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Photochemical dissociation of HOBr. A nonadiabatic dynamics study
Accepted Manuscript Title: Photochemical dissociation of HOBr. A nonadiabatic dynamics study Author: Saadullah G. Aziz Abdulrahman O. Alyoubi Shaaban A. Elroby Rifaat H. Hilal PII: DOI: Reference:
S1010-6030(16)30074-0 http://dx.doi.org/doi:10.1016/j.jphotochem.2016.02.024 JPC 10153
To appear in:
Journal of Photochemistry and Photobiology A: Chemistry
Received date: Revised date: Accepted date:
31-1-2016 24-2-2016 27-2-2016
Please cite this article as: Saadullah G.Aziz, Abdulrahman O.Alyoubi, Shaaban A.Elroby, Rifaat H.Hilal, Photochemical dissociation of HOBr.A nonadiabatic dynamics study, Journal of Photochemistry and Photobiology A: Chemistry http://dx.doi.org/10.1016/j.jphotochem.2016.02.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Photochemical Dissociation of HOBr. A Nonadiabatic Dynamics Study Saadullah G. Aziz1, Abdulrahman O. Alyoubi 1, Shaaban A. Elroby 1,2, and Rifaat H. Hilal 1,3* Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah B.O. 208203, Saudi Arabia; E‐Mails: [email protected] (S.G.A.); [email protected] (A.O.A.); [email protected] (S.A.E.) 2 Chemistry Department, Faculty of Science, Beni‐Suef University, Beni‐Suef 6251, Egypt 3 Chemistry Department, Faculty of Science, Cairo University, Cairo 12613, Egypt 1
[email protected]
Highlights The excited state properties and photochemical dissociation of hypobromous acid, HOBr were investigated using equation of motion coupled cluster (EOM‐CCSD ) and time‐dependent density functional theory (TDDFTThe decay of the excited states of HOBr in the gas phase was examined . The spectrum, composed of 10 excited states, was simulated with the nuclear ensemble approximation, sampling a Wigner distribution with 500 points. Dynamics simulations were done with the surface hopping method. ). Results are in good agreement with experimental data.
Abstract A number of single‐reference post Hartree‐Fock methods, namely CIS, symmetry adopted cluster configuration interaction (SAC‐CI), equation of motion coupled cluster (EOM‐CCSD ) and time‐dependent density functional theory (TDDFT), were used to investigate the excited state properties and photochemical dissociation of hypobromous acid, HOBr. Results are in good agreement with experimental data. The decay of the excited states of HOBr in the gas phase was examined by simulating the UV photoabsorption spectrum and nonadiabatic dynamics at the TDDFT M06‐2X level of theory. The spectrum, composed of 10 excited states, was simulated with the nuclear ensemble approximation, sampling a Wigner distribution with 500 points. Dynamics simulations were done with the surface hopping method, started in two separate spectral windows, at 4.0 ± 0.25 eV and 8.0 ± 0.25 eV, to be compared to experimental UV spectral data. Three hundred trajectories were considered from each of these windows according to their excitation probabilities. The excited‐state lifetime was determined. The main photochemical channel observed were HO and Br eliminations, representing 67% of all processes. Key words: HOBr‐ Excited state dynamics‐ TDDFT – photodissociation – non‐adiabatic dynamics
1. Introduction
The important role played by the different bromine species in ozone depletion, was recently recognized [1,2]. This is especially important in the Arctic spring and in areas where there exist high concentration of HOX species ( e.g. OH radical) [3‐ 6]. The depletion of ozone by BrO and OH radical was in investigated in the laboratory [7‐9] where it was concluded that such a process would increase the recycling of bromine. The photolysis of HOBr was suggested to be the most important channel in this respect[10]. and may be written as HOBr + hv HO + Br This photodissociation reaction was investigated near the threshold of dissociation at 490 and 510 nm. Characterization of the OH photofragment was carried out via Doppler and polarization spectroscopy using laser‐induced fluorescence [11]. The UV‐VIS spectrum of HOBr was, measured over the 200‐420 nm range. Two main absorption bands centered near 280 and 350 nm were observed[12,14]. A third long wave length band, centered near 440 nm was later detected by monitoring the yield of OH radicals as the wavelength of an excitation laser is scanned over the region from 440 to 650 nm. This band has been assigned to a transition to a triplet state, and although its peak absorption cross section is very small, its influence on determining the photochemical lifetime of HOBr is large due to its proximity to the peak of the solar actinic flux[9]. Motivated by the fact that very little is known about the photolysis of HOBr, its photochemical and photophysical dissociation mechanism, the present research project is launched with a focus on the calculation of excited state properties, using different correlated single‐reference methods. The reduced computational cost of
such methods has allowed us to extend our investigations to nonadiabatic dynamics processes [1] starting at highly excited states (S7−S11), where photochemical reactions of HOBr has been experimentally studied. It should be noted here that, although the molecule at hand is triatomic small and can in principle be handled by quantum dynamics, yet inclusion of this number of excited states in the quantum dynamics simulations is practically impossible. Based on these nonadiabatic dynamics simulations, we have been able to provide a much better insight into the photolysis of this molecule. 2. Computational Details The ground‐state geometry was optimized at the MP2 level with the aug‐cc‐pVTZ basis set[17,18] using GAUSSIAN 09[19]. This geometry was used for further calculations of the vertical excitations using the same basis set. The diffuse character of this basis set enables it to give the correct description of Rydberg orbitals. Excited state calculations started at the low level CIS [20] , and then the more accurate and involving symmetry adopted cluster configuration interaction (SAC‐CI)[16] and equation of motion coupled cluster with single and double excitations (EOM‐CCSD)[21], methods. TDDFT (time‐dependent density functional theory) calculations were also carried out with M06‐2X [22] and ωB97XD [23] functionals, using GAUSSIAN 09. For each method, 10 singlet excited states were computed. The Cs symmetry was enforced in all static calculations. In a second part of the investigation, relaxed potential energy‐curve calculations along two internal coordinates, namely the BrO‐H and the HO‐Br coordinates, have been performed. The ground and 10 excited states (5A′ and 5A″) have been computed on ground‐state relaxed geometries. The calculations have been carried out at the EOM‐CCSD method.
In the last part of the study, UV photoabsorption spectrum and nonadiabatic dynamics simulations were carried out to understand the ultrafast decay of the excited states of HOBr in the gas phase. Computations were performed using Newton‐X program package [24,25] at the TDDFT / M06‐2X level of theory. In order to simulate the photoabsorption spectrum, 500 points were sampled with the nuclear ensemble approximation [25]. The same number of excited states computed in the relaxed potential energy curves (10) was considered here. Dynamics simulations were started in two spectral windows at 4.0 ± 0.25 and 8.0 ± 0.25 eV. Three hundred trajectories were stochastically sampled from each of these windows according to their excitation probabilities. Dynamics simulations were done with the surface hopping method [26,27]. Classical equations were integrated with 0.5 fs time‐step, while quantum equations were integrated with 0.025 fs. For the quantum integration, all necessary quantities were interpolated between classical steps. Nonadiabatic effects between excited states were taken into account by the fewest switches algorithm [28] with decoherence corrections (α = 0.1 Hartree) [29]. Nonadiabatic couplings between excited states were computed by finite differences with the method proposed by Hammes‐Schiffer and Tully[30]. 3. Results and Discussion 3.1.Excitation Energies and Oscillator Strengths
The results obtained for vertical‐excitation energies, oscillator strengths, and state assignments computed with the TD‐M06‐2X and ωB97XD functionals and EOM‐ CCSD method, are shown in Table 1. With respect to the vertical excitation energies, all three methods are in good agreement with the observed spectrum of HOBr. All calculated excited states are in the range up to >10 eV. Two main band
systems dominate the computed spectrum. The first long wave length band system is centered on 3.5 eV and is composed of one configuration, namely the HOMO‐LUMO transition. The MO’s involved are displayed in Figure S3 of the supplementary material (SM). These KS MO’s were computed at the M06‐2X /aug‐ cc‐pVTZ level of theory. For visualization and to make the assignment of the delocalized KS MO’s more straightforward, a full natural orbital treatment (nbo) has been performed and the resulting orbitals are those displayed in Figure S3. The long wave length absorption at 3.39 eV is of very low intensity as compared to the short wave length one. This transition is of the combination of nBr – Ryd and ‐ * type localized on the O‐Br bond region. Whereas, the short wavelength absorption, which spans the 7.5‐8.5 eV range, may be attributed to a transition from a nBr–*. The Symmetry Adapted Cluster/Configuration Interaction (SAC‐CI) methods of Nakatsuji and coworkers[21] have been also used to explore the excited state space for the singlet, triplet and ionized states of HOBr. Results are summarized in table 2. SAC‐CI computations predicted two singlet states, one triplet and two ionized states in the region < 11.5 eV. The singlet states are heavily mixed with several configurations. These singlet states are contaminated by 1.7% and 0.53% of doublet states. The triplet state, on the other hand, is pure. The first ionized state is of symmetry A” and is characterized by ionization potential (I.P.) = 10.6 eV, leading to the formation of a cation. This state results in the removal of an electron from the HOMO (MO 22; nonbonding Br orbital). Ionization from the HOMO‐1 (MO 21) is responsible for the second ionized state ( A’) of I.P. =11.3 eV. This MO is also of the n‐ type representing the lone pair of the pπorbitals on the Br with little interaction with the p orbital of oxygen.
3.2.Photodissociation pathways of HOBr The presence of radical species such as OH, Br and OBr reveals two possible pathways for the photodissociation of HOBr, viz., OH stretching and OBr stretching pathways. The question arise is that how the excited singlet and triplet states of HOBr are populated along these two pathways. In order to examine the ordering of these excited states along these stretching pathways, the potential energy profile was computed at the EOM‐CCSD/ aug‐cc‐pVTZ level of theory, along the HO and the OBr coordinates. Results are depicted in Figure S1 of the supplementary materials (SM), for the ground and lowest excited states in the Franck‐Condon region. The O‐H distance is stretched up to 3.1 Å, while the O‐Br distance is stretched up to 3.7 Å. Excited singlet states all show parallel repulsive behavior along the O‐H stretching coordinate with the profiles of states S1 – S4 are closely approaching in the 2.0 ‐2.2 Å. All states are showing a dissociative behavior. The energy profile of the triplet states along the O‐H stretching coordinate is different, however. The lowest triplet state T1 intersects the ground state at RO‐H of 2.366 Å. This seems to pinpoint the deactivation pathway of the excited HOBr. The energy profiles along the O‐Br stretching coordinate show, however, a different behavior where both T1 and T2 contribute to the deactivation pathway. Both triplet states intersect the ground state at 3.02 Å. In conclusion, upon photo‐excitation, one would expect deactivation through intersection of the low‐lying triplet with the ground state whereas, on the singlet PES, however, surface hoping may take place between S2/S3 states and dissociation is the dominant behavior. A question may arise at this point is that how these triplets get populated?. To answer this question, the potential energy profile along both RO‐H and RO‐Br for the lowest singlet and triplet states are displayed in Figure 1. Along the O‐Br coordinate S1 approaches and intersects T1 at a RO‐Br distance of 2.62 Å just before T1 intersects the ground state at a RO‐Br
distance of 2.82 Å . This seems to explain how T1 gets populated. This is in agreement with Minaev’s [9,31,32] excellent work on the spectra of HOX (
X=Cl, Br and I). Along the RO‐H coordinate, however, the situation is not that straightforward. Indeed, T1 intersect the ground state at RO‐H of 2.367 Å , however, T1 intersects S1 at a larger O‐H distance. That is, T1 cannot be populated along this coordinate 3.3.UV‐Photoabsorption Spectrum simulation The photoabsorption spectrum of HOBr in the UV region, calculated at the TDDFT level with the M06‐2X functional using the aug‐cc‐pVTZ, is shown in Figure 2. In the region up to 10 eV, the absorption spectrum shows two main bands, one with high intensity with peaks at 8.37 eV (cross‐section=0.47 in Å2 per molecule‐1. ) and a short wavelength absorption with much lower intensity at 4.37 eV ( cross‐section = 0.003 in Å2 per molecule‐1). Moreover, the 4.37 eV band has a clear tail at 3.8 eV whereas, a more diffuse low intensity shoulder at the low‐energy tail of the 8.37 eV band is predicted at ∼7.4 eV. The comparison of these spectral features with the vertical spectrum of Table 1 allows the direct assignment of most of these features. Experimentally, excitation laser scanning studies [15] show that excitation at 440 nm is responsible for the photodissociation of HOBr leading to the increase of OH concentration. The photochemical lifetime of troposphere HOBr in polar regions, is suggested to be shortened by a factor of 2 compared to values based on the near‐UV absorption bands alone. Furthermore, experimental observations suggest that absorption into this band is responsible for up to 50% of the total photolysis rate of HOBr [10].
Dynamics simulations starting from two energy windows centered at 4.0 and 8.0 eV show reaction pathways, leading to two main products. The dynamics in the spectral window centered about 4.0 eV show 54% probability to originate from excited state 3 (n*). Whereas, dynamics in the spectral windows centered about 8.0 eV, show 67% probability to originate from state 7 (nRyd*). One should also bear in mind that due to methodological limitations (trajectories were stopped just before conversion to the ground state), only excited‐state dissociation processes are accounted for in the present study. Two dissociation channels were observed with the above probability values, namely , elimination of H and the consequent formation of OBr and a second channel where the OH is eliminated leaving Br. Let us examine the dynamics took place at the spectral windows 4.0 eV. Figure 3a displays the evolution of the energies of the three states S0, S1 and S2 with time. The trajectories show different behavior, however. The evolution of both S1 and S2 show slight attractive behavior in the first 25 fs where S1 starts a repulsive decay much steeper than that of S2 leading to crossing S1/S2 at 35 fs. These dynamics corresponds to a dissociation channel leading to the formation of the OH radical in agreement with experimental observation [11,34]. At time 33.50 fs the molecule was on surface 3 (S2). The energy gap to S1 was 0.03 eV. At time 34.00 fs, the molecule was on surface 2 (S1), therefore a surface hopping took place. The energy gap with S0 was 0.63 eV and with S1 was 0.07eV. This seems to be the only surface hopping taking place just before dissociation. Let us examine this hopping process more closely, in substep 1341 belonging to step 68 , the molecule still on surface 3 with population in this state of 85.7% is ready for hopping into surface 2. Upon hopping into S1 the population of surface 2 increase to 34% and remains populated in the next substeps, and in fact population increases to about 50% until the termination of the trajectories. The dynamics at the spectral window 8.0 eV is much more involving, however. We simulated the dynamics while the system is
in surface 7 for 500 fs. Figure 3b displays the evolution of the energies of the 7 states within the time domain studied. Note that the trajectories are all broken in 80 fs time interval due to the dissociation of the molecule. The molecule starts at S7 and soon under goes the first surface hopping in step 16 after 8.0 fs to S6 where it remains on this surface until step 64 after 32.0 fs where it hops into surface 5 which is immediately followed by another hopping into S4 at 33.0 fs. However, due to the crowdness of the energy profiles in this region, the molecule reverts back into surface 5 after 1.5 fs. At 38.0 fs it undergoes a hopping with high probability into S4 then a final hopping with even higher probability took place to S3 at 48.5 fs. The system remains on S3 until 78 fs where all trajectories were broken. The energy profiles of all surfaces underwent drastic change at the 48.0 – 53.0 fs range and at the 68.0‐ 72.0 fs range. In these two time domains S4, S5 and S7 show a steep repulsive rise whereas; all other surfaces show an opposite trend. The very idea of on‐fly dynamics is based on nonadiabatic couplings between excited states which were computed, in the present work, by finite differences with the method proposed by Tully[28].Unfortunately, Newton‐X software package does handle spin‐orbit coupling so far, although efforts are being carried out to include it. The importance of SOC has been discussed for different HOX (X=Cl, Br, and I) species by Minaev[9,31,32]; where he pinpointed the importance of SOC and quadrapole coupling constants for spectral interpretation of HOI molecule in a way which is more marked than the other hypohalaous molecules. 4. Conclusion The photochemical‐dissociation process of HOBr an important atmospheric pollutant, was investigated with quantum‐chemical methods, including vertical spectrum and potential energy curves at CIS, EOM‐CCSD, SAC‐CI and TDDFT
levels, as well as vibrationally broadened spectrum simulations and nonadiabatic dynamics with TDDFT. Energy ordering and excited‐state characters calculated with single‐reference methods, especially TDDFT, are in good agreement with experimental results. Deactivation of excited HOBr through intersection of T1 with the ground state takes place along the O‐Br coordinate. T1 is populated by intersection with S1 earlier on the O‐Br coordinate. Internal conversion S1to the ground state is not observed in both cases studied, namely at the spectral windows at 4.0 and 8.0 eV. Photodissociation occurred through two different reaction pathways with two main products, including atomic elimination (Br, or H), and multifragmentation (Br+OH,or OBr+H), mechanism. The main photochemical channel observed were OH +Br, representing 67% of all processes. 5. Acknowledgements This project was funded by the National Plan for Science, Technology and Innovation (MAARIFAH) – King Abdulaziz City for Science and Technology ‐ the Kingdom of Saudi Arabia – award number (11‐ENV
1995‐03). The authors also, acknowledge with thanks Science and Technology Unit, King Abdulaziz University for technical support.
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10. Michael Lock, Rhett J. Barnes, and Amitabha Sinha , Near‐Threshold Photodissociation Dynamics of HOBr: Determination of Product State Distribution, Vector Correlation, and Heat of Formation, J. Phys. Chem. 100(1996), 7972‐7980. 11. John J. Orlando and James B. Burkholder, Gas‐Phase UV Visible Absorption Spectra of HOBr and BrO, J. Phys. Chem.,99(1995),1143‐1150. 12. Trevor Ingham, Dieter Bauer, Jochen Landgraf, and John N. Crowley, Ultraviolet‐Visible Absorption Cross Sections of Gaseous HOBr , J. Phys. Chem. A102(1998), 3293‐3298. 13. Michael R. Hand and Ian H. Williams ,and Joseph S. Francisco Ab Initio Study of the Electronic Spectrum of HOBr, J. Phys. Chem. 100(1996), 9250‐ 9253. 14. Rhett J. Barnes, Michael Lock, Jack Coleman, and Amitabha Sinha, Observation of a New Absorption Band of HOBr and Its Atmospheric Implications, J. Phys. Chem. 100(1996),453‐457. 15. Yarkony, D. R. Nonadiabatic, Quantum Chemistry‐Past, Present, and Future. Chem. Rev. 112(2011), 481−498. 16. K. Toyota, I. Mayumi, M. Ehara, M. J. Frisch, and H. Nakatsuji, “Singularity‐ free analytical energy gradients for the SAC/SAC‐CI method: Coupled perturbed minimum orbital‐deformation (CPMOD) approach,” Chem. Phys. Lett., 367 (2003),730‐36. 17. Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. Electron Affinities of the First‐Row Atoms revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 96(1992), 6796−6807. 18. Dunning, T. H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron Through Neon and Hydrogen. J. Chem. Phys. 90(1989),1007−1023.
19. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision D.01; Gaussian, Inc.: Wallingford, CT, 2013. 20. Foresman J. B., Head‐Gordon M., Pople J. A., Frisch M. J. Toward a Systematic Molecular Orbital Theory for Excited States, J. Phys. Chem., 96 (1992) 135‐49. 21. Kállay M. and Gauss J. Calculation of excited‐state properties using general coupled‐cluster and configuration‐interaction models. J. Chem. Phys., 121 (2004) 9257. 22. Y. Zhao and D. G. Truhlar, “Comparative DFT study of van der Waals complexes: Rare‐gas dimers, alkaline‐earth dimers, zinc dimer, and zinc‐ rare‐gas dimers,” J. Phys. Chem., 110 (2006), 5121‐29. 23. Chai, J.‐D.; Head‐Gordon, M. Long‐Range Corrected Hybrid Density Functionals with Damped Atom−Atom Dispersion Corrections. Phys. Chem. Chem. Phys. 10(2008),6615−6620. 24. Barbatti, M.; Ruckenbauer, M.; Plasser, F.; Pittner, J.; Granucci, G.; Persico, M.; Lischka, H. Newton‐X: A Surface‐Hopping Program for Nonadiabatic Molecular Dynamics. WIREs: Comp. Mol. Sci. 4(2014), 26−33. 25. Barbatti, M.; Granucci, G.; Ruckenbauer, M.; Plasser, F.; Crespo‐Otero, R.; Pittner, J.; Persico, M.; Lischka, H. NEWTON‐X: A package for Newtonian Dynamics Close to the Crossing Seam. Available via the Internet at www.newtonx.org, 2013. 26. Crespo‐Otero, R.; Barbatti, M. Spectrum Simulation and Decomposition with Nuclear Ensemble: Formal Derivation and Application to Benzene, Furan and 2‐Phenylfuran. Theor. Chem. Acc. 131(2012), 1237. 27. Tully, J. C. Molecular‐Dynamics with Electronic‐Transitions. J. Chem. Phys. 93(1990),1061−1071.
28. Barbatti, M. Nonadiabatic Dynamics with Trajectory Surface Hopping Method. WIREs: Comp. Mol. Sci. 1(2011), 620−633. 29. Granucci, G.; Persico, M. Critical Appraisal of the Fewest Switches Algorithm for Surface Hopping. J. Chem. Phys. 126(2007), 134114−134111. 30. Hammes‐Schiffer, S., Tully, J. C. Proton‐Transfer in Solution ‐ Molecular‐ Dynamics with Quantum Transitions. J. Chem. Phys. 101(1994), 4657−4667. 31. Boris Minaev and Elena Bilan, Spin‐Orbit Coupling Effects in Ozone Depletion Spectroscopy, Bull. Polish Acad. Sci.,Theor.Chem.,49 (2001),134‐ 163. 32. B. Minaev and H. Agren, Ab initio study of the singlet‐triplet transitions in hypobromous acid, J. Mol. Str. (Theochem), 492 (1999),53‐66.
7 6 5 4 3 2 G
S1
S2
T1
1 0 1.5
2
2.5
3 RBr‐O
10 9 8 7 6 5 4 3 2 1 0 1
1.5
4
Å
G
0.5
3.5
2
RO‐H Å
S1
2.5
S2
3
T1
3.5
Figure 1: Potential energy profile along the O‐H and O‐Br stretching coordinates (in angstrom) for the lowest singlet and triplet states of HOBr, computed at the EOM‐CCSD/aug‐cc‐pVTZ level of theory.
Figure 2 : Photoabsorption cross‐section in Å2.molecule‐1 as a function of the excitation energy (eV) of HOBr simulated at the M06‐2X/aug‐cc‐pVTZ level of theory.
(a)
(b) Figure 3: Potential energies of the ground and (a) states S1, S2 and S3 at the spectral window 4.0 eV ;(b) states S1‐S7 at the spectral window 8.0 eV, as a function of time.
Table 1 : Vertical‐Excitation Energies, Oscillator Strengths and main configurations obtained for HOBr with different methods and aug‐cc‐pVTZ basis Set. B97‐XD Sy E,e m V 3.58 A” 4.43
A’
6.77
A”
6.88
A”
8.43
A’
9.11
A”
10.31
A”
F
0.00 2 0.01 8 0.00 6 0.01 1 0.12 0.00 2 0.04 4
M06‐2X E,e Sy V m
Assignmen t nBr–*
weigh t 0.70
3.45
A”
nBr – *
0.70
4.33
A’
nBr ‐ * nO ‐* nO ‐ * nBr ‐ * nBr ‐5p ‐ * nBr ‐5p
0.60 0.25 0.64 ‐ 0.22 0.60 0.33 0.69
6.69
A”
7.40
A’
8.60
A’
9.15
A”
nBr ‐Ryd nBr‐ *
0.60 ‐0.24
8.85
A”
f
0.00 1 0.01 7 0.01 2 0.03 7 0.08 1 0.02 9 0.01
Assignmen t nBr –*
weigh t
EOM‐CCSD E,e Sy V m
0.68
3.77
A”
nBr –*
0.68
4.63
A’
0.00 2 0.02
nBr ‐*
0.64
7.015
A”
0.02
nBr ‐ * nBr ‐ Ryd ‐ * nBr ‐ Ryd nBr Ryd nBr ‐ Ryd
0.66 0.48 ‐0.38 0.49 ‐0.41 ‐0.51
7.78
A’
0.05
8.42
A”
0.08
8.64
A’
0.18
8.85
A”
0.01
f
Assignmen t nBr–* n– * nBr – * nBr – * ‐* nBr‐* ‐* nBr ‐ * n‐ Ryd nBr ‐Ryd nBr ‐ Ryd n ‐ Ryd nBr ‐ Ryd
weigh t 0.32 0.45 0.33 0.47 ‐0.39 ‐0.33 ‐0.39 ‐0.33 0.41 0.39 0.41 0.39 ‐0.51
Table 2: Transition energies of singlet, triplet and ionized states of HOBr computed at the SAC‐CI /aug‐cc‐pVTZ level of theory.
Spin
symm
E,eV
S2 S1 T1 Ionized cation doublet
Aʹ A” A’ A’ A”
4.635 3.776 3.790 11.324 10.604
Transition dipole, au x y ‐0.0852 0.1695 0.0 0.0 0.0 0.0
f z 0.0000 0.0085 0.0
0.0041 0.000 0.0 0.955 0.948
S1010-6030(16)30074-0 http://dx.doi.org/doi:10.1016/j.jphotochem.2016.02.024 JPC 10153
To appear in:
Journal of Photochemistry and Photobiology A: Chemistry
Received date: Revised date: Accepted date:
31-1-2016 24-2-2016 27-2-2016
Please cite this article as: Saadullah G.Aziz, Abdulrahman O.Alyoubi, Shaaban A.Elroby, Rifaat H.Hilal, Photochemical dissociation of HOBr.A nonadiabatic dynamics study, Journal of Photochemistry and Photobiology A: Chemistry http://dx.doi.org/10.1016/j.jphotochem.2016.02.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Photochemical Dissociation of HOBr. A Nonadiabatic Dynamics Study Saadullah G. Aziz1, Abdulrahman O. Alyoubi 1, Shaaban A. Elroby 1,2, and Rifaat H. Hilal 1,3* Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah B.O. 208203, Saudi Arabia; E‐Mails: [email protected] (S.G.A.); [email protected] (A.O.A.); [email protected] (S.A.E.) 2 Chemistry Department, Faculty of Science, Beni‐Suef University, Beni‐Suef 6251, Egypt 3 Chemistry Department, Faculty of Science, Cairo University, Cairo 12613, Egypt 1
[email protected]
Highlights The excited state properties and photochemical dissociation of hypobromous acid, HOBr were investigated using equation of motion coupled cluster (EOM‐CCSD ) and time‐dependent density functional theory (TDDFTThe decay of the excited states of HOBr in the gas phase was examined . The spectrum, composed of 10 excited states, was simulated with the nuclear ensemble approximation, sampling a Wigner distribution with 500 points. Dynamics simulations were done with the surface hopping method. ). Results are in good agreement with experimental data.
Abstract A number of single‐reference post Hartree‐Fock methods, namely CIS, symmetry adopted cluster configuration interaction (SAC‐CI), equation of motion coupled cluster (EOM‐CCSD ) and time‐dependent density functional theory (TDDFT), were used to investigate the excited state properties and photochemical dissociation of hypobromous acid, HOBr. Results are in good agreement with experimental data. The decay of the excited states of HOBr in the gas phase was examined by simulating the UV photoabsorption spectrum and nonadiabatic dynamics at the TDDFT M06‐2X level of theory. The spectrum, composed of 10 excited states, was simulated with the nuclear ensemble approximation, sampling a Wigner distribution with 500 points. Dynamics simulations were done with the surface hopping method, started in two separate spectral windows, at 4.0 ± 0.25 eV and 8.0 ± 0.25 eV, to be compared to experimental UV spectral data. Three hundred trajectories were considered from each of these windows according to their excitation probabilities. The excited‐state lifetime was determined. The main photochemical channel observed were HO and Br eliminations, representing 67% of all processes. Key words: HOBr‐ Excited state dynamics‐ TDDFT – photodissociation – non‐adiabatic dynamics
1. Introduction
The important role played by the different bromine species in ozone depletion, was recently recognized [1,2]. This is especially important in the Arctic spring and in areas where there exist high concentration of HOX species ( e.g. OH radical) [3‐ 6]. The depletion of ozone by BrO and OH radical was in investigated in the laboratory [7‐9] where it was concluded that such a process would increase the recycling of bromine. The photolysis of HOBr was suggested to be the most important channel in this respect[10]. and may be written as HOBr + hv HO + Br This photodissociation reaction was investigated near the threshold of dissociation at 490 and 510 nm. Characterization of the OH photofragment was carried out via Doppler and polarization spectroscopy using laser‐induced fluorescence [11]. The UV‐VIS spectrum of HOBr was, measured over the 200‐420 nm range. Two main absorption bands centered near 280 and 350 nm were observed[12,14]. A third long wave length band, centered near 440 nm was later detected by monitoring the yield of OH radicals as the wavelength of an excitation laser is scanned over the region from 440 to 650 nm. This band has been assigned to a transition to a triplet state, and although its peak absorption cross section is very small, its influence on determining the photochemical lifetime of HOBr is large due to its proximity to the peak of the solar actinic flux[9]. Motivated by the fact that very little is known about the photolysis of HOBr, its photochemical and photophysical dissociation mechanism, the present research project is launched with a focus on the calculation of excited state properties, using different correlated single‐reference methods. The reduced computational cost of
such methods has allowed us to extend our investigations to nonadiabatic dynamics processes [1] starting at highly excited states (S7−S11), where photochemical reactions of HOBr has been experimentally studied. It should be noted here that, although the molecule at hand is triatomic small and can in principle be handled by quantum dynamics, yet inclusion of this number of excited states in the quantum dynamics simulations is practically impossible. Based on these nonadiabatic dynamics simulations, we have been able to provide a much better insight into the photolysis of this molecule. 2. Computational Details The ground‐state geometry was optimized at the MP2 level with the aug‐cc‐pVTZ basis set[17,18] using GAUSSIAN 09[19]. This geometry was used for further calculations of the vertical excitations using the same basis set. The diffuse character of this basis set enables it to give the correct description of Rydberg orbitals. Excited state calculations started at the low level CIS [20] , and then the more accurate and involving symmetry adopted cluster configuration interaction (SAC‐CI)[16] and equation of motion coupled cluster with single and double excitations (EOM‐CCSD)[21], methods. TDDFT (time‐dependent density functional theory) calculations were also carried out with M06‐2X [22] and ωB97XD [23] functionals, using GAUSSIAN 09. For each method, 10 singlet excited states were computed. The Cs symmetry was enforced in all static calculations. In a second part of the investigation, relaxed potential energy‐curve calculations along two internal coordinates, namely the BrO‐H and the HO‐Br coordinates, have been performed. The ground and 10 excited states (5A′ and 5A″) have been computed on ground‐state relaxed geometries. The calculations have been carried out at the EOM‐CCSD method.
In the last part of the study, UV photoabsorption spectrum and nonadiabatic dynamics simulations were carried out to understand the ultrafast decay of the excited states of HOBr in the gas phase. Computations were performed using Newton‐X program package [24,25] at the TDDFT / M06‐2X level of theory. In order to simulate the photoabsorption spectrum, 500 points were sampled with the nuclear ensemble approximation [25]. The same number of excited states computed in the relaxed potential energy curves (10) was considered here. Dynamics simulations were started in two spectral windows at 4.0 ± 0.25 and 8.0 ± 0.25 eV. Three hundred trajectories were stochastically sampled from each of these windows according to their excitation probabilities. Dynamics simulations were done with the surface hopping method [26,27]. Classical equations were integrated with 0.5 fs time‐step, while quantum equations were integrated with 0.025 fs. For the quantum integration, all necessary quantities were interpolated between classical steps. Nonadiabatic effects between excited states were taken into account by the fewest switches algorithm [28] with decoherence corrections (α = 0.1 Hartree) [29]. Nonadiabatic couplings between excited states were computed by finite differences with the method proposed by Hammes‐Schiffer and Tully[30]. 3. Results and Discussion 3.1.Excitation Energies and Oscillator Strengths
The results obtained for vertical‐excitation energies, oscillator strengths, and state assignments computed with the TD‐M06‐2X and ωB97XD functionals and EOM‐ CCSD method, are shown in Table 1. With respect to the vertical excitation energies, all three methods are in good agreement with the observed spectrum of HOBr. All calculated excited states are in the range up to >10 eV. Two main band
systems dominate the computed spectrum. The first long wave length band system is centered on 3.5 eV and is composed of one configuration, namely the HOMO‐LUMO transition. The MO’s involved are displayed in Figure S3 of the supplementary material (SM). These KS MO’s were computed at the M06‐2X /aug‐ cc‐pVTZ level of theory. For visualization and to make the assignment of the delocalized KS MO’s more straightforward, a full natural orbital treatment (nbo) has been performed and the resulting orbitals are those displayed in Figure S3. The long wave length absorption at 3.39 eV is of very low intensity as compared to the short wave length one. This transition is of the combination of nBr – Ryd and ‐ * type localized on the O‐Br bond region. Whereas, the short wavelength absorption, which spans the 7.5‐8.5 eV range, may be attributed to a transition from a nBr–*. The Symmetry Adapted Cluster/Configuration Interaction (SAC‐CI) methods of Nakatsuji and coworkers[21] have been also used to explore the excited state space for the singlet, triplet and ionized states of HOBr. Results are summarized in table 2. SAC‐CI computations predicted two singlet states, one triplet and two ionized states in the region < 11.5 eV. The singlet states are heavily mixed with several configurations. These singlet states are contaminated by 1.7% and 0.53% of doublet states. The triplet state, on the other hand, is pure. The first ionized state is of symmetry A” and is characterized by ionization potential (I.P.) = 10.6 eV, leading to the formation of a cation. This state results in the removal of an electron from the HOMO (MO 22; nonbonding Br orbital). Ionization from the HOMO‐1 (MO 21) is responsible for the second ionized state ( A’) of I.P. =11.3 eV. This MO is also of the n‐ type representing the lone pair of the pπorbitals on the Br with little interaction with the p orbital of oxygen.
3.2.Photodissociation pathways of HOBr The presence of radical species such as OH, Br and OBr reveals two possible pathways for the photodissociation of HOBr, viz., OH stretching and OBr stretching pathways. The question arise is that how the excited singlet and triplet states of HOBr are populated along these two pathways. In order to examine the ordering of these excited states along these stretching pathways, the potential energy profile was computed at the EOM‐CCSD/ aug‐cc‐pVTZ level of theory, along the HO and the OBr coordinates. Results are depicted in Figure S1 of the supplementary materials (SM), for the ground and lowest excited states in the Franck‐Condon region. The O‐H distance is stretched up to 3.1 Å, while the O‐Br distance is stretched up to 3.7 Å. Excited singlet states all show parallel repulsive behavior along the O‐H stretching coordinate with the profiles of states S1 – S4 are closely approaching in the 2.0 ‐2.2 Å. All states are showing a dissociative behavior. The energy profile of the triplet states along the O‐H stretching coordinate is different, however. The lowest triplet state T1 intersects the ground state at RO‐H of 2.366 Å. This seems to pinpoint the deactivation pathway of the excited HOBr. The energy profiles along the O‐Br stretching coordinate show, however, a different behavior where both T1 and T2 contribute to the deactivation pathway. Both triplet states intersect the ground state at 3.02 Å. In conclusion, upon photo‐excitation, one would expect deactivation through intersection of the low‐lying triplet with the ground state whereas, on the singlet PES, however, surface hoping may take place between S2/S3 states and dissociation is the dominant behavior. A question may arise at this point is that how these triplets get populated?. To answer this question, the potential energy profile along both RO‐H and RO‐Br for the lowest singlet and triplet states are displayed in Figure 1. Along the O‐Br coordinate S1 approaches and intersects T1 at a RO‐Br distance of 2.62 Å just before T1 intersects the ground state at a RO‐Br
distance of 2.82 Å . This seems to explain how T1 gets populated. This is in agreement with Minaev’s [9,31,32] excellent work on the spectra of HOX (
X=Cl, Br and I). Along the RO‐H coordinate, however, the situation is not that straightforward. Indeed, T1 intersect the ground state at RO‐H of 2.367 Å , however, T1 intersects S1 at a larger O‐H distance. That is, T1 cannot be populated along this coordinate 3.3.UV‐Photoabsorption Spectrum simulation The photoabsorption spectrum of HOBr in the UV region, calculated at the TDDFT level with the M06‐2X functional using the aug‐cc‐pVTZ, is shown in Figure 2. In the region up to 10 eV, the absorption spectrum shows two main bands, one with high intensity with peaks at 8.37 eV (cross‐section=0.47 in Å2 per molecule‐1. ) and a short wavelength absorption with much lower intensity at 4.37 eV ( cross‐section = 0.003 in Å2 per molecule‐1). Moreover, the 4.37 eV band has a clear tail at 3.8 eV whereas, a more diffuse low intensity shoulder at the low‐energy tail of the 8.37 eV band is predicted at ∼7.4 eV. The comparison of these spectral features with the vertical spectrum of Table 1 allows the direct assignment of most of these features. Experimentally, excitation laser scanning studies [15] show that excitation at 440 nm is responsible for the photodissociation of HOBr leading to the increase of OH concentration. The photochemical lifetime of troposphere HOBr in polar regions, is suggested to be shortened by a factor of 2 compared to values based on the near‐UV absorption bands alone. Furthermore, experimental observations suggest that absorption into this band is responsible for up to 50% of the total photolysis rate of HOBr [10].
Dynamics simulations starting from two energy windows centered at 4.0 and 8.0 eV show reaction pathways, leading to two main products. The dynamics in the spectral window centered about 4.0 eV show 54% probability to originate from excited state 3 (n*). Whereas, dynamics in the spectral windows centered about 8.0 eV, show 67% probability to originate from state 7 (nRyd*). One should also bear in mind that due to methodological limitations (trajectories were stopped just before conversion to the ground state), only excited‐state dissociation processes are accounted for in the present study. Two dissociation channels were observed with the above probability values, namely , elimination of H and the consequent formation of OBr and a second channel where the OH is eliminated leaving Br. Let us examine the dynamics took place at the spectral windows 4.0 eV. Figure 3a displays the evolution of the energies of the three states S0, S1 and S2 with time. The trajectories show different behavior, however. The evolution of both S1 and S2 show slight attractive behavior in the first 25 fs where S1 starts a repulsive decay much steeper than that of S2 leading to crossing S1/S2 at 35 fs. These dynamics corresponds to a dissociation channel leading to the formation of the OH radical in agreement with experimental observation [11,34]. At time 33.50 fs the molecule was on surface 3 (S2). The energy gap to S1 was 0.03 eV. At time 34.00 fs, the molecule was on surface 2 (S1), therefore a surface hopping took place. The energy gap with S0 was 0.63 eV and with S1 was 0.07eV. This seems to be the only surface hopping taking place just before dissociation. Let us examine this hopping process more closely, in substep 1341 belonging to step 68 , the molecule still on surface 3 with population in this state of 85.7% is ready for hopping into surface 2. Upon hopping into S1 the population of surface 2 increase to 34% and remains populated in the next substeps, and in fact population increases to about 50% until the termination of the trajectories. The dynamics at the spectral window 8.0 eV is much more involving, however. We simulated the dynamics while the system is
in surface 7 for 500 fs. Figure 3b displays the evolution of the energies of the 7 states within the time domain studied. Note that the trajectories are all broken in 80 fs time interval due to the dissociation of the molecule. The molecule starts at S7 and soon under goes the first surface hopping in step 16 after 8.0 fs to S6 where it remains on this surface until step 64 after 32.0 fs where it hops into surface 5 which is immediately followed by another hopping into S4 at 33.0 fs. However, due to the crowdness of the energy profiles in this region, the molecule reverts back into surface 5 after 1.5 fs. At 38.0 fs it undergoes a hopping with high probability into S4 then a final hopping with even higher probability took place to S3 at 48.5 fs. The system remains on S3 until 78 fs where all trajectories were broken. The energy profiles of all surfaces underwent drastic change at the 48.0 – 53.0 fs range and at the 68.0‐ 72.0 fs range. In these two time domains S4, S5 and S7 show a steep repulsive rise whereas; all other surfaces show an opposite trend. The very idea of on‐fly dynamics is based on nonadiabatic couplings between excited states which were computed, in the present work, by finite differences with the method proposed by Tully[28].Unfortunately, Newton‐X software package does handle spin‐orbit coupling so far, although efforts are being carried out to include it. The importance of SOC has been discussed for different HOX (X=Cl, Br, and I) species by Minaev[9,31,32]; where he pinpointed the importance of SOC and quadrapole coupling constants for spectral interpretation of HOI molecule in a way which is more marked than the other hypohalaous molecules. 4. Conclusion The photochemical‐dissociation process of HOBr an important atmospheric pollutant, was investigated with quantum‐chemical methods, including vertical spectrum and potential energy curves at CIS, EOM‐CCSD, SAC‐CI and TDDFT
levels, as well as vibrationally broadened spectrum simulations and nonadiabatic dynamics with TDDFT. Energy ordering and excited‐state characters calculated with single‐reference methods, especially TDDFT, are in good agreement with experimental results. Deactivation of excited HOBr through intersection of T1 with the ground state takes place along the O‐Br coordinate. T1 is populated by intersection with S1 earlier on the O‐Br coordinate. Internal conversion S1to the ground state is not observed in both cases studied, namely at the spectral windows at 4.0 and 8.0 eV. Photodissociation occurred through two different reaction pathways with two main products, including atomic elimination (Br, or H), and multifragmentation (Br+OH,or OBr+H), mechanism. The main photochemical channel observed were OH +Br, representing 67% of all processes. 5. Acknowledgements This project was funded by the National Plan for Science, Technology and Innovation (MAARIFAH) – King Abdulaziz City for Science and Technology ‐ the Kingdom of Saudi Arabia – award number (11‐ENV
1995‐03). The authors also, acknowledge with thanks Science and Technology Unit, King Abdulaziz University for technical support.
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28. Barbatti, M. Nonadiabatic Dynamics with Trajectory Surface Hopping Method. WIREs: Comp. Mol. Sci. 1(2011), 620−633. 29. Granucci, G.; Persico, M. Critical Appraisal of the Fewest Switches Algorithm for Surface Hopping. J. Chem. Phys. 126(2007), 134114−134111. 30. Hammes‐Schiffer, S., Tully, J. C. Proton‐Transfer in Solution ‐ Molecular‐ Dynamics with Quantum Transitions. J. Chem. Phys. 101(1994), 4657−4667. 31. Boris Minaev and Elena Bilan, Spin‐Orbit Coupling Effects in Ozone Depletion Spectroscopy, Bull. Polish Acad. Sci.,Theor.Chem.,49 (2001),134‐ 163. 32. B. Minaev and H. Agren, Ab initio study of the singlet‐triplet transitions in hypobromous acid, J. Mol. Str. (Theochem), 492 (1999),53‐66.
7 6 5 4 3 2 G
S1
S2
T1
1 0 1.5
2
2.5
3 RBr‐O
10 9 8 7 6 5 4 3 2 1 0 1
1.5
4
Å
G
0.5
3.5
2
RO‐H Å
S1
2.5
S2
3
T1
3.5
Figure 1: Potential energy profile along the O‐H and O‐Br stretching coordinates (in angstrom) for the lowest singlet and triplet states of HOBr, computed at the EOM‐CCSD/aug‐cc‐pVTZ level of theory.
Figure 2 : Photoabsorption cross‐section in Å2.molecule‐1 as a function of the excitation energy (eV) of HOBr simulated at the M06‐2X/aug‐cc‐pVTZ level of theory.
(a)
(b) Figure 3: Potential energies of the ground and (a) states S1, S2 and S3 at the spectral window 4.0 eV ;(b) states S1‐S7 at the spectral window 8.0 eV, as a function of time.
Table 1 : Vertical‐Excitation Energies, Oscillator Strengths and main configurations obtained for HOBr with different methods and aug‐cc‐pVTZ basis Set. B97‐XD Sy E,e m V 3.58 A” 4.43
A’
6.77
A”
6.88
A”
8.43
A’
9.11
A”
10.31
A”
F
0.00 2 0.01 8 0.00 6 0.01 1 0.12 0.00 2 0.04 4
M06‐2X E,e Sy V m
Assignmen t nBr–*
weigh t 0.70
3.45
A”
nBr – *
0.70
4.33
A’
nBr ‐ * nO ‐* nO ‐ * nBr ‐ * nBr ‐5p ‐ * nBr ‐5p
0.60 0.25 0.64 ‐ 0.22 0.60 0.33 0.69
6.69
A”
7.40
A’
8.60
A’
9.15
A”
nBr ‐Ryd nBr‐ *
0.60 ‐0.24
8.85
A”
f
0.00 1 0.01 7 0.01 2 0.03 7 0.08 1 0.02 9 0.01
Assignmen t nBr –*
weigh t
EOM‐CCSD E,e Sy V m
0.68
3.77
A”
nBr –*
0.68
4.63
A’
0.00 2 0.02
nBr ‐*
0.64
7.015
A”
0.02
nBr ‐ * nBr ‐ Ryd ‐ * nBr ‐ Ryd nBr Ryd nBr ‐ Ryd
0.66 0.48 ‐0.38 0.49 ‐0.41 ‐0.51
7.78
A’
0.05
8.42
A”
0.08
8.64
A’
0.18
8.85
A”
0.01
f
Assignmen t nBr–* n– * nBr – * nBr – * ‐* nBr‐* ‐* nBr ‐ * n‐ Ryd nBr ‐Ryd nBr ‐ Ryd n ‐ Ryd nBr ‐ Ryd
weigh t 0.32 0.45 0.33 0.47 ‐0.39 ‐0.33 ‐0.39 ‐0.33 0.41 0.39 0.41 0.39 ‐0.51
Table 2: Transition energies of singlet, triplet and ionized states of HOBr computed at the SAC‐CI /aug‐cc‐pVTZ level of theory.
Spin
symm
E,eV
S2 S1 T1 Ionized cation doublet
Aʹ A” A’ A’ A”
4.635 3.776 3.790 11.324 10.604
Transition dipole, au x y ‐0.0852 0.1695 0.0 0.0 0.0 0.0
f z 0.0000 0.0085 0.0
0.0041 0.000 0.0 0.955 0.948