potential-energy function of the B⁺ state correlates with the upper ²P_3/2 threshold. Between these two thresholds, high-lying vibrational levels of the B⁺ state can predissociate into the Mg⁺²P_1/2 + Rg continuum, allowing one to observe the vibrational levels in the Mg⁺ PFI signal (illustrated by the red shaded area in the upper inset in Figure 1). The sharp onset of the observed signal thus corresponds to the position of the Mg⁺²P_1/2 + Rg dissociation threshold. The two vertical bars in Figure 4 mark the positions of the two dissociation thresholds, derived from the spectra, i.e., 37,772(7) and 37,861(7) cm^–1, and the red areas indicate the uncertainty of the position of these thresholds. Using the experimentally determined dissociation thresholds together with the atomic Mg⁺(3p) ²P_1/2,3/2 term values,³⁵ one can determine the dissociation energy of the metastable a ³Π₀ state of MgXe [D₀(a) = 618(7) cm^–1], the X⁺ state of MgXe⁺ [D₀(X⁺) = 2970(7) cm^–1], and the A_Ω⁺ states of MgXe⁺ [D₀(A_1/2⁺) = 9781(7) cm^–1 and D₀(A_3/2⁺) = 9603(7) cm^–1]. The dissociation energy of the X⁺ state determined in this way is slightly higher than the ab initio value [D₀(X⁺) = 2905.8 cm^–1] reported by Gardner et al.⁶ Considering the discrepancy between the ab initio and the experimental values of D₀ for the X⁺ state of MgAr⁺ (0.7 cm^–139) and MgKr⁺ (30.8 cm^–127) and the larger number of electrons in MgXe, the values may be regarded as being in good agreement. The dissociation energies for the X⁺ and the A⁺ states of MgXe⁺ reported by Pilgrim et al.⁴ [D₀(X⁺) = 4182 cm^–1 and D₀(A_1/2⁺) = 11,026 cm^–1] are larger than our values but were extracted in a Birge–Sponer extrapolation, which can be inaccurate when the potential curves are subject to spin–orbit coupling and long-range interactions.

For the X⁺²Σ⁺(v⁺) ← a ³Π₀ transitions to be observed when monitoring the Mg⁺-PFI signal, the X⁺-state ion must absorb one or two additional photons to reach the repulsive wall of a higher-lying electronic state with a Mg⁺ + Xe asymptote (blue arrows in Figure 1). The X⁺(5) level is the lowest vibrational level for which the X⁺(v⁺) – a(0) excitation wavenumber is high enough to reach the Mg⁺²P_1/2,3/2 + Xe ¹S₀ dissociation threshold with one additional photon alone. The very strong Mg⁺-PFI signal for v⁺ = 5 indicates a sufficient overlap of the wave function of the X⁺(5) vibrational level with the repulsive wall of the B⁺ state. Transitions to X⁺²Σ⁺(v⁺ < 5) can only be detected following the absorption of three or more photons and are, therefore, much weaker or not observed at all.

In MgAr⁺ and MgKr⁺, the lowest vibrational levels of the B⁺ state were observed in the Mg⁺-PFI dissociation signal.^26,27 The suggested mechanism leading to dissociation in these ions involves the excitation of the B⁺ vibrational states with a second photon to the outer repulsive wall of the Mg⁺(3dσ)Rg state (see Figure 1 and refs (26 and 27) for details). In MgXe⁺, we do not observe low-lying vibrational levels of the B⁺ state, suggesting that this dissociative decay channel is not efficient in this case. Absorption of a second photon of wavenumber from B⁺(v⁺) levels indeed accesses an energy range located above the local maximum in the potential of the Mg⁺(3σ)Xe state (see dashed orange arrow in Figure 1), implying low Franck–Condon densities for direct dissociation.

4. Conclusions

In this article, we presented the spectroscopic characterization of the X⁺²Σ⁺ ground and A⁺²Π_Ω and B⁺²Σ⁺ electronically excited states of MgXe⁺ by photoelectron and photodissociation spectroscopy. The measurements were performed using a rotationally cold beam of metastable a ³Π₀ MgXe molecules produced in a laser-ablation supersonic beam source.

The vibrational structure of the X⁺²Σ⁺ state of MgXe⁺ was characterized using PFI-ZEKE PE spectroscopy following single-photon excitation from the ³Π₀ metastable state of MgXe. We derived the adiabatic ionization energy of the ³Π₀ state [E_I/(hc) = 37,468.3(6) cm^–1]. The potential-energy function and vibrational constants of the X⁺ state were determined through least-squares fits of the experimental term values. The observed and calculated positions and intensities of the vibrational bands are in good agreement. Additionally, the study revealed the presence of channel interactions affecting the intensities of transitions to low-lying vibrational levels of the X⁺ state.

The A⁺_Ω and B⁺ states were investigated by using ICRD spectroscopy. Our measurement of the A⁺_Ω states confirms previous results obtained on these states by Pilgrim et al.⁴ We observed the B⁺ state of MgXe⁺ for the first time and could determine the position of the Mg⁺(3p) ²P_1/2 + Xe ¹S₀ dissociation threshold. Using thermochemical cycles and the term values of Mg and Mg⁺³⁵, we could determine the dissociation energies of the a [D₀(a) = 618(7) cm^–1], X⁺ [D₀(X⁺) = 2970(7) cm^–1], and A_Ω⁺ [D₀(A_1/2⁺) = 9781(7) cm^–1 and D₀(A_3/2⁺) = 9603(7) cm^–1] states. Further investigation is needed to fully characterize the 3p complex of MgXe⁺. In particular, experimental data on the low vibrational levels of the B⁺ state would be needed for a global treatment of the 3p complex of MgXe⁺.

The authors declare no competing financial interest.