Multiple-State Nonadiabatic Dynamics Simulation of

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Multiple-state nonadiabatic dynamics simulation of photoisomerization of acetylacetone with the direct ab initio QTMF approach Binbin Xie, Ganglong Cui, and Wei-Hai Fang J. Chem. Theory Comput., Just Accepted Manuscript • Publication Date (Web): 24 Apr 2017 Downloaded from http://pubs.acs.org on April 24, 2017

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Journal of Chemical Theory and Computation

Multiple-state nonadiabatic dynamics simulation of photoisomerization of acetylacetone with the direct ab initio QTMF approach Binbin Xie, Ganglong Cui, and Wei-Hai Fang* Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China

Abstract In the present work, quantum trajectory mean-field (QTMF) approach is numerically implemented by ab initio calculation at the level of the complete active space self-consistent field, which is used to simulate photoisomerization of acetylacetone at ~265 nm. The simulated results shed light on the possible nonadiabatic pathways from the S2 state and mechanism of the photoisomerization. The in-plane proton transfer and the subsequent S2oS1 transition through the E-S2/S1-1 intersection region are the predominant route to the S1 state. Meanwhile, the rotational isomerization occurs in the S2 state, which is followed by internal conversion to the S1 state in the vicinity of the E-S2/S1-2 conical intersection. As a minor pathway, the direct S2oS1oS0 transition can take place via the E-S2/S1/S0 three-state intersection region. The rotamerization in the S1 state was determined to be the key step for formation of non-chelated enolic isomers. The final formation yield is predicted to be 0.57 within the simulated period. The time constant for the S2 proton transfer was experimentally inferred to be ~70.0 fs in the gas phase and ~50.0 fs in dioxane, acetonitrile, and n-hexane, which is well reproduced by the present QTMF simulation. The S1 lifetime of 2.11 ps simulated here is in excellent agreement with the experimentally inferred value of 2.12, 2.13, and 2.25 ps in n-hexane, acetonitrile, and dioxane respectively. The present study provides a clear evidence that direct ab initio QTMF approach is a reliable tool for simulating multiple-state nonadiabatic dynamics processes.

*

Author to whom correspondence should be addressed. Email: [email protected], Tel: +86-010-58805382. 1

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1. INTRODUCTION The Born-Oppenheimer (B-O) approximation is one of the most fundamental hypotheses in the fields of chemistry and physics, and is the basis of understanding chemical and physical phenomena. Although the B-O approximation is at the heart of quantum mechanical treatment of molecular structures and properties,1-4 there are a great many chemical, physical, and biological events that cannot be adequately described within the B-O approximation.4-8 Actually, nonadiabatic transitions among potential energy surfaces of different electronic states play an important role in many areas of physics, chemistry and biology, and are often dominant factors in photochemical processes such as photo-induced electron and proton migration, photo-damage and photo-repair of nucleic acids,9-12 and photo-catalytic reactions at metal or semiconductor surface.13-16 The accurate treatment of nonadiabatic processes for chemical and biological systems is currently a formidable challenge for dynamical simulation. A complete description must be based on the full quantum mechanical time evolution equations. Because of the insurmountably computational scaling with the size of the system, the full quantum dynamics simulations are only applicable to very small molecules.3 Alternatively, the mixed quantum-classical (MQC) dynamical approaches have been developed to investigate the nonadiabatic dynamics of a complex system in the last half century, which treat the nuclear subsystem classically and the electronic subsystem quantum mechanically.2 A major issue is how to deal with the feedback between the quantum and classical subsystems. Ehrenfest mean field (EMF)18-20 and trajectory surface-hopping (TSH)5,20-24 are the most widely used MQC dynamical methods for investigating nonadiabatic processes in the field of chemistry, physics, or biology. In the TSH algorithm, the nuclei move always 2


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on the potential energy surface of a single B-O electronic state, but allow to hop into other B-O states. The hopping is determined stochastically in a way to maintain internal consistency, which requires that the fraction of trajectories running on each electronic state equals the corresponding probability computed by solving the electronic time-dependent Schrödinger equation (TDSE) and averaging over all trajectories.22 However, this requirement is not always satisfied for the TSH simulations. Unlike the TSH method, classical trajectories are propagated along weighted averages of potential energy surfaces for the related B-O states in the EMF scheme. Since the nuclear motion is represented by one point in phase space for all the electronic states, the mean-field trajectory can be dramatically different from the behavior of the quantum wave-packets if the potential energy surfaces have very different slopes for the related B-O states. As pointed out in the previous study,25 the presence of classical nuclei in the MQC system induces nonadiabatic coupling that causes the TDSE to evolve wave functions of a single B-O state into quantum-mechanical superpositions. The quantum decoherence can be caused by the interaction of a quantum superposition with the classical nuclei. Actually, the classical nuclei can be viewed as a classical observer and the nuclear motion acts as continuous quantum measurements to the electronic subsystem. As a consequence, the quantum superposition of electronic states is resolved into a single B-O electronic state.25 Inspired by the aforementioned understanding for the MQC dynamics, recently we proposed a quantum trajectory mean-field (QTMF) approach for simulation of non-adiabatic dynamics proceses.26 The concept of continuous quantum measurement involved in the QTMF scheme can keep the reasonable feature of quantum coherence in the coupling region and can resolve the quantum superposition into a single B-O electronic state, leading to the physical asymptotic region where the coherence is very weak or disappear. It is evident that the QTMF method takes the advantage of the EMF 3



and TSH algorithms and provides a natural interface between the separate quantum and classical subsystems, without invoking any artificial surface-hopping algorithm. More recently, the QTMF method was employed to explore photodissociation dynamics of diazirinone (N2CO).27 The QTMF simulated excited-state lifetime, time constant of the C-N fission, and branching radio of different channels were compared with those from the TSH and AIMS (ab initio multiple spawning) dynamical simulations as well as the available experimental findings, which gives a clear evidence that the QTMF method is a reliable tool for exploring non-adiabatic dynamics. Since the N2CO photodissociation starts from the first excited singlet state (S1) and the final products of N2 + CO are in the ground state (S0), only two states were involved in the QTMF dynamics simulations.27 As emphasized in the previous study,26 the Schrödinger equation is replaced with a master equation in the QTMF scheme, where the quantum decoherence is automatically fulfilled by the stochastic process. In principle, the QTMF method is more suitable for simulating non-adiabatic processes that involve more than two B-O states. Experimentally, it has been established that at least the lowest three singlet states are involved in photodynamics of acetylacetone (AcAc, CH3COCH2COCH3) at ~265 nm. Therefore, we take CH3COCH2COCH3 as a representative system to carry out direct ab initio QTMF nonadiabatic dynamics simulation in the present work. Beta-dicarbonyl compounds are of versatile photochemical reactivities28 and were extensively used in commercial sunscreen products owing to a high UV absorption and the fast deactivation after UV irradiation.29 In addition, they can be produced in the atmospheric oxidation of volatile organic compounds and their degradation can be initiated by photolysis.30 As the simplest symmetric E-diketone, acetylacetone has been a subject of numerous theoretical31-38 and experimental studies,31,39-45 which mainly focused on its structures in the ground state, the intramolecular proton transfer, and the 4


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keto-enol tautomerism in the gas phase,31-36,46-49 various solvents,35 the isolated matrices,31,49 and nano-confinement environments.37 Although AcAc is a prototype of E-diketones, it exists mainly as the enolic form32,34-36,40 and actually belongs to the category of D,E-enone systems. The reason for this comes from the stabilizing effect of the intramolecular H-bond coupled with a S-electronic delocalization over the O-C-C-C-O pseudo-cycle backbone in the chelated enolic form. A lot of experimental investigations have been performed in order to examine the ultrafast dynamics of acetylacetone.41-45 The second excited singlet state (S2) of the AcAc enolic form is initially populated upon photoexcitation at ~265 nm, which has the 1ŒŒ* character. Subsequently, there are multiple steps for the enolic form to deactivate from the S2 state. The first step is the departure from the Franck-Condon (FC) region, which was determined to occur in the period of 60 - 80 fs in the gas phase41 and within 50 fs in dioxane, acetonitrile, and n-hexane.44 This ultrafast initial step was speculated to involve the proton transfer and complex deformation in structure. The second step of the S2oS1 internal conversion proceeds in the coupling regions of the two electronic states and a time constant of about 1.4 ps was assigned as the full transfer of the wavepacket from the S2(1ŒŒ*) to S1(1nŒ*) state in the gas phase.41 Contrary to what was observed in the gas phase, isomerization among the different non-chelated enolic forms was observed to be the main processes upon ~265 nm irradiation of acetylacetone and the related systems in various solvents44,45 or isolated in matrices.42,43

2. THE QTMF METHOD AND AB INITIO IMPLEMENTATION The QTMF method has been described in detail in the previous studies,26,27 only a brief introduction is presented here. In the B-O representation, the time-dependent Schrödinger equation for the coherent electronic evolution can be expressed as, 5




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The initial nuclear coordinates R(t0 ) and the conjugated velocities R(t0 ) in the S2 state are generated by means of randomly sampling from Wigner distribution of harmonic vibrations in the ground state (S0). Meanwhile, the initial diagonal and off-diagonal elements of the density matrix are set as zero, Uij (t0 )

0 (i, j = 0, 1, and 2)

except for U 22 (t0 ) 1 . Once the initialization is complete, energies, energy gradients, non-adiabatic coupling vectors d ij at the initial conditions are computed for the S2, S1, and S0 states. Then the velocity-Verlet method is employed for integration of the trajectories with the time step ( 't ) of 0.5 fs and the mean force is obtained from Eq. (7),

F (t )

¦U

ii

(t )’Ei (t )

¦ U (t )>E (t ) ij

j

@

Ei (t ) d ji (t )

(7)

For propagation of the electronic wave function, the fourth-order Runge-Kutta method was used with the integration step of 0.0125 fs, where the energies, velocities, and non-adiabatic coupling vectors were interpolated for the intermediate steps. Ab initio calculation is carried out at the level of the complete active space self-consistent field (CASSCF), which allows for the balanced representation of several electronic

states

simultaneously.50,51

The

three-state-averaged

(SA3)

CASSCF

calculations have been performed to determine the stationary and intersection structures in the S0, S1, and S2 states. Ten electrons in nine orbitals are included in the active space for the SA3-CASSCF calculation, referred to as SA3-CAS(10,9) hereafter, which is mainly composed of the C=C and C=O S and S* orbitals, the O-H V and V* orbitals, and the non-bonding orbital at the O atom. Graphical representation of the active orbitals are given in Supporting Information (SI). To validate the reliability of the SA3-CAS(10,9) calculations, the single-point energies were calculated with the multi-state second order perturbation theory (MS-CASPT2)52 on the basis of the SA3-CAS(10,9) wave functions, referred

to

as

MS-SA3-CASPT2(10,9)

hereafter.

7


The

SA3-CAS(10,9)

and


MS-SA3-CASPT2(10,9) calculations are performed with 6-31G*, 6-31G**, and 6-31++G** basis sets by using the Molpro 2012 software package.53

3. RESULTS AND DISCUSSION Structures and relative energies Although there is a rich debate as to whether the hydrogen bond has an asymmetric O-H˜˜Õ (CS) or symmetric O˜˜˜H˜˜Õ (C2V) configuration for the chelated enolic form in the S0 state,33,35,48 the asymmetric CS structure has been determined experimentally with the gas-phase electron diffraction technique,35 which is supported by numerous ab initio calculations at different levels of theory.31-36 However, the geometric structures of enolic form in the S1 and S2 states have not been experimentally determined up to now and the previous calculations focused mainly on the S0 stationary structures. Here, the chelated enolic forms in the S0, S1, and S2 states, which are respectively referred to as E-S0, E-S1, and E-S2 hereafter, are optimized at the SA3-CAS(10,9) level of theory with 6-31G*, 6-31G**, and 6-31++G** basis sets. The detailed results are given in Table S1 and Figure S1 of Supporting Information. The SA3-CAS(10,9)/6-31G* optimized structures are schematically shown in Figure 1, together with the key bond parameters and an atom-labeling scheme in E-S0, and their relative energies are listed in Table 1. Besides the most stable chelated form, five non-chelated enolic isomers in the S0 state were confirmed to be local minima by the SA3-CAS(10,9)/6-31G* calculation. Their structures and relative energies are given in Figure S2 and Table S2 of Supporting Information. The O5-H6 bond length and the H6˜˜Õ1 distance are predicted to be respectively 0.977 and 1.916 Å in the E-S0 structure by the SA3-CAS(10,9) optimization with the 6-31G* basis set. These bond parameters are nearly unchanged when the 6-31G** and 6-31++G** basis sets are used for the SA3-CAS(10,9) optimizations. The present

8


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calculations reproduce the asymmetric O-H˜˜Õ (CS) configuration for the E-S0 structure. Meanwhile the symmetric O˜˜˜H˜˜Õ (C2V) structure was confirmed to be the transition state, which connects the two equivalent E-S0 minima with a barrier of ~2.0 kcal/mol.31-36 The SA3-CAS(10,9) calculations reveal that the initial noS* excitation is mainly localized on the C2=O1 carbonyl group and subsequently the Œ electrons are redistributed on the O5-C4-C3-C2-O1 framework, which results in the diradical character of the S1 state with one unpaired electron localized at the O1 atom and the other distributed in the delocalized S* orbital. In the E-S1 structure, the O5-H6 bond is shrunk to 0.968, 0.964, and 0.962 Å, while the H6˜˜Õ1 distance is elongated to 2.103, 2.111, and 2.130 Å at the levels

of

SA3-CAS(10,9)/6-31G*,

SA3-CAS(10,9)/6-31G**,

and

SA3-CAS(10,9)/6-31++G** respectively. As shown in Figure 1, the hydrogen bond in the E-S1 structure has an asymmetric O-H˜˜Õ (CS) configuration, which is the same as that in the S0 state. Analogously, the symmetric O˜˜˜H˜˜Õ (C2V) structure was confirmed to be the transition state in the S1 state, referred to as E-S1-TS hereafter, which connects the two equivalent E-S1 minima. The barrier height is calculated to be 13.3 kcal/mol at the

MS-SA3-CAS(10,9)/6-31G*//SA3-CAS(10,9)/6-31G*

level

for

the

in-plane

hydrogen exchange in the S1 state. Analogous to the S0 state, five non-chelated enolic structures in the S1 state were determined by the SA3-CAS(10,9)/6-31G* calculations, which are 3.0 - 4.3 kcal/mol higher than the E-S1 structure in energy, as listed in Table S2 of Supporting Information. The change of the H-bond (O5-H6˜˜Õ1) structure from S0 to S1 shows that the H-bond interaction in the E-S1 structure is weaker than that in the E-S0 structure. The reason for this comes from the 1nS* character of the S1 state. The H-bond strength is to large extent dependent on a donation of the lone-pair electrons of the O1 atom to the 9



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O5-H6 V* orbital. One of the lone-pair electrons distributed in the O1 atom is excited to the Œ* orbital in the S1(1nS*) state, which leads to a considerable decrease of the electron density on the O1 atom. As a result, the H-bond is significantly weakened in the S1(1nS*) state, as compared with that in the S0 state. Because of the redistribution of the Œ electrons, the bond parameters on the O5-C4-C3-C2-O1 framework are adjusted in the E-S1 structure. Unlike the E-S1 structure, the S2 state originates from the delocalized SoS* excitation and the S electrons are distributed on the O5-C4-C3-C2-O1 pseudo-cycle. As a consequence, the symmetric (C2V) structure was determined to be the local S2 minimum in the present study, which is referred to as E-S2-1 hereafter. In the E-S2-1 structure, both the O5˜˜˜H6 and H6˜˜Õ1 distances are predicted to be 1.258 Å by the SA3-CAS(10,9) calculations with the 6-31G* basis set and they become 1.256 and 1.255 Å respectively, when the 6-31G** and 6-31++G** basis sets are used. Actually, a similar E-S2-1 structure was characterized in the previous ab initio study at the CAS(10,8)/cc-pVDZ level.32 Another minimum-energy structure was found in the S2 state, referred to as E-S2-2 hereafter. The rotational isomerization takes place from the chelated E-S2-1 to the non-chelated

E-S2-2

structure,

which

involves

a

large

deformation

of

the

O5-C4-C3-C2-O1 framework and a rotation of the CH3-C4-O5-H6 group. Finally, It should be pointed out that the SA3-CAS(10,9) optimized E-S0, E-S1, and E-S2 structures exhibit small dependence on the size of basis sets (see Figure S1 of SI). On the basis of the SA3-CAS(10,9)/6-31G* optimized E-S0 structure, the vertical excitation energies to the S1 and S2 states were calculated to be respectively 99.0 and 116.2 kcal/mol at the MS-SA3-CASPT2(10,9)/6-31G* level, which are close to those obtained by the MS-SA3-CASPT2(10,9) calculations with 6-31G** and 6-31++G** basis sets. The electronic spectra of AcAc have been measured with various spectral 10


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techniques (see Ref. 32 for early investigations). The relatively strong band with a peak at around 4.67 eV (107.8 kcal/mol) was assigned to be the first Œ:Œ* transition of the chelated enolic form, while the lowest n:Œ* transition was determined to be 4.04 eV (93.2 kcal/mol).54 In comparison with the experimental findings, the vertical excitation energies are a little overestimated by the MS-SA3-CASPT2(10,9)//SA3-CAS(10,9) calculations. As listed in Table S1 of Supporting Information, the S0:61/S0:62 adiabatic excitation energies are predicted to be 84.4/99.2, 84.7/98.6, and 82.6/97.7 kcal/mol by the combined MS-SA3-CASPT2(10,9)//SA3-CAS(10,9) calculations with 6-31G*, 6-31G**, and 6-31++G** basis sets respectively, which indicates that the basis-set change has only a little influence on the calculated excitation energies. In addition to the vertical and adiabatic excitation energies, single-point energy calculations were performed at the MS-SA3-CASPT2(10,9)/6-31G* level of theory for a wide range of geometric structures that were generated by the QTMF dynamical simulation for two distinctive initial conditions (the QTMF dynamical simulation will be discussed below). With respect to the S0 minimum, the MS-SA3-CASPT2(10,9)/6-31G* and SA3-CAS(10,9)/6-31G* calculated relative energies for the S1 and S2 state were plotted in Figure 2 as a function of time, which corresponds to a change of the S1 and S2 relative energies with nuclear configuration. The S1 and S2 relative energies are overestimated by ~10.0 kcal/mol at the SA3-CAS(10,9)/6-31G* level of theory, as compared with those from the MS-SA3-CASPT2(10,9)/6-31G* calculations, which is the expected result of the limited inclusion of dynamic electron correlation in the SA3-CAS(10,9)/6-31G* calculations. However, the potential energy curves calculated at the two levels of theory are nearly parallel to each other and exhibit the same energy change tendency with respect to nuclear configuration. This change tendency is tightly related to energy gradients or forces, which determines time evolution of nuclear 11



configuration. The SA3-CAS(10,9)/6-31G* calculations can give a reliable description on the energy gradients, which are required for accurate QTMF dynamical simulation. Several surface-crossing structures among the S2, S1, and S0 states are determined for the enolic form by the SA3-CAS(10,9)/6-31G* calculations, which include two minimum-energy conical intersections between the S2 and S1 states (E-S2/S1-1 and E-S2/S1-2) and one minimum-energy conical intersection between the S1 and S0 states (E-S1/S0). In addition, one minimum-energy intersection among the S2, S1, and S0 states (E-S2/S1/S0) is determined with a penalty function-based three-state intersection optimization approach.55 The optimized structures for these intersections are shown in Figure 1, along with the key bond parameters. Local topological shapes of the E-S2/S1-1, E-S2/S1-2, and E-S1/S0 conical intersections were represented by the two vectors of energy gradient difference ( gij ) and non-adiabatic coupling ( d ij ) with a linear approximation,56 which are shown in Figure S4 of Supporting Information. The local topological shapes reveal that E-S2/S1-1 is a peaked conical intersection, while E-S2/S1-2 is of the sloped character. Qualitatively, the S2oS1 internal conversion occurs in the E-S2/S1-1 region with higher efficiency than that in the vicinity of the E-S2/S1-2 intersection,56 which is confirmed by the dynamical simulation discussed below. As shown in Figure 1, the E-S2/S1-1 conical intersection is similar to the local E-S2-1 minimum in structure. Meanwhile, they have nearly the same relative energy with respect to the E-S0 minimum. As discussed before, the symmetric O˜˜˜H˜˜Õ (C2V) structure is the transition state (E-S1-TS) in the S1 state, which connects the two equivalent E-S1 minima. This transition state is also similar to E-S2-1 or E-S2/S1-1 in structure and is about 1.0 kcal/mol lower than E-S2-1 or E-S2/S1-1 in energy. From Table 1 and Figure 1, it can be seen that the relative energy of the E-S2/S1-2 is close to that of E-S2-2, and E-S2/S1-2 is similar to E-S2-2 in structure. As pointed out before, the E-S0 12


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and E-S1 structures have the CS symmetry, and E-S2-1, E-S2/S1-1, and E-S1-TS have their backbone structures in the C2V symmetry. However, E-S2-2, E-S2/S1-2, and E-S1/S0 have non-planar structures, which originate from a rotation of the H6-O5-C4-CH3 group with respect to the O1-C2(CH3)-C3 moiety. An analogous intramolecuar rotation of ~90.0° leads to the three-state E-S2/S1/S0 intersection structure, which is a little lower than the E-S2-2 or E-S2/S1-2 structure in energy. A similar three-state intersection was discovered by Coe and Martinez in the previous studies for malonaldehyde.57,58 They pointed out that for D,E-unsaturated enones such as acetylacetone, the intramolecuar rotation lowers the energy of S2 state and raises the energy of the S0 state. However, the energy of the S1(1nS*) state is significantly less affected by this intramolecuar rotation. Therefore, it can be expected that the S2, S1, and S0 states become degenerate at about 90.0° rotation and a small changes of other bond parameters.58 Nonadiabatic dynamics The SA3-CAS(10,9)/6-31G* calculation was confirmed to be reliable for describing structures and properties of acetylacetone in the low-lying electronic states, which is employed to perform on-the-fly QTMF nonadiabatic simulations. Dynamics results are reported for an ensemble of 298 trajectories and the initial conditions in the S2 state are generated by randomly sampling from the Wigner distribution of harmonic vibrations in the S0 state. Upon a close examination of the distribution of the QTMF simulated 298 trajectories, it was found that most of them (224 trajectories) are initially propagated into the E-S2-1 region and decay to the S1 state in the vicinity of the E-S2/S1-1 conical intersection. There are 51 trajectories that relax to E-S2-2 directly, which is followed by the S2oS1 transition in the region of the E-S2/S1-2 conical intersection. Meanwhile, the S2oS1oS0 transition was observed to take place in the vicinity of the E-S2/S1/S0 three-state intersection for the remaining 23 trajectories. Overall, three types of nonadiabatic processes from the S2 Franck-Condon (FC) region 13



were determined by the combined ab initio calculation and QTMF dynamical simulation, referred to as types I, II, and III. Their branching ratios are predicted to be 75.2%, 17.1%, and 7.7% respectively. The diagonal element ( U 00 , U11 , or U 22 ) of the density matrix reflects the population of the S0, S1, or S2 state, while the off-diagonal element ( U 01 or U12 ) defines the coherence of the related states. Time evolution of energies, the O-H distances, the diagonal and the off-diagonal elements are plotted in Figures 3, 4, and 5 for the representative trajectories respectively. Upon irradiation at ~265 nm, the S2 state is populated initially. The proton transfer was observed to occur immediately for most of the simulated trajectories (type I). These trajectories are propagated into the E-S2-1 or E-S2/S1-1 region. As can be seen from Figure 3, the U12 value is about 0.5 in the propagation period of 40 fs, which reflects a strong coherence between the S 1 and S2 states in the initial process of proton transfer. The complete decoherence takes place in the subsequent 100.0 fs and the superposition state is collapsed to the S1 state. The S electrons are redistributed in the O-C-C-C-O pseudo-cycle backbone and the H-O, C-O, and C-C bond distances are alternately changed in the initial process from S2(FC) to E-S2-1. But the system keeps the chelated enolic form in this process and the O-C-C-C-O pseudo-cycle backbone is co-planar. A close examination of the QTMF simulated 224 trajectories of type I reveals that the rotational isomerization takes place once decaying to the S1 state via the E-S2/S1-1 intersection region. Several non-chelated rotamers were observed to be formed in the S1 state. As discussed before, the chelated enolic structure of E-S1 is the most stable in the S1 state. However, there are five non-chelated enolic structures in the S1 state, which are only 3.0 - 4.3 kcal/mol higher than the E-S1 structure in energy. As a result, the enolic form in the S1 state has some preference for the non-chelated structures. As shown in 14


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Figure 3, the trajectory is propagated in the S1 state for ~2200.0 fs before the S1oS0 transition, although the strong coherence between S1 and S0 was observed for a few times in the S1 propagation process. Within the simulated period of 3.0 ps, there are 117 trajectories that are finally propagated to the S0 state via the E-S1/S0 region, either yielding chelated enolic form of E-S0 or leading to the non-chelated enolic form (NE-S0). The whole process for type I can be summarized as S2(FC) o E-S2-1 o E-S2/S1-1 o S1 o E-S1/S0 oE-S0 + NE-S0, which is the predominant route upon irradiation of the chelated enolic form to the S2 state. Besides the in-plane proton transfer in the S2 state, the rotational isomerization is another initial process from the S2(FC) region, which produces the non-planar E-S2-2 structure firstly. Among the QTMF simulated 298 trajectories, fifty-one of them were observed to propagate into the E-S2-2 or E-S2/S1-2 structural region directly, which is referred to as type II hereafter. Time evolution of energies, the O-H distances, the diagonal and the off-diagonal elements is plotted in Figure 4 for one representative trajectory of type II. The trajectory is propagated in the S2 and S1 superposition state for the initial period of ~125.0 fs, which is similar to the initial in-plane proton transfer. After the S2oS1 transition in the vicinity of the E-S2/S1-2 conical intersection, a strong coherence between the S1 and S0 state appears in the subsequent ~100.0 fs, which is followed by automatic decoherence to the S1 state. Upon a close examination of the 51 trajectories of type II, it is found that the S1oS0 internal conversion takes place in the E-S1/S0 region for 41 trajectories within the simulated period of 3.0 ps. The chelated enolic form and the non-chelated enolic isomers are finally produced in the S0 state. The whole process for type II can be represented as S2(FC) o E-S2-2 o E-S2/S1-2 o S1 o E-S1/S0 o E-S0 + NE-S0. Unlike type I and II processes discussed above, there exists deactivation pathway 15



type III for the chelated enolic form in the S2 state, which involves three-state E-S2/S1/S0 intersection and can be represented as S2(FC) o E-S2/S1/S0 o E-S0(NE-S0). Upon close examination of 23 trajectories that belong to type III, it was found that the relaxation process from S2(FC) to E-S2/S1/S0 involve a large rotation of the H6-O5-C4-CH3 group with respect to the O1-C2(CH3)-C3 moiety. As shown in Figure 5, the nuclear motion is mainly governed either by the S2 or S1 potential energy surface with U 22 | 1 or U11 | 1 in the initial period of 0.0 - 150.0 fs, although there is a strong S2 and S1 coherence. Subsequently the trajectory oscillates in the three-state intersection region for about 100.0 fs. The strong coherence among the S2, S1, and S0 states is observed in this period and the S2oS1oS0 transition occurs. Finally, twenty-three trajectories are propagated to the S0 state via the E-S2/S1/S0 region. It should be pointed out that the nonadiabatic decay from S2 to S0 through the E-S2/S1/S0 region is not direct S2oS0 transition, but a sequential process of the S2oS1oS0 transition with a short stop in the S1 state. The QTMF simulated results corroborate that the in-plane proton transfer is the predominant route upon irradiation of the chelated enolic form to the S2 state, while the rotational isomerization in the S2 state is a minor process with the percentage of 24.8%. The two analogous pathways from the initially populated S2 state of malonaldehyde were determined by the AIMS dynamical simulation.57 Among the QTMF simulated 275 trajectories that propagate in the S1 state, the non-chelated isomer was observed to be formed in the 158 trajectories within the simulated period of 3.0 ps. Although the chelated enolic structure of E-S1 is the most stable in the S1 state, there are five non-chelated isomers that are only 3.0 - 4.3 kcal/mol higher than E-S1 in energy (see Table S2 of SI). As a result, the non-chelated isomers are formed in the S1 state with the percentage of 57.5%, which is larger than that for the chelated enolic form. Experimentally, it has been established that the rotamerization takes place in the S1 state 16


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within a few picoseconds and is the key step in the relaxation dynamics for the formation of the non-chelated enolic isomers.44 As pointed out before, five non-chelated enolic isomers were determined to be local minima in the S0 state by the SA3-CAS(10.9)/6-31G* calculations. Some of them have been identified in different kinds of matrices by the combined infrared spectroscopy and electronic structure calculations.31,32,42,43,59 With respect to the E-S0 minimum, however, these non-chelated isomers have their relative energies of 10.0 - 19.0 kcal/mol at the MS-SA3-CAS(10,9)/6-31G*//SA3-CAS(10,9)/6-31G* level of theory. Thus, the AcAc molecule exists mainly as the chelated enolic form in the S0 state. Within the simulated period of 3.0 ps, there are 181 trajectories that are propagated to the S0 state. Among them, 104 trajectories lead to formation of the non-chelated enolic isomers. The formation yield for the non-chelated isomers is estimated to be 0.57 by the direct ab initio QTMF simulation, which is defined as the ratio between the trajectories in non-chelated form and the total number of trajectories in the S0 state. The formation yield was experimentally measured to be 0.36, 0.29, and 0.15 in acetonitrile, dioxane, and n-hexane respectively.44 In comparison with the experimental values, this yield is significantly overestimated by the present QTMF simulation. Since the solvent effect is not considered in the present simulation, the AcAc molecule possesses a large quantity of internal energies once it is populated in the S0 state. In addition, the simulated period of 3.0 ps is not long enough for the complete recovery to the most stable chelated enolic form in the S0 state. These are main reasons why formation of the non-chelated isomer in the S0 state is overestimated by the present QTMF simulation. Once E-S0 is excited to the S2 state, the subsequent relaxation processes were observed to have a multi-exponential character in the previous femtosecond pump-probe experiment.41 A simple linear kinetic model was used to fit the time dependencies of the 17



Page 18 of 38

observed signals, which is a sequential decay involving four transients, W

W

W

C A B A •• • o B ••o C ••o D

(8)

In Eq. (8), transients A and D were definitely assigned to the S2(FC) structure and the enolic isomer in the S1 state respectively, while transients B and C were speculated to correspond to an ionization-resonance state and the coupling region between the S2 and S1 state respectively.41 The present electronic structure calculations reveal that transients B and C are respectively the local and global minima of E-S2-1 and E-S2-2 in the S2 state, which are further confirmed by ab initio QTMF dynamic simulations. The measured transient absorption signal was fitted with a sequential one-exponential model and only one time constant was reported as the S2 lifetime for three symmetrical -diketones of malonaldehyde, acetylacetone, and dibenzoylmethane in acetonitrile, dioxane, or n-hexane.44 However, when dibenzoylmethane in n-hexane is subjected to near- or deep-UV irradiation, two time constants were found to be needed for description of the S2 dynamics.45 As discussed before, there is a strong coherence between the S2 and S1 states in the initial processes and the nuclear motion is governed by the S2 and S1 superposition state upon irradiation at ~265 nm. It is a difficult task to distinguish experimentally whether the rotational isomerization proceeds in the S2 or S1 state, which is probably the reason why a considerable difference in the S2 time constants was reported in the previous experimental studies.41,44,45 The S0, S1, and S2 populations are plotted in Figure 6 as a function of time, which come from the time evolution of the diagonal elements ( U 00 , U11 , and U 22 ) for the QTMF simulated 298 trajectories. Since E-S2/S1-2 and E-S2/S1/S0 have similar backbone structures and there is a large overlap between the E-S2/S1-2 and E-S2/S1/S0 intersection regions, the S2 relaxation to the E-S2/S1-2 and E-S2/S1/S0 regions can be considered as

18


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There exists a minor relaxation pathway from the S2(FC) structure with a branching ratio of 24.8%, which originates from a rotation of the H6-O5-C4-CH3 group with respect to the O1-C2(CH3)-C3 moiety and a redistribution of S electrons in the O1-C2-C3-C4-O5 backbone. This minor S2 process is also predicted to be ultrafast with a time constant of 217.2 fs, which leads to the E-S2-2 region. The second time constant of W B was fitted to be 100.0 r 20.0 fs in the experimental study.

41

The present QTMF

dynamic simulation reveals that the transient C should be the global minimum of E-S2-2 in the S2 state and AoC is a direct process of the rotational isomerization from S2(FC) to E-S2-2(E-S2/S1-2) or to E-S2/S1/S0. Thus, the fitted second time component of 217.2 fs should be compared with a sum of W A and W B (170.0 r 30.0 fs) inferred experimentally.41 Experimentally it has been established that two time constants of ~50.0 and ~330.0 fs are needed for describing the S2 dynamics of dibenzoylmethane in n-hexane.45 The previous experimental studies41,44,45 and the present QTMF simulation agree well in the first time constant of the S2 dynamics. However, there is a considerable difference in the second time constant of the S2 state. The reason for this comes from occurrence of the rotamerization in the S2 and S1 superposition state, which can be either assigned as the S2 or S1 process. The S2oS1 population transfer results in an increase of the S1 population initially, and then it is decreased due to the S1oS0 transition. Time evolution of the S1 population ( P( St)1 ) can be approximately described by the kinetic model of a consecutive reaction, W

W

S2 S1 o S1 ••• o S0 S2 •••

(12)

and is fitted with the analytical formula, P( St)1

ª t t º ) exp( )» «exp( 1 W S2 ¬« W S2 W S1 ¼»

1 W S2 1 W S1

20


(13)

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The fitted lifetime ( W S1 ) is 2109.3 fs for the S1 state with W S2 fixed at the S2 lifetime of 101.2 fs. The transient D in Eq. (8) was assigned as the enolic isomer in the S1 state and the time constant of W C was experimentally fitted to be 1.4r0.2 ps with the kinetic model expressed by Eq. (8).41 This time constant ( W C ) can be considered as an approximation to the S1 lifetime. A sequential one-exponential model was used to fit time dependencies of the observed signals upon UV (~265 nm) irradiation of acetylacetone in the nonpolar solvent of n-hexane.44 The S2 and S1 lifetimes were experimentally inferred to be 50.0 and 2120.0 fs respectively,44 which are well reproduced by the present ab initio QTMF simulations. It should be pointed out that the S2 decay was considered as a single-exponential process in the previous experimental study44 and the time constant of W B in Eq. (8) is merged into W C as the S1 lifetime.

Summary In the present work, the QTMF approach is numerically implemented by ab initio calculation at the CASSCF level, which is used to simulate photodynamics of the AcAc enolic form. Upon irradiation at ~265 nm, the S2 state is initially populated in the Franck-Condon region. Three types of nonadiabatic processes were determined by the combined ab initio calculation and QTMF dynamical simulation, which are summarized as follows, E-S0 + hQ o S2(FC) o E-S2-1o E-S2/S1-1 o S1 o E-S1/S0 o E-S0 + NE-S0 o E-S2-2 o E-S2/S1-2 o S1 o E-S1/S0 o E-S0 + NE-S0 o E-S2/S1/S0 o E-S0 + NE-S0 There is a strong coherence between the S2 and S1 states in the initial two processes of the in-plane proton transfer and the rotational isomerization. Subsequently decoherence takes place mainly in the E-S2/S1-1 intersection region, which is the predominant route to 21



the S1 state. Meanwhile, the S1 state is populated through the S2oS1 transition in the conical intersection E-S2/S1-2 region. The chelated enolic form produced in the S1 state via the E-S2/S1-1 region is gradually changed into the non-chelated isomers. Although the chelated enolic structure of E-S1 is the most stable in the S1 state, five non-chelated isomers can be formed in the S1 state with a total percentage of 57.5%. Within the simulated period of 3.0 ps, the yield of isomerization to the non-chelated isomer in the S0 state is predicted to be 0.57 by the ab initio QTMF simulation, which is nearly same as that in the S1 state. Since the solvent effect is not included in the present QTMF simulation, a large quantity of excess energies are left in the internal degrees of freedom once enolic isomers return from the S2 to S0 state. In addition, the simulated period is relatively short and the recovery to the most stable chelated isomer is not complete within 3.0 ps. These are main reasons why formation of the non-chelated isomer in the S0 state is considerably overestimated by the present QTMF simulation, as compared with the experimental findings. Upon excitation to the S2 state, the first time component was experimentally inferred to be 70.0 r 10.0 fs in the gas phase and ~50.0 fs in dioxane, acetonitrile, and n-hexane. The first time component is not only well reproduced by the present QTMF dynamical simulation, but also the related process is exclusively assigned as the in-plane proton transfer from the S2 Franck-Condon structure to the local minimum (E-S2-1). However, a considerable difference in the second time constant of the S2 state was reported in the previous experimental studies. The underlying process for the second time constant was determined to be the rotational isomerization to the global minimum (E-S2-2) by the present QTMF simulation. This rotamerization was characterized to proceed in the S2 and S1 superposition state, which is probably the reason for the difference reported experimentally for the second time constant of the S2 state. The S1 22


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lifetime was estimated to be 2.11 ps by the present ab initio QTMF simulation, which is in excellent agreement with the experimentally inferred value of 2.12, 2.13, and 2.25 ps for acetylacetone in n-hexane, acetonitrile, and dioxane respectively.

Acknowledgment: This work was supported by grants from the NSFC (Grant Nos. 21421003, 21688102, 21520102005, and 21590801). Supporting Information Stationary and intersection structures, their relative energies, and graphical representation of the active orbitals are available free of charge via the Internet at http://pubs.acs.org.

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29



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Table 1 The relative energies (Rel-E) calculated at the level of MS-SA3-CASPT2(10,9)/6-31G* on the basis of the SA3-CAS(10,9)/6-31G* optimized stationary and intersection structures

Stationary Structures

Rel-E (kcal/mol)

Intersection Structures

Rel-E (kcal/mol)

E-S0

0.0

E-S1/S0

86.0

E-S1

84.6

E-S2/S1-1

99.6

E-S2-1

99.2

E-S2/S1-2

97.0

E-S2-2

96.6

E-S2/S1/S0

93.7

E-S1-TS

97.9

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Table 2 The fitted first ( W S1 ) and second (W S2 ) time constants for the S2 2

2

state and lifetime ( W S ) for the S1 state, together with the related values inferred experimentally 1

Time constants (fs)

This work

Exp.(a)

2

48.5

70.0 r 10.0

”50.0

~50.0

W S2

217.2

170.0 r 30.0

--

~330.0

WS

2109.3

1400 r 200.0

2110.0

--

W S1

2

1

Exp.(b)

Exps.(a), (b), and (c) :Taken from Refs. 41, 44, and 45 respectively

31


Exp.(c)


Figure 1. T he optimized stationary and intersection structures are shown schematically, together with the selected bond parameters (bond length in Å and dihedral angle in degree) and an atom-labeling scheme in E-S0.

32


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Table of Contents Graphic

38


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Multiple-State Nonadiabatic Dynamics Simulation of

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