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Roaming and chaotic behaviors in collisional and photo-initiated molecular-beam reactions: a role of classical vs. quantum nonadiabatic dynamics

  • The Quantum World of Molecules
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Abstract

A new reaction scheme is proposed to account for roaming and chaotic behaviors in collisional and photo-initiated molecular-beam reactions, where nonadiabatic dynamics plays a key role and the collapse of superposition of wave functions is considered to be important in the beginning of the present scheme. Since the feature of molecular orbitals of reagents is crucial in reaction, we showed how to map out the spatial distribution of the relevant HOMO molecular orbitals of CH3Cl in the impact of fast electrons. We identified by experiment that the multiple overlap of nearby molecular orbitals affects even the vibrational motion of adjacent molecule DCl of the transient [ClDCl] chemical species. We also showed dynamical steric effects in the HBr + OH four-atom reaction as a manifestation of the nonadiabatic dynamics in complex systems. The roaming mechanism in the photo-initiated reaction of methyl formate is clarified in detail by experiment as well as the QCT trajectory calculation, where the conical intersection region plays an essential role. We suggest that two types of roaming trajectories coexist, i.e., deterministic and chaotic roaming trajectories based on classical trajectory calculations. To clarify the nonadiabatic dynamics in the roaming mechanism for non-collinear three-dimensional (3D) collisions, a new model of the 3D Polanyi rule is proposed as the extension of the well-established 2D Polanyi rule. In the 3D Polanyi rule, it is expected that the curvature and torsion of Frenet–Serret formulas in three-dimensional space would provide us key concepts in understanding reaction dynamics.

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Fig. 1

[adapted from (Kasai et al. 1993)]

Fig. 2

[adapted from (Kasai et al. 1995)]

Fig. 3

[adapted from Kasai et al. (1995)]

Fig. 4
Fig. 5

[adapted from (Mitani et al. 2004)]

Fig. 6

(adapted from Tsai et al. (2010, 2011)]

Fig. 7

[adapted from (Tsai et al. 2011)]

Fig. 8

[adapted from Bonnet et al. (2007)]

Fig. 9

[adapted from Tsai et al. (2011)]

Fig. 10
Fig. 11

[adapted from Polanyi (1972) and Polanyi and Wong (1969)]

Fig. 12

[adapted from Kasai and Kuwata (1978)]

Fig. 13
Fig. 14

[adapted from Kasai and Lin (2017)]

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References

  • Agmon N (1982) Fine structure in the dependence of final conditions on initial conditions in classical collinear H2 + H dynamics. J Chem Phys 76:1309

    Article  CAS  Google Scholar 

  • Anderson PN, Hits RA (1996) OH radical reactions: the major removal pathway for polychlorinated biphenyls from the atmosphere. Environ Sci Technol 30:1756

    Article  CAS  Google Scholar 

  • Aquilanti V (1995) Elementary chemical processes: how quantum and semiclassical mechanics avoid classical catastrophes and chaos. In: Costa G, Calucci G, Giorgi M (eds) Conceptual tools for understanding nature. World Scientific, Singapore, pp 76–92

    Google Scholar 

  • Aquilanti V, Cavalli S, Grossi G (1985) Semiclassical analysis of regular and irregular modes of coupled quantum oscillators. In: Casati G (ed) Chaotic behaviour in quantum systems. Plenum Press, New York, pp 299–308

    Chapter  Google Scholar 

  • Aquilanti V, Cavalli S, Grossi G (1989) Quantum behavior at a cusp, or how wave mechanics avoids a catastrophe. Chem Phys Lett 162:173

    Article  CAS  Google Scholar 

  • Aquilanti V, Pirani F, Cappelletti D, Vecchiocattivi F, Kasai T (2004) Theory of chemical reaction dynamics ed. by A. Lagana and G. Lendvay. NATO Sci Ser II Math Phys Chem 145:243

    Article  CAS  Google Scholar 

  • Atkinson DB, Jaramillo VI, Smith MA (1997) Low-temperature kinetic behavior of the bimolecular reaction OH + HBr (76–242 K). J Phys Chem A 101:3356

    Article  CAS  Google Scholar 

  • Bonnet L, Larregaray P, Duguay B, Rayez JC, Che D-C, Kasai T (2007) Stereoselectivity as a probe of unexpected reaction pathways. Bull Chem Soc Jpn 80:707

    Article  CAS  Google Scholar 

  • Brooks PR (1988) Spectroscopy of transition region species. Chem Rev 88:407

    Article  CAS  Google Scholar 

  • Butkovskaya NI, Setser DW (1996) Dynamics of OH and OD radical reactions with HI and GeH4 as Studied by infrared chemiluminescence of the H2O and HDO products. J Chem Phys 106:5028

    Article  Google Scholar 

  • Butkovskaya NI, Setser DW (1998) Vibrational excitation of H2O and HOD molecules produced by reactions of OH and OD with cyclo-C6H12, n-C4H10, neo-C5H12, HCl, DCl and NH3 as studied by infrared chemiluminescence. J Chem Phys 108:2434

    Article  CAS  Google Scholar 

  • Chao MS, Tornero J, Lin KC, Stolte S, Urena AG (2013) Decoherence cross-section in NO + Ar collisions: experimental results and a simple model. J Phys Chem A 117:8119

    Article  CAS  Google Scholar 

  • Che D-C, Hashinokuchi M, Shimizu Y, Ohoyama H, Kasai T (2001) Photodissociation of DCl dimer selected by an eletrostatic hexapole field combined with a Doppler-selected time-of-flight technique: observation of [ClDCl] transient species. Phys Chem Chem Phys 3:4979

    Article  CAS  Google Scholar 

  • Che D-C, Matsuo T, Yano Y, Bonnet L, Kasai T (2008) Negative collision energy dependence of Br formation in the OH + HBr reaction. Phys Chem Chem Phys 10:1419

    Article  CAS  Google Scholar 

  • Che D-C, Doi A, Yamamoto Y, Okuno Y, Kasai T (2009) Collision energy dependence for the Br formation in the reaction of OD + HBr. Phys Scr 80:048110

    Article  CAS  Google Scholar 

  • Clary DC, Nyman G, Hernandez R (1994) Mode selective chemistry in the reactions of OH with HBr and HCl. J Chem Phys 101:3704

    Article  CAS  Google Scholar 

  • Coutinho ND, Silva VHC, de Oliveira HCB, Camargo AJ, Mundim KC, Aquilanti V (2015) Stereodynamical origin of anti-arrhenius kinetics: negative activation eneregy and roaming for a four-atom reaction. J Phys Chem Lett 6:1553

    Article  CAS  Google Scholar 

  • Coutinho ND, Aquilanti V, Silva VHC, Camargo AJ, Mundim KC, de Oliveira HCB (2016) Stereodirectional origin of anti-Arrhenius kinetics for a tetraatomic hydrogen exchange reaction: born-oppenheimer molecular dynamics for OH + HBr. J Phys Chem A 120:5408

    Article  CAS  Google Scholar 

  • de Broglie L (1923) Quanta de Lumiere, diffraction et interferences. Comptes Rendus Acad Sci 177:548

    Google Scholar 

  • Garcia RR, Solomon SJ (1994) A New numerical model of the middle atmosphere: 2. Ozone and related species. J Geophys Res 99:12937

    Article  CAS  Google Scholar 

  • Giulini D, Joos E, Kiefer C, Kupsch J, Stamatescu I-O, Zeh HD (1996) Decoherence and the appearance of a classical world in quantum theory. Springer, Berlin, p 47

    Book  Google Scholar 

  • Grzybowski BA (2009) Chemistry in motion for micro- and nonotechnology. Wiley, New York

    Book  Google Scholar 

  • Han Y-C, Tsai P-Y, Bowman JM, Lin K-C (2017) Photodissociation of CH3CHO at 248 nm: identification of the channels of roaming, triple fragmentation and the transition state. Phys Chem Chem Phys 19:18628

    Article  CAS  Google Scholar 

  • Harrison JC, Ham JE, Wells JR (2007) Citronellal reactions with ozone and OH radical: rate constants and gas-phase products detected using pfbha derivatization. Atmospheric Environment 41:4482

    Article  CAS  Google Scholar 

  • Heisenberg W, Northrop FSC (1999) Physics and philosophy: the revolution in modern science. Great minds series. Prometheus Books

  • Hering P, Brooks PR, Curl RF, Judson RS, Lowe RS (1980) Chemiluminescent reaction channel opened by photon absorption during collision. Phys Rev Lett 44:687

    Article  CAS  Google Scholar 

  • Hilborn RC (1994) Chaos and nonlinear dynamics, an introduction for scientists and engineers. Oxford University Press, Oxford

    Google Scholar 

  • Hung K-C, Tsai P-Y, Li H-K, Lin K-C (2014) Photodissociation of CH3CHO at 248 nm by time-resolved Fourier-transform infrared emission spectroscopy: verification of roaming and triple fragmentation. J Chem Phys 140:064313

    Article  CAS  Google Scholar 

  • Imura K, Kasai T, Ohoyama H, Naaman R (1999) Focusing of DCl and HCl Dimers by an electrostatic hexapol field—the role of the tunneling motion. J Chem Phys 110:355

    Article  CAS  Google Scholar 

  • Jaramillo VI, Smith MA (2001) Temperature-dependent kinetic isotope effects in the gas-phase reaction: OH + HBr”. J Phys Chem A 105:5854

    Article  CAS  Google Scholar 

  • Jaramillo VI, Gougeon S, Picard SDL, Canosa A, Smith MA, Rowe BR (2002) A consensus view of the temperature dependence of the gas phase reaction: OH + HBr → H2O + Br. Int J Chem Kinet 34:339

    Article  CAS  Google Scholar 

  • Karplus M, Porter RN, Sharma RD (1965) Exchange reactions with activation energy. I. Simple barrier potential for (H, H2). J Chem Phys 43:3259–3287

    Article  CAS  Google Scholar 

  • Kasai T, Kuwata K (1978) Classical trajectory calculations of chemical reaction. Newsl Osaka Univ Large Scale Comput Cent 37(31):36

    Google Scholar 

  • Kasai T, Lin K-C (2017) Coordinate analysis for interpreting the decoherence in the coherent-NO with Ar collision: a physico-mathematical picture using the stereographic projection and the cusp catastrophe. J Chin Chem Soc 64:25

    Article  CAS  Google Scholar 

  • Kasai T, Matsunami T, Fukawa T, Ohoyama H, Kuwata K (1993a) Effect of molecular orientation on indirect ionization by electron impact of CH3Cl in the |111> eigenstate. Phys Rev Lett 70:3864

    Article  CAS  Google Scholar 

  • Kasai T, Fukawa T, Matsunami T, Che D-C, Ohashi K, Ohoyama H, Kuwata K (1993b) Formation of an intense pulsed beam of CH3Cl in the |111> state using a 2-m electrostatic hexapole field. Rev Sci Instrum 64:1150

    Article  CAS  Google Scholar 

  • Kasai T, Matsunami T, Fukawa T, Ohoyama H, Kuwata K (1995) Alignment and Orientation effects for the indirect ionization of CH3Cl in the |111> rotational state by fast electron impact. J Phys Chem 99:13597

    Article  CAS  Google Scholar 

  • Kasai T, Stolte S, Chandler D, Urena AG (2006) Editorial: stereodynamics of chemical reactions. Eur Phys J D 38:1

    Article  CAS  Google Scholar 

  • Kasai T, Che D-C, Tsai P-Y, Lin K-C (2012) Reaction dynamics with molecular beams and oriented molecular beams: a tool for looking closer to chemical reactions and photodissociations. J Chin Chem Soc 59:338

    Article  CAS  Google Scholar 

  • Kasai T, Che D-C, Okada M, Tsai P-Y, Lin K-C, Palazzetti F, Aquilanti V (2014) Directions of chemical change: experimental characterization of the stereodynamics of photodissociation and reactive processes. Phys Chem Chem Phys (Perspect) 16:9776

    Article  CAS  Google Scholar 

  • Kasai T, Muthiah B, Lin K-C (2017) Role of cooperative network interaction in transition region of roaming reactions: non-equilibrium steady state vs. thermal equilibrium reaction scheme. AIP Conf Proc 1906:030009

    Article  CAS  Google Scholar 

  • Kreyszig Erwin (1991) Differential geometry. Dover, New York, pp 40–43

    Google Scholar 

  • Kuwata K, Kasai T (1995) The chemical dynamics and kinetics of small radicals, part II. Adv Ser Phys Chem (World Scientific) 6:842–935

    Article  CAS  Google Scholar 

  • Lai L-H, Che D-C, Liu K (1996) Photodissociative pathways of C2H2 at 121.6 nm revealed by a Doppler-selected time-of-flight (a 3-D mapping) technique. J Phys Chem 100:6376

    Article  CAS  Google Scholar 

  • Li H-K, Tsai P-Y, Hung K-C, Kasai T, Lin K-C (2015) Photodissociation of CH3CHO at 308 nm: observation of H-roaming, CH3-roaming, and transition state pathways together along the ground state surface. J Chem Phys (Commun) 142:041101

    Article  CAS  Google Scholar 

  • Lin K-C (2016) Regulation of nonadiabatic processes in photolysis of some carbonyl compounds. Phys Chem Chem Phys (Perspect) 18:6980

    Article  CAS  Google Scholar 

  • Liu JY, Li ZS, Dai ZW, Huang XR, Sun CC (2001) Direct ab initio dynamics calculations of the reaction rates for the hydrogen abstraction OH + HBr → H2O + Br. J Phys Chem A 105:7707

    Article  CAS  Google Scholar 

  • Lombardi A, Palazzetti F, Aquilanti V, Li H-K, Tsai P-Y, Kasai T, Lin K-C (2016) Rovibrationally excited molecules on the verge of a triple breakdown: molecular and roaming mechanisms in the photodecomposition of methyl formate. J Phys Chem A 120:5155

    Article  CAS  Google Scholar 

  • Maguire TC, Brooks PR, Curl RF, Spence JH, Ulvic SJ (1986) Photoexcitation of reaction complexes in the reaction K + NaCl → KCl + Na. J Chem Phys 85:844

    Article  CAS  Google Scholar 

  • Metz RB, Weaver A, Bradforth SE, Kitsopoulous TN, Neumark DM (1990) Probing the transition state with negative ion photodetachment: the chlorine atom + hydrogen chloride and bromine atom + hydrogen bromide reactions. J Phys Chem 94:1377

    Article  CAS  Google Scholar 

  • Mitani M, Yoshioka Y, Che D-C, Kasai T (2004) Vibrational analysis with the symmetrically combined morse potential model for antisymmetiric stretching in [ClDCl] formed by photodissociation of (DCl)2. J Phys Chem A 108:5220

    Article  CAS  Google Scholar 

  • Molina MJ, Rowland FS (1974) Stratospheric sink for chlorofluoromethanes: chlorine atom-catalysed destruction of ozone. Nature 249:810

    Article  CAS  Google Scholar 

  • Nakamura M, Che DC, Tsai PY, Lin KC, Kasai T (2013) Alignment selection of the metastable CO(a3Π1) Molecule and the steric effect in the aligned CO(a3Π1) + NO collision. J Phys Chem A 117:8157

    Article  CAS  Google Scholar 

  • Nakamura M, Tsai P-Y, Kasai T, Lin K-C, Palazzetti F, Lombardi A, Aquilanti V (2015) Dynamical, spectroscopic and computational imaging of bond breaking in photodissociation: roaming and role of conical intersections. Faraday Discuss 177:77

    Article  CAS  Google Scholar 

  • Neumark DM (1993) Transition-state spectroscopy via negative ion photodetachment. Acc Chem Res 26:33

    Article  CAS  Google Scholar 

  • Nizamov B, Setser DW (1996) Quasiclassical trajectory calculations for the OH(X 2Π) and OD(X 2Π) + HBr reactions: energy partitioning and rate constants. J Chem Phys 105:9897

    Article  CAS  Google Scholar 

  • Pines D, Bohm DA (1952) Collective description of electron interactions: II. Collective vs individual particle aspects of the interactions. Phys Rev 85:338

    Article  CAS  Google Scholar 

  • Polanyi JC (1972) Some concepts in reaction dynamics. Acc Chem Res 5:161

    Article  CAS  Google Scholar 

  • Polanyi JC, Wong WH (1969) Location of energy barriers. I. Effect on the dynamics of reactions A + BC. J Chem Phys 51:1439

    Article  CAS  Google Scholar 

  • Poston T, Stewart I (1975) Catastrophe theory and its applications. Pitman Publishing, London

    Google Scholar 

  • Rankin CC, Miller WH (1971) Classical S matrix for linear reactive collisions of H + Cl2. J Chem Phys 55:3150

    Article  CAS  Google Scholar 

  • Schreel K, Meulen JJ (1997) State-to-state scattering of oriented OH. J Phys Chem A 101:7639

    Article  CAS  Google Scholar 

  • Sims IR, Smith IWM, Clary DC, Bocherel P, Rowe BR (1994) Ultra-low temperature kinetics of neutral-neutral reactions: new experimental and theoretical results for OH + HBr between 295 and 23 K. J Chem Phys 101:1748

    Article  CAS  Google Scholar 

  • Skouteris D, Manopoulos DE, Bian W, Werner H-J, Lai L-H, Liu K (1990) van der Waals interactions in the Cl + HD reaction. Science 286:1713

    Article  Google Scholar 

  • Thom R (1978) Structural stability and morphogenesis. Benjamin, Reading

    Google Scholar 

  • Townsend D, Lahankar SA, Lee SK, Chambreau SD, Suits AG, Zhang X, Rheinecker J, Harding LB, Bowman JM (2004) The roaming atom: straying from the reaction path in formaldehyde decomposition. Science 306:1158

    Article  CAS  Google Scholar 

  • Tsai P-Y, Lin K-C (2015a) Insight into the photodissociation dynamical feature of conventional transition state and roaming pathways by an impulsive model. J Phys Chem A 119:29

    Article  CAS  Google Scholar 

  • Tsai P-Y, Lin K-C (2015b) Insight into photofragment vector correlation by multi-center impulsive model. Phys Chem Chem Phys 17:19592

    Article  CAS  Google Scholar 

  • Tsai P-Y, Che D-C, Nakamura M, Lin K-C, Kasai T (2010) Orientation dependence in the four-atom reaction of OH + HBr using the single-state oriented OH radical beam. Phys Chem Chem Phys (Commun) 12:2532

    Article  CAS  Google Scholar 

  • Tsai P-Y, Che D-C, Nakamura M, Lin K-C, Kasai T (2011) Orientation dependence for Br formation in the reaction of oriented OH radical with HBr molecule. Phys Chem Chem Phys 13:1419

    Article  CAS  Google Scholar 

  • Tsai P-Y, Chao M-H, Kasai T, Lin K-C, Lombardi A, Palazzetti F, Aquilanti V (2014a) Road leading to roam. Role of triple fragmentation and of conical intersections in photochemical reactions: experiments and theory on methyl formate. Phys Chem Chem Phys 16:2854

    Article  CAS  Google Scholar 

  • Tsai P-Y, Hung K-C, Li H-K, Lin K-C (2014b) Photodissociation of propionaldehyde at 248 nm: roaming pathway as an increasingly important role in large aliphatic aldehydes. J Phys Chem Lett 5:190

    Article  CAS  Google Scholar 

  • Tsai P-Y, Li H-K, Kasai T, Lin K-C (2015) Roaming as the dominant mechanism for molecular products in photodissociation of large aliphatic aldehydes. Phys Chem Chem Phys 17:23112

    Article  CAS  Google Scholar 

  • Wayne RP (1991) Chemistry of the atmospheres, 3rd edn. Oxford University, Oxford

    Google Scholar 

  • Wormer PES, Ktos JA, Groenenboom GC, van der Avoird AD (2005) Ab initio computed diabatic potential energy surfaces of OH–HCl. J Chem Phys 122:244325

    Article  CAS  Google Scholar 

  • Zewail AH (1988) Laser femtochemistry. Science 242:1645

    Article  CAS  Google Scholar 

  • Zurek WH (1991) Decoherence and the transition from quantum to classical. Phys Today 44(10):36–44

    Article  Google Scholar 

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Acknowledgements

The authors sincerely would like to dedicate the present work to Emeritus professor of Osaka University Keiji Kuwata who passed away on March 6, 2018. Prof. Kuwata was a pioneer and guided them to this exciting research field. They are grateful to Prof. Wilson Agerico Dino, and Jeffrey Tanudji, Department of Applied Physics, Graduate School of Engineering, Osaka University for stimulating discussion. TK thanks Prof. Hikaru Kobayashi, Institute of Scientific and industrial Research, Osaka University for his valuable comments, and appreciates Department of Chemistry, National Taiwan University for a financial support to carry out this work.

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Authors and Affiliations

  1. Department of Chemistry, National Taiwan University, Taipei, 10617, Taiwan

    Toshio Kasai, Masaaki Nakamura, Balaganesh Muthiah & King-Chuen Lin

  2. Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka, 567-0047, Japan

    Toshio Kasai

  3. Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, 560-0043, Japan

    Dock-Chil Che

  4. Department of Chemistry, National Chung-Hsing University, Taichung, 10402, Taiwan

    Po-Yu Tsai

  5. Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, 10617, Taiwan

    King-Chuen Lin

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  1. Toshio Kasai
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  2. Dock-Chil Che
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  3. Po-Yu Tsai
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  4. Masaaki Nakamura
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  5. Balaganesh Muthiah
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  6. King-Chuen Lin
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Correspondence to Toshio Kasai.

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Kasai, T., Che, DC., Tsai, PY. et al. Roaming and chaotic behaviors in collisional and photo-initiated molecular-beam reactions: a role of classical vs. quantum nonadiabatic dynamics. Rend. Fis. Acc. Lincei 29, 219–232 (2018). https://doi.org/10.1007/s12210-018-0709-4

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