Wave Packet Dynamics at an Extended Seam of Conical Intersection

Letter pubs.acs.org/JPCL

Wave Packet Dynamics at an Extended Seam of Conical Intersection: Mechanism of the Light-Induced Wolff Rearrangement Quansong Li, Annapaola Migani,§ and Lluís Blancafort* Institut de Química Computacional and Departament de Química, Universitat de Girona, Campus de Montilivi, 17071 Girona, Spain S Supporting Information *

ABSTRACT: Quantum dynamics calculations on a model surface based on CASPT2//CASSCF calculations are carried out to probe the traversal of a wave packet through an extended seam of conical intersection during the light-induced Wolff rearrangement of diazonaphtoquinone. The reaction is applied in the fabrication of integrated circuits. It consists of nitrogen elimination and ring rearrangement to yield a ketene. After excitation, the wave packet relaxes and reaches the extended seam. A fraction of the wave packet decays to the ground state at a region of the seam connected to a carbene intermediate, while the remaining part decays at a region leading to the ketene. The passage of the wave packet through the extended seam explains the competition between concerted ketene formation and a stepwise mechanism involving a carbene. The two primary photoproducts are formed in the first 100 fs of the simulation, in agreement with recent ultrafast spectroscopy measurements. SECTION: Spectroscopy, Photochemistry, and Excited States

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essential, and wave packet propagations give insight into the traversal of the seam that goes beyond what can be understood from the potential energy surface or from mixed quantum classical dynamics. The 5-sulfonated derivative of DNQ is the photoactive compound of photoresists used in photolithography, and it is used in the fabrication of more than 80% of today’s integrated circuits. The Wolff rearrangement is at the basis of this application. It consists of the conversion of an α-diazo ketone into a ketene, mediated by loss of a nitrogen molecule, and the transformation of a six- to a five-membered ring (see Figure 1). Almost 70 years after its discovery, its mechanism remains to be fully clarified. The latest spectroscopic results point to the coexistence of the concerted and stepwise mechanisms,

onical intersections (CIs) are crossings between potential energy surfaces of the same multiplicity that play a key role in photochemical and photophysical processes in biology and industrial applications1−4 by providing an efficient funnel to access the ground state from the excited state. They are the doorway for formation of a photoproduct or recovery of the reactant. Experimentally, the signature of a CI is usually given by short excited-state lifetimes of tens of picoseconds or less.5 More direct experimental evidence of the dynamics at the CI is beginning to appear using different highly resolved techniques,6−9 which calls for an improved theoretical description. Such a description can be obtained best describing the dynamics in terms of a wave packet evolving on several potential energy surfaces.10 One also has to consider that conical intersections are not isolated points but form part of multidimensional seams of intersection.1−4,11 On the basis of these ideas, we focus on the wave packet dynamics along an extended seam of conical intersection.12,13 Such extended seams are composed of several segments, associated with different photoproducts. This topological feature has been invoked previously to explain excited-state processes.13−20 However, its role in the dynamics remains to be clarified because wave packet dynamics calculations considering an extended seam are rare and have been limited to small models16 or cases where there is no photochemical reactivity.21 Here, we simulate a reaction of technological relevance, the light-induced Wolff rearrangement of 2-diazo-1-naphthoquinone (DNQ).22 The mechanism of this complex reaction is associated with an extended seam, where dynamical and quantum effects are © 2012 American Chemical Society

Figure 1. Wolff rearrangement of 2-diazo-1-naphthoquinone (DNQ). Received: February 28, 2012 Accepted: April 5, 2012 Published: April 5, 2012 1056

dx.doi.org/10.1021/jz300235z | J. Phys. Chem. Lett. 2012, 3, 1056−1061

The Journal of Physical Chemistry Letters

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Figure 2. Main decay pathways for the bright (π,π*) state of DNQ (S2 at the FC geometry), obtained from intrinsic reaction coordinate calculations using the CASPT2//CASSCF approach: from the FC structure to (S2/S1)X, from (S2/S1)X to the two segments of the (S1/S0) seam of intersection, and from segment 1 to the ground-state species. Segment 1 is represented by a series of double cones. For illustration, we include three structures along the seam at different C−N distances (1.5 Å, 2.0 Å, and 2.5 Å). The whole segment is energetically accessible from (S2/S1)X (see CASPT2 energies in eV in brackets). The relaxation paths on S0, calculated from the three CI structures, lead to the species shown at the bottom of the figure. The decay paths from segment 2 (not shown; see SI) lead to the FC, carbene, and ketene structures. The insets on the left- and right-hand sides of the figure show the orbitals involved in the excitations at the FC structure and segment 1, respectively.

involving a carbene intermediate.23 Thus, the carbene intermediate postulated in the stepwise path was detected within 8 ps after excitation and trapped by alcohols, suggesting a stepwise mechanism.24 On the other hand, in a recent femtosecond resolved spectroscopic study of the DNQ 5sulfonate derivative, the appearance of the ketene product was monitored with transient IR spectroscopy, and the ketene appeared within 300 fs after irradiation with UV light of 400 nm.23 Similar results, which point to the coexistence of the concerted and stepwise mechanisms, were reached for two acyclic analogues of DNQ, 5-diazo Meldrum’s acid25 and αbiphenyl-α-diazo acetone.26 The main focus of this work is how the competition between the two mechanisms occurs. In ground-state reactions, this could be due to different paths involving different transition structures or to a single transition structure with a bifurcation along the path to the products.27 Here, we follow a different line of thought. The short time scale of formation of the two primary photoproducts suggests that an extended seam is involved in the product formation and raises the question about the dynamics along the seam. To answer this question, we have characterized the reaction paths for the photochemical Wolff rearrangement of DNQ with high-level quantum chemistry calculations, and we have constructed a three-dimensional model surface to carry out the wave packet dynamics. The excited-state potential energy surface has been characterized with the CASPT2//CASSCF approach28 using the Gaussian29 and Molcas30 programs. In this approach, critical points and minimum-energy paths are optimized at the complete active space self-consistent field (CASSCF) level, and the energies are recalculated at the complete active space second-order perturbation (CASPT2)

level to account for dynamic correlation (see Supporting Information, SI, for details). We use a (10,10) active space for the CASSCF calculations (10 electrons in 10 orbitals) and a (14,13) one for the CASPT2 calculations. The calculations are carried out in the gas phase because solvent effects on the initial part of the photodynamics are small, as shown by the similar subpicosecond dynamics of DNQ in methanol and water23 or those of a related α-diazoketone in acetonitrile.26 Moreover, the computed solvent-induced shifts of the vertical excitations in water are less than 0.1 eV for the relevant states.31 In the most recent experimental study, the light-induced Wolff rearrangement is initiated by excitation at 400 nm.23 The red edge of the UV/vis spectrum of DNQ, around this wavelength, contains two transitions;31 one of them corresponds to a (π,π*) state and the other one to a (π,π*NN) one where an electron is promoted to the in-plane antibonding π orbital of the diazo group, labeled π*NN (see orbitals in Figure 2). The (π,π*) state is bright and has an oscillator strength of approximately 0.4, while the (π,π*NN) state has an oscillator strength smaller than 0.001. Therefore, one can assume that the initial excitation populates the bright (π,π*) state, which is S2 at the Franck− Condon (FC) structure. The calculated minimum-energy paths are summarized in Figure 2. The (π,π*) state relaxation from the FC structure is barrierless and leads to a conical intersection with the (π,π*NN) state, (S2/S1)X. The relaxation involves bond stretching modes in the ring, an out-of-plane bending of the diazo group, and a stretching of the C−N bond from 1.32 to 1.48 Å (see structures in Figure 2). There are two paths for further relaxation from (S2/S1)X on S1. The main path continues on the (π,π*) state along the C−N stretch coordinate until it reaches a (S1/S0) 1057



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where the coordinates Q are treated as normal modes and μi is the reduced mass of Qi. W is a modified version of the [2 × 2] vibronic coupling Hamiltonian35

seam of intersection labeled segment 1. This segment has been mapped with constrained conical intersection optimizations, fixing the C−N distance to different values and the C3−C2− N12−N13 dihedral angle to 90° (see SI for the atom numbering). The seam lies along the C−N stretch coordinate, with the diazo group bent out of the plane. The minimumenergy path from (S2/S1)X hits the seam at a structure where the C−N distance is 1.65 Å, but the whole segment is accessible from the energetic point of view. A first idea of the dynamics at the seam can be obtained by studying the ground-state decay paths at different regions of segment 1, which lead to different species. At the region where the C−N distance is 1.65 Å, the decay path leads to the reactant (FC structure). At shorter C− N distances (1.5 Å), there is one path that reverts to the reactant and one that leads to a diazirine side product. This product must be formed in low yields because it arises from the high-energy region of the seam, and therefore, it has not been detected experimentally. It has not been considered further here because our focus is the carbene versus ketene alternative. At intermediate C−N distances (2.0 Å), the decay path leads to the carbene intermediate, while at longer C−N distances (2.5 Å), also the ketene can be formed. On the ground state, the carbene is separated from the ketene by a barrier of 0.3 eV, and the ketene is more stable by 2.3 eV (see SI). The barrier explains the estimated lifetime of the carbene, which lies in the range of 10−20 ps.23,24 During the passage through the (S2/S1)X intersection, a fraction of the wave packet is bifurcated to the (π,π*NN) state. It will follow another barrierless decay path that leads to a segment of the (S1/S0) seam where the diazo group is bent in the plane of the ring (segment 2 in Figure 2). Apart from the orientation of the diazo group, segment 2 is similar to segment 1. It lies along the C−N dissociation coordinate, and the decay paths lead to the reactant and the carbene and ketene species. The dynamics at segment 2 has not been considered further because access to segment 1 will be the dominant channel, and a similar behavior can be expected in segment 2. The quantum dynamics at the seam are carried out on a reduced surface, using the multiconfigurational time-dependent Hartree (MCTDH)32 method. This method is well-suited to treat the nonadiabatic effects associated with the traversal of the seam. The alternative is mixed classical quantum dynamics on a surface calculated on-the-fly. These calculations can be carried out on the full dimensional surface, but the passage through the seam is treated in a more approximate way with trajectory surface hopping or similar algorithms. In addition, the model surfaces for the quantum dynamics can be fitted to high-level ab initio calculations (CASPT2 in the present case), whereas onthe-fly dynamics are bound to lower-level methods that are known to give rise to artifacts.33 The propagation is carried out by integrating the timedependent Schrödinger equation of the form ⎛ d ⎞ ⎛|Ψ d(t )⟩⎞ ∂ |Ψ1 (t )⟩⎟ ⎟ ⎜ 1 ( W T ) iℏ ⎜⎜ = + ⎟ ⎟ ⎜ d ∂t ⎝|Ψ d(t )⟩⎠ ⎝|Ψ 2(t )⟩⎠ 2

⎛ W11 W12 ⎞ ⎟ W=⎜ ⎝W12 W22 ⎠

The diabatic states are obtained from the ab initio calculations using the regularized diabatic states approach, where the couplings are expressed through the off-diagonal potential terms W12.36 The diabatic states correspond to a closed-shell electronic configuration that correlates with the ketene and an open-shell configuration correlating with the carbene. Choosing the coordinates and constructing the potential is particularly challenging because the Wolff rearrangement involves large-amplitude motions along many highly correlated coordinates, and the surface is highly anharmonic. To make the problem tractable, we make use of the fact that the initial relaxation from the FC structure to (S2/S1)X is barrierless, and we do not consider it in the dynamics. Therefore, we have constructed a minimal three-dimensional model describing the region of the potential energy surface spanned by the three key structures, (S2/S1)X, the open-shell carbene, and the ketene. The first two coordinates of our model (Q1 and Q2, respectively) are the C−N dissociation coordinate and the rearrangement coordinate from the six- to the five-membered ring. The subspace formed by Q1 and Q2 (Q3 = 0) corresponds to geometries where the ring is planar and the orientation of the diazo moiety is fixed to the values at (S2/S1)X. Q3 is the coupling coordinate, which consists of an out-of-plane motion of the ring atoms. Our diabatization scheme is based on the symmetry of the states at the diazo dissociation limit, where the ring is planar and has Cs symmetry. The two lowest states have A′ and A″ symmetry and correlate with the ketene and carbene configurations, respectively. Because of their different symmetry, the diabatic and adiabatic states coincide. In our model, this is the case at planar ring geometries for large values of Q1. We assume that this holds for all values of Q1 and Q2, as long as Q3 is 0. On the basis of this approximation, the diabatic surfaces in the subspace of planar geometries (Q3 = 0) can be fitted directly from the adiabatic CASPT2 energies, obtained from atomic displacements along Q1 and Q2 centered on (S2/S1)X. The interstate coupling only occurs along the ring symmetry breaking coordinate Q3. W12 is linear along Q3, and the strength of the coupling, κ12, depends parametrically on Q1 W12 = κ12(Q 1) ·Q 3

∑ i = 1,3

TQ̂ i = −

1 2

∑ i = 1,3

1 ∂2 μi ∂Q i2 i

(4)

The coupling coordinate Q3 is derived from the CASSCF interstate coupling vector ic, calculated in the full-dimensional space of coordinates at different points on the seam ic = ∇Q ⟨Ψ0|Ĥ ele|Ψ⟩ 1

(5)

In eq 5, Ĥ ele is the electronic Hamiltonian, and Ψi is the adiabatic electronic wave function for state i. Because the ic vector changes along the seam, Q̂ 3 is obtained as the average of the ic vectors at three structures on segment 1 (C2−N12 values of 1.60, 2.00, and 2.50 Å). The ic vectors at these structures are mainly composed of out-of-plane motions of the ring atoms (see Figure SI4, SI). This validates our approach of approximating the diabatic states by the adiabatic ones at planar geometries. To obtain the parameters of W involving Q3,

(1)

A diabatic basis is used, which is more suitable for surfaces centered on conical intersections.34 T is approximated by a diagonal kinetic energy operator T̂ =

(3)

(2) 1058



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we have carried out atomic displacements along Q3 centered at different points on the seam. The parameters of Wii are obtained by fitting the average of the adiabatic energies at the resulting structures, while the parameters of the interstate coupling term W12 are obtained by fitting the square of the adiabatic energy difference. More details about the construction of the model are given in the SI. Overall, the parameters of W have been fitted to 249 points, and the root-mean-square of the error is 0.37 eV. This error is calculated on the basis of all points with energy lower than a threshold of 0.1 hartree with respect to the ground-state minimum. The threshold lies above the initial relative potential energy of the wave packet on the excited-state surface, which is approximately 0.08 hartree. The error is relatively large because the rearrangement coordinate is very complex. However, it is acceptable for our purpose of providing a qualitative picture of the traversal of the wave packet through the seam. The model surface along Q1 and Q2 is shown in Figure 3. It reproduces the ab initio data because it contains the seam,

many more highly correlated and anharmonic degrees of freedom. Parametrizing such a surface and carrying out quantum dynamics on it is beyond the present state of the art. The results of our wave packet propagation are presented in Figures 3 and 4. The wave packet is equilibrated on the ground

Figure 3. Two-dimensional plot of the model surface for the dynamics along Q1 (C−N dissociation coordinate) and Q2 (ring rearrangement coordinate) (projection for Q3 = 0; m.w.a.d.: mass-weighted atomic displacements). The purple and blue−green surfaces correspond to the closed- and open-shell diabatic states, correlating with the ketene and carbene products, respectively. The minima for the two photoproducts are found at large values of Q1 on either side of the plot. Snapshots of the wave packet evolution at different time steps are also shown on the surface. The wave packet at the beginning of the dynamics is shown in blue. The red wave packet corresponds to the fraction that decays at the region of the seam leading to the carbene minimum, and the yellow one corresponds to the fraction that decays at the region leading to the ketene.

Figure 4. Snapshots of the wave packet propagations on the contour plots of the model surfaces along Q1 and Q2 (integrated density along Q3; coordinates in mass-weighted atomic displacements). Energy scale shown in the right upper corner; wave packet density plotted in grayscale. (Left column) Open-shell surface, correlating with the carbene ground-state configuration; (right column) closed-shell surface, correlating with the ketene configuration. The seam is displayed as a dashed line. On the open-shell diabatic surface, the adiabatic ground state is the part that lies below the line of the seam in plots (a−e), and the excited state is the part lying above the seam; the opposite applies for the closed-shell surface. The time evolution of the diabatic state populations is shown in the SI.

which lies almost parallel to Q1, along the C−N dissociation coordinate. The third coordinate (Q3) couples the two states, and every point of the seam becomes a conical intersection when this coordinate is taken into account. Overall, this threedimensional model contains several approximations because the dynamics are not started at the FC structure and we only consider seam segment 1; the coordinate that leads to formation of the diazirine side product is also not considered. Therefore, our results are not quantitative, but they provide fundamental new insights into the wave packet dynamics at the seam. A quantitative treatment of the photodynamics at the quantum dynamics level would need a model surface including

state, and the excited-state propagation is initiated by transferring the equilibrated wave packet to the excited state. The propagation is run for 100 fs. Initially, the wave packet is on the green−blue surface of Figure 3, which corresponds to the open-shell configuration of DNQ ((π,π*) state) and correlates with the carbene after C−N cleavage. To form the ketene, the wave packet has to access the purple surface, which corresponds to the closed-shell configuration. In Figure 4, we present several snapshots of the wave packet propagation on the diabatic surfaces plotted along Q1 and Q2. The left and right 1059



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columns provide contour plots of the open- and closed-shell state surfaces, respectively, and the seam is shown as a dashed line. The wave packet dynamics start on S1 (open-shell state), reached after decay through (S2/S1)X (Figure 4a). The start of the dynamics corresponds to the blue wave packet shown in Figure 3. The wave packet reaches the (S1/S0) seam very quickly, after approximately 20 fs, at a region with short C−N distance (Figure 4b). Part of the wave packet, which corresponds to the red wave packet in Figure 3, remains on the open-shell surface and decays to the ground state, where it evolves to the carbene minimum (Figure 4b−e). The remaining fraction, which corresponds to the yellow wave packet in Figure 3, is transferred to the closed-shell surface (Figure 4g) and decays to the ground state at a region with a longer C−N distance, at around 40 fs (Figure 4h). This fraction evolves to the ketene minimum (Figure 4i,k). According to the state populations (see SI), the ratio between carbene and ketene is approximately 4:1. Both primary photoproducts are formed within 100 fs. Hence, the results agree with the latest experiments that report the formation of the ketene in less than 400 fs and hypothesize that the carbene is also involved in the mechanism.23 The carbene fraction evolves to the ketene in a time that exceeds the time scale of our dynamics because its estimated lifetime is 10−20 ps.23,24 Apart from DNQ, a mechanism involving the seam of intersection along the C−N coordinate must be also important for other excited-state rearrangements of diazo compounds, where the alternative between the concerted and stepwise mechanisms is also discussed.37−39 The wave packet propagation gives some aspects from the picture of the dynamics at the seam that cannot be deduced from the “static” picture provided by the potential energy surface or may not be well reproduced by more approximate dynamics. Thus, during the first traversal of the seam, the fraction of the wave packet that switches to the closed-shell surface (Figure 4g) does not follow the gradient of that surface, which points to the reactant minimum. Instead, the inertia of the wave packet takes it in the direction of increasing Q1 to complete the C−N dissociation. Moreover, the fraction of the wave packet that evolves to the ketene undergoes two consecutive passages through different points of the seam (Figure 4g and h) because the seam lies along the initial reaction coordinate Q1. The quantum dynamics approach guarantees that this is not an artifact due to the dynamics treatment. More importantly, the extended seam is a common dominant feature of other ultrafast photochemical reactions,13−20 and similar effects to those described here must occur in those cases. Our study is very timely, at a point where theoretical and experimental groups are attempting to simulate optical control using mechanistic ideas and knowledge of the potential energy surface, rather than optimal control strategies.16,19,40−43 It has been suggested that control strategies should focus on passage through the conical intersection.16,40 To apply such an approach successfully, a detailed picture of the potential energy surface and the photodynamics through the seam is necessary. Our work provides such a description, and it shows that the extended seam is an ideal target for optical control of photochemical reactions.

Letter

ASSOCIATED CONTENT

S Supporting Information *

Complete refs 29 and 30, computational details, and Cartesian coordinates for all optimized structures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address

́ Centro de Fisica de Materiales CSIC-UPV/EHU, 20018 Donosti-San Sebastián, Spain. §

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by Grants CTQ2008-06696 and CTQ2011-26573 from the Spanish Ministerio de Ciencia e Innovación (MICINN), SGR0528 from the Catalan Agència de Gestió d’Ajuts Universitaris i de Recerca (AGAUR), and UNGI08-4E-003 from MICINN and the FEDER fund (European Fund for Regional Development). Q.L. acknowledges a Juan de la Cierva fellowship of the MICINN and A.M. a Beatriu de Pinós fellowship of the Generalitat de Catalunya (Spain).

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