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# Rotational and nuclear-spin level dependent photodissociation dynamics of H2S

## Abstract

The detailed features of molecular photochemistry are key to understanding chemical processes enabled by non-adiabatic transitions between potential energy surfaces. But even in a small molecule like hydrogen sulphide (H2S), the influence of non-adiabatic transitions is not yet well understood. Here we report high resolution translational spectroscopy measurements of the H and S(1D) photoproducts formed following excitation of H2S to selected quantum levels of a Rydberg state with 1B1 electronic symmetry at wavelengths λ ~ 139.1 nm, revealing rich photofragmentation dynamics. Analysis reveals formation of SH(X), SH(A), S(3P) and H2 co-fragments, and in the diatomic products, inverted internal state population distributions. These nuclear dynamics are rationalised in terms of vibronic and rotational dependent predissociations, with relative probabilities depending on the parent quantum level. The study suggests likely formation routes for the S atoms attributed to solar photolysis of H2S in the coma of comets like C/1995 O1 and C/2014 Q2.

## Introduction

Sulphur is a relatively abundant element in the Universe (the S/H ratio in the solar photosphere is 1.3 × 10−5 (refs. 1,2) but the abundances of known sulphur-containing molecules in the interstellar medium (ISM) sum to much less than this value3. Estimates based on the limited range of S-containing compounds detected in low-density diffuse clouds imply sulphur fractions similar to the cosmic value4, that decrease markedly on moving into denser regions of the ISM5,6,7. The abundances of S-containing species in the outer layers of the photodissociation region in the Horsehead nebula, for example, are thought to be only about one quarter of the cosmic value8 and orders of magnitude lower values have been suggested in cold molecular clouds9. Given the high hydrogen abundances and the mobility of hydrogen in the ice matrix, sulphur atoms incident on interstellar ice mantles are expected to favour formation of H2S, the chemical- and photo-induced desorption of which is considered the main source of gas-phase H2S molecules10,11. H2S has been detected in the atmospheres of comets P/Halley12, C/1995 O1 (Hale-Bopp)13,14, C/2014 Q2 (Lovejoy)15 and 67P/Churyumov–Gerasimenko16,17 and, where comparisons are possible, the returned H2S densities are significantly greater than those of any other sulphur-containing species. Gaseous H2S has also been detected in the Jovian atmosphere18 and above the cloud deck in the atmospheres of Uranus19 and (probably) Neptune20.

The electronic spectrum of H2S displays weak continuous absorption at wavelengths λ < 260 nm and stronger absorption features at λ < 155 nm associated with excitations to Rydberg states21,22,23, as illustrated in Fig. 1 and shown in more detail in Supplementary Fig. 1. Photodissociation by solar ultraviolet (UV) radiation is an important destruction route for H2S molecules in the ISM. Photolysis studies in the long-wavelength continuum24 and at λ = 157.6 nm25 reveal prompt S–H bond fission and formation of ground (X2Π) state SH radicals. Lyman-α (λ = 121.6 nm) photolysis, in contrast, yields SH radicals in the excited A2Σ+ state26,27. These earlier data guide the current astrochemical models28,29, which assume a very simple description of this photophysics: dissociation exclusively to H + SH fragments, supplemented by photoionization at energies above the first ionisation potential (84432 ± 2 cm−1, ref. 30, with relative probabilities determined by the respective cross-sections31. Recent photofragment translational spectroscopy (PTS) measurements of the H and S(1D) atoms from photolysis of jet-cooled H2S molecules at many wavelengths in the range 122 ≤ λ ≤ 155 nm hint at a much richer photochemistry, however, involving multiple excited electronic states, a range of non-adiabatic inter-state couplings, and fragmentation to many of the spin-allowed dissociation limits illustrated in Fig. 1 and detailed in Table 132. Of particular astrophysical significance, the PTS study showed that only ~25% of H2S photoexcitation events induced by the general interstellar radiation field (ISRF)33 would yield SH(X) products; sequential fragmentation to three atoms is the most likely outcome32. This finding provides a plausible explanation for (i) prior rotational spectroscopy measurements directed at the W49 massive star-forming region, which deduced SH/H2S abundance ratios lower than would be predicted by the standard models in turbulent dissipation regions and shocks34 and (ii) the detection of UV emission from S atoms attributed to H2S photodissociation in the comas of, for example, C/1995 O1(Hale-Bopp)35 and C/2014 Q2 (Lovejoy)36.

Inspection of Fig. 1 reveals an intense absorption feature at λ~139.1 nm, which lies in the middle of the range where the branching into SH(A)/SH(X) primary photoproducts shows a strong wavelength dependence32. This absorption is attributable to excitation from the $$\tilde{X}$$1A1 ground state to a predissociated Rydberg state of H2S with 1B1 symmetry21,23,37,38,39. The excited state has a near-integer quantum defect, encouraging assignment in terms of excitation from the highest occupied, non-bonding 3pb1 orbital to a 3da1 Rydberg orbital21,23, and predissociates sufficiently slowly to allow excitation to specific rotational (JKaKc) levels of the 1B1 state. Earlier resonance enhanced multiphoton ionisation (REMPI) studies involving this 1B1 state identified both homogeneous (i.e. vibronic) and heterogeneous (i.e. Coriolis induced) predissociation mechanisms23,39 but were silent with regard to the products.

Here, we show the rich quantum state-dependent photofragmentation dynamics that prevail when exciting within the manifold of levels associated with just this one predissociated electronic state of H2S and serves to highlight the over-simplicity of the current astrochemistry model descriptions. The present data comprise excitation spectra for forming H and S(1D) atoms, and H2 molecules in selected vibration, rotation (v”, J”) levels, (i.e. photofragment excitation (PHOFEX) spectra) and translational energy distributions of H and S(1D) atom products derived using H-atom Rydberg tagging29,40 and velocity map ion imaging41 techniques, respectively (detailed in the ‘Methods’ section). These results provide a lens through which the rich photofragmentation dynamics of H2S can begin to be appreciated. Processes I–V all contribute to the decay of the photoexcited H2S(1B1) molecules, but with parent rotational level-dependent efficiencies. The data also confirm nuclear spin conservation in dissociation pathway V and show that some products are formed via more than one route. The details of the excited-state-resolved, multi-channel fragmentations revealed for this prototypical three-atom system are ripe for quantitative interpretation by contemporary electronic structure and excited-state dynamics studies.

## Results

### PHOFEX spectra

Figure 2 shows excitation spectra for forming H and S(1D) atoms following excitation of a jet-cooled sample of H2S (30% in Ar) across the wavenumber range 71,865–71,950 cm−1 (139.15–138.99 nm). Both spectra show four features, but with clearly different relative intensities. The features can be assigned using the spectral simulation programme PGOPHER42 and the appropriate spectroscopic parameters23 (Supplementary Fig. 2). Each comprises one (or more) lifetime broadened transitions. The feature at 71,877.7 cm−1 is a single rovibronic transition (the 000-110 line), the 71,916.5 cm−1 feature is dominated by the 110–000 transition, while the major contributors to the more heavily blended features centred at ~71,897 cm−1 and ~71,936 cm−1 are, respectively, the 111-101 and 211-101/220-110 transitions. Supplementary Table 1 gives further details of the contributing transitions, the relative populations of the various ground state rotational levels at two different parent rotational temperatures (Trot = 3 K and 15 K) and the values of <Jq2> (the expectation values of the square of the angular momentum about the q = a, b and c-inertial axes in the excited rotational level).

Several factors influence the relative intensities of these features. First, we note that these are excitation spectra for forming specific products; they report a convolution of the parent absorption probability and the branching ratio for forming the target fragment. Prior work32 suggests that the H atom loss processes (I–IV) are dominant at these wavelengths, so the H atom PHOFEX spectrum (Fig. 2a) is likely to better approximate the parent absorption spectrum. The rate of Coriolis-driven predissociation of this 1B1 excited state has previously been shown to scale with <Jb2> 23, so simulations of the 1B1$$\tilde{X}$$1A1 band have to recognise both the homogeneous and heterogeneous (i.e. rotational level independent and dependent) contributions to the excited state decay rate, and thus to the lifetime broadened peak linewidths and, via conservation of transition probability, the peak heights.

Symmetry dictates that each rotational level of H2S satisfies either ortho- or para-nuclear spin statistics. The former levels (for which Ka + Kc = odd in the $$\tilde{X}$$state) have three times higher statistical weight, and transitions involving ortho-H2S molecules are highlighted in bold in Supplementary Table 1a, b. Ortho- and para-H2S molecules do not interconvert during the supersonic expansion, so any simulation of the jet-cooled excitation spectra must employ different rotational (Trot) and nuclear spin (Tns) temperatures. Supplementary Fig. 2a, c shows H atom PHOFEX spectra recorded under different expansion conditions which, as confirmed by the accompanying PGOPHER-simulated absorption spectra (Supplementary Figs. 2b, d), afford different degrees of rotational cooling and different Trot values. Under the most dilute expansion conditions (yielding Trot~3 K), almost all the parent population has relaxed to the lowest energy para- (000) and ortho- (101) levels of the ground state (see Supplementary Table 1b), the 000–110 line at 71,877.7 cm−1 is no longer observed and the blended features clearly narrow.

The H and S(1D) atom PHOFEX spectra shown in Fig. 2 were recorded under comparable expansion conditions, wherein Trot~15 K, yet the 000–110 line is clearly much weaker and the blended ~71,936 cm−1 feature relatively more intense in the latter. Supplementary Fig. 2e, f show, respectively, the 1 (λ~139 nm) + 1′ (λ = 532 nm) parent REMPI spectrum and a PHOFEX spectrum for forming ortho-H2 products (in the v” = 10, J” = 1 level). As expected, the 71,916.5 cm−1 feature associated with para-H2S molecules is absent in the ortho-H2 PHOFEX spectrum (nuclear spin is conserved in the fragmentation process, as also found in studies of photoinduced H2 elimination from the H2S+ parent cation43. But the 000–110 line, which samples ortho-H2S molecules, is barely discernible either. These differences confirm that the predissociation rates and the branching into the various predissociation products both depend on the excited state rotational level.

### H atom product translational energy distributions

H atom time-of-flight (TOF) spectra were recorded following photolysis of H2S at wavelengths within each of the four main features in Fig. 2. As before32, these TOF data (Supplementary Fig. 3) were converted to the corresponding total H + SH translational energy distributions, P(ET), as described in the ‘Methods’ section. Fig. 3 contrasts the P(ET) spectra obtained at λ = 139.125 nm (exciting the 000–110 transition) and 139.051 nm (110–000 transition), with the polarisation vector of the photolysis laser radiation (εphot) aligned, respectively, parallel (θ = 0°) and perpendicular (θ = 90°) to the detection axis. The P(ET) spectra obtained when exciting within the blended features at λ = 139.085 and 139.015 nm are shown in Supplementary Fig. 4.

These P(ET) spectra all look rather similar at high ET (>10,000 cm−1). The θ = 0° and 90° spectra obtained when exciting at 139.125 nm (Fig. 3a) are essentially identical (reflecting the isotropy of the J′ = 0 wavefunction) but, at all other wavelengths, the high-ET signal is consistently more intense when detecting at θ = 90°. Such recoil anisotropy is consistent with the perpendicular transition assignment (1B1$$\tilde{X}$$1A1, i.e. the transition dipole moment lies perpendicular to the molecular plane) and subsequent homogeneous predissociation on a timescale (~picosecond) that is shorter than the parent rotational period.

Given the threshold energies for the various fragmentation paths (Table 1 and illustrated also in Fig. 1), the structured envelope with ET > 11,000 cm−1 must be associated with SH(X) co-fragments formed via process I in a spread of vibrational (v”) and rotational (N”) quantum states. The best-fit simulation of this spectrum is shown in Supplementary Fig. 5. The higher energy part (with ET > 18,000 cm−1) is attributable to formation of SH(X) fragments with 0 ≤ v” ≤ 10 and a spread of low N” values (peaking at N”~10). These SH(X, v”, N”) population distributions have similarities with those reported when exciting H2S at λ = 157.6 nm25. The lower energy part, with 11000 < ET < 18,000 cm−1, spanning beyond the three-body dissociation limit to H + H + S(3P) atoms (process III), is attributable to formation of H + SH(X, low v”, high N”) products with energies extending beyond the SH(X) state bond dissociation energy, D0(S–H). The broad maximum in Fig. 3a centred at ET~8000 cm−1 is likely to include contributions from H atoms formed with primary SH(X) fragments in ‘super-rotor’ levels, i.e. quasi-bound levels supported by the accompanying centrifugal potential energy barrier. Population of analogous OH(X) super-rotor levels in the photolysis of H2O has been reported44. Many of these SH(X) super-rotors will predissociate by tunnelling through the centrifugal barrier within the short (<5 ns) time delay between the photolysis and probe (H Rydberg tagging) laser pulses to yield a second (slow) H atom. The broad peak centred at ET ~ 2500 cm−1 in Fig. 3a is attributed to such secondary H atom products.

The spectra obtained at wavelengths that sample 1B1 state levels with J' > 0 show another structured component at ET ≤ 10,000 cm−1. To highlight these features, the distribution shown in Supplementary Fig. 5a has been used as a basis function (P(ET)vib) that represents the contribution from homogeneous (i.e. purely vibronic) predissociation pathways and a suitably weighted amount of this P(ET)vib function subtracted from the P(ET) distributions obtained at λ = 139.085, 139.051 and 139.015 nm, so as to minimise the signal at ET > 10,000 cm-1. The resulting P(ET)Cor distributions (Supplementary Fig. 6) describe the Coriolis-induced predissociation yields and confirm formation of H + SH(A) products (process II).

These SH(A) fragments are mainly formed in the v’ = 0 level, in a broad spread of rotational (N’) levels extending to (and just beyond) the SH(A) state bond dissociation energy (i.e. to energies above the threshold for forming H + S(1D) atoms)—as shown by the comb included in Fig. 3b32 – and with an N-dependent recoil anisotropy: H + SH(A, v′ = 0, low N’) products recoil preferentially along the axis parallel to εphot, whereas H + SH(A, v’ = 0, high N’) products appear with greater probability along axes perpendicular to εphot.

All SH(A) radicals predissociate on a nanosecond (or shorter) timescale to yield H + S(3PJ) atom products45. Thus the primary SH(A) photoproducts revealed in Fig. 3b and Supplementary Fig. 4 must decay to yield a second H atom within the time that the Rydberg tagging laser radiation is present, and these secondary H atoms must also contribute to the P(ET)Cor distribution and the total P(ET) spectra. The predissociation of SH(A) radicals favours population of ground (J = 2) spin-orbit state S(3PJ) products45, and combs indicating the ET values of H + S(3P2) products expected from predissociation of selected SH(A, v’ = 0, N’) photoproducts are also included in Supplementary Fig. 6. Astute readers will recognise weak structure attributable to H + SH(A) products in Fig. 3a. This is attributed to dissociation following excitation to the weak absorption continuum that underlies the 1B1$$\tilde{X}$$1A1 band, since similar signal is also evident in P(ET) spectra obtained when exciting at wavelengths off-resonant with the 000–110 transition (e.g. at λ = 139.117 nm, Supplementary Fig. 7).

In summary, the H Rydberg atom photofragment translational spectroscopy (HRA-PTS) measurements reveal formation of (i) H + SH(X) products via vibronic predissociation from the 1B1 Rydberg state, (ii) H + SH(A) products via Coriolis-induced predissociation of excited state levels with <Jb2 >> 0 and (iii) S(3P) atoms via sequential decay of primary SH(X) and SH(A) photoproducts (i.e. net process III, by tunnelling from ‘super-rotor’ levels and by electronic predissociation, respectively).

### S(1D) atom product translational energy distributions

Figure 4a, b shows time-sliced velocity map images of the S(1D) photofragments measured following photolysis of H2S at λ = 139.125 and 139.051 nm, respectively, and subsequent resonant ionisation at λ = 130.092 nm. Image analysis yields the corresponding P(ET) distributions (Fig. 4c, d), derived assuming momentum conservation and H2 as the partner fragment.

The structure in these P(ET) spectra reveals population of specific H2(v′′, J′′) levels, which are clearly very different in the two cases. Best-fit simulations of these spectra (Fig. 4c, d) return the H2(v′′) population distributions shown in Fig. 4e, f. Rotational (J”) distributions for representative v′′ = 0 and v′′ = 10 state products are shown in Fig. 4g, h. The H2 products formed when exciting the 000–110 transition show an isotropic velocity distribution, and an inverted vibrational state population distribution spanning all bound vibrational levels of H2 (i.e. all levels with v′′ ≤ 14), peaking at v′′ = 10, but only modest rotational excitation. The H2 products formed from the 110–000 transition, in contrast, have anisotropic velocity distributions and a bimodal vibrational state population distribution comprising not just an inverted vibrationally ‘hot’, rotationally ‘cold’ component (again peaking at v′′~10) but also a substantial yield of vibrationally ‘cold’ (i.e. v′′ = 0 and 1) products. These H2(low v′′) products show highly inverted rotational state population distributions; the P(ET) spectrum shows structure at low ET values, beyond the S(1D) + 2H dissociation limit, consistent with formation of super-rotor levels of H2(v′′ = 0). Fig. 4g, h) confirm the expected conservation of nuclear spin symmetry: the H2 products from excitation of (a) ortho- and (b) para-H2S molecules are formed in, respectively, odd and even J” levels.

Supplementary Fig. 8 shows images obtained following excitation at λ = 139.085 and 139.015 nm, along with the derived P(ET) and H2 internal energy distributions. The H2(v′′, J′′) distributions measured at λ = 139.085 nm are reminiscent of those found when exciting to the 000 level (Fig. 4e, g); excitation at this wavelength populates primarily the 111 level (another level of ortho-H2S and the only other excited level for which <Jb2 > = 0). The H2(v′′, J′′) distributions derived from the image recorded at λ = 139.015 nm, in contrast, are more like those found when exciting to the 110 level (Fig. 4f, h). Again, the dominant excitations at this wavelength populate levels with <Jb2 >> 0, though these levels (211 and 220) are levels of ortho-H2S and the H2 products thus have odd J′′. Supplementary Fig. 9 shows S(1D) images recorded at other wavelengths near λ~139.09 nm, which illustrate the extreme sensitivity of the product energy disposal to the exact choice of excitation wavelength within these blended features.

These ion imaging studies reveal formation of S(1D) + H2 products (i.e. process V) via both vibronic and Coriolis-induced predissociation pathways. The H2 products arising via the former route carry substantial vibrational but little rotational excitation. Previous REMPI studies have reported formation of H2 products in high v′′, low J′′ states following excitation of H2S to similar total energies46,47,48,49,50. The P(ET) distributions measured when exciting parent levels with <Jb2 >> 0 reveal a rival Coriolis-induced pathway yielding additional H2 products, characterised by little vibrational but massive rotational excitation—including population of super-rotor levels of H2.

## Discussion

The present study affords detailed views of different photofragmentation pathways in a prototypical triatomic molecule. Photoexcitation to the predissociated 1B1 state of H2S at λ~139.1 nm allows definition of the initial rovibrational level(s) from which dissociation occurs (i.e. their rotational angular momentum and nuclear spin symmetry), while the excitation and PTS detection methods yield quantum-state-resolved information on the dissociation products. Qualitatively, the deduced dynamics can all be reconciled within the framework illustrated in Fig. 5, but a complete interpretation will require much better knowledge of the topographies of, and non-adiabatic couplings between, the various excited-state potential energy surfaces (PESs). Hopefully, the scope of the present data will inspire state-of-the-art computational studies of H2S, enabling it to acquire status as a reference molecule within the photophysics and chemical reaction dynamics communities—comparable to that enjoyed by its lighter analogue H2O51.

Previous REMPI52 and OH(A) PHOFEX53 spectroscopy and HRA-PTS studies54 following excitation to the analogous $$\tilde{C}$$1B1 state of H2O have also revealed competitive homogeneous (vibronic) and heterogeneous (Coriolis-induced) predissociation pathways. These have been rationalised by non-adiabatic coupling from the $$\tilde{C}$$ state to dissociative states of, respectively, 1B1 and 1A1 symmetry (labelled the $$\tilde{A}$$ and $$\tilde{B}$$ states of H2O)51 and, from hereon, it proves helpful to discuss the fragmentation dynamics of H2S revealed by the present work in the context of existing knowledge relating to the fragmentation of H2O.

### Vibronically-induced predissociation

The topography of the $$\tilde{A}$$1B1 PES of H2O ensures that direct population of this state by vertical photoexcitation from the ground state equilibrium geometry leads to prompt O–H bond fission, yielding H + OH(X) fragments with modest rovibrational excitation of the latter55,56,57. The $$\tilde{C}$$ and $$\tilde{X}$$states of H2O have similar equilibrium geometries, yet vibronic predissociation from the $$\tilde{C}$$, v = 0, 000 level yields OH(X) products in a wide range of vibrational levels (0 ≤ v” ≤ 13). Wavepacket calculations58 provide an explanation for this striking energy disposal: non-adiabatic coupling between the $$\tilde{C}$$ and $$\tilde{A}$$ state PESs is mediated by sampling an intermediate 1A2 state PES59, most efficiently at compressed O–H bond lengths, and this compression of the surviving O–H bond maps into the final product vibration.

The present data for H2S show obvious parallels, but also some differences. Additionally, the present data inform on the competing H2 elimination channel—the possible O(1D) + H2 product channel following VUV photoexcitation of H2O has yet to be studied in any detail. Prior studies of H2S photoexcitation within its long-wavelength absorption band (see Fig. 1), the analogue of the $$\tilde{A}$$$$\tilde{X}$$ absorption of H2O, reveal the first important difference: Vertical excitation of H2S samples not one but two near degenerate excited states (with 1B1 and 1A2 symmetry in C2v, i.e. both 1A″ in Cs), only one of which is dissociative upon H–SH bond extension60. The increasing vibrational excitation of the SH(X) products observed when exciting at shorter wavelengths within this continuum25 has been attributed to efficient electronic predissociation of molecules initially excited to the higher-lying, quasi-bound state61,62.

Thus, the analogue of the $$\tilde{A}$$ state of H2O in H2S is probably better viewed as a ‘lumpy continuum’ of quasi-bound resonances embedded in a dissociative continuum, all with 1A″ symmetry, appropriate for accession by vibronic (i.e. rotation-independent) coupling from the 1B1 state of current interest. High-level ab initio calculations of these coupled excited state PESs and accompanying wavepacket propagations would likely reveal whether the foregoing explanations (i.e. compression of the S–H bonds at the point of optimal non-adiabatic coupling to the 1A″ continuum, and/or a legacy of the resonance structure within the 1A″ continuum) can account for the observed vibrationally excited SH(X) fragments from vibronic predissociation of H2S(1B1) molecules. These same calculations should also inform on the dynamics of S(1D) + H2(X, high v”, low J′′) product formation after coupling to the 1A″ continuum, which has been predicted to be a barrierless process at near-C2v (i.e. T-shaped) geometries63. We return later to consider potential sources of the H + SH(X, low v”, very high N”) and S(3P) + 2H products via a vibronic coupling mechanism (as implied by the data shown in Fig. 3 and Supplementary Fig. 5).

### Coriolis-induced predissociation

Analogy with H2O again provides a useful starting point. Vertical excitation to the $$\tilde{B}$$1A1 state of H2O also results in prompt dissociation, but the O–H bond extension occurs in tandem with rapid opening of the HOH bond angle: some of the photoexcited molecules evolve on the adiabatic $$\tilde{B}$$ state PES and undergo H–OH bond fission to yield electronically excited OH(A) fragments with little vibrational but very high rotational excitation—the legacy of the strong angular forces imposed by the topography of the $$\tilde{B}$$ state PES. However, the dominant decay processes for H2O($$\tilde{B}$$) molecules involve non-adiabatic couplings (i) via a Renner–Teller seam of degeneracy between the $$\tilde{B}$$ and $$\tilde{A}$$ state PESs at linear geometries and (ii) at either of two conical intersections (CIs) between the $$\tilde{B}$$ and $$\tilde{X}$$state PESs at linear H….OH and H….HO configurations—all of which yield OH(X, low v”, high N”) products64,65. H2O molecules accessing the $$\tilde{B}$$ state PES by Coriolis-enabled predissociation from rovibrational levels of the $$\tilde{C}$$1B1 state54 show similar propensities for forming both OH(A) and OH(X) photofragments in low v, high N quantum states.

Figure 3 confirms formation of H + SH(A, low v’, high N′) products by rotationally-mediated predissociation from H2S(1B1) state levels with <Jb2 >> 0. Rotation about the b axis (the z inertial axis in C2v) transforms as a2 and can thus promote non-adiabatic coupling of the 1B1 state to a continuum of 1B2 symmetry. This highlights another difference cf. H2O. The above discussion of the long-wavelength absorption suggests that, in H2S, the analogue of the $$\tilde{B}$$ state of H2O will also comprise two nested states, of 1A1 and 1B2 symmetry in C2v (i.e. both 1A′ in Cs). These are the upper components of the Renner–Teller pairs with, respectively, the lower-lying 1B1 and 1A2 states. Both 1A′ states will have linear minimum energy geometries at short RH–SH bond lengths and the coupled states should manifest as a series of quasi-bound resonances embedded in a continuum that correlates adiabatically to the H + SH(A) asymptote. The topography of the dissociative 1A′ PES will encourage H–SH bond extension in concert with opening of HSH, consistent with the observed H + SH(A, low v′, high N′) products.

The imaging data (Fig. 4b) reveal that formation of S(1D) + H2(low v′′, high J′′) products also requires Coriolis-coupling to the 1A′ continuum and that these products recoil preferentially parallel to εphot. Both observations can be explained assuming a set of dissociative trajectories on the 1A′ PES for which the balance of axial and tangential forces allows the molecule to evolve outside the region of the CI at linear H….SH geometries (CI-1 in Supplementary Fig. 10) and thus remain on the 1A′ PES but not dissociate fully. Rather, the emerging H and SH(A) fragments are held in a centrifugally-bound complex and are drawn into a seam of intersection between the 1A′ and $$\tilde{X}$$ state PESs at linear H….HS geometries. This seam, which includes the CI-2 depicted in Supplementary Fig. 10 but spans a wide range of H…H and S…H separations, enables H atom transfer and ultimate formation of the observed S(1D) atoms and H2 fragments. The experimental data show that this fragmentation route favours massive rotation of the H2 products and an extension of such dynamics could contribute to the observed S(1D) + 2H fragment yield.

### Another vibronic predissociation mechanism

We now consider possible routes to the observed H + SH(X, low v”, high N”) and S(3P) + 2H products. Many VUV photolysis studies of H2O have identified H + OH(X, low v”, high N”) products but, in all cases, the high product rotation is seen as a legacy of initial motion (opening of HOH) on the $$\tilde{B}$$ state PES prior to non-adiabatic coupling to the $$\tilde{A}$$ or $$\tilde{X}$$state PESs. But the H + SH(X, low v”, high N”) products revealed in Fig. 3 are deduced to arise via a vibronic predissociation mechanism. As at shorter excitation wavelengths26,27,32, non-adiabatic coupling to the 1A′ PES provides an efficient route to H + SH(A, low v’, high N’) products, but not to H + SH(X, low v”, high N”) products—probably because the balance of angular and radial forces prevailing on the 1A′ PES carry all dissociating molecules outside the region of configuration space that supports non-adiabatic transfer to the lower energy states (i.e. preclude type I trajectories whereby excited molecules achieve linearity at shorter RH–SH values than CI-1 in Supplementary Fig. 10)32. But it is hard to envisage any route to very highly rotationally excited SH fragments that do not depend on the angular acceleration provided by the topography of the 1A′ PES.

Detailed understanding must await future high-level theoretical studies, but we can suggest a possible rotation-independent mechanism. The photoexcited 1B1 molecules undergo vibronic predissociation to the 1A″ ‘lumpy continuum’. Some survive in quasi-bound bending levels long enough to sample a broader range of configuration space, including near-linear geometries that enable non-adiabatic coupling to the upper (1A′) Renner–Teller components. Further angular acceleration is then generated by passage through CI-1 between the 1A′ PES and the $$\tilde{X}$$ state PES at linear H….SH geometries (Supplementary Fig. 10), ultimately yielding H + SH(X, low v”, high N”) products – as observed. The non-observation of H + SH(A) fragments via this vibronic predissociation route can be understood by recognising that the execution of this more tortuous route to the 1A′ PES partitions sufficient energy into other degrees of freedom to ‘close off’ the excited product asymptote.

### Product branching

Recent PTS studies showed the progressive switch from single S–H bond fission (process I), which dominates at λ > 150 nm, to three body dissociation at shorter photolysis wavelengths32. The predissociated 1B1-$$\tilde{X}$$1A1 band investigated here falls at a wavelength where processes I–V all contribute to the product yield, via a range of non-adiabatic coupling pathways, with excited rotational level-dependent efficiencies. Only two excited state rotational levels have <Jb2 > = 0 (the 000 and 111 levels), so higher temperature H2S samples will contain a larger fraction of molecules with <Jb2 >> 0 and higher average <Jb2 > values—both of which will increase the probability of heterogeneous predissociation. Using PGOPHER42, along with the previous parameterisation of the vibronic and Coriolis-induced predissociation rates from the 1B1 state23, suggests that the cross-section for absorption that results in heterogeneous predissociation (σhetero) contributes only ~17% of the total 1B1$$\tilde{X}$$1A1 cross-section (σtot) at temperatures T ≤ 30 K but starts to dominate once T = 300 K, where σhetero/σtot~0.52.

Increasing the relative probability of coupling to the 1A′ continuum can be expected to reduce the relative yield of H + SH(X) products, but more quantitative discussions would also require better knowledge of how the rotational angular momentum of the photoexcited molecule may continue to influence the nuclear motions after initial non-adiabatic coupling to the 1A′ or 1A continua. Qualitatively, however, the current data suggest that the initial non-adiabatic coupling has a major influence on the eventual product branching. For example, the decomposition of P(ET) spectra when exciting the four main features (Fig. 2) and detecting along an axis at θ = 54.7° (the magic angle variants of the spectra shown in Fig. 3 and Supplementary Fig. 4) shows the P(ET)Cor/P(ET)vib ratio increasing from 0 at λ = 139.125 nm (when exciting the 000 level) to >1 at λ = 139.015 nm (when exciting levels with <Jb2> in the range 2.5–4). Similarly, if we attribute the S(1D) + H2(v” = 0 and 1, high J”) products observed at λ = 139.051 and 139.015 nm to the Coriolis-induced predissociation pathway, and all other S(1D) + H2(high v”, low J”) products to vibronic predissociation, then the ratio of the heterogeneous to homogeneous contributions to the total S(1D) + H2 yield increases from 0 at λ = 139.125 nm to ~0.5 at λ = 139.015 nm.

In summary, this work provides one of the most complete experimental studies of molecular photofragmentation processes reported to date, affording initial parent quantum state selection and detailed investigation of competing product channels. Predissociation of the 1B1 Rydberg state of H2S populated by photoexcitation at λ ~139.1 nm is initiated via both rotation-free (vibronic) and rotation-induced non-adiabatic couplings, thus ensuring that the relative yields of H, S, SH and H2 products, their velocity distributions and respective quantum state population distributions are sensitively dependent on the chosen parent quantum state. The fragmentation mechanisms are rationalised based on available knowledge regarding the topographies of, and non-adiabatic couplings between, the PESs of the lower-lying valence excited states of H2S. Similarities and differences with the photofragmentation dynamics of the more thoroughly studied homologue, H2O, are highlighted. The time is now ripe for a thorough investigation of the excited state photophysics of H2S combining cutting-edge experiments of the types described here and state-of-the-art quantum chemistry methods.

From an astrophysical perspective, recent studies have shown that H2S photoexcitation by the general ISRF should favour triple fragmentation to the constituent atoms (the dominant process at wavelengths λ < 130 nm) over binary dissociation to H + SH(X) radicals (which dominates at λ > 150 nm) by a factor of ~3:132. The present study explores the fate of H2S molecules excited on a strong absorption feature in the intermediate wavelength region, where the branching between two- and three-body dissociation is changing rapidly with wavelength, and reveals that this branching is also highly parent quantum state dependent. The 1B1 state molecules prepared with <Jb2> = 0 dissociate predominantly to H + SH(X) products, whereas molecules with <Jb2> > 0 can also decay to H + SH(A) (and thence to H  +H + S(3P)) and S(1D) + H2 products, with probabilities that scale with <Jb2>. Thus, the fate of H2S molecules following excitation on the strong 1B1-$$\tilde{X}$$1A1 absorption (and, most probably, on any of the other neighbouring Rydberg resonances evident in Fig. 1) will be sensitive to the local temperature. Any S(1D) photoproducts formed in rarefied interstellar environments will decay radiatively (via the spin-forbidden 1D→3P transition, with Einstein A-coefficient A ~2.1 × 10−2 s−1 (ref. 66)), adding to the S(3P) yield from the various three-body fragmentation pathways of H2S and the secondary photolysis of primary SH(X) fragments that are predicted15 to be the main sources of the S atoms detected in the coma of several comets35,36.

## Methods

### The H atom product translational energy distributions

The H atom product translational energy distributions were recorded using a tuneable VUV pump source along with the H-atom Rydberg tagging time-of-flight (HRTOF) probe technique67. In the HRTOF detection method, the H atom products were excited from the ground state to a high n Rydberg state via a two-step excitation. Step one involves resonant excitation from the n = 1 to n = 2 state at the Lyman-α wavelength (λ = 121.6 nm), while step two uses UV laser excitation at λ~365 nm to further excite the H atom from the n = 2 state to a high-n (n = 30–80) Rydberg state, lying slightly below the ionisation threshold. Coherent 121.6 nm radiation was generated by difference four-wave mixing (DFWM) involving two 212.556 nm photons and one 845 nm photon overlapped in a stainless steel cell filled with a 3:1 ratio Ar/Kr gas mixture. Laser light at λ = 212.556 nm was produced by doubling the output of a 355 nm (Nd:YAG laser, Spectra Physics Pro-290) pumped dye laser (Sirah, PESC-G-24) operating at λ~425 nm. Half of the 532 nm output of the same Nd:YAG laser was used to pump another dye laser (Continuum ND6000) which operated at λ~845 nm. The λ~365 nm laser radiation used in the second step of the H-atom Rydberg tagging was generated by doubling the output of a third dye laser (Radiant Dye Laser-Jaguar, D90MA) operating at λ~730 nm, which was pumped by the remaining 532 nm output of the Nd:YAG laser. To eliminate background signals arising from λ = 212.556 nm photolysis of H2S in the interaction region, the 121.6, 212.556 and 845 nm beams were passed through a biconvex LiF lens positioned off-axis at the exit of the Ar/Kr gas cell thereby ensuring that only the VUV beam was dispersed through the interaction region.

The tuneable VUV photolysis source for H2S photodissociation at λ~139.1 nm was also generated by DFWM using 212.556 nm photons and tuneable radiation with λ~450 nm in another mixing cell, which was coupled to the other side of the main chamber. The 212.556 nm and 450 nm photons were generated using the second Nd:YAG laser to pump two further dye lasers, respectively. The same dispersion strategy employing an off-axis mounted LiF lens was also used to ensure that the 139.1 nm (but not the 212.556 nm) radiation passed through the interaction region. Since 121.6 nm photons also induce H2S photolysis and thus generate H atom signals, it was necessary to use a background subtraction method, whereby the λ~139.1 nm photolysis laser was alternated on and off. The parallel (θ = 0o) and perpendicular (θ = 90o) signals were recorded by tuning the polarisation of the 139.1 nm radiation, using a rotatable half-waveplate to rotate the polarisation of the tuneable (λ ~ 450 nm) radiation.

The neutral Rydberg-tagged H atom photofragments flew a known distance d (~280 mm) before reaching a grounded mesh-mounted close in front of Z-stack micro-channel plate (MCP) detector, where they were field-ionised immediately by the ~2000 V cm−1 electric field. The signal detected by the MCP was then amplified by a fast pre-amplifier and counted by a multichannel scaler. The recorded TOF data (shown in Supplementary Fig. 3) were converted to the corresponding H atom kinetic energy distributions. Momentum conservation arguments were then used to derive the total translational energy distributions P(ET), where

$${E}_{{{{\rm{T}}}}}=\frac{1}{2}{m}_{H}{\left(\frac{d}{t}\right)}^{2}(1+{m}_{H}/{m}_{SH}),$$
(1)

m is the photofragment mass, d is the flight distance and t is the TOF measured over this distance. The H atom PHOFEX spectra were recorded by integrating the H atom signals while scanning through a range of photolysis wavelengths.

### The S(1D) atom product translational energy distributions

The S(1D) atom product translational energy distributions were recorded using the VUV pump—time-sliced velocity map imaging (TSVMI) probe technique32. Briefly, the pulsed supersonic beam was generated by expanding a mixture of 30% H2S and Ar into the source chamber where it was skimmed before entering (through a 2 mm hole in the first electrode), and propagating along the centre axis of, the ion optics assembly mounted in the reaction chamber. The molecular beam was intersected at right angles by the photolysis and probe laser beams between the second and the third plates of the ion optics assembly. The λ ~139 nm photolysis photons were generated by DFWM, as described above, with εphot fixed in the horizontal plane and thus parallel to the front face of the MCP detector. The S(1D2) photoproducts were probed by one photon excitation at λ = 130.092 nm, which populates the autoionizing 3p3(2Do)5 s; 1D2o level. These photons were also generated by DFWM, by combining the frequency doubled output from one dye laser (at λ = 212.556 nm) with the fundamental output of a second dye laser (at λ = 580.654 nm) in a Kr/Ar gas mixture. The resulting S+ ions are accelerated through the remaining ion optics and travel through a 740 mm long field-free region before impacting on a 70 mm-diameter chevron double MCP detector coupled with a P43 phosphor screen. Transient images on the phosphor screen were recorded by a charge-coupled device camera, using a 30 ns gate voltage pulse to acquire time-sliced images.

### Parent REMPI spectra and H2(v′′, J′′) PHOFEX spectra

Parent REMPI spectra and H2(v′′, J′′) PHOFEX spectra were recorded at UNSW Sydney using an ion-imaging apparatus68. Briefly, a molecular beam of 10% H2S in helium was generated using a pulsed valve (General Valve Series 9, 0.5 mm orifice, controlled by an Iota One valve driver) and passed through a 1 mm diameter skimmer into an ion-imaging spectrometer configured in spatial mapping mode. The early-time component of the molecular beam was intersected with a λ~139.1 nm laser pulse generated by DFWM in a stainless-steel gas cell charged with 5 mbar of krypton. The λ = 212.556 nm and λ~450 nm precursor laser pulses were generated using two different Sirah Cobra-Stretch dye lasers (2 × 1800 g/mm grating). The λ = 212.556 nm radiation was generated by frequency-tripling the output of one dye laser running DCM dye in ethanol and pumped with the Nd:YAG 2nd harmonic (532 nm). The λ~450 nm light was the fundamental output of the other dye laser pumped by the Nd:YAG 3rd harmonic (355 nm) and operating with Coumarin-450 laser dye. To record REMPI spectra of the H2S parent molecule, the λ~139.1 nm pulse and final probe (ionisation) laser pulse, provided by the 2nd harmonic (532 nm) of a Nd:YAG laser (Quantel Brilliant B), were overlapped in space and time. The (multiphoton) probe pulse for recording H2 PHOFEX spectra was provided by the doubled output (λ~293 nm) of a 532 nm pumped Lambda-Physik LPD3000 dye laser running Pyromethene 597 dye and, in this case, the probe pulse was delayed by ~40 ns relative to the parent pump pulse. All wavelengths were verified using a Toptica WS5 wavelength-metre.

## Data availability

The source data underlying Figs. 2, 3 and 4 are provided as a Source Data file. All other data supporting this study are available from the authors upon request. Source data are provided with this paper.

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## Acknowledgements

The work in Dalian was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB17000000), the Chemical Dynamics Research Center (Grant No. 21688102), the National Natural Science Foundation of China (NSFC Nos. 21873099 and 21922306), the Key Technology Team of the Chinese Academy of Sciences (Grant No. GJJSTD20190002), the international partnership programme of Chinese Academy of Sciences (No. 121421KYSB20170012), and Liaoning Revitalization Talents Program (Grant Nos. XLYC1907154). C.S.H. is grateful for an Australian Research Council Discovery Early Career Award (DE200100549), M.N.R.A. is grateful for funding from the UK Engineering and Physical Sciences Research Council (EPSRC, EP/L005913) and both C.S.H. and M.N.R.A. are grateful to the NSFC Center for Chemical Dynamics for the award of Visiting Fellowships. We thank the DCLS staff for technical support.

## Author information

Authors

### Contributions

K.J.Y., C.S.H. and M.N.R.A. designed the experiments. Y.R.Z., Z.J.L., Y.C., Y.C.W., S.Z., Z.X.L., J.S.C., C.S.H. and K.J.Y. performed the experiments. K.J.Y., M.N.R.A., S.W.C., C.M.W., Y.R.Z., Z.J.L. and C.S.H. analysed the data. K.J.Y., M.N.R.A., C.S.H., H.B.D., G.R.W. and X.M.Y. discussed the experimental results. K.J.Y., C.S.H. and M.N.R.A. prepared the manuscript.

### Corresponding authors

Correspondence to Christopher S. Hansen or Michael N. R. Ashfold or Kaijun Yuan.

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Zhao, Y., Luo, Z., Chang, Y. et al. Rotational and nuclear-spin level dependent photodissociation dynamics of H2S. Nat Commun 12, 4459 (2021). https://doi.org/10.1038/s41467-021-24782-6

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