Competing quantum tunneling processes of heavy and light particles in isocyanic acid radical anions

Domain: physics
Published: 2025-11-27
Editorial outcome: minor_revision

Abstract
Quantum tunneling is known to be mass dependent. Here we report an unexpected mass effect on tunneling reactions in isocyanic acid radical anions (HNCO·−), which exhibit negative electron affinities. The cis- and trans- isomers of HNCO·− were generated in a solid neon matrix and their interconversion and electron-detachment tunneling kinetics were investigated using infrared absorption spectroscopy. The results reveal that electron tunneling, which involves some degree of nuclear motion of HNCO·− to neutral HNCO, occurs at a slower rate than the cis-to-trans isomerization of HNCO·−, with the latter following a distinct bond angle inversion pathway driven by the heavy carbon atom. This contrasts to the typical dominance of light hydrogen atom tunneling in cis-trans isomerization systems. These findings are rationalized by instanton theory calculations. Our model, which explicitly includes the neon matrix via a QM/MM approach, reveals that the carbon-driven pathway is favored by a lower barrier and shorter tunneling distance.

Introduction
Quantum tunneling is a fundamental phenomenon that allows particles, such as electrons or atoms, to pass through energy barriers that, classically, they would be unable to overcome. It is well established that the probability of a particle tunneling through a barrier decreases exponentially with the square-root of the effective mass of the particle involved in tunneling1, making it most prominent for low-mass particles like electrons and protons. Since its introduction in chemistry, quantum tunneling has been recognized as playing a crucial role in various hydrogen/proton transfer reactions2–8. Heavy-atom tunneling, involving elements like carbon, nitrogen, and oxygen, has also been observed in certain reactions, especially under low-temperature conditions9–16.

Isomerization is one area where tunneling plays a key role, especially in molecular systems undergoing cis-trans transformations17. While more complex mechanisms, such as bond-angle inversion (BAI), have been identified in many thermally or photochemically induced isomerization processes18–21, cis-trans isomerization reactions governed by tunneling are primarily driven by simpler rotation about single bonds involving light hydrogen atoms. This phenomenon has been observed in high-lying conformers of various molecular systems, including carboxylic acids and their derivatives (such as amino acids)22,23, diacids like oxalic acid24, phenol derivatives25, hydroxycarbenes26,27, metaphosphorous acid (HOPO)28, and carboxyl radical (HOCO)29.

In this work, the isocyanic acid radical anion offers a fascinating system for studying mass-dependent tunneling dynamics, owing to its unique electronic structure and the presence of multiple potential tunneling mechanisms. The radical anion exhibits negative electron affinity, enabling it to release an electron and form neutral HNCO through electron tunneling. The cis- and trans- isomers of HNCO·− exhibit distinct stabilities and can interconvert via two possible tunneling pathways: one involves N−H bond rotation through hydrogen tunneling, while the other involves NCO BAI via the tunneling of the heavier carbon atom (Fig. 1). In addition to its fundamental interest, the HNCO·− anion holds practical significance in astrochemistry. Isocyanic acid is a key molecule in understanding the evolution of prebiotic chemistry, including the formation of peptides, amino acids, and proteins30,31.

Results
The HNCO·− anions were produced through high-frequency discharge of neutral HNCO in the gas phase and then trapped in a solid neon matrix (See “Methods” for details). After 30 min of sample deposition at 3 K, two distinct groups of product absorptions, labeled as a and b, were detected. Group a displayed five absorptions at 2883.3, 2718.9, 1637.2, 1198.8 and 1090.8 cm−1, while group b showed six absorptions at 3267.4, 1645.4, 1218.8, 1120.2, 654.8 and 636.1 cm−1. The IR difference spectrum presented in Fig. 2A (comparing the spectrum acquired after the sample kept in the dark for a period of time with that obtained immediately after sample deposition) demonstrates a decline in the absorptions of group a, while those of group b and HNCO neutral (c) increased. Over time, the absorptions of group a almost disappeared, group b absorptions started to decrease, and the absorptions of neutral HNCO continued to increase (Fig. 2B). These observations suggest spontaneous conversions of species a to species b and to neutral HNCO in the dark at 3 K. Notably, as illustrated in Supplementary Fig. 1, species b can convert back to species a upon red light (625 nm) irradiation, while both groups of absorptions disappear under blue light irradiation, accompanied by an increase in neutral HNCO absorptions (Supplementary Fig. 2). These results suggest that species a and b are charged forms of HNCO32–34. Experiments with isotopically labeled H15NCO, HN13CO and DNCO samples were also conducted, and their IR difference spectra in selected regions are presented in Supplementary Figs 4–6. The band positions of both groups and their isotopic counterparts are listed in Table 1.

The strongest absorption at 1637.2 cm−1 for species a and for species b at 1645.4 cm−1 exhibited significant carbon-13 isotopic frequency shifts of −42.1 cm−1, alongside minor shifts for deuterium (−8.0 and −8.9 cm−1) and nitrogen-15 (−2.1 and −2.9 cm−1), suggesting that these absorptions are due to an NCO antisymmetric stretching vibration. The band positions (1637.2 and 1645.4 cm−1) are notably lower than that of the neutral HNCO molecule at 2268.5 cm−1, suggesting that species a and b are HNCO·− anion isomers. This is comparable to the isoelectronic CO2·− anion, which also exhibits a lower OCO antisymmetric stretching vibration mode (1658.3 cm−1, Ne matrix) than that of neutral CO2 (2348.2 cm−1, Ne matrix)33.

Quantum chemistry calculations using the XYGJ-OS functional, an accurate doubly hybrid density functional, with the jul-cc-pVTZ basis set, were performed to validate the experimental assignments (See “Methods” for details). The neutral HNCO molecule exhibits a single conformer, which has a quasi-linear N=C=O structure. In contrast, the HNCO·− anion is predicted to be bent, with two isomeric forms: cis and trans. The trans-isomer is 17.5 kJ mol−1 more stable than the cis-isomer, confirming that the group a absorptions correspond to the less stable cis-isomer, while the group b absorptions are associated with the more stable trans-isomer (Table 1). The calculated vibrational frequencies and isotopic frequency shifts are listed in Table 1, which provides strong support for the experimental assignments. For the cis-isomer, the band at 1637.2 cm−1 aligns well with the theoretically calculated IR frequency of 1689.5 cm−1 for the NCO antisymmetric stretching mode (ν2). Compared to neutral HNCO (2141.0 cm−1), this mode shows a significant red-shift of 631.3 cm−1, consistent with the calculated shift of 612.5 cm−1. The 2883.3 cm−1 absorption observed in cis-isomer is attributed to the N−H stretching mode (ν1)35. The absorption at 1198.8 cm−1 is assigned to the in-plane HNC bending mode (ν3). A similar mode of the isoelectronic HNNO molecule is observed at 1166.9 cm−1 in the Xe matrix36. The absorption at 1090.8 cm−1 is attributed to the in-plane N−H bending mode (ν4). The weak absorption at 2718.9 cm−1 is assigned to a combination mode (ν2 + ν4) based on its band position and isotopic shifts. For the trans-isomer, the N−H stretching mode is observed at 3267.4 cm−1, and the 1218.8 and 1120.2 cm−1 absorptions are assigned to the in-plane HNC bending and in-plane N−H bending modes, respectively, both of which occur at slightly higher frequencies than those observed in the cis-isomer.

The spontaneous cis-to-trans and anion-to-neutral conversions observed in the dark at 3 K suggest that the cis-to-trans isomerization and electron detachment reactions possibly proceed via quantum mechanical tunneling, as the available energy (kBT ≈ 0.25 meV) is several orders of magnitude lower than the calculated barrier for cis-to-trans isomerization (see below) and is insufficient to drive these processes thermally. Kinetics for these reactions were investigated by monitoring the intensity changes of the IR bands corresponding to the three species over time (Fig. 3). The strongest absorption associated with the NCO antisymmetric stretching mode was used for each species. The experimental data were fitted using exponential decay and/or growth equations (See “Methods” for details), with the resulting rate constants summarized in Supplementary Tables 1, 2. The cis-to-trans isomerization reaction has a rate of 8.5 ± 0.4 × 10−5 s−1, which is larger than those of the electron detachment reactions, determined to be 5.0 ± 0.2 × 10−5 and 4.9 ± 0.2 × 10−6 s−1 for cis- and trans-HNCO·−, respectively. To assess whether the observed processes are stimulated by the IR radiation from the spectrometer, additional comparative experiments with IR filter or under distinct conditions were performed. The results are shown in Supplementary Figs 8–10, respectively, which demonstrate that globar IR radiation has negligible influence on both the cis-to-trans HNCO·− isomerization and the cis-HNCO·− → HNCO electron-detachment kinetics, while it promotes the trans-HNCO·− → HNCO detachment process.

To elucidate the tunneling reaction mechanism for the cis-to-trans isomerization of HNCO·− and the electron-detachment of HNCO·− to HNCO, rate constants for the isotopically labeled H15NCO·−, HN13CO·−, and DNCO·− species were measured (Supplementary Figs 4–6), and kinetic isotope effects (KIEs) were determined. The KIE of nitrogen was determined to be 1.1 ± 0.1, indicating minimal nitrogen involvement in the tunneling process. The KIE of H/D was determined to be 9.9 ± 1.0, which is significantly lower than those typically observed for hydrogen-atom tunneling-controlled cis-trans isomerization reactions in cryogenic matrices under similar conditions (for oxalic acid, kH / kD > 103)24,37. In contrast, the KIE of carbon (1.7 ± 0.1) is substantially larger than those observed in typical carbon-atom tunneling reactions38,39. For instance, the KIE of carbon in the ring-opening of cyclopropylcarbinyl radical at −100 °C was determined to be only 1.238. This KIE value suggests significant involvement of the carbon atom in the tunneling process, indicating that the isomerization reaction follows the BAI mechanism rather than the N−H bond rotation mechanism. It’s interesting to note that electron detachment tunneling reactions also exhibit notable kinetic isotope effects for carbon. For instance, the cis-HNCO·− to HNCO reaction shows a KIE of 1.3 ± 0.1, while the trans-HNCO·− to HNCO reaction has a KIE of 1.2 ± 0.1. These values suggest that the electron detachment tunneling processes involve nuclear motion of the carbon atom, which drives the significant structural changes from the bent HNCO·− to neutral HNCO with a quasi-linear N=C=O moiety.

Quantum chemistry calculations predicted that the BAI pathway for cis-to-trans isomerization features a quasi-linear intermediate with a barrier of 21.3 kJ mol−1 (Fig. 4A). For both the cis- and trans-HNCO·− isomers, electron detachment, concurrent with nuclear rearrangement, is exothermic but requires passage through the crossing between the negatively charged and the neutral quasi-diabatic states. Two crossing points were identified on the potential energy surface (Fig. 4A): one for the cis-HNCO·− anion isomer, located ~14.3 kJ mol−1 above cis-HNCO·−, and another for the trans-HNCO·− isomer, positioned ~9.2 kJ mol−1 above trans-HNCO·−. Notably, both crossing points lie below the energy of the transition state (TS) in the BAI pathway. The observed electron detachment rates, which are lower than the cis-to-trans isomerization rates, suggest that curve crossing occurs with low probability—possibly due to matrix effects localizing the electron. However, the complexity of the matrix environment makes it challenging to compute this probability.

To understand why the conventional N−H bond rotation isomerization mechanism was not observed, we extensively performed TS searches for both in-plane and out-of-plane N−H rotation mechanisms40. No TSs were found for either mechanism. The in-plane N−H rotation has a second order stationary point rather than a TS. Meanwhile, we show through a 2D scan (Supplementary Fig. 13) that out-of-plane N−H rotation is energetically unfavorable compared to BAI, which might be rationalized as follows. Orbital analysis reveals that in the planar cis- and trans-HNCO·− isomers, the nitrogen atom adopts sp2 hybridization. If the isomerization were to occur via N−H bond rotation, the hybridization would need to transition to sp3 hybridization at the pseudo-TS, where the hydrogen atom is oriented perpendicular to the NCO plane. This change in hybridization necessitates the breaking of the N−C π bond, which is energetically unfavorable. In contrast, along the BAI pathway, no change in bonding occurs. Furthermore, the unpaired electron of the HNCO·− radical anion occupies an NCO anti-bonding π* orbital, which weakens both the N−C and C−O bonds compared to those in neutral HNCO, making this pathway energetically favorable. The combination of these two factors makes the isomerization mechanism via N−H bond rotation in HNCO·− quite unusual.

Nevertheless, a reaction with an energy barrier of 21.3 kJ mol−1 would not occur classically at cryogenic temperatures without the assistance of tunneling. To explore tunneling in HNCO·−, we performed ring-polymer instanton theory41–43 calculations (see Supplementary Materials for the full computational details and discussions). Instanton reveals significant carbon tunneling on the BAI pathway (Fig. 4B). Specifically, carbon contributes about 64.7% of the squared mass-weighted tunneling path length (defined as ∑i,j mj(xij − xi+1,j)2, where i and j are indices for the instanton beads and atoms, respectively), while hydrogen, nitrogen, and oxygen contribute relatively small percentages of 11.5%, 8.5% and 15.3%, respectively. Interestingly, due to corner-cutting, instantons for the N−H bond rotation pathway also exist (Fig. 4B), despite that the classical TS does not exist. Although the barrier of the BAI pathway via carbon tunneling is less than half of that of the N−H bond rotation pathway via hydrogen tunneling, carbon’s mass is 12 times larger than that of hydrogen. According to the Jeffreys-Wentzel-Kramers-Brillouin (JWKB) semiclassical picture of tunneling, the tunneling probability depends not only on the barrier height, but also on the effective mass and tunneling distance of the atoms involved1,9. Carbon tunnels only 0.54 Å in the BAI process, which is considerably shorter than the hydrogen tunneling distance of 1.43 Å in the N−H bond rotation process. As a result, as shown in Fig. 4B, the squared mass-weighted tunneling path lengths (∑i,j mj(xij − xi+1,j)2) for both pathways are similar (at ~2 amu1/2 Å), with the shorter tunneling distance of carbon compensating for its greater mass.

The calculated reaction rate constants using the ring-polymer instanton theory and the classical transition state theory, for temperatures ranging from 30 to 100 K, are compared in Supplementary Fig. 14. The instanton rate constants for the isomerization reaction via carbon atom tunneling along the NCO BAI pathway remain near-temperature-independent below 50 K (Supplementary Tables 7, 8). These rates are many orders of magnitude higher than those calculated using classical transition state theory, indicating that tunneling dominates the reaction at low temperatures. Instanton theory predicts that the tunneling rate constant of BAI is nearly three orders of magnitude faster than that of the N−H bond rotation, suggesting that BAI is the more favorable pathway. Furthermore, instanton theory estimates a very large H/D KIE (~105) for the N−H bond rotation pathway (Supplementary Tables 7–9), which contrasts sharply with the experimentally observed value of only 9.9 ± 1.0. In contrast, the KIEs predicted by instanton theory for the BAI mechanism align semi-quantitatively with the experimental values (Table 2).

Despite the good semi-quantitative agreement between the theoretical and experimental KIEs, the instanton rates calculated in the gas phase at the DFT level exceed the observed rates by six orders of magnitude. Two primary factors may account for this discrepancy: the accuracy of the electronic structure and the neglect of the solid neon matrix environment. To understand their impact, firstly, we performed multireference calculations. As detailed in Supplementary Materials, while the cis- and trans-HNCO·− isomers do not exhibit multireference characteristics, strong multireference effects appear along the isomerization pathway. Supplementary Fig. 12 show that multireference methods predict higher barriers than both DFT and CCSD(T). After applying a correction at the MRCI level using the dual-level approach44, the instanton rates decrease by over three orders of magnitude, bringing them much closer to the experimental results (Table 2). Secondly, to quantitatively assess the influence of the matrix environment on tunneling, we performed instanton calculations that explicitly model the HNCO·− anion embedded within a neon lattice using a QM/MM setup45 (see Supplementary Materials for full details). The results show that the presence of the neon matrix dramatically suppresses the tunneling rate to 2.2 × 10−3 s−1, a value significantly closer to the experimental observation. Analysis shows that this substantial rate reduction is caused by the matrix environment altering the instanton pathway, elongating the tunneling path meanwhile increasing the potential energy along the path (Fig. 4C). This finding provides direct theoretical evidence for the key role of the neon matrix and is consistent with the established theory of dissipative quantum tunneling, which predicts that the environment can suppress tunneling rates46,47. The small remaining discrepancy can be attributed to a combination of the aforementioned multi-reference character, the idealizations within the matrix model, and perhaps the approximations in instanton theory.

Methods
Experimental details
Matrix-isolation spectroscopy. The isocyanic acid anion (HNCO·−) was prepared by high-frequency discharge of the HNCO/Ne mixtures. The HNCO/Ne gas stream was subjected to discharge from a Tesla coil. The tip of the Tesla coil was connected to a copper cap on one end of a quartz tube extending into the vacuum chamber. The other end of the quartz tube was connected to a copper tube with ground potential. Discharge takes place between the cap and the copper tube. The discharged products were deposited onto a cryogenic gold-plated copper block, which was maintained at 3 K with a closed-cycle helium refrigerator. After 30 min of sample deposition at 3 K, IR absorption spectra in the mid-infrared region (4000−450 cm−1) were recorded with a Bruker Vertex 70V spectrometer with a 0.5 cm−1 resolution using a liquid nitrogen cooled broad band HgCdTe (MCT) detector. Bare mirror backgrounds, recorded prior to sample deposition, were used as references for processing the sample spectra. The spectra were subjected to baseline corrections to compensate for infrared light scattering and interference patterns. For selected samples, photo-excitation (625 nm) was performed through a quartz window mounted on the assembly. The HNCO/Ne mixtures were prepared in a stainless-steel vacuum line using a standard manometric technique.

Sample preparation. HNCO was prepared by heating a mixture of stearic acid (0.57 g, 2 mmol) and sodium cyanate (0.13 g, 2 mmol) at 90 °C in a glass vessel (25 mL), which was connected to a dynamic vacuum line (0.1 Pa) through a poly (tetrafluoroethylene) Young-valve48. All of the volatile products were condensed in a liquid nitrogen trap and then purified by fractional distillation through three successive cold U-traps at −80, −135, and −196 °C. Pure isocyanic acid was retained in the middle trap, and its quality was checked with gas-phase IR spectroscopy (Bruker, Tensor 27). Isotopically-labeled HN13CO and H15NCO were prepared from 13C and 15N-labelled potassium cyanate, which were synthesized as a precipitate by heating 13C and 15N-labeled urea with potassium phenoxide in 4-methyl-2-pentanol at 135 °C for 2 h, followed by filtration, washing with cold ethanol, and drying49. DNCO was prepared by allowing a saturated solution of potassium cyanate in D2O to drop onto a saturated aqueous solution of phosphoric acid (85% D3PO4 in D2O) under vacuum50.

Kinetic measurement. For the kinetic measurements, the matrix was carefully shielded from visible light and maintained at the lowest achievable temperature of the cryostat (~3 K). IR spectra were recorded at 30-min intervals over a total period of 90 h. The integrated areas of the absorption bands corresponding to the NCO antisymmetric stretching modes were extracted from the corresponding IR difference spectra (ΔA) and used for the kinetic analysis. To ensure clarity, the integrated band intensities were normalized to the integral of the corresponding peaks.

The experimental results show that the cis-HNCO·− anion (a) can spontaneously convert to the more stable trans-HNCO·− anion isomer (b) via nuclear tunneling, as described in reaction (1). Additionally, both anion isomers can undergo electron detachment to form the neutral HNCO molecule (c), as represented in reactions (2) and (3).

cis-HNCO·− → trans-HNCO·− (1)

trans-HNCO·− → HNCO + e− (2)

cis-HNCO·− → HNCO + e− (3)

The entire process can be described by three rate constants: k1, k2, and k3 corresponding to reactions (1) to (3), respectively. Since each species participates in two independent reactions, the experimentally measured kinetic curves for each species were fitted using double exponential decay/growth equations, as shown in Eqs. (4–6):

y = A0 exp(−k1x) − B0 exp(−k2x) + y0 (4)

y = −A0 [exp(−k1x) − exp(−k3x)] + y0 (5)

y = B0 exp(−k2x) + A0 exp(−k3x) + y0 (6)

We first fitted the experimental data for trans-HNCO·− (b) with the double exponential decay equation (Eq. 4) to determine the rate constants k1 and k2. Using k1, the rate constant k3 for the conversion from cis-HNCO·− (a) to HNCO (c) was obtained by fitting the experimental kinetic decay curve of cis-HNCO·− with Eq. (5). To verify the accuracy of k2 and k3, the coefficients of determination (R2) were obtained by fitting the kinetic growth curve of HNCO (c) using Eq. (6), where k2 and k3 had already been determined from Eqs. (4) and (5), respectively. All fitted curves yielded coefficients of determination (R2 ≥ 0.999), confirming the reliability of the kinetic rate constants.

Kinetic measurements for the isotopologues HNCO·−, H15NCO·− and HN13CO·− were conducted in duplicate. The rate constants for each species from the different experiments are listed in Supplementary Tables 1, 2, with the average values used to calculate the kinetic isotope effect (KIE) values.

Computation details
Electronic structure calculations. All quantum chemistry calculations were performed with the Gaussian09 program51, locally modified to implement the XYGJ-OS doubly hybrid density functional52, and the Molpro 2019 package53. Unless specified otherwise, geometry optimizations were carried out using the XYGJ-OS functional with the jul-cc-pVTZ basis set54, as this functional showed the best agreement with experimental results among several tested double-hybrids. Harmonic and anharmonic vibrational frequencies were calculated at this level.

Instanton rate calculations. Quantum tunneling rates were computed using ring-polymer instanton theory41–43, which provides a practical path-integral formulation of semiclassical instanton theory55. Instanton pathways, which represent the optimal tunneling paths, are first-order saddle points on the ring-polymer potential energy surface. This theory inherently accounts for zero-point energy and corner-cutting effects.

Ab initio instanton calculations were performed using a Python program developed based on the instanton program of Prof. J. O. Richardson's. The instanton rates were converged with respect to the number of beads, and all the instanton pathways were optimized to a convergence criterion of 2.6 kJ mol−1 Å−1 on the total gradient norm. For gas-phase calculations, a dual-level approach44 was employed: the pathway was optimized at the XYGJ-OS level, and the action was subsequently refined with single-point energy corrections at the CCSD(T) and MRCI levels. The temperature-independent plateau rates below 50 K were used for comparison with experimental results.

Modeling of the neon matrix environment. To quantitatively assess the influence of the neon matrix, a quantum mechanics/molecular mechanics (QM/MM) approach was adapted for instanton calculations.

QM/MM Crystal Model Construction: The model was constructed from 88 Ne atoms surrounding the HNCO·− anion within a face-centered cubic (fcc) lattice. This set of atoms was partitioned into a flexible inner shell of 22 Ne atoms and a fixed outer shell of 66 Ne atoms to simulate the bulk lattice while allowing for local relaxation.

QM/MM Energy Decomposition Scheme: The total potential energy of the system was calculated as a sum of two components, Etotal = EQM+Pauli + EvdW. The primary term, EQM+Pauli, was calculated with Gaussian09 and includes the full quantum mechanical energy of the HNCO·− anion (XYGJ-OS/AVTZ) and its electrostatic and Pauli repulsion interactions with the 88 Ne atoms, which were represented by repulsive effective core potentials (ECPs). The ECP parameters were benchmarked against a small full-quantum cluster model to ensure accuracy. The missing long-range van der Waals dispersion interactions, EvdW, were computed separately using the LAMMPS package56 with a classical Lennard-Jones potential.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The central thrust of the paper by Tang et al, is to establish by a combination of experimental and theoretical methods the\nmechanism of the cis to trans isomerization of the HNCO- anion. They note that there are two central paths leading from cis\nto trans, one may be described as the rotation of the H atom about the NC bond, the second would be inversion about the\nNCO bond, as shown in their Fig. 1. They also studied the electron detachment from both trans and cis isomers. Their\ncentral conclusions are:\n1. Electron detachment occurs via tunneling but the rate is smaller than the nuclear isomerization rate.\n2. The nuclear isomerization rate is a heavy atom process, inversion about the NCO bond rather the H atom rotation, which\nintuitively due to the light mass of the H atom would be expected to be the favorable route.\n3. The theoretical kinetic isotope effect agree reasonably well with the measured one, “proving” the dominance of the heavy\natom tunneling process.\nThese conclusions are interesting and would justify publication in Nature Communications, with one perhaps heavy proviso.\nAs the authors themselves honestly note, the magnitude of the theoretical rates are orders of magnitude larger that the\nmeasured experimental ones. They consider two possibilities one is the difficulty in computing the force field, the other,\nwhich to my mind is the more important one has to do with the fact that the experiment is in a matrix while the theoretical\ncomputations are for the isolated molecule . It is well understood that “friction” will exponentially reduce rates. But it is also\nwell understood that it can significantly change reaction pathways. It is difficult to recommend publication ss long as this\npoint is not resolved.\nTo my mind, the authors have two choices. One is to undertake the instanton computation in the presence of the Ne matrix.\nFor this purpose, it is not necessary to use highly accurate ab-initio potential for the Ne matrix, a Lennard Jones potential for\nthe Ne atoms should suffice, but it would establish the effect of the matrix on the tunneling mechanism. The other, is to\npublish the experimental findings in a different, perhaps less high profile journal such as the Journal of Chemical Physics\nand then later on publish the theoretical results based on a computation in the presence of the Ne matrix.", "reviewer_2": "This manuscript reports a fascinating discovery of competitive quantum mechanical tunneling (QMT) reactions in isocyanic\nacid radical anions (HNCO•‒). The cis and trans isomers of HNCO•‒ were generated in a neon matrix at 3 K. Subsequent\nspontaneous transformations were observed: cis-HNCO•‒ isomerizes to the more stable trans-HNCO•‒, whereas both cis\nand trans HNCO•‒ undergo electron detachment to form quasilinear HNCO. The identification of the species were clearly\nestablished by IR spectroscopy, supported by data from isotopically labeled H15NCO, HN13CO, and DNCO, as well as by\nquantum chemical calculations. Kinetic measurements established that QMT electron detachment occurs at a slower rate\nthan the QMT isomerization reaction. Based on kinetic isotope effects (KIEs) and computations, the isomerization reaction\nwas established to occur via an unconventional bond-angle inversion that consists mainly of the movement of the carbon\natom, rather than a putative NH bond rotation. This demonstrates an extraordinary example of competitive QMT reactivity,\nwhere electron QMT proceeds more slowly than a heavy-atom QMT reaction. Quantum chemical calculations combined with\ninstanton theory provided support for this remarkable discovery. The overall experimental and theoretical approaches are of\nexcellent quality and well crafted. The conclusions and claims are well supported and clearly written. The work is of high\nscientific quality and of great significance to the field. Therefore, I support the publication of these pioneering results in\nNature Communications.\nA few minor issues should be addressed before publication:\n1. In line 38, reference 25 does not correspond to H-atom tunneling in phenol derivatives, nor does reference 27\ncorresponds to H-atom tunneling in hydroxycarbenes.\n2. The sentence in line 58 feels off - “adapted” does not seem like the appropriate verb in this context and should be\nreconsidered.\n3. It is indicated that the electron detachment reaction proceeds via QMT, as there is no available energy to drive the process\nthermally. The computations presented (Figure 4) show that electron detachment requires a nonadiabatic crossing from the\nnegatively charged diabatic state to the neutral diabatic state of HNCO: 14.3 kJ/mol from cis-HNCO•⁻ and 9.2 kJ/mol from\ntrans-HNCO•⁻. This indicates that the transformation is not strictly a simple electron detachment process, but involves some\ndegree of molecular rearrangement, which is in agreement with the KIEs observed. I think point should be clarified\nthroughout the text to avoid the misleading impression that the electron detachment via QMT is a process involving only the\nejection of an electron without molecular rearrangement.\n4. During the kinetic measurements, the samples were exposed to the full IR light of the FTIR spectrometer. It is well known\nthat such IR radiation can, in some cases, promote conformational isomerization of matrix-isolated species, potentially\noccurring alongside QMT processes. See, for instance: “Effects of Entangled IR Radiation and Tunneling on the\nConformational Interconversion of 2-Cyanophenol” (DOI: 10.1021/acs.jpca.9b01382) and “Conformational Switching in\nPyruvic Acid Isolated in Ar and N₂ Matrixes: Spectroscopic Analysis, Anharmonic Simulation, and Tunneling” (DOI:\n10.1021/jp509578c). Therefore, it is important to assess whether the processes reported are stimulated by IR spectrometer\nlight, as in this case the kinetic data would not strictly reflect QMT processes.", "reviewer_3": "The paper investigates tunneling reactions in isocyanic acid radical anions in the solid neon matrix experimentaly.\nSpecifically, interconversion between its cis and trans isomers is observed to proceed faster than the electron detachment\nreaction and via the bond-angle inversion mechanism rather than NH bond rotation. The paper is clearly written, it\nshowcases interesting dynamics on a simple system that could serve as a future benchmark for dynamical theories. The\nexperiment is backed up by instanton rate calculations that give support to the observed kinetic isotope effect, although the\nabsolute numbers are in a clear disagreement (as rationalized in the paper). In my opinion, paper is suitable for publication in Nat. Commun. after the\ncomments, listed below, are addressed.\n1) Line 48 and 49: reformulate without repetitions of \"prebiotic chemistry\"\n2) Line 58: explain the phrase \"adapted in the dark\" for broad readership\n3) Line 78 states that \"_these_\" experimental observations support assignment of \"different vibrational modes\". Which\nexperimental observations do you refer to? The text above was about asymmetric NCO stretch. Please, reformulate or\nexplain.\n4) Line 110: \"To elucidate\" which reaction mechanism?\n5) Line 116: please, cite \"typical\" KIE observations of cis-trans isomerization.\n6) Line 157: what is square mass-weighted tunneling path? Is it sqrt(m)x Euclidean distance in Cartesian coordinates?\n7) Line 140-152: NH bond rotation could be in-plane motion or out-of-plane motion. It seems only out-of-plane motion was\nconsidered here? E.g. in vinyl radical both paths exist and the out-of-plane bond-rotation path is much higher in energy [J.\nChem. Phys. 152, 204311 (2020)]. Instanton theory can easily be used to locate both paths if they exist.\n8) Instanton rate calculations have not been described in sufficient detail. Please, provide details of which partition functions\nhave been used and how they have been estimated, as well as the details of convergence parameters and instanton path\ncharacteristics (length, potential barrier, etc).", "reviewer_4": "The manuscript of J. Tang et al. documents and interprets carefully conducted spectroscopic and computational studies of a\ntetratomic radical anion when held in a cryogenic Neon matrix. Under such conditions there are slow spectroscopic changes\nwhich allow for a kinetic analysis and, in conjunction with quantum chemical modelling, convincingly manifest tunneling\ndynamics of competing isomerization and detachment processes: heavy atom versus H-atom tunneling, and electron\ndetachment. The noteworthy finding of these studies is, that the Carbon atom tunneling across a shallow barrier exceeds that of the light Hydrogen atom.\nThese findings are significant and go beyond those of current studies. It is of conceptual value to know about a less slow\nheavy atom tunneling to surpass a much slower light atom tunneling, and to surpass metastable electron detachment alike.\nAll of the found conclusions are fully supported by the documented results, and there is no further evidence needed. Some\nclaims are stated in a too strong manner that needs to tone down (see below). Publication is not hampered by these\ndeficiencies, once they are helped.\nThe documented work has been conducted in a sound manner and sets standards in its field. By virtue of the submitted\ndocumentation, it is possible to reproduce all findings.\nDeficiencies that need to be helped upon revision are as follows:\n(In general)\nStrength’ of claims is occasionally too strong. Some part of the experimental description and interpretation seems to imply\nknowledge of computational results without stating it and ahead of their presentation in the manuscript. In cases where this\nis unavoidable cross reference is necessary, e.g. via a simple “see below” or an “as to be discussed in the following”\nstatement. Find explicit example in the following.\n(in detail)\nP3, line 66: “The results imply…” -> “These results suggest…”, and some reference on charge detection methodology in\nmatrix isolation spectroscopy\nP3, line 74: The NCO antisymmetric stretching vibration needs additional justification. Maybe by reference to the\ncomputations.\nP3, line 75: “than that” -> “than those”\nP3, line 83: The XYGJ-OS method is NOT known to each future reader of this paper. Need to introduce it by a few words (…\ndouble hybrid density functional …)\nP4, line 91: Similar mode -> A similar mode\nP4, line 100: reactions proceed -> reactions possibly proceed\nP4, line 101, “…, as the available energy is insufficient to drive these processes thermally”: This is an assumption, unless\nthe outcome of the quantum chemical knowledge is invoked – which is not discussed yet at this stage of the manuscript.\nNeed to rephrase / clarify where this assumption comes from.\nP4/5, lines 107-126: alle of the k and KIE values need to indicate uncertainty limits/error bars – which are absent as of now.\nP5, lines 130/131: The authors mix up the concepts of diabatic and adiabatic states by stating “… requires nonadiabatic\ncrossing from the … diabatic state to the … diabatic state”. The authors wish to look up the concepts of adiabatic and\ndiabatic states once more and correct their statement accordingly.\nP5, line 137: likely -> possibly\nP5, line 141: “…searches for this pathway.” Requires some cross reference to that instance in the supplement where the\napplied search method is documented.\nDirectly afterwards: “Surprisingly, no TSs were found for N-H bond rotation” : (1) Drop surprisingly, and (2) add “…which\nmight be rationalized as follows:…”\nP6, line 151: “… the isomerization mechanism …” -> “… the isomerization mechanism via N-H bond rotation …\"\nP8, line 208: “… for carbon’s mass disadvantage …” -> “… for carbon’s higher mass …\"\nP16, caption to figure 4, line 356: “percentage contributions” How evaluated? Need to indicate!\nSupplement P4, 4th line from the bottom: “… are account …” -> “… are accounted …\"\nSupplement P14, heading: “Theoretical Plots” -> “Plots of Computational Results\"\nIn summary the present contribution is significant and it documents results of value. The novelty of its findings is such that it\nwarrants publication in the chosen journal, once the above stated deficiencies are helped for. The published manuscript will\nsurely attract a high attention by a broad audience of scientists which share an interest in molecular phenomena."}, "author_response": "Responses to the review comments\nWe would like to express our sincere gratitude to the reviewers for their time and effort\nin thoroughly reviewing and evaluating our manuscript. We deeply appreciate their\npositive feedback, as well as the constructive comments and suggestions, which have\ngreatly contributed to improving the quality of our work. Below, we provide our point-\nby-point responses to the review comments. All changes made to the manuscript have\nbeen highlighted in yellow in the revised version.\nReviewer 1: The central thrust of the paper by Tang et al, is to establish by a\ncombination of experimental and theoretical methods the mechanism of the cis to trans\nisomerization of the HNCO- anion. They note that there are two central paths leading\nfrom cis to trans, one may be described as the rotation of the H atom about the NC bond,\nthe second would be inversion about the NCO bond, as shown in their Fig. 1. They also\nstudied the electron detachment from both trans and cis isomers. Their central\nconclusions are:\n1. Electron detachment occurs via tunneling but the rate is smaller than the nuclear\nisomerization rate.\n2. The nuclear isomerization rate is a heavy atom process, inversion about the NCO\nbond rather the H atom rotation, which intuitively due to the light mass of the H atom\nwould be expected to be the favorable route.\n3. The theoretical kinetic isotope effect agree reasonably well with the measured one,\n“proving” the dominance of the heavy atom tunneling process.\nThese conclusions are interesting and would justify publication in Nature\nCommunications, with one perhaps heavy proviso. As the authors themselves honestly\nnote, the magnitude of the theoretical rates are orders of magnitude larger that the\nmeasured experimental ones. They consider two possibilities one is the difficulty in\ncomputing the force field, the other, which to my mind is the more important one has to\ndo with the fact that the experiment is in a matrix while the theoretical computations\nare for the isolated molecule. It is well understood that “friction” will exponentially\nreduce rates. But it is also well understood that it can significantly change reaction\npathways. It is difficult to recommend publication ss long as this point is not resolved.\nTo my mind, the authors have two choices. One is to undertake the instanton\ncomputation in the presence of the Ne matrix. For this purpose, it is not necessary to\nuse highly accurate ab-initio potential for the Ne matrix, a Lennard Jones potential for\nthe Ne atoms should suffice, but it would establish the effect of the matrix on the\ntunneling mechanism. The other, is to publish the experimental findings in a different,\nperhaps less high profile journal such as the Journal of Chemical Physics and then\nlater on publish the theoretical results based on a computation in the presence of the\nNe matrix.\nAuthor response: We are extremely grateful to the reviewer for the constructive\nsuggestion to perform instanton calculations in the presence of the neon matrix, treating\nthe interactions of the Ne atoms with a Lennard-Jones (LJ) potential. Following this\nvaluable suggestion, we have implemented a QM/MM approach to model the system\nand recalculated the instanton tunneling pathway for the HNCO•‒ anion embedded in a\nneon matrix.\nOur QM/MM model is designed to address two primary types of intermolecular\ninteractions separately. At the QM level, the HNCO•‒ anion is modeled using DFT at\nthe XYGJ-OS/AVTZ level. To mitigate the well-known “electron spill-out” issue,\nwhere the anion's diffuse excess electron unphysically delocalizes into the MM region\nwhen large basis sets are used, we model the interaction between HNCO•‒ and Ne by\ntreating the Ne atoms as pure repulsive effective core potentials (ECPs) within the DFT\ncalculations. This approach, inspired by the methodology in Ref. [J. Chem. Theory\nComput. 2020, 16, 3, 1373–1381], provides the essential Pauli repulsion to confine the\nwavefunction (i.e., electron) to the HNCO molecule during the isomerization reaction,\neven when using the large AVTZ basis set. At the MM level, long-range van der Waals\n(dispersion) interactions for both Ne-Ne and HNCO•‒-Ne pairs are described using\nclassical Lennard-Jones (LJ) potentials, as suggested by the reviewer.\nThe new calculations reveal a significant matrix effect on the tunneling process.\nThe presence of the neon matrix dramatically suppresses the tunneling rate to 2.2×10−3\ns−1, which significantly narrows the gap between the computed and experimental rates.\nOur analysis shows that this substantial rate reduction arises from the matrix\nenvironment altering the instanton pathway, elongating the tunneling path and\nsimultaneously increasing the potential energy along the path. This finding provides\ndirect theoretical evidence for the pivotal role of the neon matrix and is consistent with\nthe established theory of dissipative quantum tunneling, which predicts that the\nenvironment can suppress tunneling rates (Phys. Rev. A 1990, 41, 5366–5382; Phys.\nRev. E 2007, 75, 041103). The small remaining discrepancy can be attributed to a\ncombination of the multi-reference character, idealizations in the matrix model, and\npotential approximations in instanton theory.\nWe believe that this major addition, prompted by the reviewer’s suggestion,\nprovides a quantitative and physically sound understanding of how the matrix\nenvironment governs ion tunneling. Additionally, it introduces a methodology that\ncould be broadly applied to simulations of ions in matrices in the future. In the revised\nmanuscript, we have:\n1) Incorporated the above discussions and new references into the main text (Page 8,\nlast yellow highlighted paragraph);\n2) Added new plots to Figure 4, showing the optimized instanton in the neon matrix;\n3) Updated Table 2 with the results from the matrix calculations;\n4) Included full computational details of the QM/MM instanton calculations in the\nSupplementary Materials Computational Details section.\n----------------------------------------End of responses #1---------------------------------------\nReviewer 2: This manuscript reports a fascinating discovery of competitive quantum\nmechanical tunneling (QMT) reactions in isocyanic acid radical anions (HNCO•‒). The\ncis and trans isomers of HNCO•‒ were generated in a neon matrix at 3 K. Subsequent\nspontaneous transformations were observed: cis-HNCO•‒ isomerizes to the more stable\ntrans-HNCO•‒, whereas both cis and trans HNCO•‒ undergo electron detachment to\nform quasilinear HNCO. The identification of the species were clearly established by\nIR spectroscopy, supported by data from isotopically labeled H15NCO, HN13CO, and\nDNCO, as well as by quantum chemical calculations. Kinetic measurements\nestablished that QMT electron detachment occurs at a slower rate than the QMT\nisomerization reaction. Based on kinetic isotope effects (KIEs) and computations, the\nisomerization reaction was established to occur via an unconventional bond-angle\ninversion that consists mainly of the movement of the carbon atom, rather than a\nputative NH bond rotation. This demonstrates an extraordinary example of competitive\nQMT reactivity, where electron QMT proceeds more slowly than a heavy-atom QMT\nreaction. Quantum chemical calculations combined with instanton theory provided\nsupport for this remarkable discovery. The overall experimental and theoretical\napproaches are of excellent quality and well crafted. The conclusions and claims are\nwell supported and clearly written. The work is of high scientific quality and of great\nsignificance to the field. Therefore, I support the publication of these pioneering results\nin Nature Communications. A few minor issues should be addressed before publication.\nComment 1: In line 38, reference 25 does not correspond to H-atom tunneling in\nphenol derivatives, nor does reference 27 corresponds to H-atom tunneling in\nhydroxycarbenes.\nAuthor response: We sincerely thank the reviewer for pointing out the confusion\nregarding references 25 and 27. These references have been updated as follows:\nReference 25 is now: \"Roque, J. P. L. et al. Switching on H-tunneling through\nconformational control. J. Am. Chem. Soc. 143, 8266-8271 (2021).\"\nReference 27 is now: \"Quanz, H., Bernhardt, B., Erb, F. R., Bartlett, M. A., Allen, W.\nD., & Schreiner, P. R. Identification and reactivity of s-cis, s-cis-dihydroxycarbene, a\nnew [CH O ] intermediate. J. Am. Chem. Soc. 142, 19457-19461 (2020).\"\n2 2\nComment 2: The sentence in line 58 feels off - “adapted” does not seem like the\nappropriate verb in this context and should be reconsidered.\nAuthor response: The word \"adapted\" has been replaced with \"kept\" to better align\nwith the context.\nComment 3: It is indicated that the electron detachment reaction proceeds via QMT,\nas there is no available energy to drive the process thermally. The computations\npresented (Figure 4) show that electron detachment requires a nonadiabatic crossing\nfrom the negatively charged diabatic state to the neutral diabatic state of HNCO: 14.3\nkJ/mol from cis-HNCO•− and 9.2 kJ/mol from trans- HNCO•−. This indicates that the\ntransformation is not strictly a simple electron detachment process, but involves some\ndegree of molecular rearrangement, which is in agreement with the KIEs observed. I\nthink point should be clarified throughout the text to avoid the misleading impression\nthat the electron detachment via QMT is a process involving only the\nejection of an electron without molecular rearrangement.\nAuthor response: We agree with the reviewer that the electron detachment process\ninvolves some degree of nuclear motion. To clarify this point, we have revised the text\nas follows:\n1. Abstract: The results reveal that electron tunneling, which involves some\ndegree of nuclear motion of HNCO•− to neutral HNCO, occurs at a slower rate\nthan the cis-to-trans isomerization of HNCO•−, with the latter following a\ndistinct bond angle inversion pathway driven by the heavy carbon atom.\n2. Page 6, first paragraph: These values suggest that the electron detachment\ntunneling processes involves nuclear motion of the carbon atom, which drives\nthe significant structural changes from the bent HNCO•− to neutral HNCO with\na quasi-linear N=C=O moiety.\n3. Page 6, second paragraph: For both the cis- and trans-HNCO•− isomers,\nelectron detachment, concurrent with nuclear rearrangement, is exothermic.\n4. Conclusion: Contrary to conventional expectations, electron tunneling\ninvolving some degree of nuclear motion proceeds more slowly than pure\nnuclear tunneling.\nComment 4: During the kinetic measurements, the samples were exposed to the full IR\nlight of the FTIR spectrometer. It is well known that such IR radiation can, in some\ncases, promote conformational isomerization of matrix-isolated species, potentially\noccurring alongside QMT processes. See, for instance: “Effects of Entangled IR\nRadiation and Tunneling on the Conformational Interconversion of 2-Cyanophenol”\n(DOI: 10.1021/acs.jpca.9b01382) and “Conformational Switching in Pyruvic Acid\nIsolated in Ar and N₂ Matrixes: Spectroscopic Analysis, Anharmonic Simulation,\nand Tunneling” (DOI: 10.1021/jp509578c). Therefore, it is important to assess whether the\nprocesses reported are stimulated by IR spectrometer light, as in this case the kinetic\ndata would not strictly reflect QMT processes.\nAuthor response: We thank the reviewer for raising this important point regarding the\npotential influence of the FTIR spectrometer's IR radiation on conformational\nisomerization kinetics (cis-to-trans and trans-to-cis). To assess the effect of the globar\nIR source, we conducted additional parallel experiments, and the results are shown in\nFigure S8. In the first experiment, following the references provided by the reviewer,\nwe installed a filter blocking IR radiation above 1818 cm⁻¹ (~21 kJ/mol) and subjected\nthe sample to continuous filtered irradiation (Figures S8 and S9). The observed cis-to-\ntrans decay rate (k = 7.5 × 10−5 s−1, Figure S8, orange line) is very close to the rate\nmeasured under unfiltered exposure (8.9 × 10−5 s⁻¹, Figure S8, blue line). In another\nexperiment, the sample was kept in the dark for 15.5 hours and exposed to the globar\nsource only during spectral acquisition (~0.5 hours total). Exponential fitting yielded a\nsimilar rate constant of 8.1×10−5 s−1 (Figure S8, purple line). The very small rate\ndifferences among these experiments demonstrate that the spectrometer’s IR radiation\nhas negligible influence on the cis-to-trans isomerization kinetics.\nWe also investigated the impact of IR irradiation on the electron detachment process\nof HNCO•−. In the comparative experiment with a filter blocking IR radiation above\n1818 cm⁻¹, the detachment rates were measured as k = 8.5×10−7 s−1 (trans-HNCO•− →\n3\nradiation resulted in a 6-fold decrease in the trans-HNCO•− detachment rate (k ), while\n2\nthe cis-HNCO•− → HNCO rate (k ) remained virtually unchanged.\nMaterials (Figures S8-S10) and are discussed in the main text: “To assess whether the\nobserved processes are stimulated by the IR radiation from the spectrometer, additional\ncomparative experiments with IR filter or under distinct conditions are performed. The\nresults are shown in Figures S8-S10, respectively, which demonstrate that globar IR\nradiation has negligible influence on both the cis-to-trans HNCO•− isomerization and\nthe cis-HNCO•− → HNCO electron-detachment kinetics, while it promotes the trans-\nHNCO•− → HNCO detachment process.” (Page 5, first yellow highlighted paragraph).\n----------------------------------------End of responses #2---------------------------------------\nReviewer 3: The paper investigates tunneling reactions in isocyanic acid radical\nanions in the solid neon matrix experimentally. Specifically, interconversion between\nits cis and trans isomers is observed to proceed faster than the electron detachment\nreaction and via the bond-angle inversion mechanism rather than NH bond rotation.\nThe paper is clearly written, it showcases interesting dynamics on a simple system that\ncould serve as a future benchmark for dynamical theories. The experiment is backed up\nby instanton rate calculations that give support to the observed kinetic isotope effect,\nalthough the absolute numbers are in a clear disagreement (as rationalized in the\npaper). In my opinion, paper is suitable for publication in Nat. Commun. after the\ncomments, listed below, are addressed.\n1) Line 48 and 49: reformulate without repetitions of \"prebiotic chemistry\"\nAuthor response: The first occurrence of 'prebiotic chemistry' has been removed to\navoid repetition.\n2) Line 58: explain the phrase \"adapted in the dark\" for broad readership\nAuthor response: The word \"adapted\" has been replaced with \"kept\" to better align\nwith the context.\n3) Line 78 states that \"_these_\" experimental observations support assignment of\n\"different vibrational modes\". Which experimental observations do you refer to? The\ntext above was about asymmetric NCO stretch. Please, reformulate or explain.\nAuthor response: For clarity, the sentence “These experimental observations support\nthe assignment of group a and b absorptions to different vibrational modes of the\nHNCO•− anion isomers” has been removed. The text has been revised to: “The band\npositions (1637.2 and 1645.4 cm–1) are notably lower than that of the neutral HNCO\nmolecule at 2268.5 cm–1, suggesting that species a and b are HNCO•− anion isomers.\nThis is comparable to the isoelectronic CO •− anion, which also exhibits a lower OCO\n2\nantisymmetric stretching vibration mode (1658.3 cm−1, Ne matrix) than that of neutral\nCO (2348.2 cm−1, Ne matrix)33” (Page 3, last paragraph, yellow highlighted sentences).\nadded: “For the cis-isomer, the band at 1637.2 cm−1 aligns well with the theoretically\ncalculated IR frequency of 1689.5 cm−1 for the NCO antisymmetric stretching mode\n(ν ). Compared to neutral HNCO (2141.0 cm−1), this mode shows a significant red-shift\n2\nof 631.3 cm−1, consistent with the calculated shift of 612.5 cm−1.” (See Page 4, yellow\nhighlighted sentences in the middle)\n4) Line 110: \"To elucidate\" which reaction mechanism?\nAuthor response: The reaction mechanism refers to the cis-to-trans isomerization of\nHNCO•− and the electron-detachment of HNCO•− to HNCO. To clarify, we have revised\nthe text to: \"To elucidate the tunneling reaction mechanism for the cis-to-trans\nisomerization of HNCO•− and the electron-detachment of HNCO•− to HNCO\".\n5) Line 116: please, cite \"typical\" KIE observations of cis-trans isomerization.\nAuthor response: The relevant references have been added, and the sentence has been\nrevised to: “The KIE of H/D was determined to be 9.9±1.0, which is significantly lower\nthan those typically observed for hydrogen-atom tunneling-controlled cis-trans\nisomerization reactions in cryogenic matrices under similar conditions (for oxalic acid,\nk /k > 103)24,36.\nH D\n6) Line 157: what is square mass-weighted tunneling path? Is it sqrt(m)x Euclidean\ndistance in Cartesian coordinates?\nAuthor response: The squared mass-weighted tunneling path length is the squared\nEuclidean distance in Cartesian coordinates, computed as\nwhere i is the instanton bead index and j is the atom index. We use the squared path\nlength instead of the path length for two reasons: (1) The squared path lengths of\nindividual atoms add up to the total squared path length, whereas the squared path\nlengths of individual atoms do not; (2) The squared path length is related to the\ninstanton action. In the revised manuscript, we added the expression for the squared\nmass-weighted tunneling path length (Page 7, second yellow highlighted sentence).\n7) Line 140-152: NH bond rotation could be in-plane motion or out-of-plane motion. It\nseems only out-of-plane motion was considered here? E.g. in vinyl radical both paths\nexist and the out-of-plane bond-rotation path is much higher in energy [J. Chem. Phys.\n152, 204311 (2020)]. Instanton theory can easily be used to locate both paths if they\nexist.\nAuthor response: We thank the reviewer for this insightful comment. We searched for\nin-plane isomerization transition states for HNCO•− but did not find any. The in-plane\nN-H bond rotation path has a stationary point of second order, which does not qualify\nas a transition state. Additionally, in response to the reviewer’s suggestion, we\nperformed instanton optimization but were unable to locate any instantons for this\nmechanism. These findings have been incorporated into the revised manuscript. (Page\n6, third paragraph, yellow highlighted sentences)\n8) Comment: Instanton rate calculations have not been described in sufficient detail.\nPlease, provide details of which partition functions have been used and how they have\nbeen estimated, as well as the details of convergence parameters and instanton path\ncharacteristics (length, potential barrier, etc).\nAuthor response: Following the reviewer’s comment, we have added more details on\nthe ring-polymer instanton theory calculations, including the full rate expression in the\nring-polymer formulation and how each term (e.g. the partition functions and the\nEuclidean action) is computed in the Supplementary Materials. We have carefully tested\nthe convergence of the instanton calculations, and these results are presented in Table\nS7. In the revised manuscript, we added the following sentence to direct the reader to\nthe SI: 'See Supplementary Materials for the full computational details and convergence\ndiscussions.' While the instanton characteristics are shown in Figure 3b, we agree with\nthe reviewer that listing these quantities in a table would be informative. Therefore, we\nhave added Table S10 in the revised SI, presenting the tunneling path length, Euclidean\naction, and the highest energy point along the instanton path.\n----------------------------------------End of responses #3---------------------------------------\nReviewer 4: The manuscript of J. Tang et al. documents and interprets carefully\nconducted spectroscopic and computational studies of a tetratomic radical anion when\nheld in a cryogenic Neon matrix. Under such conditions there are slow spectroscopic\nchanges which allow for a kinetic analysis and, in conjunction with quantum chemical\nmodelling, convincingly manifest tunneling dynamics of competing isomerization and\ndetachment processes: heavy atom versus H-atom tunneling, and electron detachment.\nThe noteworthy finding of these studies is, that the Carbon atom tunneling across a\nshallow barrier exceeds that of the light Hydrogen atom.\nThese findings are significant and go beyond those of current studies. It is of conceptual\nvalue to know about a less slow heavy atom tunneling to surpass a much slower light\natom tunneling, and to surpass metastable electron detachment alike.\nAll of the found conclusions are fully supported by the documented results, and there is\nno further evidence needed. Some claims are stated in a too strong manner that needs to\ntone down (see below). Publication is not hampered by these deficiencies, once they\nare helped.\nThe documented work has been conducted in a sound manner and sets standards in its\nfield. By virtue of the submitted documentation, it is possible to reproduce all findings.\nDeficiencies that need to be helped upon revision are as follows:\n(In general)\nStrength’ of claims is occasionally too strong. Some part of the experimental description\nand interpretation seems to imply knowledge of computational results without stating\nit and ahead of their presentation in the manuscript. In cases where this is unavoidable\ncross reference is necessary, e.g. via a simple “see below” or an “as to be discussed in\nthe following” statement. Find explicit example in the following.\nComment 1: P3, line 66: “The results imply…” -> “These results suggest…”, and\nsome reference on charge detection methodology in matrix isolation spectroscopy.\nAuthor response: The suggested changes have been incorporated into the revised\nmanuscript: “These results suggest that species a and b are charged forms of HNCO32,33.”\nAdditionally, two references on charge detection methodology in matrix isolation\nspectroscopy have been included.\nComment 2: P3, line 74: The NCO antisymmetric stretching vibration needs additional\njustification. Maybe by reference to the computations.\nAuthor response: As suggested by the reviewer, additional justification has been added\non page 4: “For the cis-isomer, the band at 1637.2 cm−1 aligns well with the theoretically\ncalculated IR frequency of 1689.5 cm−1 for the NCO antisymmetric stretching mode\n(ν ). Compared to neutral HNCO (2141.0 cm−1), this mode shows a significant red-shift\n2\nof 631.3 cm−1, consistent with the calculated shift of 612.5 cm−1.”\nComment 3: P3, line 75: “than that” -> “than those”\nAuthor response: There are two conformers for the HNCO•− anion (cis and trans), but\nonly one conformer for neutral HNCO. Therefore, we use the singular 'that' when\ncomparing to the single reference band of neutral HNCO. For clarity, the sentence has\nbeen revised to: “These two band positions (1637.2 and 1645.4 cm−1) are notably lower\nthan that of the neutral HNCO molecule at 2268.5 cm−1.”\nComment 4: P3, line 83: The XYGJ-OS method is NOT known to each future reader of\nthis paper. Need to introduce it by a few words (… double hybrid density functional …)\nAuthor response: Following the reviewer’s suggestion, we have added a brief\nintroduction to the XYGJ-OS functional: “an accurate doubly hybrid density functional.”\nComment 5: P4, line 91: Similar mode -> A similar mode; P4, line 100: reactions\nproceed -> reactions possibly proceed\nAuthor response: The corrections have been made accordingly: “A similar mode” and\n“reactions possibly proceed”.\nComment 6: P4, line 101, “…, as the available energy is insufficient to drive these\nprocesses thermally”: This is an assumption, unless the outcome of the quantum\nchemical knowledge is invoked – which is not discussed yet at this stage of the\nmanuscript. Need to rephrase / clarify where this assumption comes from.\nAuthor response: The reaction system was maintained at 3 K under dark conditions,\nlimiting the average thermal energy (k T) to approximately 0.25 meV. This energy is\nB\nseveral orders of magnitude lower than the calculated barrier for cis-to-trans\nisomerization of 21.3 kJ/mol (≈ 0.22 eV). To clarify this point, the original statement\nhas been revised to: “as the available energy (k T ≈ 0.25 meV) is several orders of\nB\nmagnitude lower than the calculated barrier for cis-to-trans isomerization (see below)\nand is insufficient to drive these processes thermally.”(Page 4, last paragraph, yellow\nhighlighted sentences)\nComment 7: P4/5, lines 107-126: alle of the k and KIE values need to indicate\nuncertainty limits/error bars – which are absent as of now.\nAuthor response: The standard deviations for all rate constants (k) and kinetic isotope\neffects (KIE) have been included in Table S2. Additionally, the relevant text and Table\n2 in the manuscript have been revised accordingly.\nComment 8: P5, lines 130/131: The authors mix up the concepts of diabatic and\nadiabatic states by stating “… requires nonadiabatic crossing from the … diabatic state\nto the … diabatic state”. The authors wish to look up the concepts of adiabatic and\ndiabatic states once more and correct their statement accordingly.\nAuthor response: We thank the reviewer for pointing out this issue. In the revised\nmanuscript, we have corrected the statement to: “Electron detachment requires passage\nthrough the crossing between the negatively charged and neutral quasi-diabatic states”.\nComment 9: P5, line 137: likely -> possibly\nAuthor response: Correction has been made accordingly.\nComment 10: P5, line 141: “…searches for this pathway.” Requires some cross\nreference to that instance in the supplement where the applied search method is\ndocumented.\nAuthor response: We have added more details on the transition state and instanton\nsearch/optimization algorithm in the Supplementary Materials.\nComment 11:\n(a) Directly afterwards: “Surprisingly, no TSs were found for N-H bond rotation”: (1)\nDrop surprisingly, and (2) add “…which might be rationalized as follows:…”\n(b) P6, line 151: “… the isomerization mechanism …” -> “… the isomerization\nmechanism via N-H bond rotation …\"\n(c) P8, line 208: “… for carbon’s mass disadvantage …” -> “… for carbon’s higher\nmass …\"\nAuthor response: As suggested by the reviewer, the changes have been made\naccordingly.\nComment 12: P16, caption to figure 4, line 356: “percentage contributions” How\nevaluated? Need to indicate!\nAuthor response: The percentage contribution for each atom is evaluated based on its\ncontribution to the total mass-weighted squared path length of the instanton pathway. A\nhigher percentage indicates that the atom undergoes a greater displacement along the\ninstanton pathway.\nComment 13: Supplement P4, 4th line from the bottom: “… are account …” -> “…\nare accounted …”; Supplement P14, heading: “Theoretical Plots” -> “Plots of\nComputational Results\"\nAuthor response: As suggested by the reviewer, the changes have been made\naccordingly.\n----------------------------------------End of responses #4---------------------------------------\nResponses to the review comments\nAll four reviewers have agreed that the manuscript is suitable for publication.\nReviewer #3 provided two additional minor comments:\n1) Instanton action depends on the square root distance rather than distance\nsquared, in S=\\int p dx through dx.\nAuthor response: As suggested, we have clarified the relationship between the\ninstanton action, mass, and tunneling distance in the revised manuscript.\n2) It is possible to find the minimum action path (instanton) for the in-plane motion,\nif it exists (and it is possible it does not), even if it is passing near a second-order\nsaddle point of the potential energy surface. Sometimes (not always), instanton\ncalculation may fail due to that (if the region with two negative hessian\neigenvalues is long). Even in the case that instanton calculations fail, if the\nminimum action path exists, it is sometimes possible to state that the path does\nnot contribute significantly to the overall rate is its action is large.\nAuthor response: We agree with the reviewer that such a path, if it exists, would\nlikely have a very high action, rendering its contribution negligible. We have added\na statement in the Supplementary Materials addressing this point, which can be\nfound in the last paragraph of the Instanton Theory section (Page 3,\nSupplementary Materials)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have undertaken a substantial effort to address my previous remarks. It is gratifying to see that the guess that\nthe matrix might be responsible for the previous differences between the theoretical and measured rates turns out to be\nreasonable. The paper as it now stands is sutiable for publication.", "reviewer_2": "The authors have addressed all the points I raised. A key aspect was the assessment of whether IR radiation from the FTIR\nspectrometer could affect the kinetics of the reported processes. To evaluate this, additional experiments were conducted\nusing an IR radiation filter cutting above 1818 cm⁻¹. The sample was either subjected to continuous filtered IR radiation or\nkept in the dark except during the filtered IR measurements. The results showed that IR radiation promotes a six-fold\nincrease in the trans-HNCO•− detachment rate (i.e., when comparing measurements performed under unfiltered versus\nfiltered IR light). In contrast, for cis-HNCO•− detachment and cis-to-trans isomerization kinetics, the spectrometer’s IR\nradiation had a negligible influence. Thus, the main conclusion regarding tunneling remains unaffected. With these\nclarifications now provided in the revised version, I am pleased to recommend this excellent work for publication in Nature\nCommunications.", "reviewer_3": "The authors have responded to all reviewer's requests, which includes performing additional experiments and non-trivial\ncalculations. The paper contains a thorough and clear discussions now and is of exceptional quality and, in my opinion,\nsuitable for publication.\nI have two small comments:\n1) Instanton action depends on the square root distance rather than distance squared, in S=\\int p dx through dx.\n2) It is possible to find the minimum action path (instanton) for the in-plane motion, if it exists (and it is possible it does not),\neven if it is passing near a second-order saddle point of the potential energy surface. Sometimes (not always), instanton\ncalculation may fail due to that (if the region with two negative hessian eigenvalues is long). Even in the case that instanton\ncalculations fail, if the minimum action path exists, it is sometimes possible to state that the path does not contribute\nsignificantly to the overall rate is its action is large.", "reviewer_4": "This is a sound revision of the manuscript on Competing Quantum Tunneling Processes in Isocyanic Radical Anions. I see\nthat all concerns of all four reviewers been taken care of in an approprate manner. The manuscript is ready for publication in\nNature Comm., and I congratulated all authors to this nice piece of work.\nGet is published!"}, "author_response": ""}]

Decision letter