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Observation of geometric phase effect induced photodissociation dynamics in phenol
Chemical Physics Letters 463 (2008) 305–308
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Observation of geometric phase effect induced photodissociation dynamics in phenol M.G.D. Nix *, A.L. Devine, R.N. Dixon, M.N.R. Ashfold School of Chemistry, University of Bristol, Cantocks Close, Bristol BS8 1TS, UK
a r t i c l e
i n f o
Article history: Received 10 July 2008 In final form 22 August 2008 Available online 27 August 2008
a b s t r a c t Dynamical effects attributable to the geometric phase have been observed in UV photo-induced O–H bond fission in jet cooled phenol. Phenoxyl radicals are formed with an odd quanta progression in a00 mode m16a. This mode specific product formation is reproduced by 2D wavepacket simulations and discussed in terms of quantum interference resulting from the geometric phase effect at the conical intersection between the ground and first excited state potential energy surfaces at extended O–H bond lengths. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The geometric phase effect (GPE) [1] in molecular systems occurs at points of degeneracy such as conical intersections (CIs) of potential energy surfaces (PESs), due to the non-adiabatic nature of the vibronic interactions. Herzberg and Longuet-Higgins [2] first showed that the phase of the adiabatic electronic wavefunction (we) in a 2-state system changes by p with a nuclear motion of 2p around a CI. A sign change occurs in we and, as the overall wavefunction (W) must remain single valued throughout configuration space, an opposite phase change is required in the nuclear wavefunction (wNUC). Under the adiabatic approximation, this nuclear phase change (du) is neglected and must be re-introduced into wNUC as du = h/2, where h represents the angular transit about the CI. Nuclear wavefunctions which encircle a CI (h = 2p) an odd number of times exhibit a p relative phase shift; an even number of circuits are required to recover the original phase [3]. Observable GPEs result from re-combination and interference of two components of a wavefunction with differing du. This occurs when the CI is encircled by wNUC as it moves in the (2D) branching space of the CI. GPEs in molecular systems have recently received much attention [4–10], as the importance of CIs in reaction dynamics has increasingly become recognised. Reactive scattering systems, such as H + D2, in which the nuclear wavefunction is confined to one adiabatic PES in the vicinity of a CI have been predicted [9] to show a GPE, although no conclusive experimental demonstrations have yet been reported. Recent theoretical studies of the H + H2 system [4] suggest that, although the wavefunction bifurcates and encircles the CI, the bifurcation is asymmetric, with only 1% of the amplitude in the minor channel. The magnitude of any interference effect would thus necessarily be small. Furthermore,
* Corresponding author. Fax: +44 117 9250612. E-mail address: [email protected] (M.G.D. Nix). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.08.085
the two components are predicted to scatter into different regions of configuration space, precluding interference effects at long range, where detection would occur. An ideal system for experimental observation of a GPE would have a single exit channel from the CI region, forcing the two components of the wavefunction to recombine in configuration space and remain so thereafter, causing observable interference. Photodissociations often originate from a well-defined nuclear configuration and proceed via a single exit channel, removing many of the dynamical complications associated with full collisions. In an ‘ideal’ system, therefore, a well-characterised nuclear wavepacket would be prepared photolytically and dissociate via bifurcation around a CI, remaining on a single adiabatic PES throughout. We recently reported [11] the total kinetic energy release (TKER) spectra of the H + phenoxyl products resulting from UV photolysis of phenol via its S1 S0 000 transition. The phenoxyl products were observed to be formed in an odd-quanta progression in an out-of-plane (a00 ) vibrational mode. These dynamics were originally interpreted in a diabatic framework, involving symmetry restrictions on wNUC and we, with the odd quanta progression resulting from the off-diagonal H’’ coupling term between diabatic states (1pp (A0 ) and 1pr* (A00 )). [For clarity, we choose to describe the electronic states using either adiabatic (S0, S1, S2) or diabatic (1pp, 1pp*, 1pr*) labels, as in Fig. 1]. The data can also be interpreted in an adiabatic representation however, wherein they represent a manifestation of the GPE in dynamics on the S0 PES. This Letter illustrates the equivalence of the two interpretations and examines the significance of GPE in such systems, particularly where symmetry plays a role. 2. Observation and discussion The discussion here will focus on photodissociation of phenol via its S1 S0 origin transition, as this is representative of
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The electronic ground state of phenoxyl has 2A00 symmetry, whereas the ground state of phenol (which correlates to the first excited state of phenoxyl upon extending the O–H bond length, RO–H) has 1A0 symmetry (Fig. 1). The level populated by exciting the S1 S0(p* p) 000 band has A0 electronic (and vibronic) symmetry, and a reported fluorescence lifetime of 2 ns [12]. Most of the S1(v = 0) population transfers to the S0 PES (presumably on this same timescale) by internal conversion (IC), conserving the A0 (i.e. A0 a0 ) vibronic symmetry. The dominant acceptor modes following IC are (lifetime broadened) O–H stretch overtones of a0 symmetry [12], which allow direct access to the region of the 1pp/1pr* CI during the first vibrational period on the S0 PES and, subsequent O– H bond fission. We now consider this evolution in, respectively, a diabatic and an adiabatic framework. 2.1. Diabatic model
Fig. 1. Dissociation mechanism showing (a) initial excitation to the 1pp* PES and (b) mO–H specific IC to S0, followed by predissociation of S0 molecules at the 1 pp/1pr* CI at RO–H 1.9 Å. All subsequent dynamics (dashed arrow) occur on the S0 PES.
dynamics at higher photon energies also [11]. The TKER distribution (Fig. 2b) recovered from the recorded H atom time of flight (TOF) spectrum (Fig. 2a) is expanded and re-plotted (Fig. 2c) in terms of the internal energy of the phenoxyl co-fragment, Eint. The populated vibrational levels of the phenoxyl products were assigned [11] by fitting the observed peak separations in terms of the calculated (B3LYP/6-311+g(d,p)) wavenumbers for the (anharmonic) normal modes of vibration. The product distribution is dominated by m16a (an a00 mode), and the in-plane CO wag m18(a0 ), as shown in Fig. 2c. m18b is excited as a result of the recoil of the H atom as it departs from a non-coaxial COH geometry.
To form ground state phenoxyl + H products, the wavepacket must remain on the lower cone of the CI, switching electronic configuration and symmetry from 1pp (A0 ) to 1pr*(A00 ) in the process. The vibrational symmetry must also change (from a0 to a00 ) in order to maintain the overall A0 vibronic symmetry and allow the dissociation to occur. However, this is merely a symmetry requirement. A force is needed to produce such a change in the dissociating wavepacket. In the absence of coupling between the (diabatic) surfaces (i.e. with non-adiabatic interactions turned off), the population would remain on the 1pp PES and (assuming insufficient energy to access the excited phenoxyl (2A0 ) + H asymptote) revisit the Franck Condon region, as the symmetry would be incorrect to allow access to the 1pr*(A00 ) PES. Consider the interaction of the diabatic |1ppi and |1pr*i states in terms of the first order non-adiabatic coupling term, H00 . wNUC associated with the 1pr* state must necessarily gain a node at the CI, due to the fact that H00 is zero at the intersection point, where its sign changes. we(S0) becomes 1pr*(A00 ) in character and wNUC(S0) becomes a00 . we(S1) becomes 1pp (A0 ) and wNUC(S1) becomes a0 , conserving the symmetry of the full wavefunction. Of course, W evolves in a continuous (rather than sudden) fashion, necessitating the gradual application of H00 with h. 2.2. Adiabatic model
Fig. 2. (a) TOF and (b) TKER spectra following excitation of phenol at the S1–S0 origin (275.113 nm). (c) Assignment of phenoxyl product vibrational states in terms of internal energy (Eint).
In the adiabatic picture, the electronic structure of the S0 PES evolves smoothly from 1pp(A0 ) to 1pr*(A00 ) with increase in the angle h relative to the CI degenerate point, as shown in Fig. 3. No arbitrary coupling term is applied, but the nuclear phase information is missing and must be recovered. This is the GPE, which causes the phase of wNUC to change by p on encircling the CI. Consider a system such as that depicted in Fig. 3, where the coupling coordinate is an out-of-plane (a00 ) ring twisting mode such as m16a, and the initial, CI and final geometries are all planar. A wavepacket travelling from reactant (phenol) to product (phenoxyl + H) along RO–H on the S0 PES will bifurcate symmetrically and pass around the CI via two equivalent routes. Recombination of these components leads to overlap of the two bifurcated pieces of the time-dependent wavepacket, which is equivalent to complete encirclement of the CI by the time-independent wavefunction. Whilst no part of the wavepacket explicitly encircles the CI, the two components travel +p and p, respectively, with associated phase shifts du = ±p/2 in wNUC. Thus, the phase difference between the two components of wNUC in the exit channel is p and, due to the 50:50 bifurcation, complete destructive interference occurs on recombination at the plane of symmetry in the exit channel. A node is thus introduced into wNUC at large RO–H, causing the wavepacket that was initially
M.G.D. Nix et al. / Chemical Physics Letters 463 (2008) 305–308
Fig. 3. Schematic 2D equipotential plot of the S0 adiabatic PES. The wavepacket (shown above) bifurcates on approaching the CI, undergoes a phase change (du = ±h/2) and recombines in the exit channel, with a node at mcoupling = 0 (at the symmetry plane).
even (a0 ) to become odd (a00 ) in the coupling coordinate. The requirement for an a00 nuclear symmetry change is thus satisfied and access to the extended part of the adiabatic S0 PES (with 1 pr*(A00 ) electronic character) is allowed. The involvement of the GPE is crucial, else symmetry constraints would force the wavepacket to remain on the 1pp diabatic surface, preventing dissociation to the lowest asymptote (see Fig. 1a). That dissociation to this asymptote occurs at all is evidence of the GPE, but there is also a signature of the coupling in the phenoxyl product vibrational state distribution, which we have modelled. 2.3. Wavepacket simulations The system is represented by a 2D model involving RO–H and
m16a. We specifically consider the dynamics induced by the CI in m16a, so bifurcation will displace the wavepacket in m16a. Given that the GPE changes the parity of wNUC, a m16a = 0 wavepacket approaching the CI, bifurcating, and then recombining at large RO–H should produce a superposition of odd quanta in m16a. A diabatic model was chosen for computational ease, but is entirely equivalent to the adiabatic representation. To prepare the
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PESs, analytic functions were fitted first to ab initio DFT (B3LYP/ 6-311+g(d,p)) points, and the model PESs were subsequently fitted to the experimentally determined energetics (e.g. S1S0 origin, D0(C6H5OH)). It was also considered valid to use a continuously driven oscillator model to choose the initial wavefunction (rather than a time-dependent gaussian wavepacket) since ns laser pulses were employed experimentally and because IC from the S1(v = 0) level to the S0 PES occurs to broadened S0 levels on a ns timescale. The subsequent dissociation is expected to occur promptly (i.e. without significant IVR on S0). Driving high mO–H modes of the S0 PES into resonance near the S1 S0 origin excitation energy, we selected a wavefunction, corresponding to a single broadened eigenstate of the model S0 PES, to use as a starting point for the time-dependent propagation. The mO–H resonance in S0 was chosen to best represent the energy of the S1 zero point level. The off-diagonal non-adiabatic coupling parameter required to reproduce the observed product state distribution in (odd quanta of) m16a is V12 (q16a/q0 = 1) 1150 cm1. The exit channel (diabatic) wavefunction produced by the model (Fig. 4 (right panel)) clearly shows a node at planar geometries at large RO–H, reflecting the GPE induced interference between the two components of wNUC. The resulting vibrational progression can be examined by projecting the 1pr* wavefunction onto a basis of the (harmonic) vibrational wavefunctions of m16a. Experimental integrated intensities were obtained by subtracting a background function from the spectrum in Fig. 2c to eliminate contributions from the unimolecular decay channel, fitting gaussian peaks to the features assigned to the m16a progression and integrating the area under each function. The observed intensity pattern of the odd quanta progression is well reproduced by our simple model, as shown in Fig. 5. No peaks were observed for even quanta, although background signal, underlying the structured component, could in principle mask some weak contributions. The simulation predicts zero intensity in the even states as expected, due to the node at planarity in the exit channel wave. The oscillatory nature of the unbound wavefunction in the mO–H coordinate (Fig. 4b) indicates a kinetic energy release of 6000 cm1, also in excellent accord with the experimental data (see Fig. 2b). The question arises as to why similar dynamics have not been noted in previous photodissociation experiments, but the situation in phenol is rather unusual. The dissociation (following IC at an energy above that of the CI) occurs on a single adiabatic PES (S0) and
Fig. 4. Left: A continuously driven oscillator wavefunction, representing mO–H = 13 on the 1pp diabatic PES. Right: Population on the diabatic 1pr* state, following coupling at the 1pp/1pr* CI. The GPE induced node at q16a/q0 = 0 is clearly evident.
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3. Conclusion The odd quanta progression in m16a in the phenoxyl products resulting from UV photolysis of phenol is arguably the first experimental demonstration of molecular dynamics induced by GPEs. By employing photodissociation rather than bimolecular scattering, it has been possible to exert much tighter control over the initial wavefunction and to ensure that wNUC recombines fully following bifurcation and passage around the CI into the exit channel. GPEs are intrinsic to dynamics occurring adiabatically around a CI, but two distinct cases can be recognised
Fig. 5. Comparison of simulated and experimental integrated peak intensities for the progression in m16a. Experimental intensities were determined from the average integrated intensities over all available datasets. Experimental and simulated intensities were normalised at the m16a = 1 level.
the wavepacket encircles the CI before recombining in the exit channel. This situation must occur in many systems following IC, and the effects described above should be ubiquitous whenever there is a CI along the minimum energy pathway to products. However, IC will typically populate a wide spread of S0 vibrational levels, involving motions that do not correspond to the reaction coordinate. Significant IVR must occur in such cases in order that the minimum energy required to reach the product asymptote is transferred into the dissociation coordinate (in this case RO–H). Any residual energy in such cases will likely be retained as internal (vibrational) energy in the fragments, resulting in a broad distribution of populated product states and, in the limit, an unresolvable distribution of vibrationally hot products (and thus an unresolvable TKER spectrum). In phenol, however, the specific transfer of population into S0 levels with mO–H 13 allows direct access to the CI without significant IVR. Hence wNUC approaching the CI is unusually simple, and the GPE induced progression in m16a is resolved in the measured TKER spectra. Domcke et al. [6] have suggested that GPEs in the photodissociation of phenol could also affect the branching between product electronic states. Indeed, electronically excited phenoxyl products would be expected in the limit that the recoil velocity was sufficient to support non-adiabatic ‘hopping’ between the PESs; the present modelling would predict selective formation of excited phenoxyl products with m16a = 0, 2, 4, . . . Experimentally [11], however, we have not identified formation of such excited products, even at shorter photolysis wavelengths, suggesting that the surface-hopping probability is low and that most of the population dissociates adiabatically to the lower asymptote within one (or a few) vibrational periods of the IC step. However, Crim et al. [13] have proposed that this electronically excited channel is open following vibrational pre-excitation to mO–H = 1 in S0. The product TKER increases by 3500 cm1 in this case, presumably enhancing the surface hopping probability.
(1) Symmetry allowed CIs (e.g. A0 /A00 ): The CI lies at the symmetric configuration of an asymmetric coupling mode and a double well potential results (as in phenol). The GPE allows the system to meet the symmetry change required so that it stays on the lower adiabat and allows predissociation of the (e.g. A0 ) state by the (e.g. A00 ) state. (2) Accidental (same symmetry) CI: The CI in this case involves same symmetry states and thus need not be located at a symmetric point in the coupling coordinate [14]. The GPE is not needed to meet a symmetry requirement in order to couple the surfaces, but must still occur and cause interference, leading to the introduction of an additional node in the coupling coordinate on recombination of wNUC after passing the CI. This node need not occur at the equilibrium position and thus may not cause a parity switch (e.g. odd to even quanta of product vibration). Despite this, the GPE induced node will remain in wNUC and should reveal itself in, for example, dispersed emission or product state branching ratios, due to Franck-Condon like arguments.
Acknowledgments The authors are grateful to Prof. G.G. Balint-Kurti and Drs. S.C. Althorpe, W.S. Hopkins and E. Wrede for very helpful discussions and to EPSRC for financial support through the Portfolio Partnership LASER. References [1] M.V. Berry, Proc. R. Soc. London A 392 (1984) 45. [2] G. Herzberg, H.C. Longuet-Higgins, Discuss. Faraday Soc. 35 (1963) 77. [3] J.C. Juanes-Marcos, S.C. Althorpe, E. Wrede, J. Chem. Phys. 126 (2007) 17286480. [4] J.C. Juanes-Marcos, S.C. Althorpe, E. Wrede, Science 309 (2005) 1227. [5] D.C. Clary, Science 309 (2005) 1195. [6] M. Abe, Y. Ohtsuki, Y. Fujimura, Z. Lan, W. Domcke, J. Chem. Phys. 124 (2006) 224316. [7] S.C. Althorpe, J. Chem. Phys. 124 (2006) 084105. [8] D. Babikov, B.K. Kendrick, P. Zhang, K. Morokuma, J. Chem. Phys. 122 (2005) 1. [9] B.K. Kendrick, J. Phys. Chem. A 107 (2003) 6739. [10] J.C. Juanes-Marcos, S.C. Althorpe, E. Wrede, Chem. Phys. Lett. 381 (2003) 743. [11] M.G.D. Nix, A.L. Devine, B. Cronin, R.N. Dixon, M.N.R. Ashfold, J. Chem. Phys. 125 (2006) 133318. [12] A. Sur, P.M. Johnson, J. Chem. Phys. 4 (1986) 1206. [13] M.L. Hause, Y.H. Yoon, A.S. Case, F.F. Crim, J. Chem. Phys. 128 (2008) 104307. [14] D.R. Yarkony, Rev. Mod. Phys. 68 (1996) 985.
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Observation of geometric phase effect induced photodissociation dynamics in phenol M.G.D. Nix *, A.L. Devine, R.N. Dixon, M.N.R. Ashfold School of Chemistry, University of Bristol, Cantocks Close, Bristol BS8 1TS, UK
a r t i c l e
i n f o
Article history: Received 10 July 2008 In final form 22 August 2008 Available online 27 August 2008
a b s t r a c t Dynamical effects attributable to the geometric phase have been observed in UV photo-induced O–H bond fission in jet cooled phenol. Phenoxyl radicals are formed with an odd quanta progression in a00 mode m16a. This mode specific product formation is reproduced by 2D wavepacket simulations and discussed in terms of quantum interference resulting from the geometric phase effect at the conical intersection between the ground and first excited state potential energy surfaces at extended O–H bond lengths. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The geometric phase effect (GPE) [1] in molecular systems occurs at points of degeneracy such as conical intersections (CIs) of potential energy surfaces (PESs), due to the non-adiabatic nature of the vibronic interactions. Herzberg and Longuet-Higgins [2] first showed that the phase of the adiabatic electronic wavefunction (we) in a 2-state system changes by p with a nuclear motion of 2p around a CI. A sign change occurs in we and, as the overall wavefunction (W) must remain single valued throughout configuration space, an opposite phase change is required in the nuclear wavefunction (wNUC). Under the adiabatic approximation, this nuclear phase change (du) is neglected and must be re-introduced into wNUC as du = h/2, where h represents the angular transit about the CI. Nuclear wavefunctions which encircle a CI (h = 2p) an odd number of times exhibit a p relative phase shift; an even number of circuits are required to recover the original phase [3]. Observable GPEs result from re-combination and interference of two components of a wavefunction with differing du. This occurs when the CI is encircled by wNUC as it moves in the (2D) branching space of the CI. GPEs in molecular systems have recently received much attention [4–10], as the importance of CIs in reaction dynamics has increasingly become recognised. Reactive scattering systems, such as H + D2, in which the nuclear wavefunction is confined to one adiabatic PES in the vicinity of a CI have been predicted [9] to show a GPE, although no conclusive experimental demonstrations have yet been reported. Recent theoretical studies of the H + H2 system [4] suggest that, although the wavefunction bifurcates and encircles the CI, the bifurcation is asymmetric, with only 1% of the amplitude in the minor channel. The magnitude of any interference effect would thus necessarily be small. Furthermore,
* Corresponding author. Fax: +44 117 9250612. E-mail address: [email protected] (M.G.D. Nix). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.08.085
the two components are predicted to scatter into different regions of configuration space, precluding interference effects at long range, where detection would occur. An ideal system for experimental observation of a GPE would have a single exit channel from the CI region, forcing the two components of the wavefunction to recombine in configuration space and remain so thereafter, causing observable interference. Photodissociations often originate from a well-defined nuclear configuration and proceed via a single exit channel, removing many of the dynamical complications associated with full collisions. In an ‘ideal’ system, therefore, a well-characterised nuclear wavepacket would be prepared photolytically and dissociate via bifurcation around a CI, remaining on a single adiabatic PES throughout. We recently reported [11] the total kinetic energy release (TKER) spectra of the H + phenoxyl products resulting from UV photolysis of phenol via its S1 S0 000 transition. The phenoxyl products were observed to be formed in an odd-quanta progression in an out-of-plane (a00 ) vibrational mode. These dynamics were originally interpreted in a diabatic framework, involving symmetry restrictions on wNUC and we, with the odd quanta progression resulting from the off-diagonal H’’ coupling term between diabatic states (1pp (A0 ) and 1pr* (A00 )). [For clarity, we choose to describe the electronic states using either adiabatic (S0, S1, S2) or diabatic (1pp, 1pp*, 1pr*) labels, as in Fig. 1]. The data can also be interpreted in an adiabatic representation however, wherein they represent a manifestation of the GPE in dynamics on the S0 PES. This Letter illustrates the equivalence of the two interpretations and examines the significance of GPE in such systems, particularly where symmetry plays a role. 2. Observation and discussion The discussion here will focus on photodissociation of phenol via its S1 S0 origin transition, as this is representative of
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The electronic ground state of phenoxyl has 2A00 symmetry, whereas the ground state of phenol (which correlates to the first excited state of phenoxyl upon extending the O–H bond length, RO–H) has 1A0 symmetry (Fig. 1). The level populated by exciting the S1 S0(p* p) 000 band has A0 electronic (and vibronic) symmetry, and a reported fluorescence lifetime of 2 ns [12]. Most of the S1(v = 0) population transfers to the S0 PES (presumably on this same timescale) by internal conversion (IC), conserving the A0 (i.e. A0 a0 ) vibronic symmetry. The dominant acceptor modes following IC are (lifetime broadened) O–H stretch overtones of a0 symmetry [12], which allow direct access to the region of the 1pp/1pr* CI during the first vibrational period on the S0 PES and, subsequent O– H bond fission. We now consider this evolution in, respectively, a diabatic and an adiabatic framework. 2.1. Diabatic model
Fig. 1. Dissociation mechanism showing (a) initial excitation to the 1pp* PES and (b) mO–H specific IC to S0, followed by predissociation of S0 molecules at the 1 pp/1pr* CI at RO–H 1.9 Å. All subsequent dynamics (dashed arrow) occur on the S0 PES.
dynamics at higher photon energies also [11]. The TKER distribution (Fig. 2b) recovered from the recorded H atom time of flight (TOF) spectrum (Fig. 2a) is expanded and re-plotted (Fig. 2c) in terms of the internal energy of the phenoxyl co-fragment, Eint. The populated vibrational levels of the phenoxyl products were assigned [11] by fitting the observed peak separations in terms of the calculated (B3LYP/6-311+g(d,p)) wavenumbers for the (anharmonic) normal modes of vibration. The product distribution is dominated by m16a (an a00 mode), and the in-plane CO wag m18(a0 ), as shown in Fig. 2c. m18b is excited as a result of the recoil of the H atom as it departs from a non-coaxial COH geometry.
To form ground state phenoxyl + H products, the wavepacket must remain on the lower cone of the CI, switching electronic configuration and symmetry from 1pp (A0 ) to 1pr*(A00 ) in the process. The vibrational symmetry must also change (from a0 to a00 ) in order to maintain the overall A0 vibronic symmetry and allow the dissociation to occur. However, this is merely a symmetry requirement. A force is needed to produce such a change in the dissociating wavepacket. In the absence of coupling between the (diabatic) surfaces (i.e. with non-adiabatic interactions turned off), the population would remain on the 1pp PES and (assuming insufficient energy to access the excited phenoxyl (2A0 ) + H asymptote) revisit the Franck Condon region, as the symmetry would be incorrect to allow access to the 1pr*(A00 ) PES. Consider the interaction of the diabatic |1ppi and |1pr*i states in terms of the first order non-adiabatic coupling term, H00 . wNUC associated with the 1pr* state must necessarily gain a node at the CI, due to the fact that H00 is zero at the intersection point, where its sign changes. we(S0) becomes 1pr*(A00 ) in character and wNUC(S0) becomes a00 . we(S1) becomes 1pp (A0 ) and wNUC(S1) becomes a0 , conserving the symmetry of the full wavefunction. Of course, W evolves in a continuous (rather than sudden) fashion, necessitating the gradual application of H00 with h. 2.2. Adiabatic model
Fig. 2. (a) TOF and (b) TKER spectra following excitation of phenol at the S1–S0 origin (275.113 nm). (c) Assignment of phenoxyl product vibrational states in terms of internal energy (Eint).
In the adiabatic picture, the electronic structure of the S0 PES evolves smoothly from 1pp(A0 ) to 1pr*(A00 ) with increase in the angle h relative to the CI degenerate point, as shown in Fig. 3. No arbitrary coupling term is applied, but the nuclear phase information is missing and must be recovered. This is the GPE, which causes the phase of wNUC to change by p on encircling the CI. Consider a system such as that depicted in Fig. 3, where the coupling coordinate is an out-of-plane (a00 ) ring twisting mode such as m16a, and the initial, CI and final geometries are all planar. A wavepacket travelling from reactant (phenol) to product (phenoxyl + H) along RO–H on the S0 PES will bifurcate symmetrically and pass around the CI via two equivalent routes. Recombination of these components leads to overlap of the two bifurcated pieces of the time-dependent wavepacket, which is equivalent to complete encirclement of the CI by the time-independent wavefunction. Whilst no part of the wavepacket explicitly encircles the CI, the two components travel +p and p, respectively, with associated phase shifts du = ±p/2 in wNUC. Thus, the phase difference between the two components of wNUC in the exit channel is p and, due to the 50:50 bifurcation, complete destructive interference occurs on recombination at the plane of symmetry in the exit channel. A node is thus introduced into wNUC at large RO–H, causing the wavepacket that was initially
M.G.D. Nix et al. / Chemical Physics Letters 463 (2008) 305–308
Fig. 3. Schematic 2D equipotential plot of the S0 adiabatic PES. The wavepacket (shown above) bifurcates on approaching the CI, undergoes a phase change (du = ±h/2) and recombines in the exit channel, with a node at mcoupling = 0 (at the symmetry plane).
even (a0 ) to become odd (a00 ) in the coupling coordinate. The requirement for an a00 nuclear symmetry change is thus satisfied and access to the extended part of the adiabatic S0 PES (with 1 pr*(A00 ) electronic character) is allowed. The involvement of the GPE is crucial, else symmetry constraints would force the wavepacket to remain on the 1pp diabatic surface, preventing dissociation to the lowest asymptote (see Fig. 1a). That dissociation to this asymptote occurs at all is evidence of the GPE, but there is also a signature of the coupling in the phenoxyl product vibrational state distribution, which we have modelled. 2.3. Wavepacket simulations The system is represented by a 2D model involving RO–H and
m16a. We specifically consider the dynamics induced by the CI in m16a, so bifurcation will displace the wavepacket in m16a. Given that the GPE changes the parity of wNUC, a m16a = 0 wavepacket approaching the CI, bifurcating, and then recombining at large RO–H should produce a superposition of odd quanta in m16a. A diabatic model was chosen for computational ease, but is entirely equivalent to the adiabatic representation. To prepare the
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PESs, analytic functions were fitted first to ab initio DFT (B3LYP/ 6-311+g(d,p)) points, and the model PESs were subsequently fitted to the experimentally determined energetics (e.g. S1S0 origin, D0(C6H5OH)). It was also considered valid to use a continuously driven oscillator model to choose the initial wavefunction (rather than a time-dependent gaussian wavepacket) since ns laser pulses were employed experimentally and because IC from the S1(v = 0) level to the S0 PES occurs to broadened S0 levels on a ns timescale. The subsequent dissociation is expected to occur promptly (i.e. without significant IVR on S0). Driving high mO–H modes of the S0 PES into resonance near the S1 S0 origin excitation energy, we selected a wavefunction, corresponding to a single broadened eigenstate of the model S0 PES, to use as a starting point for the time-dependent propagation. The mO–H resonance in S0 was chosen to best represent the energy of the S1 zero point level. The off-diagonal non-adiabatic coupling parameter required to reproduce the observed product state distribution in (odd quanta of) m16a is V12 (q16a/q0 = 1) 1150 cm1. The exit channel (diabatic) wavefunction produced by the model (Fig. 4 (right panel)) clearly shows a node at planar geometries at large RO–H, reflecting the GPE induced interference between the two components of wNUC. The resulting vibrational progression can be examined by projecting the 1pr* wavefunction onto a basis of the (harmonic) vibrational wavefunctions of m16a. Experimental integrated intensities were obtained by subtracting a background function from the spectrum in Fig. 2c to eliminate contributions from the unimolecular decay channel, fitting gaussian peaks to the features assigned to the m16a progression and integrating the area under each function. The observed intensity pattern of the odd quanta progression is well reproduced by our simple model, as shown in Fig. 5. No peaks were observed for even quanta, although background signal, underlying the structured component, could in principle mask some weak contributions. The simulation predicts zero intensity in the even states as expected, due to the node at planarity in the exit channel wave. The oscillatory nature of the unbound wavefunction in the mO–H coordinate (Fig. 4b) indicates a kinetic energy release of 6000 cm1, also in excellent accord with the experimental data (see Fig. 2b). The question arises as to why similar dynamics have not been noted in previous photodissociation experiments, but the situation in phenol is rather unusual. The dissociation (following IC at an energy above that of the CI) occurs on a single adiabatic PES (S0) and
Fig. 4. Left: A continuously driven oscillator wavefunction, representing mO–H = 13 on the 1pp diabatic PES. Right: Population on the diabatic 1pr* state, following coupling at the 1pp/1pr* CI. The GPE induced node at q16a/q0 = 0 is clearly evident.
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3. Conclusion The odd quanta progression in m16a in the phenoxyl products resulting from UV photolysis of phenol is arguably the first experimental demonstration of molecular dynamics induced by GPEs. By employing photodissociation rather than bimolecular scattering, it has been possible to exert much tighter control over the initial wavefunction and to ensure that wNUC recombines fully following bifurcation and passage around the CI into the exit channel. GPEs are intrinsic to dynamics occurring adiabatically around a CI, but two distinct cases can be recognised
Fig. 5. Comparison of simulated and experimental integrated peak intensities for the progression in m16a. Experimental intensities were determined from the average integrated intensities over all available datasets. Experimental and simulated intensities were normalised at the m16a = 1 level.
the wavepacket encircles the CI before recombining in the exit channel. This situation must occur in many systems following IC, and the effects described above should be ubiquitous whenever there is a CI along the minimum energy pathway to products. However, IC will typically populate a wide spread of S0 vibrational levels, involving motions that do not correspond to the reaction coordinate. Significant IVR must occur in such cases in order that the minimum energy required to reach the product asymptote is transferred into the dissociation coordinate (in this case RO–H). Any residual energy in such cases will likely be retained as internal (vibrational) energy in the fragments, resulting in a broad distribution of populated product states and, in the limit, an unresolvable distribution of vibrationally hot products (and thus an unresolvable TKER spectrum). In phenol, however, the specific transfer of population into S0 levels with mO–H 13 allows direct access to the CI without significant IVR. Hence wNUC approaching the CI is unusually simple, and the GPE induced progression in m16a is resolved in the measured TKER spectra. Domcke et al. [6] have suggested that GPEs in the photodissociation of phenol could also affect the branching between product electronic states. Indeed, electronically excited phenoxyl products would be expected in the limit that the recoil velocity was sufficient to support non-adiabatic ‘hopping’ between the PESs; the present modelling would predict selective formation of excited phenoxyl products with m16a = 0, 2, 4, . . . Experimentally [11], however, we have not identified formation of such excited products, even at shorter photolysis wavelengths, suggesting that the surface-hopping probability is low and that most of the population dissociates adiabatically to the lower asymptote within one (or a few) vibrational periods of the IC step. However, Crim et al. [13] have proposed that this electronically excited channel is open following vibrational pre-excitation to mO–H = 1 in S0. The product TKER increases by 3500 cm1 in this case, presumably enhancing the surface hopping probability.
(1) Symmetry allowed CIs (e.g. A0 /A00 ): The CI lies at the symmetric configuration of an asymmetric coupling mode and a double well potential results (as in phenol). The GPE allows the system to meet the symmetry change required so that it stays on the lower adiabat and allows predissociation of the (e.g. A0 ) state by the (e.g. A00 ) state. (2) Accidental (same symmetry) CI: The CI in this case involves same symmetry states and thus need not be located at a symmetric point in the coupling coordinate [14]. The GPE is not needed to meet a symmetry requirement in order to couple the surfaces, but must still occur and cause interference, leading to the introduction of an additional node in the coupling coordinate on recombination of wNUC after passing the CI. This node need not occur at the equilibrium position and thus may not cause a parity switch (e.g. odd to even quanta of product vibration). Despite this, the GPE induced node will remain in wNUC and should reveal itself in, for example, dispersed emission or product state branching ratios, due to Franck-Condon like arguments.
Acknowledgments The authors are grateful to Prof. G.G. Balint-Kurti and Drs. S.C. Althorpe, W.S. Hopkins and E. Wrede for very helpful discussions and to EPSRC for financial support through the Portfolio Partnership LASER. References [1] M.V. Berry, Proc. R. Soc. London A 392 (1984) 45. [2] G. Herzberg, H.C. Longuet-Higgins, Discuss. Faraday Soc. 35 (1963) 77. [3] J.C. Juanes-Marcos, S.C. Althorpe, E. Wrede, J. Chem. Phys. 126 (2007) 17286480. [4] J.C. Juanes-Marcos, S.C. Althorpe, E. Wrede, Science 309 (2005) 1227. [5] D.C. Clary, Science 309 (2005) 1195. [6] M. Abe, Y. Ohtsuki, Y. Fujimura, Z. Lan, W. Domcke, J. Chem. Phys. 124 (2006) 224316. [7] S.C. Althorpe, J. Chem. Phys. 124 (2006) 084105. [8] D. Babikov, B.K. Kendrick, P. Zhang, K. Morokuma, J. Chem. Phys. 122 (2005) 1. [9] B.K. Kendrick, J. Phys. Chem. A 107 (2003) 6739. [10] J.C. Juanes-Marcos, S.C. Althorpe, E. Wrede, Chem. Phys. Lett. 381 (2003) 743. [11] M.G.D. Nix, A.L. Devine, B. Cronin, R.N. Dixon, M.N.R. Ashfold, J. Chem. Phys. 125 (2006) 133318. [12] A. Sur, P.M. Johnson, J. Chem. Phys. 4 (1986) 1206. [13] M.L. Hause, Y.H. Yoon, A.S. Case, F.F. Crim, J. Chem. Phys. 128 (2008) 104307. [14] D.R. Yarkony, Rev. Mod. Phys. 68 (1996) 985.