Photolytic mechanisms of hydroxylamine

The photodissociation of small molecules has been extensively studied because of the increase in environmental problems related to the atmosphere of the Earth. In this work, the photodissociation mechanisms of hydroxylamine (NH2OH) as a model molecule in its lowest singlet-excited (S1) state were systematically studied using the complete active space second-order perturbation theory (CASPT2) and transition state theory (TST). In particular, this study focused on nonradiative relaxation processes that convert the S0 → S1 excited-state molecule to its products in their respective electronic ground states. The potential energy curves obtained from relaxed scans suggest that O–H dissociation is the preferred process in the S1 state. For the N–O and N–H dissociation pathways, thermally excited precursors were hypothesized to form in the S0 state to circumvent O–H dissociation. Thus, S0 → S1 vertical excitations lead to transition structures in the S1 state, which fragment to their respective electronic-ground-state products. The thermodynamic and kinetic results confirmed the precursor hypothesis, showing that the exothermic energy caused by the formation of HNO and H2 is sufficient to generate such precursors in the S0 state. Additionally, the TST confirmed that unimolecular isomerization–dissociation is a two-step process that generates products effectively by direct photolysis of the corresponding covalent bonds. In particular, the process consists of O–H bond dissociation, followed by spontaneous isomerization and formation of H2 in its electronic ground state, resulting in the high quantum yield observed in the UV absorption experiments in the preferential formation of HNO and H2. The configuration interaction coefficients of the characteristic structures on the potential energy curves revealed considerable changes in the multiconfigurational character of the wavefunctions, especially for the transition structures. These are characterized by the development of Rydberg orbitals, being produced at the intersection of the S0 and S1 states. The present study highlights the effects of thermal selectivity and the multiconfigurational character of the wavefunctions on photodissociation. Because detailed information on the photolytic mechanisms of isolated NH2OH is limited both theoretically and experimentally, these results provide fundamental insight into unimolecular photodissociation, posing ground for future studies on related systems.


Introduction
The photodissociation of small molecules has been extensively studied both theoretically and experimentally because environmental problems related to the atmosphere of the Earth are increasing. 1 Because it has O-H and N-H groups, as well as lone-pair electrons, hydroxylamine (NH 2 OH) has oen been employed as a prototypical molecule in mechanistic studies of gas-phase photodissociation processes. [2][3][4][5][6][7] For isolated NH 2 OH, two types of unimolecular photodissociation mechanisms have been reported: (i) direct photolysis of the O-H, N-O, and N-H covalent bonds, 3 which can generate the nitroxyl (NH 2 O), hydroxylamino (NHOH), amino (NH 2 ), hydroxyl (OH) radical groups, and hydrogen (H); (ii) intramolecular isomerization/ dissociation, which can produce, e.g., nitrosyl hydride (HNO) [8][9][10] and ammonia oxide (NH 3 O). [11][12][13][14] In the direct photolysis pathway, ultraviolet (UV) absorption experiments have shown that the H-atom channel, in which two H atoms are generated with a quantum efficiency greater than one (1.7), is the preferred process at an absorption wavelength of 193 nm. In this pathway, N-O dissociation is a minor process, with a quantum efficiency of less than 0.1. 5 Instead, photolysis by UV absorption at 240 nm leads mainly to the dissociation of N-O and formation of NH 2 and OH in their electronic ground states. 7 Thus, though the O-H dissociation was rst proposed, both O-H and N-O dissociation have been reported as primary processes (representing 60% and 40%, respectively) in the direct photolysis of NH 2 OH vapor at 298 K, because of the possible thermal decomposition. 3 Limited evidence suggests that the N-H dissociation of eqn (3) occurs rst. 5 To study the photodissociation of NH 2 OH, ab initio calculations have been previously performed on low-lying singlet states using the complete active space self-consistent eld (CASSCF) method. 7 The potential energy curves obtained from the freezescan method, in which the remaining coordinates were xed at their MP2/6-31G** equilibrium values in the electronic ground state, showed that excitations from the two lowest-lying singlet states (n orb ¼ 8 and 9) are possible and can lead to fragmentations through the H-atom, NH 2 , and OH channels. It was concluded that these two dissociation processes result from excitations with different wavelengths rather than different excitation mechanisms. 7 This is consistent with other ab initio calculations based on the coupled electron pair approximation, which showed that the two highest occupied orbitals, 2a 00 and 7a 0 , are associated with the 2p lone-pair orbitals of the O and N atoms, respectively, with an energy difference of less than 1 eV. 15 The end product of NH 2 OH photolysis at 193 nm (6.42 eV) 5 is HNO, which is an important intermediate in the formation of NO by combustion 16 and by the catalytic decomposition of ozone (O 3 ) in the stratosphere and reaction with HNOH. 17 HNO is a reactive radical with a rather long lifetime (0.1 s), 18 and it has been studied extensively both experimentally and theoretically. 8 Although computational studies have suggested the formation of triplet HNO ( 3 HNO), the bent structure in the singlet state ( 1 HNO) was concluded to be the most stable, 19 with a singlet-triplet energy gap of 77 kJ mol À1 . 20 Using thermodynamic data, the threshold wavelength (l thres ) for the formation of HNO and H 2 aer excitation of NH 2 OH by 193 nm-UV radiation was predicted to be 891 nm (1.39 eV). 5 The interconversion between NH 2 OH and NH 3 O is a prototypical model for unimolecular chemical transformations (i.e., isomerization). 11 Although the energy barrier associated with intramolecular hydrogen/proton transfer from the O atom to N is rather high in the electronic ground state of this system ($234 kJ mol À1 ), 11 mass spectroscopic experiments and ab initio calculations conrmed the existence of neutral NH 3 O in the gas phase, 12 and structure-reactivity analysis of the equilibrium constants suggested that $20% of aqueous NH 2 OH solution is composed by NH 3 O. 13 In this work, the photolytic mechanisms of a single NH 2 OH molecule in the lowest singlet-excited (S 1 ) state were studied using ab initio calculations through the complete active space second-order perturbation theory (CASPT2) with the aug-cc-pVDZ basis set. Different from previous ones, this study focuses on nonradiative relaxation processes that convert the excited-state molecule to its electronic-ground-state products and on the effects of thermal energy on photodissociation. The structures and energetics of the precursors, and the transition structures of the seven dissociation channels, shown in Fig. 1, were studied in detail using the S 0 and S 1 potential energy curves obtained from CASPT2 and relaxed scans. To determine the contributions of the different electronic states to photodissociation, we analyzed the conguration interaction (CI) coefficients corresponding to the multicongurational character of each structure on the potential energy curves. Because of the limited theoretical and experimental information, the role of thermal energy in the photolytic mechanisms was discussed using the transition state theory (TST), 21,22 considering the 200-1200 K temperature range.

Ab initio calculations
Because the photodissociation of NH 2 OH involves fragmentation and formation of covalent bonds, closed-and open-shell congurations must be considered. 23 To account for the mul-ticongurational character of NH 2 OH photolysis, ab initio calculations were performed using CASPT2, which is a widely recognized method for excited-state calculations. 24 It should be mentioned that although the multistate complete-active-space second-order perturbation (MS-CASPT2) method is more accurate, MS-CASPT2 calculations are computer intensive and therefore applicable only to small systems. In this work, because the energy gradients with respect to degrees of freedom and Hessian had to be computed extensively, the CASPT2 method was employed to optimize the computational resources.
The electronic ground state of NH 2 OH in its equilibrium structure with C s symmetry is represented by (1a 0 ) 2 (2a 0 ) 2 (3a 0 ) 2 (4a 0 ) 2 (1a 00 ) 2 (5a 0 ) 2 (6a 0 ) 2 (2a 00 ) 2 (7a 0 ) 2 . The active space was dened by assigning ten electrons (n ¼ 10) to nine active orbitals (m ¼ 9), and hereaer abbreviated as the (10,9) active space. The remaining electrons were assigned to four doubly occupied orbitals (close ¼ 4). For NH 2 OH, CASPT2 (10,9) calculations involved 5292 CASSCF reference wavefunctions. The aug-cc-pVDZ basis set was satisfactorily used to optimize computational resources. Indeed, augmented basis sets with diffuse functions are reportedly suitable for singlet-state calculations, 24 and in our previous study, CASPT2/aug-cc-pVDZ calculations were shown to yield reasonable potential energy curves and S 0 / S 1 vertical excitation energies for water clusters. 25 The ab initio CI calculations in the CASSCF framework 7 revealed that the rst two electronic excited states involve excitations of a single electron from the two highest occupied orbitals, 2a 00 (n orb ¼ 8) and 7a 0 (n orb ¼ 9), to the two lowest unoccupied ones, 8a 0 (n orb ¼ 10) and 9a 0 (n orb ¼ 11), and that these low-lying excited states possess Rydberg and dissociativevalence character, which results from adiabatic excitation. 26 Because of this, the S 1 state was calculated adiabatically. Schematic diagram showing doubly occupied and active spaces used in CASPT2 (10,9) calculations and spatial distributions of the orbitals potentially involved in the S 0 / S 1 excitation of NH 2 OH are illustrated in Fig. S1. † Additionally, because previous ab initio calculations suggested that the products of photodissociation forming at conical intersections do not necessarily have C s symmetry, 26 and because nonradiative relaxations of the excited structures are our primary interest, the CASPT2(10,9) geometry was optimized with no geometrical constraints (C 1 symmetry). To study the effects of the multicongurational wavefunctions in the photolysis of NH 2 OH, the CI coefficients of the equilibrium, transition, and nal structures on the potential energy curves were examined. The CASPT2 (10,9) calculations were performed using the MOLPRO soware package 27,28 and applying the Werner-Meyer-Knowles nonlinear method in the orbital/state optimization. [29][30][31] Potential energy curves and equilibrium structures To obtain information on the equilibrium structures and elementary photodissociation steps, the potential energy curves of the direct O-H, N-O, and N-H dissociations were constructed as relaxed scans in the S 1 state. Here, the structural parameters of the potential energy curves were optimized using the CASPT2 (10,9) and quadratic steepest descent (QSD) methods, 32 and the same geometries were used to calculate the energies of the S 0 potential energy curves. All degrees of freedom used in these ab initio calculations are included in Fig. 1.
Because our preliminary CASPT2 (10,9) results showed that the O-H dissociation of channel (1) occurs preferentially along a purely repulsive potential energy curve in the S 1 state, the S 1 potential energy curves for the N-O and N-H dissociation of channels (2)-(4) were constructed by constraining the O-H(5) distance at the equilibrium value of the ground (S 0 ) state (R O-H(5) ¼ 0.97Å). These calculated potential energy curves were used to characterize the potential precursors in their electronic ground state outside the Franck-Condon region of the equilibrium structure. From these, the S 0 / S 1 vertical excitations could provide the transition and nal structures in their respective ground state.
Because mass spectroscopy measurements conrmed the existence of neutral NH 3 O in the gas phase, 12 and because intramolecular isomerization is one of the most common radical reactions in electronic excited states, the unimolecular isomerization potential energy curve 11 for the formation of ammonia oxide (NH 2 OH / NH 3 O) of channel (5) was constructed in the S 1 state by transferring the dissociated H(5) atom of channel (1) to the N atom ( Fig. 1). Similarly, because HNO and H 2 are the dominant products of photolysis at the lowest absorption wavelength (193 nm), 5 and because O-H dissociation is the primary process, an intramolecular isomerization that generates HNO and H 2 (channel (6)) was assumed by transferring the dissociated H atom of channel (1) (H(5)) to one of the H atoms (H(2) or H(3)) of the NH 2 group (Fig. 1). A high energy barrier caused by intramolecular rearrangement was assumed for the H 2 generation mechanisms. 7 Although NH was not detected during UV photolysis at 193 nm, 7 it is interesting to calculate the transition structures and energetics of the H(2) / O and H(3) / O isomerization of channel (7) and compare them with those of the H(5) / N isomerization of channel (5). Similar to the approach used for N-O and N-H dissociation, the unimolecular isomerizationdissociation process that underlies the formation of NH and H 2 O was simulated by constraining the O-H(5) distance at 0.97 A and transferring the dissociated H atom of channel (3) or (4) (H(2) or H(3)) to the O atom.

The effects of thermal energy on photodissociation
Because the potential energy curves obtained by CASPT2 (10,9) calculations represent the reaction paths at 0 K, the effects of temperature must be incorporated in the model. The mechanisms represented in Fig. 1 involve covalent bond dissociation and isomerization of a single molecule. Therefore, unimolecular rate constants (k) were used, calculating them in the 200-1200 K temperature range according to TST, 21,22 which can be applied when the energy barrier is higher than the thermal energy (k B T). 33 Although some of the direct covalent bond dissociations involve transferring the H atom, the S 0 and S 1 potential energy curves evidenced that the S 0 state has a broad energy barrier, whereas S 1 is barrierless, implying that quantum mechanical tunneling has no signicant role. Therefore, the classical (k Class ) and quantized-vibrational (k Q-vib , which includes the zero-point vibrational energies) rate constants were initially computed. For the one-dimensional energy prole, the classical transition rate constant is expressed as 34 where Q s and Q R are the partition functions of the transition and reactant structures, respectively, and DE s is the potential energy barrier obtained from the relaxed-scan potential energy curve. k B and h are the Boltzmann and Planck constants, respectively. To calculate the rate constant with quantized vibrations, the barrier height obtained with the zero-point vibrational energy (DE s ZPE ) is used, and the partition functions are calculated in the harmonic oscillator approximation: Here, Q s ZPE and Q R ZPE are the partition functions of the transition and reactant structures obtained with respect to their zero-point vibrational energies. Additionally, the crossover temperature (T c ), i.e., the temperature below which the transition states are dominated by quantum mechanical tunneling, was computed as 35,36 where U s is the imaginary frequency of the transition structure.
Although the effects of thermal energy are discussed only for the highest temperature (1200 K), i.e., the temperature at which high energy precursors could be populated, the rate constants with quantized vibrations and second-order Wigner correction (k S-Wig ) 35,36 were calculated to verify the insignicance of quantum mechanical tunneling. Assuming that tunneling occurs at the top of the barrier, the Wigner correction to the rate constant is where k S-Wig is the Wigner transmission coefficient, which is 1 in the classical limit (h ¼ 0). Then, the Wigner corrected rate constant is Finally, the enthalpy changes (DH) in the elementary reactions were computed. For the reactions with energy barrier higher than k B T, the linear relationship between ln k Q-vib (T) and 1/T was used to calculate the activation enthalpy (DH s ) through the Eyring equation, 34 where DS s is the activation entropy, and R is the gas constant. In these cases, DH s was extracted from the slope of the plot. For the elementary reactions with energy barrier lower than k B T (or barrierless), the conventional expression for the relative Gibbs free energy (DG Rel ¼ DH Rel À TDS Rel ) was used to approximate the exothermic enthalpy (DH Rel ) as the y-intercept of the linear regression of DG Rel as a function of T.
The results conrmed that, for direct covalent bond dissociation at 1200 K, k S-Wig is at most 8% higher than k Q-vib , con-rming the applicability of k Q-vib to this system. All the transition state calculations were performed using the DL-FIND program 37 included in the ChemShell package. 38

Results and discussion
The characteristic structures of NH 2 OH, identied on the S 0 and S 1 potential energy curves, are labeled with a three-character code as Gk-[l], Ek-[l] s , or Ek-[l]*, where G indicates a structure in the S 0 state, E indicates one in the S 1 state, and k indicates dissociation channels (1)- (7). Different NH 2 OH structures in the same dissociation channel are labeled [1], [2], etc. The *, §, and s symbols denote vertically excited structures, those at the intersection of the S 0 and S 1 potential energy curves, and transition structures, respectively. For instance, structures G1- [1]* and E1- [1]* are identical structures (l ¼ 1) computed in the S 0 (G) and S 1 (E) states, respectively, involved in channel (1) * and E2- [4] § are different structures (l ¼ 2 and 4) on the S 1 potential energy curve of N-O dissociation (k ¼ 2); they are a vertically excited structure (*) and a structure at the S 0 -S 1 state intersection ( §), respectively.
The equilibrium structures of NH 2 OH in the electronic ground (S 0 ) and lowest singlet-excited (S 1 ) states, obtained from CASPT2 (10,9) geometry optimizations, are shown in Fig. 2. The relax-scan potential energy curves and proposed mechanisms for the direct covalent bond dissociations are shown in Fig. 3 and 4, respectively. The relax-scan potential energy curves and proposed mechanisms for the unimolecular-isomerization dissociations are illustrated in Fig. 5 and 6, respectively. The calculated CI coefficients are reported in Tables 1 and S1-S7 of the ESI. † Note that J 0 and C 0 indicate the electronic ground state, J r a and C r a indicate the a / r singly excited state (S-type), and J r,s a,b and C r,s a,b indicate the a / r and b / s doubly excited state (D-type). Indices a/r and b/s correspond to occupied and virtual (or unoccupied) spin orbitals, respectively; the presence or absence of a bar denotes beta (b) or alpha (a) spin orbitals, respectively. The classical and quantum rate constants and relative Gibbs free energies of the elementary reactions are reported in Tables S8-S11. † The vertical excitation energies and corresponding oscillator strengths of characteristic structures are included in Table S12. †

Equilibrium structures
Five equilibrium structures were obtained from the CASPT2 (10,9) geometry optimizations in the S 0 and S 1 states   40 For structure G1- [1], the CASPT2(10,9) method yields an S 0 / S 1 vertical excitation energy (E Ex ) of 6.38 eV (194 nm) with the highest oscillator strength compared with other characteristic structures (Table S12 †). These results are in excellent agreement with the photodissociation of NH 2 OH caused by UV absorption at 193 nm (6.42 eV). 5 Although NH 2 OH is not stable in the S 1 state and preferentially dissociates into NH 2 O and H, the CASPT2(10,9) geometry was optimized in this state, constraining the O-H distance to its ground state equilibrium value (0.97Å), because the corresponding structural and energetic data can be used to understand the photodissociation mechanisms. Although the N-H and N-O distances do not change substantially, the threedimensional (3-D) S 0 structure G1- [1] is transformed into the planar (2-D) structure E1- [1] of Fig. 2, with a considerably lower vertical excitation energy (E Ex ) of 3.02 eV (411 nm). The change of the NH 2 OH equilibrium structure upon S 0 / S 1 excitation (3-D / 2-D) makes it unreasonable to use the freeze-scan method in the construction of the potential energy curves in the excited states. 7 The CI coefficients of Table 1 evidence that, for structure G1- [1], the electronic ground state, J 0 , dominates (C 0 ¼ 0.9727), with a small contribution from the doubly excited J 11;11 8;8 state Fig. 3 The S 1 relax-scan potential energy curves for the direct covalent bond dissociations in NH 2 OH obtained from CASPT2 (10,9) calculations. The energies on the S 0 potential energy curves were calculated at the same geometries. The three-character codes are explained in the text. s ¼ transition structure; § ¼ structure at the intersection of the S 0 and S 1 potential energy curves; DE Rel ¼ relative energy with respect to the vertically excited precursor in the S 1 state; DE s ¼ energy barrier with respect to structure G1- [1]; S 0 and S 1 ¼ relative energies with respect to the total energy of structure G1- [1], obtained from CASPT2 (10,9)   ¼ 0:1207Þ: The interference of the primary electronic states with higher electronic excited states conrms the importance of describing the multicongurational character of NH 2 OH. For structure G1- [1], this interference is approximately 12% in both the S 0 and S 1 states.
CASPT2 (10,9) geometry optimizations reveal that NH 3 O with C 3v symmetry is stable in both the S 0 and S 1 states. The S 0 state of structure G5- [3], shown in Fig. 2 Table 1 shows an electronic state interference similar to the case of G1- [1]: structure G5- [3] is  18 The CI coefficients listed in Table 1 reveal that, in the S 0 state, the electronic ground state J 0 (C 0 ¼ 0.9493) dominates with $21% contributions from the closed-shell excited J 10; ¼ 0:0772Þ: In this case, the patterns of the CI coefficients differ from those of the previously discussed structures: the primary electronic states interfere with excitations of two electrons from the lone-pair orbital of the O atom (n orb ¼ 8) to a dissociated-valence orbital (n orb ¼ 11).
Excellent agreement with previous theoretical and experimental data is also found for the NH-H 2 O complex. In this case, the equilibrium geometries obtained from CASPT2 (10,9) optimization in the S 0 and S 1 states are identical, as shown for structure G7- [3] in Fig. 2 :HOH ¼ 102.9 , and E Ex ¼ 0 eV. The patterns of the CI coef-cients of structure G7- [3] are the same as those of structures G1- [1], E1- [1], and G5- [3].
Collectively, the structural results, the energetic ones, and the electronic states discussed above conrm the accuracy of the CASPT2(10,9)/aug-cc-pVDZ framework and its applicability to study the photodissociation of NH 2 OH in the S 0 and S 1 states.

O-H dissociation
The O-H dissociation in the S 1 state is represented by a purely repulsive potential energy curve, as shown in Fig. 3a. Assuming that NH 2 OH completely dissociates into NH 2 O and H in their electronic ground states at the intersection of the S 0 and S 1 states (structure E1-[3] § , with E Ex z 0 eV), the potential energy for the O-H dissociation relative to the vertically excited structure E1-[1]* is DE Rel ¼ À227 kJ mol À1 . Instead, in the S 0 state, the energy barrier (DE s ) with respect to the ground-state equilibrium structure G1- [1] is 386 kJ mol À1 . The rate constants and relative Gibbs free energies of Tables S8 and S9 † conrm that NH 2 OH becomes a photoacid through S 0 / S 1 vertical excitation at 194 nm (6.38 eV), and that the nonradiative relaxation of excited NH 2 OH into ground-state NH 2 O and H is thermodynamically favorable: for instance, at 1200 K, DG Rel ¼ À30 kJ mol À1 . Oppositely, the thermal dissociation of the O-H bond in the S 0 state is thermodynamically and kinetically unfavorable: e.g., at 1200 K, DG s ¼ 437 kJ mol À1 and k Q-vib ¼ 2.46 Â 10 À6 s À1 .
Examination of the S 0 and S 1 potential energy curves reveals inection points at O-H distance R O-H ¼ 1.15Å. Analysis of the This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 8319-8331 | 8325 CI coefficients of the characteristic structures (Table S1 †) shows that, in the S 0 state, the planar structure with R O-H ¼ 0.97Å is dominated by the electronic ground state J 0 (C 0 ¼ 0.9789), whereas the singly excited J 10 9 state ðC dissociates. In this case, the Rydberg orbital (n orb ¼ 10) is the natural orbital related to the dissociated H atom. The Gibbs free energy barrier for the Rydberg orbital evolution in the S 0 state at 1200 K is DG s ¼ 210 kJ mol À1 , with k Q-vib ¼ 1.82 Â 10 4 s À1 (Table S8 †).
It is noteworthy that the conversion of the transition structure into the dissociated products is characterized by signicant contributions from excitations of an electron in the lone-pair orbital of the O atom (n orb ¼ 8) to the Rydberg orbital (n orb ¼ 10). For example, in the S 1 state, though the contribution of primary electronic state J 10 9 gradually decreases from C 10 9 ¼ 0:9715 to 0:9659 and 0.9463 for structures E1- [1], E1- [2] s , and E1- [3] § , respectively, the contribution of the next Fig. 5 The S 1 relax-scan potential energy curves for the unimolecular-isomerization dissociations in NH 2 OH obtained from CASPT2 (10,9) calculations. The energies on the S 0 potential energy curves were calculated at the same geometries. The three-character codes are explained in the text. s ¼ transition structure; § ¼ structure at the intersection of the S 0 and S 1 potential energy curves; DE Rel ¼ relative energy with respect to precursor or transition structure; DE s ¼ energy barrier with respect to precursor; S 0 and S 1 ¼ relative energies with respect to the total energy of structure G1- [1], obtained from CASPT2 (10,9) calculations in the S 0 and S 1 states, respectively. (a-c) Unimolecular-isomerization dissociations in channels (5)-(7), respectively. excited state, J 10;10 9;8 ; increases signicantly from C 10;10 9;8 ¼ 0:0844 to 0:2441 (nearly 300%) for transition structure E1- [2] s and product E1- [3] § . These values will be used as guidelines to discuss direct covalent bond dissociation and isomerization-dissociation. (structure E2-[2]*) with DE s ¼ 11 and DE Rel ¼ À168 kJ mol À1 at the intersection of the S 0 and S 1 states, resulting in structure E2- [3] § and G2- [3] § with R N-O ¼ 1.90Å. However, the energy barrier for G2- [3] § formation through N-O dissociation in the S 0 state is DE s ¼ 317 kJ mol À1 (Fig. 3b). We recall that the S 1 potential energy curve for N-O dissociation was calculated by constraining the O-H distance to 0.97Å because, in the absence of this constraint, the reaction preferentially proceeds towards O-H dissociation. To conrm that structure E2- [2]* is the transition structure for N-O dissociation in the S 1 state, CASPT2 (10,9) geometrical optimizations were performed with no geometrical Fig. 6 Mechanisms for the unimolecular-isomerization dissociations in NH 2 OH obtained from the analysis of the S 0 and S 1 potential energy curves and transition state theories (TST). s ¼ transition structure; § ¼ structure at the intersection of the S 0 and S 1 potential energy curves; DE s ¼ energy barrier with respect to precursor; DG s ¼ relative Gibbs free energy barrier with respect to precursor at 1200 K; DG Rel ¼ relative Gibbs free energy with respect to the precursor at 1200 K; (.) ¼ dissociation channel. (a-c) Channels (5)-(7), respectively.  (10,9) method in the S 0 and S 1 states. J 0 ¼ electronic ground state; J r a ¼ a / r singly excited state (S-type); J r,s a,b ¼ a / r and b / s doubly excited state (D-type); the indices a and b, and r and s label occupied and virtual or unoccupied spin orbitals, respectively; a bar or lack of a bar is to denote beta (b) and alpha (a) spin orbitals, respectively Overall, these results imply that N-O dissociation cannot proceed directly through the S 0 / S 1 vertical excitation of structure G1- [1]. However, the S 0 and S 1 potential energy curves shown in Fig. 3b suggest an alternative pathway to avoid the O-H dissociation shown in Fig. 4a. In fact, equilibrium structure G1- [1] in the S 0 state could be thermally excited and form a precursor in the S 0 state, i.e., structure G2- [2] s . This structure can be vertically excited to structure E2- [2]* with E Ex ¼ 2.85 eV (435 nm), nonradiatively relaxing along a purely repulsive potential energy curve into products NH 2 and OH in their respective electronic ground states (structure E2-[3] § ) with DG Rel ¼ À136 kJ mol À1 (Table S9 †). Because the N-O dissociation of structure E2- [2]* is barrierless and spontaneous in the S 1 state, the thermal excitation is the process that determines the rate of generation of structure G2- [2] s ; at 1200 K, DG s ¼ 195 kJ mol À1 and k Q-vib ¼ 7.75 Â 10 4 s À1 (Table S8 †). The photolytic mechanism of the N-O bond at 435 nm is supported by the value of the threshold wavelength that generates NH 2 and OH from the photoexcitation of NH 2 OH, l thres ¼ 463 nm (2.68 eV). 7,41 The values of the CI coefficients listed in Table S2 † Fig. 3c shows that for the N-H cis dissociation, the S 1 potential energy curve with constrained O-H distance (R O-H(5) ¼ 0.97Å) has a maximum at R N-H(2) ¼ 1.20 A (structure E3-[2]*) with DE Rel ¼ À12 kJ mol À1 at the intersection of the S 0 and S 1 states, yielding structure E3- [3] § with R N-H(2) ¼ 1.45Å. In the S 0 state, the energy barrier for the N-H cis dissociation (structure G3-[3] § ) is DE s ¼ 378 kJ mol À1 (Fig. 3c). For the N-H trans dissociation, the S 1 potential energy curve with constrained O-H distance reveals a maximum at R N-H(3) ¼ 1.30 A (structure E4-[2]*) and DE Rel ¼ À43 kJ mol À1 , yielding structure E4- [3] § with R N-H(3) ¼ 1.55Å. Similar to the case of the N-O dissociation, CASPT2 (10,9) geometry optimizations conrmed that E3- [2]* and E4- [2]* are the transition structures for the N-H(2) and N-H(3) dissociation pathways, respectively, with threshold N-H distances of 1.20 and 1.30Å.
Analysis of the main electronic states of the characteristic structures on the potential energy curves (Tables S3 and S4 †) for N-H dissociation shows trends of the CI coefficients similar to the case of O-H dissociation. For N-H cis dissociation, the electronic ground state J 0 dominates (C 0 ¼ 0.9807) the S 0 state, whereas the singly excited J 10 9 state ðC 10 9 ¼ 0:9733Þ dominates the S 1 state. As the N-H(2) distance increases to R N-H(2) ¼ 1.20Å, the electronic states associated with excitations of an electron from the HOMOÀ1 (n orb ¼ 8) to the LUMO (n orb ¼ 10), J 10 8 ðC 10 8 ¼ 0:0641Þ and J 10;10 9;8 ðC 10;10 9;8 ¼ 0:0843Þ; appear in the S 0 and S 1 states, respectively. Their respective maximum, C 10 8 ¼ 0:1943 and C 10;10 9;8 ¼ 0:2240; is observed at the intersection of the S 0 and S 1 states, corresponding to dissociated N-H(2). Therefore, E3- [2] s and R N-H ¼ 1.20Å are conrmed to be the transition structure and the threshold N-H(2) distance for the evolution of the Rydberg orbitals, respectively.

HNO and H 2 formation
Intuitively, two precursors are possible for isomerization in channel (6), E1- [3] § and E3- [3] § , i.e., the O-H(5) and N-H(2) dissociated structure, respectively. Starting from either structure and using R H(2)-H(5) ¼ 1.50Å, H(5) / H(2) isomerization readily occurs at the intersection of the S 0 and S 1 states, yielding structure E6- [1] § , as shown in Fig. 5b. This suggests that O-H dissociation occurs rst. The potential energy curves for the H(5) / H(2) isomerization show two possibilities for the formation of HNO and H 2 , which are structures E6- [3] and G6- [3] in the S 1 and S 0 state, respectively. In the S 1 state, E6- [3] can form with a low free energy barrier via transition structure E6-[2] s (DG s ¼ 12 kJ mol À1 , k Q-vib ¼ 7.78 Â 10 12 s À1 , and DG Rel ¼ À328 kJ mol À1 at 1200 K, Table S11 †). The existence of E6- [3] as an equilibrium structure in the S 1 state supports the experimental nding that the reactive HNO radical has a rather long lifetime (0.1 s) and is one of the dominant products in the gasphase isolated system. 18 In contrast, the formation of HNO and H 2 from structure G6-[1] § is barrierless and spontaneous (DG Rel ¼ À363 kJ mol À1 , Table S10 †) in the S 0 state, with structure G6- [3] (E Ex ¼ 1.40 eV, corresponding to 886 nm) as the product. The value of E Ex is in excellent agreement with the threshold wavelength associated with the formation of HNO and H 2 , l thres ¼ 891 nm (1.39 eV), which was obtained experimentally from the excitation of NH 2 OH by UV photons at 193 nm and thermodynamic data. 5 The H(5) / H(2) unimolecular isomerization-dissociation mechanisms of the S 0 and S 1 states are depicted in Fig. 6b.
For H(2) / O isomerization, the CI coefficients listed in Table S7 † show the same multicongurational character along the potential energy curves of the H(5) / N and H(2) / H(5) isomerization. In the S 0 state, the contribution of the electronic ground state increases whereas the contribution of the singly excited state increases in the S 1 state.

The interplay between thermal excitations and photoexcitations
The previous sections show in detail the relative Gibbs free energies of the elementary processes and the effects of electronic conguration changes on the potential energy curves. To describe completely the role played by thermal energy in photolytic mechanisms, especially investigating the heat exchange in the endothermic and exothermic processes, the enthalpy changes (DH) were calculated in the elementary steps. For the direct photolysis of the N-O and N-H covalent bonds, which involves the formation of the precursors in the S 0 state, the linear relationship between ln k Q-vib (T) and 1/T of eqn (9) was used. For the spontaneous isomerization in the S 0 state (channels (5)-(7), negative DG Rel ), the conventional Gibbs free energy change (DG Rel ¼ DH Rel À TDS Rel ) was used to approximate the enthalpies of the exothermic processes (DH Rel ). Fig. S2a † shows that the linear relationship between ln k Q-vib (T) and 1/T is maintained over the entire temperature range. The values of DH s in Table S8 † evidence that, for the N-O and N-H cis dissociation, the thermal energies required for the formation of the precursors in the S 0 state are similar to those required for the formation of the Rydberg orbital (structure G1- [2] s ), being DH s ¼ 190, 208 and 199 kJ mol À1 with k Q-vib (T) ¼ 7.75 Â 10 4 , 8.54 Â 10 3 s À1 and 1.82 Â 10 4 , respectively.
For the barrierless, direct covalent bond dissociations in the S 1 state, the relationship between DG Rel and T is linear over the entire temperature range (Fig. S2b †). Table S9 † reveals that the heat release related to O-H and N-H dissociation in the S 1 state is not substantial, compared with that of N-O dissociation (DH Rel ¼ À3, À9 and À124 kJ mol À1 , respectively). Additionally, the exothermic energies of isomerization-dissociation in the S 0 state (Table S10 †) exceed the thermal energy required for the formation of the precursors, DH Rel ¼ À219 and À279 kJ mol À1 for channels (5) and (6), respectively. Assuming that the thermal energies generated in the exothermic processes can be transferred to other NH 2 OH molecules, the exothermic isomerization-dissociation of channel (6), which generates HNO and H 2 , could generate a relevant excess thermal energy for the formation of the precursors in the S 0 state. Thus, the source of thermal energy required to generate the precursors in the S 0 state is the formation of HNO and H 2 . This is supported by the nding that the formation of HNO and H 2 is the preferred process in UV experiments at 193 nm, and that HNO is a dominant product in the gas-phase isolated system. 18

Conclusion
The photodissociation mechanisms of NH 2 OH in the lowest singlet-excited state were studied by ab initio calculations in the CASPT2(10,9)/aug-cc-pVDZ framework. This study focused on nonradiative relaxation processes that convert the excited-state molecule to its electronic-ground-state products and on the role played by thermal excitation in photodissociation. All the important equilibrium structures in the S 0 and S 1 states were characterized, and the potential energy curves for direct covalent bond dissociation and unimolecular isomerization-dissociation were calculated. Additionally, thermodynamic and kinetic data associated with the elementary processes were extracted using the transition state theory.
The CASPT2 (10,9) geometry optimizations showed that, in the S 0 state, the NH 2 OH equilibrium structure is a 3-D structure with C s symmetry. An S 0 / S 1 vertical excitation energy of 6.38 eV (194 nm) was calculated, and NH 3 O, HNO, and the NH-H 2 O complex were found to be stable in the S 0 and S 1 states. Analysis of the CI coefficients of the equilibrium structures revealed that the interference of the primary electronic states with higher excited states is important and that the multi-congurational character of these structures must be included in ab initio studies. Because all the equilibrium structures and energetics are in good agreement with the available theoretical and experimental data, the use of the CASPT2 (10,9) method was proved to be appropriate.
The potential energy curves obtained from the CASPT2(10,9) and relaxed scan methods conrmed that O-H dissociation dominates in the S 1 state. Analysis of the CI coefficients of the characteristic structures on the potential energy curves revealed changes in the multicongurational character of the pathway upon O-H dissociation. For example, at the inection point (R O-H(5) ¼ 1.15Å) of the S 1 potential energy curve ðJ 10 9 Þ; an electronic state associated with excitation of an electron from the lone-pair orbital of the O atom to the Rydberg orbital ðJ 10;10 9;8 Þ emerges, having its maximum at the intersection of the S 0 and S 1 states. Therefore, the structure at the inection point is considered a transition structure, and R O-H(5) ¼ 1.15Å is considered to be the threshold distance for the development of Rydberg orbitals, which separates the bound and dissociated electronic states (bound-free transition). These conclusions were used as guidelines to discuss the other photodissociation processes.
Because O-H dissociation is the preferred process in the S 1 state, the S 1 potential energy curves for the N-O and N-H dissociations were initially constructed by constraining the O-H distance to its equilibrium S 0 value. To prevent O-H dissociation, the equilibrium structure in the S 0 state must be thermally excited to form appropriate precursors, as suggested by the potential energy curves. Then, the thermally excited precursors are vertically excited to form the transition structures in the S 1 state, which then relax nonradiatively along purely repulsive potential energy curves to generate the products in their respective electronic ground states. Although the required thermal energies are relatively high, according to our thermodynamic and kinetic results, the exothermic energy related to the formation of HNO and H 2 is at least equally high. Therefore, the thermal excitations in the S 0 state determine the rate of N-O and N-H dissociation. The proposed mechanisms, which involve different thermally excited precursors, are supported by experimental observations that show that different photon energies lead to different products in their electronic ground state.
The potential energy curves and thermodynamic results revealed that the unimolecular isomerization-dissociation effectively generates products in their electronic ground state through the direct photolysis of the corresponding covalent bonds. In particular, for the formation of HNO and H 2 , the potential energy curves suggested that the high quantum yield of photolysis by UV absorption at 193 nm results from a twostep process: rst, the O-H bond dissociates; then, isomerization and the formation of H 2 in its electronic ground state on a purely repulsive potential curve occur through a strong exothermic process. Overall, the mechanisms proposed in this work emphasize the roles of thermal selectivity and the multi-congurational character of the associated wavefunctions. Because detailed information on these aspects is limited both theoretically and experimentally, this work provides important insights into the photodissociation of NH 2 OH. Thus, it can be ground for future theoretical and experimental studies of similar systems.

Conflicts of interest
There are no conicts to declare.