## Introduction

Roaming is recognized as one of the hottest topics in reaction dynamics for the past decade. For the most studied roaming cases of H2CO and CH3CHO1,2,3,4,5,6,7,8,9,10,11, following photodissociation a recoiling atom or radical fragment on the ground-state surface can roam and then abstract intramolecularly another H atom to generate the H2 + CO and CH4 + CO molecular products. This pathway is expected to open within the roaming window, in which the dissociation threshold of such a radical channel and the transition state (TS) of a molecular channel are close to each other. However, the roaming dynamics turns out to be more complicated to render studies oriented in varied directions12,13,14,15,16,17,18,19,20,21,22,23,24,25. As an example using carbonyl compounds in the photodissociation, aliphatic aldehydes showed a loose roaming saddle point along the roaming dissociation coordinate26,27, whereas the roaming signature in methyl formate (HCOOCH3) was verified to involve multiple energy states via a conical intersection17,18. These two types of roaming dynamics apparently behave differently.

Formic acid (HCOOH) belongs to the family of carbonyl compounds, and its photodissociation dynamics has been popularly investigated for more than two decades28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43. When its electronic band S1 in the range 220 250 nm is excited, the dissociation channel mainly contains HCO + OH with a quantum yield of 0.70.830. Because the excited surface is dissociative, the produced fragments bear very large translational energy30,33. Kim and co-workers33 photolyzed the HCOOH molecule at 193 nm, and obtained a fraction of available energy into translational energy of OH as large as 0.82, whereas the fraction into internal energy of HCO was only 0.13. The fragments are mainly from the decomposition along the S1 surface and the resulting product energy disposals are consistent with those obtained at 225 nm29.

In the UV photodissociation of formic acid, two molecular channels are found:

$${\rm{HCOOH}}+{\rm{h}}v\to {\rm{CO}}+{{\rm{H}}}_{2}{\rm{O}}$$
(1)
$${\rm{HCOOH}}+{\rm{h}}v\to {{\rm{CO}}}_{2}+{{\rm{H}}}_{2}$$
(2)

Given photolysis of cis-formic acid at 193 nm, Khriachtchev et al.35 observed a CO/CO2 product ratio of 0.4 in an Ar-matrix absorption experiment, and a ratio of 5 when trans-formic acid was substituted. Such a CO/CO2 ratio is associated with conformational memory which is used to evaluate the extent of isomerization conversion between cis- and trans-formic acid. In contrast, Su et al.34 obtained the CO/CO2 ratio of 11 in the trans-formic acid at 193 nm by using 18 μs-resolved Fourier-transform infrared (FTIR) emission spectroscopy. In the quasiclassical trajectory calculations, Martınez-Nunez group39 evaluated a CO/CO2 ratio of 22.3 and 12.2 for trans- and cis-HCOOH, respectively, thus corresponding to a ratio of ~2 for trans-/cis-state selected in the initial excitation, which is much smaller than the absorption result of 12.5. Apart from a significant role of the Ar-matrix effect, Morokuma and co-workers42 recently suggested that the variation of CO/CO2 ratio should be closely related with the following dissociation process, in which the excited HCOOH molecules first flow through S2/S1 conical intersection and the partial dissociation H·····HCOO is followed by H-roaming on the S1 PES to form H2 + CO2. It is apparently controversial concerning a reliable evaluation of conformational memory which depends on the extent of energy randomization along the photodissociation coordinates.

The roaming pathways in photodissociation of formic acid at 193 nm were recognized theoretically a decade ago42,43. In addition to the H-roaming to form H2 + CO2 on the S1 state42, when the HCOOH molecules flow through the S1/S0 conical intersection, the molecular channel CO + H2O may be produced via the OH-roaming dynamics on the S0 state. The roaming mechanism has been examined in the recent work by Wang group44. They detected the CO(v = 0, J ≤ 20) ion imaging in photodissociation of HCOOH at 230 nm using (2 + 1) resonance-enhanced multiphoton ionization (REMPI) technique, and characterized the roaming/TS behavior for CO translational bimodality. However, it is still lacking a deep understanding of the energy disposal in CO(v ≥ 1, J) and discerning of the energy distributions between CO and H2O roaming products.

To complement the roaming results by ion imaging, this work employed time-resolved FTIR emission spectroscopy to monitor the fragments in photodissociation of trans-HCOOH at 193 nm. The ensuing FTIR spectra revealed simultaneously two molecular channels of CO + H2O and CO2 + H2. The vibrational state populations of CO (v = 1–8) accompanied by the corresponding rotational energy distributions are analyzed with the aid of spectral simulation. In addition, the ro-vibrational profile of H2O roaming co-product is simulated to understand the interplay with the CO product, especially in internal energy partitioning. Finally, the temporal dependence of CO/CO2 (v ≥ 1) ratio is obtained to deeply characterize the conformational memory and further reconcile with the previous reports which are in conflict34,35,39.

## Results and Discussion

### CO(v = 1) bimodal rotational distribution

A time-resolve FTIR spectrum with 10 cm−1 spectral resolution and 5 μs temporal resolution obtained the CO and CO2 in the region of 2000–2400 cm−1, in which the CO2 product (about 2200–2400 cm−1) relaxed rapidly within 20 μs delay time (Fig. S1). In addition, some weak signals appeared in the region of 2500–5000 cm−1 (Fig. S2). The spectra around 4000 cm−1 is ascribed to the CO overtones (Δv ≥ −2), while the region around 2950 cm−1 may be due to C-H stretching of the HCOO moiety in the H + HCOO channel45. However, the (v1,v2,v3 = 0,0,1) → (0,0,0) vibrational emission of H2O molecule fails to appear in the region 3600–3800 cm−1.

When the spectral resolution was increased to 0.5 cm−1, the CO and CO2 spectra with a 1 μs temporal resolution are shown in Fig. 1. The CO spectral intensity, spreading in the region of 1900–2220 cm−1, gradually increased with time within the initial 5 μs period, whereas the CO2 spectra with a peak at 2300 cm−1 were observed to shift to the larger wavenumber, indicating a rapid relaxation from higher vibrational states to lower states. Further, as the delay time is prolonged up to 25 μs (Fig. S1), both the CO and CO2 emission intensities reach the maximum at 5–10 μs delay and then the CO2 intensities diminish more rapidly. The CO and CO2 spectra show distinctly different temporal behavior.

As restricted to the spectral congestion, a spectral simulation of the CO population was used to resolve the rotational lines J up to 50 for each vibrational state v from 1 to 8, as shown in Fig. 2a. For lower vibrational states, the profile was found to comprise two Boltzmann rotational components. For instance, while inspecting the rotational population at v = 1 with a 1 μs resolution, a bimodal profile composed of two Boltzmann distributions was obtained with a small low-rotational component, which was ascribed to the OH-roaming on the S0 surface, and the other large high-rotational component ascribed to the TS pathway to form the same CO + H2O products (Fig. 2b). The CO low- and high-rotational temperatures were evaluated to be 280±15 and 1589±96 K at 0–1 µs delay. A series of rotational temperatures were similarly evaluated for 1–2, 2–3, 3–4, 4–5 and 5–6 µs delay time. Then, the temperatures were extrapolated to the 0 μs delay to be free from the Ar collision, thus obtaining 334 ± 153 and 1344 ± 430 K for both low- and high-rotational components. The evaluated ratio of low/high component varies slightly from 0.41 to 0.23 within 1 to 6 μs interval and is then averaged to 0.26 for v = 1 (Fig. S3).

According to the ion imaging results44, a clear bimodal translational distribution appears in the CO (v = 0, J = 9), in which the small component has a low speed peaking at ~380 m/s, in contrast to a large component peaking at ~1400 m/s. When the rotational level increases to J = 20, the low speed component diminishes to almost the minimum. Accordingly, the CO roaming product is characteristic of low rotation accompanied by small translational energy, while CO via the TS pathway is produced in the large rotational levels carrying a large translational energy. Alternatively, while inspecting the transition state structures of TS and roaming pathways on the S0 surface42, the distance between O and C in the HO···CHO intermediate was evaluated to be 1.865 and 3.005 Å, respectively. Therefore, a shorter O ··· C distance may exert a stronger torque to induce a larger rotational energy carried by the CO product via the TS pathway.

Note that the CO produced in triple fragmentation (H + CO + OH) may be neglected, because the fraction of available energy partitioning into the internal energy of HCO is 0.1333. The internal energy obtained by HCO is about 22 kJ/mol, which is close to the dissociation energy threshold of H···CO (~5300 cm−1)44,46,47. While taking into account the energy partitioning into rotational degrees of freedom and other vibrational modes, the reaction HCO → H + CO becomes negligible. It might be the reason why this channel has never been mentioned in the theoretical evaluation39,42,43.

### CO(v = 1–8) bimodal vibrational distribution

The vibrational population of a given state from v = 1 to 8 was evaluated by summing each rotational line simulated up to J = 50. Figure 3 shows the vibrational intensity as a function of vibrational energy distribution, corresponding to v = 1–8, but the zero-point energy is not included. Given the sum of vibrational population as denominator, the corresponding fraction of vibrational population (v = 1–8) appears consistent with the previous results (v = 1–6)34,38, as show in Fig. 4. Note that the vibrational fraction at v = 1 obtained by Su et al.34 is larger than either this work or theoretical calculation by Kurosaki et al.38. It might arise from partial vibrational relaxation to lower states during data acquisition by the FTIR apparatus with a prolonged temporal resolution34.

Each data point of vibrational intensity I(v) may break up with two Boltzmann vibrational profiles as expressed by,

$$I(v)=A{e}^{{E}_{v}/k{T}_{1}}+B{e}^{{E}_{v}/k{T}_{2}}$$
(3)

where A and B are weighing factors, Ev the vibrational energy at v state, k the Boltzmann constant, and T1 and T2 are the vibrational temperature at different component. To optimize the parameters A, B, T1 and T2, two slopes are plotted, yielding a low vibrational and a high vibrational temperature. Their intercepts indicate the factor of A and B. Since the vibrational energy transfer is much slower than the rotational energy transfer, the low and high vibrational temperatures remain constant within the first 6 μs period, corresponding to an average of 2700 ± 70 K and 7980 ± 220 K (Fig. S4). While inspecting the structures calculated for TS and OH-roaming saddle points42, the CO bond distance is 1.164 and 1.196 Å, respectively. Despite a slight difference of bond distance, we expect the lower vibrational temperature is ascribed to the TS pathway, while the higher temperature is caused by the roaming route. It is for the first time to find out vibrational-state dependence of the roaming signature.

Further, according to the theoretical PESs calculations as referred to Fig. 542,43, the molecules excited at 193 nm have to proceed through S1/T1 (431.5~442.0 kJ/mol) and T1/S0 (462.2 ± 2.3 kJ/mol) ISC to reach the ground state with enough energy to surpass the barrier to form CO + H2O. The rate for this route should be slowed by the multi-ISC processes such that the available energy carried may readily relax or disperse. In contrast, the excited molecules concomitantly proceed through the S1/S0 (449.9 kJ/mol) conical intersection to partially dissociate to HCO···OH in which the OH-roaming may form the same molecular products on the S0 surface. As such, the molecular channel via TS mechanism is anticipated to be slower with less internal energy partition than the molecular production via roaming pathway. In addition, upon irradiation of 193 nm, the C=O bond in HCOOH is elongated significantly. Following dissociation to form HCO and OH radicals, most internal energy carried by HCO is favorably deposited in the CO vibrational stretching40. The OH-roaming around the HCO core thus results in CO which bears large vibrational energy. The CO roaming channel should prevail over the TS pathway especially for higher vibrational states. On the contrary, at lower vibrational states such as v = 1, the Boltzmann rotational component of CO via the TS pathway becomes larger than the Boltzmann component via the roaming dynamics, as shown in Fig. 3.

Such roaming results exhibit a consistent trend as photolysis of propionaldehyde (CH3CH2CHO) leading to CO + C2H6 molecular products, in which the CO roaming behavior was theoretically recognized to be rotational cold but vibrational hot27. Nevertheless, these two roaming types are different from each other. Instead of proceeding through a conical intersection, the photodissociation process of propionaldehyde has to surpass a loose roaming saddle point which shows one small imaginary frequency along with some small frequency modes. Two radical moieties HCO and C2H5 in the roaming saddle point are weakly bound to each other such that they may have chance to roam around varied configurations prior to abstraction reaction.

### Ro-vibrational energy profile of H2O co-product

In the photodissociation of trans-HCOOH at 193 nm, a partial portion populated to the S2 state led to the HCOO + H products42, in which a small amount of HCOO was identified in the IR spectrum around 2950 cm−1. Most population dissociated rapidly along the S1 repulsive surface to the OH + HCO radical channel. In addition, a small portion flowed through the S1/S0 conical intersection to form the CO + H2O products via the OH-roaming pathways42. The feature of CO roaming product has been recognized to possess cold rotational but hot vibrational states.

As predicted in the roaming mechanism, the H2O co-product is expected to be vibrationally hot, but has not been examined yet. When OH roams around the HCO core followed by an H-atom abstraction at a long distance, the resulting H-OH should be vibrationally excited. Further, given transition lines, Einstein emission coefficients, harmonic wavenumber and anharmonicity constants for calculation of ro-vibrational intensities and energies48,49, the H2O spectrum was simulated in the range of 3300–3800 cm−1, while assumed to have vibrational temperature 8000 K and rotational temperature 300 K, as shown in Fig. 6, which is satisfactorily consistent with the experimental findings, especially in the 0–5 µs delay. The simulated counterpart has included the vibrational modes of symmetric stretching v1 = 5, bending v2 = 15 and asymmetric stretching v3 = 7. Given the emission transition only at (v1,v2,v3) = (0,0,1) → (0,0,0), the H2O spectrum simulated at 300 K is blue-shifted by >300 cm−1 to the 3600–3900 cm−1 region, while compared with the vibrationally excited water. That might be the reason why Su et al. could not identify the H2O production with similar apparatus34.

Note that the H2O product via the TS pathway is expected to lie in low vibrational states. The lack of a significant bimodal ro-vibrational distribution in Fig. 6 might rise from the fact that the low-temperature ro-vibrational component was buried in the high-temperature component. In addition, different from the CO product, the multi-atomic H2O co-product has more complicated spectra which cannot be spectrally resolved under our experimental conditions, and thus discerning ro-vibrational bimodality is more difficult.

In this work, we have characterized the internal energy distributions between the CO and H2O roaming products. To the best of our knowledge, this is the first case to spectrally simulate a multi-atomic co-product in the roaming dynamics. In comparison, for the photodissociation of CH3CHO → CO + CH4, the CO roaming product has been detected by ion imaging and time-resolved FTIR emission spectroscopy1,6, whereas the CH4 roaming co-product was detected only by the latter method and then analyzed by the principle of maximum entropy6, instead of the spectral simulation.

### Temporal dependence of conformational memory

When cis- or trans-HCOOH is initially excited at 193 nm, if the molecular decomposition is faster than the randomization of the torsion coordinate mixing of the conformers, then the conformational memory may be observed in terms of the CO/CO2 ratio which depends on the initial conformer to be excited35. Martınez-Nunez et al.39 ascribed a smaller (CO/CO2)trans/(CO/CO2)cis evaluated of 2 to the difference in funneling geometries of S1/S0 between cis and trans isomers and Ar-matrix effect in the experiment. They expected more than 30% of the H2 + CO2 reactive trajectories in the cis isomer funneled through the S1/S0 conical intersection and then the trajectories rapidly dissociated to the H2 + CO2 products without any chance to redistribute the energy on the ground state. Morokuma and co-workers42 explained conformational memory for a smaller (CO/CO2)cis ratio by finding a H-roaming on the S1 state to form additional H2 + CO2 products.

Given the Einstein emission coefficients of CO and CO2, the integrated area of the high-resolution CO and CO2 spectra (Fig. 1) yields a temporal dependence of CO/CO2 population ratio. The CO area is evaluated by summing all the rotational lines which sit above the CO2 profile. The CO spectra are easily separated from the CO2 profile within a small uncertainty, because the CO2 profile has weak spectral intensities and poor resolution which is made by the complicated multi-atomic spectra. As shown in Fig. 7, the ratio increases from 3 at 0–1 μs delay time to 10 at 5–6 μs delay, which is consistent with the value of 11 obtained by Su et al. using a similar apparatus with a 18 μs temporal resolution34. This fact lends the support to a negligible isomerization conversion between cis- and trans-HCOOH by collisions with Ar, which helps enhance the emission signals of the photofragments (see the details in Method). Further, the energy transfer between translational and vibrational degree of freedom is very inefficient, requiring about 104–107 collisions50. Thus, Ar-collision effect on the ro-vibrational energy redistribution and isomerization probability of excited state formic acid is minimized. This work provides a detailed temporal behavior of the conformational memory, thus characterizing the early time evolution of the CO and CO2 products in two molecular channels.

As mentioned above, (CO/CO2)trans yielded a ratio of 5 in the Ar-matrix absorption experiment35. In their absorption experiments, the detected population of CO and CO2 were substantially quenched to the ground state with a little amount at excited states. Since the production of the CO + H2O molecular channel dominates the CO2 + H2 products decomposed from trans-HCOOH at 193 nm, the (CO/CO2)trans ratio at v ≥ 1 by the emission method is expected to be ≤5. Such an emission result lacks to consider the ground state population. Given the (CO/CO2)trans ratio of 11 at v ≥ 1 reported by emission spectroscopy34, it is apparently in conflict with the ratio of 5 obtained at v ≥ 0 (or v = 0) by absorption spectroscopy. In comparison, a smaller nascent ratio of 3 for the (CO/CO2)trans at v ≥ 1 obtained in this work suggests that the CO/CO2 ratio at v = 0 should be larger than one which is consistent with the absorption results. As the delay time is prolonged to 6 µs, the CO emission intensity gradually increases, whereas the CO2 emission signal is quenched rapidly such that more population of CO2 may relax to the ground state, as shown in Fig. S1 and Fig. 1. That is why the (CO/CO2)trans ratio increases with increasing the delay time, as shown in Fig. 7. Thus, the temporal behavior of conformational memory plays a significant role to reconcile with the disputed data reported previously by both absorption and emission spectroscopy.

## Conclusion

By taking advantage of 1 μs-resolved FTIR emission spectroscopy, we have visualized concomitantly two molecular channels of CO + H2O and CO2 + H2, and further characterized the internal energy disposal in both CO and H2O roaming products, following photodissociation of trans-HCOOH at 193 nm.

The addition of Ar in the chamber does facilitate the collision-induced internal conversion (IC) and intersystem crossing (ISC) processes to enhance substantially the emission intensities of photofragments. With the aid of spectral simulation, the CO rotational and vibrational distributions each contain two Boltzmann profiles; one is ascribed to the roaming route and the other is due to the TS pathway. The CO roaming product is confirmed to possess the states with cold rotation but hot vibration, while the H2O roaming co-product is vibrationally excited.

This work has successfully resolved the puzzle concerning the energy correlation, roaming temperature, and internal state distributions for the CO and H2O products via the roaming route. Further, the obtained temporal behavior of conformational memory may well interpret the disputed results reported with different methods.

## Methods

Time-resolved FTIR emission spectroscopy51,52,53,54,55 with some modification was employed in this work, as illustrated in Fig. S5. A spectrometer (Bruker, IFS 66 v/s) allowing for evacuation of background air and moisture was operated in the step-scan mode, with which the movable mirror of the interferometer can be controlled to move step-by-step.

A 10 ns pulsed ArF excimer laser (GAMlaser, Ex 10) with a repetition rate of 23 Hz was used as a photolysis source emitting at 193 nm. The incident beam was optimized to the energy range of 5–8 mJ/pulse prior to focusing with a spherical lens to reduce its beam size from 8 × 4 to approximately 3 × 3 mm2. About 80% energy was remained in the center of the cubic chamber with a dimension 10 × 10 × 10 cm3. The sample formic acid (Acros, 97%) was used after several freeze-pump-thaw cycles, and a pressure of 1.0 Torr was then injected in the center of a six-way anodized aluminum cube for reaction. Ar (purity > 99.999%) at a pressure of 4.0 Torr added in the chamber may play two roles: first, to prevent the windows from contamination by the photolyzed species, and second, to enhance the rates of collision-induced IC or ISC to increase the emission intensity55.

The emission signal was further enhanced twice by a concave mirror (Thorlabs, CM254-050-P01) placed at the opposite side with respect to the propagating emission signal. The emitting signal was then guided to the FTIR instrument with a pair of 1 in. diameter silver-coated off-axis parabolic mirrors (Edmund, #36–589, and Thorlabs, MPD169-P01), which was flushed with the N2 gas to prevent spectral interference by the CO2 and moisture in the atmosphere.

An appropriate long-pass filter (Spectrogon, LP-4080 nm) was applied to block the unwanted spectral region and to shorten acquisition time. The transmitted signal was monitored with a high-speed InSb detector cooled at 77 K followed by a short-response-time amplifier (Kolmartech, KISDP-1-LJ2/PS). The output was connected to a low-noise preamplifier (SRS, SR560) which further amplified the electric signals by a factor of 104, and then the signals was recorded by a 130 MS/s transient recorder (Spectrum-Instrumentation, M4i-4410-x8). The temporal resolution can be shortened to 7.7 ns. In this work the digitized signals were repeatedly collected for 30 laser shots at a time interval 7.7 ns, and then the following 130 steps were successively moved and the acquired data were summed up. As such, the temporal resolution of obtained spectrum was prolonged to 1 μs. Experiments were repeated under the same conditions; then, the interferograms were co-added over eight times and finally Fourier transformed to give rise to a series of time-resolved spectra.

In comparison with our previous apparatus51,52,53,54,55, a 200 KHz 16-bit transient digitizer was used for signal processing, which restricted the temporal resolution of IR signal to 5 μs. Despite a slower IR response, with respect to the optical response, a detailed spectral variation can be visualized even within the initial 5 μs period.

A Mid-IR emitter inside the FTIR, corresponding to temperature of 1275 K when powered, was used as an external light source to calibrate the system before analyzing the acquired time-resolved spectra. Its spectral feature resembled a blackbody radiator. The spectral responses of beam splitter, optical filters, and detection system were all calibrated.

Why may the addition of Ar in the reaction chamber help enhance the emission intensities of the fragments? An example is shown in Fig. S6 comparing the enhancement of emission signal between 1 and 4 Torr Ar addition in the chamber. Under the experimental conditions, 1 Torr of Ar has a density of 3.5 × 1016 molecules/cm3 and a relative speed of about 5 × 104 cm/s with respect to HCOOH at 300 K. Given the collision cross section of 35 Å2, each excited HCOOH molecule may encounter 6 collisions with Ar within 1 μs when the fragments are detected. That is why the addition of Ar may facilitate the level-to-level coupling rate between S1 and the dramatically increased density of states in S0 or T1 at higher excitation energy. In this manner, the Ar-collision induced internal conversion (IC) or intersystem crossing (ISC) processes may be enhanced to remain a large available energy in the molecular channel; thus, CO may gain larger vibrational excitation energy. Note that the colliders simultaneously quench the ro-vibrational distributions of the resultant products.

In addition to enhancement of the emission intensities, the shape of the emission profile may change to some extent (Fig. S6). It may rise from the fact that the energy transfer between translational and rotational degree of freedom is fast such that the Ar collisions may readily change the spectral distribution. In addition, the relative intensities are changed during evolution in the earlier stage.