^{1}, Huasheng Wang

^{1}and Ágúst Kvaran

^{1,a)}

### Abstract

(2 + *n*) resonance enhanced multiphoton ionization mass spectra for resonance excitations to diabatic *E* ^{1}Σ^{+} (v′) Rydberg and *V* ^{1}Σ^{+} (v′) ion-pair states (adiabatic *B* ^{1}Σ^{+}(v′) states) of H^{ i }Cl (*i* = 35,37) and H^{ i }Br (*i* = 79,81) were recorded as a function of excitation wavenumber (two-dimensional REMPI). Simulation analyses of ion signal intensities, deperturbation analysis of line shifts and interpretations of line-widths are used to derive qualitative and quantitative information concerning the energetics of the states, off-resonance interactions between the *E* states and *V* states, closest in energy as well as on predissociation channels. Spectroscopic parameters for the *E* ^{1}Σ^{+} (v′)(v′ = 1) for H^{35}Cl and v′ = 0 for H^{79}Br states, interaction strengths for *E* − *V* state interactions and parameters relevant to dissociation of the *E* states are derived. An overall interaction and dynamical scheme, to describe the observations for HBr, is proposed.

The financial support of the University Research Fund, University of Iceland, the Icelandic Science Foundation as well as the Norwegian Research Council is gratefully acknowledged.

I. INTRODUCTION

II. EXPERIMENTAL

III. RESULT AND ANALYSIS

A. Spectra and energy levels

B. Signal intensities and interpretations

C. Line shifts and deperturbations

D. Line-widths

IV. CONCLUSIONS

### Key Topics

- Rydberg states
- 38.0
- Predissociation
- 14.0
- Dissociation
- 6.0
- Excited states
- 6.0
- Data analysis
- 5.0

## Figures

(a) and (b) HCl: 1D REMPI spectra for H^{+}, ^{35}Cl^{+}, H^{35}Cl^{+} and *J*′ assignments for rotational peaks corresponding to two-photon resonance excitations to the *E* ^{1}Σ^{+}(v′ = 0, 1), *V* ^{1}Σ^{+}(v′ = 10, 11, 14, 15) and *g* ^{3}Σ^{−}(v′ = 1) states for the excitation regions 83 200–84 250 cm^{−1} (a) and 85 600–86 440 cm^{−1} (b). (c) HBr: 1D REMPI spectra for H^{+}, ^{79}Br^{+}, H^{79}Br^{+} and *J*′ assignments for rotational peaks corresponding to two-photon resonance excitations to the *E* ^{1}Σ^{+}(v′ = 0), *V* ^{1}Σ^{+}(v′ = *m* + 4, m + 5) and *i* ^{3}Δ_{3}(v′ = 0) states for the excitation region 77 520–78 450 cm^{−1}.

(a) and (b) HCl: 1D REMPI spectra for H^{+}, ^{35}Cl^{+}, H^{35}Cl^{+} and *J*′ assignments for rotational peaks corresponding to two-photon resonance excitations to the *E* ^{1}Σ^{+}(v′ = 0, 1), *V* ^{1}Σ^{+}(v′ = 10, 11, 14, 15) and *g* ^{3}Σ^{−}(v′ = 1) states for the excitation regions 83 200–84 250 cm^{−1} (a) and 85 600–86 440 cm^{−1} (b). (c) HBr: 1D REMPI spectra for H^{+}, ^{79}Br^{+}, H^{79}Br^{+} and *J*′ assignments for rotational peaks corresponding to two-photon resonance excitations to the *E* ^{1}Σ^{+}(v′ = 0), *V* ^{1}Σ^{+}(v′ = *m* + 4, m + 5) and *i* ^{3}Δ_{3}(v′ = 0) states for the excitation region 77 520–78 450 cm^{−1}.

HCl: Rotational energy levels, derived from the observed REMPI rotational peaks for the *E* ^{1}Σ^{+}(v′ = 1) and *V* ^{1}Σ^{+}(v′ = 14, 15) states. Level-to-level off-resonance interactions between the *V*(v′) ion-pair states and the *E*(v′) Rydberg states are indicated by broken lines. Strength and alterations in state mixings are indicated, roughly, by varying thickness of broken lines.

HCl: Rotational energy levels, derived from the observed REMPI rotational peaks for the *E* ^{1}Σ^{+}(v′ = 1) and *V* ^{1}Σ^{+}(v′ = 14, 15) states. Level-to-level off-resonance interactions between the *V*(v′) ion-pair states and the *E*(v′) Rydberg states are indicated by broken lines. Strength and alterations in state mixings are indicated, roughly, by varying thickness of broken lines.

(a) and (b) H^{35}Cl: Spacings between rotational levels (Δ*E* _{ J } _{′,J′−1}) as a function of *J*′ for *V* ^{1}Σ^{+}(v′ = 15) ((a), top), *E* ^{1}Σ^{+}(v′ = 1) ((a), middle), *V* ^{1}Σ^{+}(v′ = 14) ((a), bottom), *V* ^{1}Σ^{+}(v′ = 11) ((b), top), *E* ^{1}Σ^{+}(v′ = 0) ((b), middle) and *V* ^{1}Σ^{+}(v′ = 10) ((b), bottom). (c) H^{79}Br: Spacings between rotational levels (Δ*E* _{ J } _{′,J′−1}) as a function of *J*′ for *V* ^{1}Σ^{+}(v′ = *m* + 5) ((c), top), *E* ^{1}Σ^{+}(v′ = 0) ((c), middle) and *V* ^{1}Σ^{+}(v′ = *m* + 4) ((c), bottom). Open circles are derived from observed *Q* lines (this work and Refs. ^{ 2 and 5 } , and ^{ 8 } ). Filled circles are derived from deperturbation calculations (see text).

(a) and (b) H^{35}Cl: Spacings between rotational levels (Δ*E* _{ J } _{′,J′−1}) as a function of *J*′ for *V* ^{1}Σ^{+}(v′ = 15) ((a), top), *E* ^{1}Σ^{+}(v′ = 1) ((a), middle), *V* ^{1}Σ^{+}(v′ = 14) ((a), bottom), *V* ^{1}Σ^{+}(v′ = 11) ((b), top), *E* ^{1}Σ^{+}(v′ = 0) ((b), middle) and *V* ^{1}Σ^{+}(v′ = 10) ((b), bottom). (c) H^{79}Br: Spacings between rotational levels (Δ*E* _{ J } _{′,J′−1}) as a function of *J*′ for *V* ^{1}Σ^{+}(v′ = *m* + 5) ((c), top), *E* ^{1}Σ^{+}(v′ = 0) ((c), middle) and *V* ^{1}Σ^{+}(v′ = *m* + 4) ((c), bottom). Open circles are derived from observed *Q* lines (this work and Refs. ^{ 2 and 5 } , and ^{ 8 } ). Filled circles are derived from deperturbation calculations (see text).

(a) and (b) H^{35}Cl: Relative ion signal intensities, *I*(^{35}Cl^{+})/*I*(H^{35}Cl^{+}) vs. *J*′ derived from *Q* rotational lines of REMPI spectra due to two-photon resonance excitations to the Rydberg states *E* ^{1}Σ^{+} (v′ = 1) (a) and *E* ^{1}Σ^{+} (v′ = 0) (b). (c) H^{79}Br: Relative ion signal intensities, *I*(^{79}Br^{+})/*I*(H^{79}Br^{+}) vs. *J*′ derived from *Q* rotational lines of REMPI spectra due to two-photon resonance excitations to the Rydberg state *E* ^{1}Σ^{+} (v′ = 0). Gray columns are experimental values. The black and white columns are calculated values for the contributions due to the interactions of the *E*(v′) states with the lower energy *V* states (*V* _{ L }) and the higher energy *V* states (*V* _{ H }), respectively.

(a) and (b) H^{35}Cl: Relative ion signal intensities, *I*(^{35}Cl^{+})/*I*(H^{35}Cl^{+}) vs. *J*′ derived from *Q* rotational lines of REMPI spectra due to two-photon resonance excitations to the Rydberg states *E* ^{1}Σ^{+} (v′ = 1) (a) and *E* ^{1}Σ^{+} (v′ = 0) (b). (c) H^{79}Br: Relative ion signal intensities, *I*(^{79}Br^{+})/*I*(H^{79}Br^{+}) vs. *J*′ derived from *Q* rotational lines of REMPI spectra due to two-photon resonance excitations to the Rydberg state *E* ^{1}Σ^{+} (v′ = 0). Gray columns are experimental values. The black and white columns are calculated values for the contributions due to the interactions of the *E*(v′) states with the lower energy *V* states (*V* _{ L }) and the higher energy *V* states (*V* _{ H }), respectively.

HBr: Rotational line-widths vs *J*′ derived from Q lines of H^{79}Br REMPI spectra for *V* ^{1}Σ^{+}(v′ = *m* + 5) (top), *E* ^{1}Σ^{+}(v′ = 0) (middle) and *V* ^{1}Σ^{+}(v′ = *m* + 4) (bottom).

HBr: Rotational line-widths vs *J*′ derived from Q lines of H^{79}Br REMPI spectra for *V* ^{1}Σ^{+}(v′ = *m* + 5) (top), *E* ^{1}Σ^{+}(v′ = 0) (middle) and *V* ^{1}Σ^{+}(v′ = *m* + 4) (bottom).

Semischematic figure, showing the HBr energetics, state interactions and energy transfers of relevance to the data presented (see text). Electrostatic, rotational and spin-orbit couplings are marked *E*, *JL* and *SO*, respectively. Red boxes represent the ion-pair states. Blue and purple boxes are Rydberg states and black curves are repulsive states. The blue box with solid lines represents a manifold of many Rydberg states, which couple with the ion-pair states. The blue boxes with broken lines are gateway states with respect to predissociation of other states. Relative importance of couplings and transfers are indicated by different boldness of arrows and broken lines as well as by use of brackets or not. The colored arrows indicate the major paths towards predissociation for the *V* and *E* states.

Semischematic figure, showing the HBr energetics, state interactions and energy transfers of relevance to the data presented (see text). Electrostatic, rotational and spin-orbit couplings are marked *E*, *JL* and *SO*, respectively. Red boxes represent the ion-pair states. Blue and purple boxes are Rydberg states and black curves are repulsive states. The blue box with solid lines represents a manifold of many Rydberg states, which couple with the ion-pair states. The blue boxes with broken lines are gateway states with respect to predissociation of other states. Relative importance of couplings and transfers are indicated by different boldness of arrows and broken lines as well as by use of brackets or not. The colored arrows indicate the major paths towards predissociation for the *V* and *E* states.

## Tables

Δ*E* _{ J }′ relevant to off-resonance interactions between *E* ^{1}Σ^{+}(v′ = 1) and *V* ^{1}Σ^{+} (v′ = 14,15) states (H^{35}Cl) (left), *E* ^{1}Σ^{+}(v′ = 0) and *V* ^{1}Σ^{+} (v′ = 10,11) states (H^{35}Cl) (middle) and *E* ^{1}Σ^{+}(v′ = 0) and *V* ^{1}Σ^{+} (v′ = *m* + 4,*m* + 5) states (HBr) (right).

Δ*E* _{ J }′ relevant to off-resonance interactions between *E* ^{1}Σ^{+}(v′ = 1) and *V* ^{1}Σ^{+} (v′ = 14,15) states (H^{35}Cl) (left), *E* ^{1}Σ^{+}(v′ = 0) and *V* ^{1}Σ^{+} (v′ = 10,11) states (H^{35}Cl) (middle) and *E* ^{1}Σ^{+}(v′ = 0) and *V* ^{1}Σ^{+} (v′ = *m* + 4,*m* + 5) states (HBr) (right).

Parameters used in analysis if relative ion signal intensities *I*(^{ i }X^{+})/*I*(H^{ i }X^{+}) (^{ i }X = ^{35}Cl, ^{79}Br) as a function of *J*′ for (2 + *n*) REMPI of *E* ^{1}Σ^{+}(v′) Rydberg states (see definitions in text).

Parameters used in analysis if relative ion signal intensities *I*(^{ i }X^{+})/*I*(H^{ i }X^{+}) (^{ i }X = ^{35}Cl, ^{79}Br) as a function of *J*′ for (2 + *n*) REMPI of *E* ^{1}Σ^{+}(v′) Rydberg states (see definitions in text).

Spectroscopic parameters derived from direct analysis of observed spectral lines (Obs.) and from deperturbation analysis (Dep.) (see text), (a) for *E* ^{ 1 }Σ^{+}(v′ = 1), *V* ^{1}Σ^{+}(v′ = 14, 15) (H^{35}Cl) by using interaction strengths *W* _{ L } = 124 cm^{−1} and *W* _{ H } = 126 cm^{−1}. Observed values are from this work (above) and from Ref. ^{ 3 } (below). (b) For *E* ^{1}Σ^{+}(v′ = 0), *V* ^{1}Σ^{+}(v′ = 10, 11) (H^{35}Cl) by using interaction strengths *W* _{ L } = 191 cm^{−1} and *W* _{ H } = 194 cm^{−1}. Observed values are from this work and from Ref. ^{ 3 } (below). (c) For *E* ^{1}Σ^{+}(v′ = 0), *V* ^{1}Σ^{+}(v′ = *m* + 4, *m* + 5) (H^{79}Br) by using interaction strengths *W* _{ L } = 57 cm^{−1} and *W* _{ H } = 97 cm^{−1}. Observed values are from this work (top) and from Refs. ^{ 8 } (middle) and ^{ 2 } (bottom).

Spectroscopic parameters derived from direct analysis of observed spectral lines (Obs.) and from deperturbation analysis (Dep.) (see text), (a) for *E* ^{ 1 }Σ^{+}(v′ = 1), *V* ^{1}Σ^{+}(v′ = 14, 15) (H^{35}Cl) by using interaction strengths *W* _{ L } = 124 cm^{−1} and *W* _{ H } = 126 cm^{−1}. Observed values are from this work (above) and from Ref. ^{ 3 } (below). (b) For *E* ^{1}Σ^{+}(v′ = 0), *V* ^{1}Σ^{+}(v′ = 10, 11) (H^{35}Cl) by using interaction strengths *W* _{ L } = 191 cm^{−1} and *W* _{ H } = 194 cm^{−1}. Observed values are from this work and from Ref. ^{ 3 } (below). (c) For *E* ^{1}Σ^{+}(v′ = 0), *V* ^{1}Σ^{+}(v′ = *m* + 4, *m* + 5) (H^{79}Br) by using interaction strengths *W* _{ L } = 57 cm^{−1} and *W* _{ H } = 97 cm^{−1}. Observed values are from this work (top) and from Refs. ^{ 8 } (middle) and ^{ 2 } (bottom).

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