A Theoretical Study on the Photodissociation of Acetone: Insight into

Jun 2, 2010 - On the basis of the results, we propose a new mechanism, slow intersystem crossing from S1 to T1 without seam of crossing, followed by C...
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A Theoretical Study on the Photodissociation of Acetone: Insight into the Slow Intersystem Crossing and Exploration of Nonadiabatic Pathways to the Ground State Satoshi Maeda,*,†,‡ Koichi Ohno,§ and Keiji Morokuma*,‡,

The Hakubi Center, Kyoto University, Kyoto 606-8103, Japan, ‡Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan, §Toyota Physical and Chemical Research Institute, Nagakute, Aichi 480-1192, Japan, and Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322 )

†

ABSTRACT Structures of transition states (TSs) and minima on seam of crossing (MSXs) for potential energy surfaces (PESs) of acetone of the S0, S1, and T1 states were explored. On the basis of the results, we propose a new mechanism, slow intersystem crossing from S1 to T1 without seam of crossing, followed by CH3 dissociation via a TS on T1; this slow pathway will be overtaken by a more efficient S1 pathway for higher energy. This is consistent with the observed long lifetime of the S1 species. Moreover, four channels, including three new ones, were found to regenerate the ground state acetone from the S1 PES, and they all may be involved in the roaming channel that has been proposed recently as a new route of CO generation in a 230 nm photolysis. There are significant differences in MSX structures and energies between the present CASPT2 results and previous CASSCF results. SECTION Dynamics, Clusters, Excited States

after generation of the S1 species.9-11 Relevant stationary structures of the S1 pathway were also examined by high-level CASPT2 and MRCISD(Q) calculations.12 If the S1 pathway is dominant and the T1 pathway is the minimum energy pathway, one question arises: Why does the system prefer the higher energy S1 pathway? Although small spin-orbit coupling and/or dynamical effects might be possible answers, there is no clear explanation so far. Very recently, a new dissociation mechanism was proposed by a dc-slice imaging experiment, in which, by detailed analyses of product energy distributions of CO, it was found that there are at least two mechanisms generating the CO product in 230 nm (520 kJ/mol) photolysis of acetone.18 One corresponds to the (conventional) stepwise pathway (i.e., CH3C(O)CH3 f CH3 þ CH3CO f CH3 þ CH3 þ CO). The second pathway generating rotationally cold CO was suggested to be similar to the roaming pathways of formaldehyde and acetaldehyde.19-21 In the roaming pathways, H or CH3 once partially dissociated, roams around the remaining HCO fragment, and abstracts H from HCO to generate CO. All of these three events are believed to happen on the S0 PES after a nonadiabatic transition from the S1 PES. Hence, one key step is regeneration of the ground-state species from the S1 PES. This step was studied extensively by several groups for formaldehyde.22-27 It was shown that the system passes through the T1 PES at low excitation energies, and all of relevant stationary

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hotodissociation of acetone is one of the most extensively studied photochemical reactions.1 Ketones and aldehydes undergo a cleavage of one of CC bonds adjacent to the CdO group after a photoexcitation, where this reaction is called a “Norrish type I reaction”. Acetone has been studied as a prototype of the Norrish type I reaction.2-12 On the other hand, acetone is one of the most abundant organics in the atmosphere. The photolysis of acetone can produce CO2 and OH by secondary reactions of CH3CO with O2 and is an important source of OH radicals in the upper troposphere.13-17 It was proposed that the dissociation occurs on the T1 PES (the T1 pathway) after intersystem crossing (ISC) from the S1 potential energy surface (PES),2-4 as long as the photon energy exceeds the barrier of CC breaking on the T1 PES but is below the S1 CC breaking barrier, and a secondary dissociation of CH3CO into CH3 and CO takes place if the excitation energy is sufficient. A theoretical calculation at the CASSCF level indicated that ISC happens around a minimum on seam of crossing (MSX) structure between the S1 and T1 PESs located below the T1 barrier, and it was suggested to be the most preferable channel (at least in terms of potential energy) starting from the Franck-Condon region of the S1 PES.5 The T1 pathway was proposed to be a main channel by an early experimental study, even when the excitation energy is much higher than the S1 barrier.4 However, in recent combined femtosecond laser experimental and theoretical studies,6-8 it was suggested that the dissociation occurs through the S1 barrier (the S1 pathway) before the ISC takes place. This was confirmed by another femtosecond laser study at 195 nm (613 kJ/mol) in which the dissociation was shown to happen on the S1 PES within 0.6 ps

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Received Date: April 29, 2010 Accepted Date: May 27, 2010 Published on Web Date: June 02, 2010

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Figure 1. Optimized MIN, TS, and MSX structures for the S0, S1, and T1 states of acetone at the (8e,7o)-CASPT2/6-31þG* level. Energy values are relative to S0-MIN1, where the total energy is -192.526348 hartree. Converged symmetry except for C1 is denoted in parentheses. Structures newly located and very different from CASSCF are marked by * and **, respectively. Cartesian coordinates of all these structures are available in the Supporting Information. CC and CO bond lengths and lengths for bonds rearranging at TSs (red thin lines) are presented in each structure in Å.

structures of this S1 f T1 f S0 pathway were discovered very recently.25,26 Three other channels (to the S0 state) open by increasing the excitation energy: (1) S1 f T1 f S0 pathway through a partially dissociated (HCO 3 3 3 H) region of T1 PES,27 (2) S1 f S0 pathway through the partially dissociated region of S1 PES,23 and (3) S1 f T1 f S0 pathway through the potential well of hydroxycarbene.24 In the case of acetone, it was suggested that a roaming CH3 abstracts another CH3 in CH3CO on the S0 PES.18 However, in the case of acetone, only a single mechanism is known for generation of the ground state, i.e., an S1f S0 pathway through a partially dissociated (CH3CO 3 3 3 CH3) region of S1 PES.6 In this letter, we report new potential energy profiles of the S0, S1, and T1 states of acetone. The term “seam of crossing” includes 3N-8 dimensional conical intersection between states with the same spin and space symmetry as well as 3N-7 dimensional seam of crossing between states of different spin or space symmetry. The critical points, i.e., local minimum (MIN) structures, transition state (TS) structures, and MSX structures were optimized at the CASPT2/6-31þG* level. Here, at least the active space (4e,3o) with four electrons and three orbitals (π, n, and π* orbitals) is necessary to describe the n f π* transition. In this study, two σ and two σ* orbitals are also taken into account to represent CC bond breaking and proton transfer, i.e., the (8e,7o) active space was employed. The multistate CASPT2 and the single-state CASPT2 were applied to the singlet states and the triplet state, respectively.28,29 The shift parameter 0.3 was applied in the CASPT2 calculations to avoid the intruder state problem.30 Energy values and gradient vectors of the CASPT2 method were computed by the MOLPRO2006 program.31 By using these quantities, critical points were optimized by an external optimization code implemented in the GRRM program,32-34

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where MSX structures were optimized by a combination of the gradient projection35 and the rational function optimization36 methods, and the branching-plane updating method37 was employed to avoid computations of nonadiabatic coupling derivative vectors (CDVs). It should be noted that our MSX optimizer without use of CDVs gives the same optimized structures as those optimized with a method using CDVs within a given optimization threshold, as demonstrated in ref 37. Figure 1 shows all obtained critical points and their energies. Figure 2 illustrates the potential energy profiles based on the critical points in Figure1, excluding some very high energy species and pathways, which are referred only in text below. In Figure 2, there is a green curve that is the steepest descent path (with mass considered, denoted SDP-X below) starting from T1-TS1 and propagating within the seam of S0/T1 crossing hyperspace by using a method explained in ref 37 (see discussions below about a meaning of the curve). Figure 2 indicates that, after the n f π* photoexcitation, the system will oscillate around the bottom of S1-MIN1. At the (8e,7o)-CASSCF/6-31G* level, the S1/T1-MSX structure is known to exist very close in geometry to S1-MIN1 with a energy slightly lower than T1-TS1,5 and ISC through this MSX structure has been believed to be a dominant process if the excitation energy is not enough to reach the S1-TS1. However, at the more reliable (8e,7o)-CASPT2/6-31þG* level (hereafter referred as the CASPT2 level) geometry optimization starting from the CASSCF MSX structure5 converged to S1/T1-MSX1 accompanied with significant elongation of the CO bond (from 1.586 Å to 1.794 Å) and considerable increase in energy. Moreover, optimization starting from the reported high energy CASSCF S0/S1-MSX5 with a very long CO bond converged to S0/S1-MSX2 at the CASPT2 level. Hence, we conclude that, at the more reliable CASPT2 level,

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Figure 2. Potential energy profiles of the S0, S1, and T1 states of acetone based on the (8e,7o)-CASPT2/6-31þG* stationary structures listed in Figure 1. The green curve gives the steepest decent path SPD-X within the S0/T1 seam of crossing hyperspace (see text for further details). The Franck-Condon (FC) energy is indicated with dotted line.

no crossing exists in the low energy region of basin of S1-MIN1. Here, we propose that the S1 f T1 transition takes place by trickling down from S1 to T1 while the molecule in the S1 state spends a long time oscillating on the S1 surface, because the two PESs, although without crossing, are very close and nearly parallel to each other in energy at any place in the basin of S1-MIN1. The transition probability at each geometry may be very small because the spin-orbital coupling between the two states belonging to the same electronic configuration is expected to be small; the spin-orbital coupling is exactly zero in structures with C2v symmetry such as the Franck-Condon point and S1/T1-MSX1 and was computed to be only 0.9 cm-1 at S1-MIN1 at the (8e,7o)-CASSCF/6-31þG* level using the MOLPRO2008 program.31 Therefore, the S1 f T1 transition in this mechanism should be very slow. A similar S1 f T1 transition mechanism was also proposed for formaldehyde very recently.24-26 In the case of acetone, the lifetime has been reported to be much longer than 15 ps at 253 nm (473 kJ/mol) excitation38 and not shorter than 100 ps at 253-288 nm (473-415 kJ/mol) excitations.39 The present conclusion that there is no explicit crossing seems to explain well these long experimental lifetimes of the S1 species. After the slow S1 f T1 transition, the dissociation takes place through T1-TS1. Although there is a low energy MSX between the S0 and T1 PESs in formaldehyde,25,26 the lowest S0/ T1-MSX1 of acetone is located in a high energy region, and the T1 f S0 transition should be a slow process. Very recently it has been shown that there is a seam of crossing hyperspace between the T1 and S0 PESs of formaldehyde starting from a partially dissociated (HCO 3 3 3 H) region and lasting to the radical dissociation limit.27 In the present study, we followed the SDP-X at the (8e,7o)-CASSCF/6-31þG* level starting from the CASPT2 T1-TS1 geometry to find a similar S0/T1 seam of crossing. It should be noted that this SDP-X is not a minimum energy path (MEP) integrated on PESs. Hence, the SDP-X is slightly higher in energy than the MEP of T1 dissociation.

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Figure 3. Potential energy profiles of the S0 and T1 states along the steepest decent path SPD-X within the seam of crossing hyperspace plotted against the dissociating CC bond distance at the (8e,7o)CASSCF/6-31þG* level. The curves were shifted so that the final point matches the CASPT2 dissociation limit in Figure 2 (345.5 kJ/mol).

However, actual trajectories with nonzero kinetic energy can have geometries deviated from MEP and are expected to pass geometries within the SDP-X sometimes, as shown in ref 27 for formaldehyde. A profile of the SDP-X is shown in Figure 3, where energy values of the two states are plotted by O and  . The energy gap is only 9.9 kJ/mol at the first point (i.e., T1-TS1). A minimization of the energy gap led to the second point, and then the SDP-X was followed by confining the geometries within the seam of crossing hypersurface until the CC bond distance became 2.88 Å, where numerical integration at a longer distance was difficult because of very flat PESs. The green curve in Figure 2 shows this SDP-X, with the CASSCF energy shifted so that the final point matches the CASPT2 dissociation limit. On the basis of the existence of this seam, we propose that the T1 pathway can also generate S0-MIN1 through the T1 f S0 transition followed by a recombination of CH3 and CH3CO on the S0 PES as shown by a dashed line from the green curve in Figure 2. In other words, there is a chance to come back to the ground state also in the T1 pathway. When the excitation energy becomes higher than the S1 barrier, the S1 pathway should become dominant as the S1 f T1 transition without an explicit crossing is very slow. This is

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consistent with the recent femtosecond laser studies.6-11 The S1 f S0 transition can take place just after the S1 barrier through S0/S1-MSX1, after which the system can either dissociate or come back to S0-MIN1 by a recombination of CH3 and CH3CO, as indicated by a dashed line in Figure 2. We just note here that the reactions of CH3CO species have been discussed in detail elsewhere.5-7,12,17 We also studied isomerizations on the S1 and T1 PESs. Figure 1 presents three types of isomerizations: (1) proton transfer from CH3 to O (S1-TS2 and T1-TS2), (2) proton transfer from CH3 to C of CdO (S1-TS3 and T1-TS3), and (3) CH3 transfer (S1-TS4 and T1-TS4). Among these, the second and third pathways are highly unlikely to compete with the dissociations (S1-TS1 and T1-TS1), as corresponding barriers are very high. The most probable one (S1-TS2) is also unlikely to compete against the dissociations, even if zero-pointenergy (ZPE) corrections and proton tunneling corrections are taken into account; the energies of S1-TS1 and S1-TS2 including harmonic CASPT2 ZPE are 440.8 and 468.3 kJ/mol, respectively, and a microcanonical rate of the proton transfer reaction (S1-MIN1 f S1-TS2 f S0/S1-MSX2) with a tunneling correction with the one-dimensional Eckart potential model40 is only 1.7  103 (s-1) when available excitation energy is 450 kJ/mol. In higher excitation energies, the dissociation is always faster than the proton transfer. We may conclude that the excited state proton transfer is just a minor channel generating the ground-state acetone via S0/S1-MSX2. MSX structures outside the potential well of acetone as well as TS and EQ structures in the present CASPT2 result are very similar to the CASSCF results in the literature.5-7 However, MSX structures inside the potential well of acetone are significantly different between the two levels. This is probably because of the importance of dynamical electron correlation in optimizations of MSX structures, as has been discussed by several groups.41,42 Even if shapes of two PESs are very similar between CASSCF and CASPT2 methods, a subtle vertical shift in energy of one of the PESs may cause a significant change in the position of a crossing seam. This problem is especially serious when gradient vectors of two PESs are pointing to similar directions, where such a crossing seam is sometimes classified as “sloped type”.43 In acetone, a well-defined potential well (i.e., S0-MIN1, S1-MIN1, and T1-MIN1) exists on every S0, S1, and T1 PES, and MSX structures in these potential wells fall into the sloped type. Similarly, one of the most important MSX structures of formaldehyde (a S0/T1-MSX structure) was missing on CASSCF PESs even if the fullvalence active-space is employed.26 Therefore, we propose Figure 2 as a new and more reliable figure of potential energy profiles for better understanding of the photodissociation dynamics of acetone. In summary, we proposed a new mechanism of the S1 f T1 ISC, in which the transition takes place very slowly, as there is no explicit low-energy crossing between these two PESs. This is consistent with the long lifetime of the S1 species38,39 and the fact that the S1 pathway becomes dominant at high excitation energies.6-11 We also proposed four pathways (among which three are new) for regeneration of the ground-state S0 from the S1 PES, in the order of increasing energy requirement: (1) S1 f T1 trickling transition followed

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by a T1 f S0 transition via a seam in the partially dissociated region (the green curve in Figure 2), (2) (known) S1 f S0 transition via S0/S1-MSX1 after a CC bond breaking through S1-TS1, (3) S1 f S0 transition via S0/S1-MSX2 after a proton transfer through S1-TS2, and (4) S1 f T1 trickling transition followed by a T1 f S0 transition via S0/T1-MSX1. In conclusion, we propose that these pathways all may be involved in the roaming dynamics of acetone, with the new pathway (1) dominating at lower energy.18

SUPPORTING INFORMATION AVAILABLE Cartesian coordinates of optimized geometries in Figure 1. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed. E-mail address: [email protected] (S.M.), [email protected] (K.M.).

ACKNOWLEDGMENT This work is partly supported by a grant from the Japan Science and Technology Agency with a Core Research for Evolutional Science and Technology (CREST) in the Area of High Performance Computing for Multiscale and Multiphysics Phenomena as well as a grant from AFOSR (Grant No. FA9550-07-1-0395). The computational resources at the Research Center for Computational Science at the Institute for Molecular Science are gratefully acknowledged.

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