Challenges in XUV Photochemistry Simulations: A Case Study on

Subscriber access provided by UNIV OF DURHAM

Article

Challenges in XUV Photochemistry Simulations: A Case Study on Ultrafast Fragmentation Dynamics of the Benzene Radical Cation Sophia Bazzi, Ralph Welsch, Oriol Vendrell, and Robin Santra J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b11543 • Publication Date (Web): 03 Jan 2018 Downloaded from http://pubs.acs.org on January 4, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry A is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Challenges in XUV Photochemistry Simulations: A Case Study on Ultrafast Fragmentation Dynamics of the Benzene Radical Cation ∗,†,‡

Sophia Bazzi,

†Center

Ralph Welsch,

∗,†

Oriol Vendrell,

∗,¶,†,§

and Robin Santra

†,‡,k,§

for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany

‡Department

of Chemistry, University of Hamburg, Grindelallee 117, 20146 Hamburg, Germany

¶Department

of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark

§The

Hamburg Centre for Ultrafast Imaging, Luruper Chausee 149, 22761 Hamburg, Germany

kDepartment

of Physics, University of Hamburg, Jungiusstrasse 9, 20355 Hamburg, Germany

E-mail: [email protected]; [email protected]; [email protected]

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The challenges of simulating extreme ultraviolet (XUV) induced dissociation dynamics of organic molecules on a multitude of coupled potential energy surfaces are discussed for the prototypical photoionization of benzene. The prospects of Koopmans' theorem based electronic structure calculations in combination with classical trajectories and Tully's fewest switches surface hopping are explored. It is found that a Koopmans' theorem based approach overestimates the CH dissociation barrier and thus underestimates the fragmentation yield. However, the non-adiabatic population dynamics are in good agreement with previous approaches indicating that the Koopmans' theorem based potentials are well described around the Franck-Condon point. This is explicitly tested for the ground state potential of the benzene cation employing CASPT2 calculations, for which very good agreement is found. This work highlights the need for ecient electronic structure approaches that can treat medium sized organic molecules with a multitude of coupled excited states and several dissociation channels.

1

Introduction

Understanding the extreme ultraviolet (XUV) induced dynamics and the subsequent fragmentation of molecular systems is important as it can provide answers to a broad range of fundamental questions such as the photochemical fate of biologically relevant molecules, which is related to the origin of life on earth, 1 the evolution and complexity of the interstellar medium, 2 and the photochemistry of atmospheric molecules. Of particular interest is the photochemical behavior of XUV irradiated polycyclic aromatic hydrocarbons (PAHs) due to their fundamental role in understanding the chemistry in the interstellar medium. Since the proposal that PAHs are the carriers of certain infrared emission bands observed in outer space, 3 these molecules have been the subject of considerable experimental 47 and theoretical work. 810 It is, however, challenging to obtain a complete picture of the dynamics and dissociation patterns of such large systems after XUV irradiation (10 124 eV), as one has to 2


Page 2 of 25

Page 3 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


deal with several nuclear degrees of freedom, as well as a broad range of excited states and fragmentation channels. There is an urgency for further development of theoretical methods that can describe the XUV photochemistry of medium-sized to large systems. For an accurate picture of nuclear dynamics and fragmentation patterns one needs to calculate the electronic structure accurately. Accurate electronic structure calculations of a large number of excited states along with several nuclear degrees of freedom including bond breaking is a very challenging task. The highest accuracy for calculating coupled potential energy surfaces over the entire range of nuclear geometries can be obtained with multireference methods, such as the multireference conguration interaction (MRCI) 11 approach. Energy gradients as well as derivative couplings can be obtained using analytic gradient techniques, 1214 which allows for the simulation of fragmentation processes. Due to the high computational cost of MRCI calculations, they are limited to simulation of a few atoms and cannot treat PAHs. Furthermore, only a few excited states can be treated with MRCI and therefore it is not a feasible approach for describing the broad range of electronic states accessed in the XUV radiation regime. Multicongurational methods have been widely used to describe ultrafast dynamics, particularly complete active space self-consistent eld (CASSCF) 15 and its second-order perturbation theory extension (CASPT2), 1621 which recovers part of the dynamical correlation energy that is missing from a CASSCF calculation. 22 However, it should be noted that the shape of the potential energy surfaces and as a result, the photoinduced dynamics can be strongly inuenced by the choice of the active space and the basis set. 23 Active space selection is a very delicate task and one needs to have a benchmark for its validation. 24 CASSCF applications are also limited by the number of atoms and the size of active spaces 24 and it becomes impractical for large active spaces, large systems, and large number of electronic states, which are typical for XUV-induced dynamics. Other wave function-based methods that have been successful in many aspects of excited state chemistry are the approximate coupled-cluster method of second order (CC2) 25 as 3



an approximation to the CCSD method, 25,26 and the algebraic-diagrammatic-construction (ADC). 2734 These methods are not as expensive as MRCI or CAS methods but they have many limitations. Both methods are based on a single reference determinant and thus cannot describe situations with static correlation. Furthermore, these methods have problems describing the topology around surface crossings. Tuna et al. 35 have previously assessed the performance of these two methods for the description of S0 and S1 reaction paths as well as the branching space of the conical intersection involved in the photoisomerization process of penta-2,4-dieniminium cation. They showed that CC2 suers from the existence of many artifacts around the surface crossing and that the ADC method is unable to describe the correct topology of the surface crossing. Plasser et al. 35,36 showed that CC2 is an unsuitable method for surface hopping molecular dynamics simulations due to numerical instabilities arising from the non-Hermitian formulation of CC2. Another approach that has been widely applied to calculate excited state properties 3741 and ultrafast dynamics 42 is time-dependent density functional theory (TDDFT), 43 which is applicable to relatively large systems. The results of TDDFT calculations strongly depend on the exchange-correlation (XC) functional employed and on the fraction of Hartree-Fock exchange included. Therefore, the excitation energies are highly dependent on the choice of functional, which makes the TDDFT calculations ambiguous if there is no benchmark to validate the excitation energies. 44,45 It is known that the typical XC functionals used in DFT ground state calculations, such as gradient-corrected BP86 46,47 or hybrid-type B3LYP, 48,49 show wrong asymptotic behavior 50 for excited states. It has been shown that TDDFT employing standard functionals leads to dramatic failures for the two lowest lying singlet π

→ π ? states of linear acenes from two (naphthalene) up to eight ring (octaacene) acenes. 51,52 Furthermore, it has been shown that the popular linear-response TDDFT approach suers from convergence problems near conical intersections and is incapable of properly describing the topography of potential energy surfaces at crossing points in the studied systems. This makes TDDFT less applicable for modeling non-adiabatic relaxation processes. 53 4


Page 4 of 25

Page 5 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


A computationally ecient ab initio treatment of excited state dynamics of cations following XUV photoionization is a Koopmans' theorem based approach, 54,55 which is applicable to the XUV induced dynamics of fairly large systems like PAHs. A Koopmans' theorem based approach does not take into account orbital relaxation and electron correlation eects which can lead to deviations in binding energies. Additionally, only states corresponding to the removal of an electron from a (valence) orbital can be treated within this approach and thus shake-up or satellite states are neglected, which become more important at higher binding energies. This approach has previously been successfully applied to describe correlated proton-electron hole dynamics of ionized [H(H2 O)21 ]+ 54 and ultrafast dynamics of acetylene cations after XUV photoionization, 55 where no fragmentation involving breakage of covalent bonds was involved. The aim of the present study is to assess the possibility of utilizing Koopmans' theorem to study the XUV induced photodissociation of medium-sized to large systems using ab initio classical trajectory calculations within the fewest switches surface hopping (FSSH) scheme. 56 To this end, we study the non-adiabatic dynamics and photodissociation of the benzene cation as a prototypical system. The paper is organized as follows. Section 2 describes the theoretical framework underlying the electronic structure and dynamics calculations. Section 3 discusses results for the benzene radical cation. Finally, Section 4 concludes and provides some outlook for future work.

2

Computational methods

Ab initio classical trajectory calculations and the fewest switches surface hopping (FSSH) scheme 56 are employed to describe the non-adiabatic ultrafast dynamics of a singly charged benzene molecule ionized into any of 15 valence ionization channels characterized by the removal of an electron from each of the 15 occupied valence molecular orbitals of benzene in the ground state. FSSH is conceptually and practically a simple method and at the same time it has a good accuracy and high computational eciency. Therefore, it has so far been one of

5



Page 6 of 25

the most utilized methods to describe non-adiabatic dynamics. In the FSSH scheme, classical trajectories are propagated on a single adiabatic potential energy surface and statistically switched to another adiabatic potential energy surface according to a hopping probability. Hopping probabilities at a given geometry R(t) are calculated as: 56

gkj =

bjk ∆t, akk

(1)

where ∆t is the time step, bjk = −2Re(a∗jk · R · djk ), akj = ck c∗j , and djk are the non-adiabatic coupling matrix elements. Please note that we chose an adiabatic basis here so that the odiagonal elements of the electronic Hamiltonian Vkj vanish. The expansion coecients ck (t) are obtained by solving the time-dependent electronic Schrödinger equation:

i¯hc˙k =

X

˙ kj ). cj (Vkj − i¯hRd

(2)

j

The hopping probability gkj is then compared to a uniformly distributed random number, ζ ,

0 < ζ < 1 and a hop occurs if gkj is larger than ζ . If a hop occurs, the velocities are adjusted along the gradient dierence direction to conserve the total energy. If not enough energy is available for this adjustment, the hop is not performed. No decoherence corrections are employed as these corrections are not relevant for the irreversible electronic decay discussed in this study. Electronic structure data, energies, energy gradients, and non-adiabatic couplings, are determined on the y on the basis of Koopmans' theorem and using the 6-31g* basis set utilizing the MOLCAS program package. 57 The fteen one-hole electronic states are created by removing a valence electron from each of the fteen Hartree-Fock (HF) valence molecular orbitals of neutral benzene. The energy of the i-th state is obtained as: 55,58

Vi,HF −K = VHF − i ,

6


(3)

Page 7 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where VHF is the ground state Hartree-Fock energy of neutral benzene and i is the energy of the i-th occupied orbital with i=0 being the highest occupied orbital. The multicongurational capabilities of MOLCAS 57 are used to generate the corresponding electronic wave functions |Ψi i with the orbitals from the HF calculation. Gradients and non-adiabatic couplings are then obtained from these congurations employing the RASSI module. 55 The initial nuclear coordinates and momenta are sampled from the vibrational ground state distribution of neutral benzene. This corresponds to the limit of T=0K. Microcanonical normal mode sampling 59 is employed to assign to each normal mode its zero-point energy. Coordinates qi and conjugated momenta pi for the i-th normal mode are chosen as:

s qi =

pi =

p

2Ei cos(2πζ), fi

(4)

2mi Ei sin(2πζ),

(5)

with ζ being a uniformly distributed random number, 0 < ζ < 1, Ei the zero-point energy, fi the force constant, and mi the mass of the i-th normal mode. Normal mode coordinates and momenta are then transformed to Cartesian coordinates for the propagation. The sampled geometries are lifted vertically to the dierent electronic states of the cation. The nuclear motion is simulated for an ensemble of fty independent trajectories for each initial electronic state. Newton's equations of motion are integrated using the velocity Verlet algorithm 60 with a time step of 0.5 fs and a total propagation time of 300 fs. Each time step takes on average 270 seconds on a single core of an Intel Xenon X5660 2.80GHz CPU. Therefore, about 45 hours of CPU time is needed for the propagation of each trajectory. We note that some of the dissociative trajectories are not propagated for the full 300 fs due to SCF convergence problems.

7



3

Results and discussion

The study reported here involves fteen coupled potential energy surfaces of the valence shell singly ionized benzene. The fteen surfaces are grouped into ten electronic states according to the degeneracy of the orbitals at the Franck-Condon region. Table 1 lists the symmetry assignments of the electronic states and the corresponding orbital energies at the equilibrium geometry of the neutral benzene. The orbital energies obtained from our Koopmans' theorem based approach are in reasonable agreement with binding energies obtained by the third-order algebraic-diagrammatic construction [ADC(3)] scheme. 61 While some quantitative deviations of the absolute energies can be found, the relative energy dierences, i.e., the energy gaps between two neighboring states, are in good agreement. The relative energy dierences among the states are more important for dynamical studies than the absolute energies. The deviation of the relative energy dierences obtained from Koopmans' theorem and from

˜ 2 E2g to the G ˜ 3 A1g states is at most 0.24 eV, but often ADC(3) 61 in the manifold of the B lower. As expected, bigger deviations are found for the higher-lying states and for the energy dierence between the ground and rst excited state. The latter, however, should not be problematic as we still nd ultrafast electronic decay to the ground state. In the following, we address two fundamental aspects of the XUV photochemistry of the benzene radical cation: the time resolved relaxation of the electronic excited states through internal conversion and the time-resolved state-specic fragmentation dynamics.

8


Page 8 of 25

Page 9 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1: The symmetry assignment of the excited electronic states of C6 H+6 and the corresponding orbital energies calculated at HF/6-31g* level at the equilibrium geometry of the neutral benzene. The dissociation probability for an initial excitation to each electronic state is also given. Half life of each of the initially excited states are given and compared to Ref. 62.

Symmetry symbol ˜ 2 E1g X

Orbital en- Dissociation Half life (fs) Half life (fs) ergy (eV) probability (%) present Ref. 62 (a)

-8.996

-

-

-

˜ 2 E2g B

-13.320

3.0

120

100 >200

C˜ 2 A2u

-13.551

0.0

15

15 15

˜ 2 E1u D

-15.897

2.0

30

>200 95

˜ 2 B2u E

-16.708

0.0

15

15 15

F˜ 2 B1u

-17.410

0.0

10

-

˜ 3 A1g G

-19.244

1.5

20

-

˜ 2 E2g H

-22.313

4.0

>300

-

I˜ 2 E1u

-27.519

2.0

>300

-

J˜ 2 A1g

-31.239 2.0 >300 a: The rst and second rows refer to the cases where an initial electronic state is coupled to two and three neighboring states, respectively.

As shown in Table 1, the dissociation probability upon valence shell ionization of benzene is a maximum of 4 % after 300 fs. This is in contrast with an experimental study on the photoionization and photodissociation of benzene, which shows more than 50 % dissociation at an UV energy of 21.21 eV. 63 Experiments in the higher excitation energies show that above 20 eV, more than 50 % of the benzene cation dissociates. 64,65 The discrepancy between the simulation and the experiment can be rationalized by comparing the calculated CH dissociation barrier for the ground state benzene cation with the value obtained at higher level of theory and through experiment (see Figure 1). The CH dissociation energy calculated at the same level of theory as employed in our classical trajectory calculations (HF/6-31g*) is 9



7.3 eV. It considerably overestimates the value obtained from CASPT2/6-31g* (see Figure 1). The CASPT2 calculations use an active space with 11 active electrons distributed in 8 molecular orbitals. An RRKM t of experimental data suggests an even lower dissociation energy of 3.66 eV. 66 Thus, the benzene radical cation may remain articially bound in our simulations. Nonetheless, we note that the CH energy prole calculated at the HF/6-31g* level matches the corresponding surface calculated at the CASPT2/6-31g* level around the equilibrium geometry. Moreover, the limited propagation time might also contribute to the low fragmentation yield observed in this study.

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

8 HF 7 6 CASPT2 5 4 3 Exp. dissociation energy 2 1 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

˚ RCH − R0 (A)

˜ 2 E1g state of C6 H+ Figure 1: Cuts through the potential energy surface for the X 6 calculated with HF/6-31g* (green), and CASPT2(12,8)/6-31g* (blue). The dissociation coordinate is obtained by changing the length of one of the CH bonds (RCH ) and maintaining the other bond lengths and the angles at the equilibrium values. R0 corresponds to the equilibrium bond length. For trajectories with enough initial energy to overcome the articially high barriers the + most frequent fragments upon dissociation of the benzene cation are: C6 H+ 5 + H, C6 H4 +

2H, and C4 H+ 4 + C2 H2 , which appear after 100 fs. These ionic fragments are also among the most abundant fragment ions observed experimentally upon valence shell ionization of the benzene molecule. 63,64 In passing we note two interesting observations in our results. The C6 H+ 4 fragment ion is produced either through a concerted dissociation mechanism or + through a stepwise process via C6 H+ 5 . The channel with two large fragments, C4 H4 +

10


Page 10 of 25

Page 11 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


C2 H2 , only appears for highly excited states of the benzene radical cation (states I˜ 2 E1u and J˜ 2 A1g ), which is in agreement with an experimental study 64 where the authors show that the contribution due to the C4 H+ 4 rapidly increases at higher photon energies. For more information about the dissociation channels along with the corresponding population dynamics see the supporting information (SI), Figure S1. Previous studies of benzene 6668 suggest that the dissociation occurs from the ground electronic state after a fast non-radiative relaxation even if higher electronic states are initially populated. A similar behavior can be found in our simulations. The only exception is found for a single trajectory on the highest valence shell excited state (J˜ 2 A1g ) where the molecule breaks apart after relaxation to the second excited state, C˜ 2 A2u (SI, Figure S1). As discussed above, the potential energy surface of the cationic ground state in the Franck-Condon region is well described by the Koopmans' theorem based approach. Based on this and earlier studies, 55 we expect the short-time non-adiabatic dynamics to be reasonably well described by the simulations presented in this study. Figure 2 shows the population dynamics for dierent initial excitations. Figure 2a presents the case of an initial excitation

˜ 2 E2g state. For this case, the B ˜ 2 E2g population gradually decreases to reach 25 to the B ˜ 2 E1g state reaches its maximum at around 73 % (Figure 2a). The % at 270 fs when the X coupling to the C˜ 2 A2u state is very weak and the corresponding population remains almost unchanged during the dynamics. The short time dynamics are in good agreement with previous theoretical work based on a reduced-dimensional quantum dynamics description using a vibronic coupling model Hamiltonian. 62,69,70 However, for longer times a faster decay to the ground state is found compared to previous work. The dierence might be attributed to the reduced dimensionality and the harmonic expansion in the previous work or to the surface hopping approximation in our simulations. In Table 1, the half life of the dierent states are given, i.e., the time it takes for the population of an initially excited state to

˜ 2 E2g state agrees very well with previous decrease to 50%. The half life computed for the B work. 62 11



Figure 2b shows the case of an initial excitation to the C˜ 2 A2u state. The half life of the

˜ 2 E2g C˜ 2 A2u state is 15 fs and in perfect agreement with previous work (see Table 1). The B state population steeply increases to its maximum of 75% within 60 fs and then gradually

˜ 2 E1g state population reaches its maximum (93 %). For decays to zero at 250 fs, when the X the rst 100 fs, the results of our study are in good agreement with previous calculations. 62 Again at longer times, a slightly faster decay to the ground state is found in our simulations compared to the previous study. 62 Experimentally, no uorescence from the C˜ 2 A2u state

˜ 2 E1g is dipole-allowed, 71 which is found although the transition from the C˜ 2 A2u to the X supports a fast radiationless transition from the C˜ 2 A2u state to the ground state. 71 In an experiment based on photo-dissociation kinetics and charge exchange ionization mass spectroscopy 72 a long lived electronic excited state was observed in the energy range of the

˜ 2 E2g and C˜ 2 A2u states, which was eventually assigned to the B ˜ 2 E2g state. However, the B authors were not absolutely certain about the assignment because of a controversy regarding

˜ 2 E2g state. 68,71 According to our results the B ˜ 2 E2g state is somewhat the lifetime of the B longer-lived than the C˜ 2 A2u state.

˜ 2 E1u state (Figure 2c), a very fast decay of the Starting the initial wave packet from the D ˜ 2 E1u state population occurs. The D ˜ 2 E1u state population dynamics considerably diers D from the previous theoretical studies, where the population gradually decays and reaches about 40 % at 200 fs and the half life is considerably longer than in the present work. 62,69 This discrepancy already at short times can be due to the reduced dimensional description employed in previous works that may not capture the dynamics of the benzene cation in the

˜ 2 E1u state adequately or it can be due to shifts in the positions of the conical intersections D ˜ 2 B2u , in our calculations. The population dynamics following initial excitation to the E ˜ 3 A1g states shows very similar behavior as for the C˜ 2 A2u and D ˜ 2 E1u states F˜ 2 B1u , and G (see SI, Figure S2). Dierent population dynamics emerge for the highest lying valence states, e.g., for the

˜ 2 E2g state shown in Figure 2d. This state has a lifetime much longer than the lower-lying H 12


Page 12 of 25

Page 13 of 25

State population

a) 1.0

b) 1.0

˜ 2 E2g B

0.8 0.6

0.2 0

c) 1.0 0.8

0.4 0.2 0.0

0

d) 1.0 ˜ 2 E1g X

0.6

0.4

0.4

0.0

0

˜ 2 E2g B ˜ 2 A2u C 50 100 150 200 250 300 Time (fs)

˜ 2 A2u C 50 100 150 200 250 300 ˜ 2 E2g H

0.8

0.6

0.2

˜ 2 E1g X

0.6

˜ 2 A2u C 50 100 150 200 250 300

˜ 2 E1u D

˜ 2 E2g B

0.8

˜ 2 E1g X

0.4

0.0

State population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.2 0.0

0

50 100 150 200 250 300 Time (fs)

˜ 2 E2g , (b) Figure 2: Internal conversion dynamics for an initial excitation to the states (a) B ˜ 2 E1u , and (d) H ˜ 2 E2g . C˜ 2 A2u , (c) D states, which was similarly observed in a theoretical study of naphthalene. 34 Similar results are also found for I˜ 2 E1u and J˜ 2 A1g states (see SI, Figure S2). This longer lifetime in our simulations can be explained based on the large energy gap of the higher-lying electronic states to any other state for the geometries sampled during the dynamics. The average gap of the higher-lying states to the next lower state is typically about 3 eV and never decreases below 0.5 eV. For more details see the SI. This large energy gap might hinder the high internal energy of the cation to convert into vibrational energy in lower-lying states. Therefore, the highly electronically excited cation is surprisingly less likely to undergo dissociation. It should be noted that including shake-up states in the electronic structure calculations could lead to a faster non-radiative decay of the high-lying states. The number of shake-up states increases above 20 eV 61 and thus they could bridge the large energy gaps seen in our simulations. No study of conical intersections at these energies has been performed. The eect of shake-up states on XUV induced photodissociation of benzene and the non-radiative decay from inner

13



to outer valence states via shake-up states requires further investigation and is beyond the scope of this paper.

4

Conclusion

In this paper, we discussed the current challenges in simulating the XUV photochemistry of medium-sized to large systems by investigating the non-adiabatic dynamics of singly ionized benzene on fteen coupled potential energy surfaces. Trajectories excited to dierent states are propagated employing the fewest switches surface hopping approach while forces and non-adiabatic couplings are obtained at the level of Koopmans' theorem excitations. We addressed two fundamental aspects of the XUV photochemistry: the time resolved relaxation of the electronically excited states through internal conversion and the time-resolved state-specic fragmentation dynamics. Good performance of the Koopmans' theorem based approach is found for the non-adiabatic relaxation process. Excitations to the lowest six states largely decay to the ground state within 100 fs, while the highest lying states are stable up to the nal propagation time of 300 fs. For most initial excitations we nd good agreement with previous simulations employing reduced-dimensional quantum dynamics ap-

˜ 2 E1u state, we nd fast decay to the proaches. Nevertheless, for initial excitation to the D ground state in contrast to previous calculations which nd a slow, gradual decay. The longer lifetime of the higher-lying states can be explained by large energy gaps to other states. Including shake-up states in the electronic structure calculations could alter the life time of the high-lying states. However, our simulations underestimated the dissociation probability compared to experiments due to an overestimation of the dissociation energies in the adopted Koopmans' theorem based electronic structure calculations. This highlights the challenges in simulating XUV induced photochemistry of medium-sized systems, where a large number of excited states as well as several dissociation channels have to be described. The challenge to develop accurate, yet ecient ab initio models that describe the fragmentation yields upon

14


Page 14 of 25

Page 15 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


XUV irradiation remains to be solved in future research. Albeit, for certain systems, it might be possible to simulate the short time non-adiabatic conversion to the ground state employing the Koopmans' theorem based approach described here and then employ a statistical theory to describe the dissociation on the ground state potential energy surface employing a highly accurate electronic structure method.

Acknowledgement The authors acknowledge NASA for the background image (NASA ID: PIA20914) used in the table of contents graphics.

Supporting Information Available Additional state populations, fragmentation dynamics, and energy gaps of the dierent states.

References (1) Tielens, A. Interstellar Polycyclic Aromatic Hydrocarbon Molecules. tron. Astrophys.

Annu. Rev. As-

2008, 46, 289337.

(2) Lundin, R.; Lammer, H.; Ribas, I. Planetary Magnetic Fields and Solar Forcing: Implications for Atmospheric Evolution.

Space Sci. Rev.

2007, 129, 245278.

(3) Leger, A.; Puget, J. L. Identication of the 'Unidentied' IR Emission Features of Interstellar Dust?

Astron. Astrophys

1984, 137, L5L8.

(4) Zhen, J.; Castillo, S.; Joblin, C.; Mulas, G.; Sabbah, H.; Giuliani, A.; Nahon, L.; Martin, S.; Champeaux, J.-P.; Mayer, P. VUV Photo-Processing of PAH Cations: Quan-

15



Page 16 of 25

titative Study on the Ionization Versus Fragmentation Processes.

Astrophys. J.

2016,

, 113120.

822

(5) Trinquier, G.; Simon, A.; Rapacioli, M.; Gadéa, F. PAH Chemistry at eV Internal Energies. 2. Ring Alteration And Dissociation.

Mol. Astrophys.

2017, 7, 3759.

(6) Allamandola, L.; Sandford, S.; Wopenka, B. Interstellar Polycyclic Aromatic Hydrocarbons and Carbon in Interplanetary Dust Particles and Meteorites.

Science

1987, 237,

5659. (7) Snow, T.; Le Page, V.; Keheyan, Y.; Bierbaum, V. The Interstellar Chemistry of PAH Cations.

Nature

1998, 391, 259260.

(8) Szczepanski, J.; Vala, M. Laboratory Evidence for Ionized Polycyclic Aromatic Hydrocarbons in the Interstellar Medium.

Nature

1993, 363, 699701.

(9) Lovas, F.; McMahon, R.; Grabow, J.-U.; Schnell, M.; Mack, J.; Scott, L.; Kuczkowski, R. Interstellar Chemistry: A Strategy for Detecting Polycyclic Aromatic Hydrocarbons in Space.

J. Am. Chem. Soc.

2005, 127, 43454349.

(10) Simon, A.; Rapacioli, M.; Rouaut, G.; Trinquier, G.; Gadéa, F. Dissociation of Polycyclic Aromatic Hydrocarbons: Molecular Dynamics Studies.

Phil. Trans. R. Soc. A

2017, 375, 20160195. (11) Werner, H.-J. Matrix-Formulated Direct Multiconguration Self-Consistent Field and Multiconguration Reference Conguration-Interaction Methods.

Adv. Chem. Phys.

1987, 69, 169. (12) Saxe, P.; Lengseld III, B.; Yarkony, D. On the Evaluation of Non-adiabatic Coupling Matrix Elements for Large Scale CI Wavefunctions. Chem. 164.

16


Phys. Lett.

1985, 113, 159

Page 17 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(13) Lischka, H.; Dallos, M.; Szalay, P. G.; Yarkony, D. R.; Shepard, R. Analytic Evaluation of Nonadiabatic Coupling Terms at the MR-CI level. I. Formalism.

J. Chem. Phys.

2004, 120, 73227329. (14) Zhu, X.; Yarkony, D. R. On the Elimination of the Electronic Structure Bottleneck in on the Fly Nonadiabatic Dynamics for Small to Moderate Sized (10-15 Atom) Molecules Using Fit Diabatic Representations Based Solely on Ab Initio Electronic Structure Data: The Photodissociation of Phenol.

J. Chem. Phys.

2016, 144, 024105.

(15) Roos, B. O. The Complete Active Space Self-Consistent Field Method and Its Applications in Electronic Structure Calculations.

Adv. Chem. Phys.

1987, 69, 399445.

(16) Andersson, K.; Malmqvist, P.-A.; Roos, B. Second-Order Perturbation Theory with a Complete Active Space Self-Consistent Field Reference Function. J. Chem. Phys. 1992, , 12181226.

96

(17) Roberts, G.; Williams, C.; Young, J.; Ullrich, S.; Paterson, M.; Stavros, V. Unraveling Ultrafast Dynamics in Photoexcited Aniline.

J. Am. Chem. Soc.

2012,

, 12578

134

12589. (18) Guo, X.; Zhao, Y.; Cao, Z. Ab Initio Study on Ultrafast Excited-State Decay of Allopurinol Keto-N9H Tautomer from Gas Phase to Aqueous Solution.

J. Phys. Chem. A

2014, 118, 90139020. (19) Cui, G.; Fang, W. Ab Initio Based Surface-Hopping Dynamics Study on Ultrafast Internal Conversion in Cyclopropanone.

J. Phys. Chem. A

2011, 115, 15471555.

(20) Schönborn, J.; Sielk, J.; Hartke, B. Photochemical Ring-Opening of Cyclohexadiene: Quantum Wavepacket Dynamics on a Global Ab Initio Potential Energy Surface. Phys. Chem. A

2010, 114, 40364044.

17


J.


Page 18 of 25

(21) Tao, H.; Levine, B.; Martínez, T. Ab Initio Multiple Spawning Dynamics Using MultiState Second-Order Perturbation Theory.

J. Phys. Chem. A

2009, 113, 1365613662.

(22) Andersson, K.; Malmqvist, P. A.; Roos, B. O.; Sadlej, A. J.; Wolinski, K. Second-Order Perturbation Theory with a CASSCF Reference Function.

J. Phys. Chem.

1990,

,

94

54835488. (23) Segarra-Martí, J.; Francés-Monerris, A.; Roca-Sanjuán, D.; Merchán, M. Assessment of the Potential Energy Hypersurfaces in Thymine within Multicongurational Theory: CASSCF Vs. CASPT2.

Molecules

2016, 21, 16661683.

(24) Keller, S.; Boguslawski, K.; Janowski, T.; Reiher, M.; Pulay, P. Selection of Active Spaces for Multicongurational Wavefunctions.

J. Chem. Phys.

2015, 142, 245278.

(25) Christiansen, O.; Koch, H.; Jørgensen, P. The Second-Order Approximate Coupled Cluster Singles and Doubles Model CC2.

Chem. Phys. Lett.

1995, 243, 409418.

(26) Purvis, G. D.; Bartlett, R. J. A Full Coupled-Cluster Singles and Doubles Model: The Inclusion of Disconnected Triples.

J. Chem. Phys.

1982, 76, 19101918.

(27) Schirmer, J. Beyond the Random-Phase Approximation: A New Approximation Scheme for the Polarization Propagator.

Phys. Rev. A

1982, 26, 23952416.

(28) Schirmer, J.; Tromov, A. Intermediate State Representation Approach to Physical Properties of Electronically Excited Molecules. J. Chem. Phys. 2004, 120, 1144911464. (29) Tromov, A.; Stelter, G.; Schirmer, J. A Consistent Third-Order Propagator Method for Electronic Excitation.

J. Chem. Phys.

1999, 111, 99829999.

(30) Tromov, A.; Stelter, G.; Schirmer, J. Electron Excitation Energies Using a Consistent Third-Order Propagator Approach: Comparison with Full Conguration Interaction and Coupled Cluster Results.

J. Chem. Phys.

18

2002, 117, 64026410.


Page 19 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(31) Mertins, F.; Schirmer, J. Algebraic Propagator Approaches and Intermediate-State Representations. I. The Biorthogonal and Unitary Coupled-Cluster Methods. Rev. A

Phys.

1996, 53, 21402152.

(32) Dreuw, A.; Wormit, M. The Algebraic Diagrammatic Construction Scheme for the Polarization Propagator for the Calculation of Excited States. Comput. Mol. Sci.

Wiley Interdiscip. Rev.:

2015, 5, 8295.

(33) Krauter, C.; Schimmelpfennig, B.; Pernpointner, M.; Dreuw, A. Algebraic Diagrammatic Construction for the Polarization Propagator with Spin-Orbit Coupling. Phys.

Chem.

2017, 482, 286293.

(34) Marciniak, A.; Despré, V.; Barillot, T.; Rouzée, A.; Galbraith, M.; Klei, J.; Yang, C.H.; Smeenk, C.; Loriot, V.; Reddy, S. et al. XUV Excitation Followed by Ultrafast Non-adiabatic Relaxation in PAH Molecules as a Femto-astrochemistry Experiment. Nat. Commun.

2015, 6, 79097914.

(35) Tuna, D.; Lefrancois, D.; Wola«ski, L.; Gozem, S.; Schapiro, I.; Andruniów, T.; Dreuw, A.; Olivucci, M. Assessment of Approximate Coupled-Cluster and AlgebraicDiagrammatic-Construction Methods for Ground- and Excited-State Reaction Paths and the Conical-Intersection Seam of a Retinal-Chromophore Model. Comput.

J. Chem. Theory

2015, 11, 57585781.

(36) Plasser, F.; Crespo-Otero, R.; Pederzoli, M.; Pittner, J.; Lischka, H.; Barbatti, M. Surface Hopping Dynamics with Correlated Single-Reference Methods: 9h-Adenine as a Case Study.

J. Chem. Theory Comput.

2014, 10, 13951405.

(37) Walter, C.; Krämer, V.; Engels, B. On the Applicability of Time-dependent Density Functional Theory (TDDFT) and Semiempirical Methods to the Computation of Excited-state Potential Energy Surfaces of Perylene-based Dye-aggregates. Quantum Chem.

2017, 117, e25337e25350. 19


Int. J.


Page 20 of 25

(38) Bauernschmitt, R.; Ahlrichs, R. Treatment of Electronic Excitations within the Adiabatic Approximation of Time Dependent Density Functional Theory. Chem. Phys. Lett.

1996, 256, 454464. (39) Zhao, J.; Yao, H.; Liu, J.; Homann, M. New Excited-State Proton Transfer Mechanisms for 1,8-Dihydroxydibenzo[A, H]Phenazine. J. Phys. Chem. A 2015, 119, 681688. (40) Chai, S.; Zhao, G.-J.; Song, P.; Yang, S.-Q.; Liu, J.-Y.; Han, K.-L. Reconsideration of the Excited-State Double Proton Transfer (ESDPT) in 2-Aminopyridine/Acid Systems: Role of the Intermolecular Hydrogen Bonding in Excited States. Phys.

Phys. Chem. Chem.

2009, 11, 43854390.

(41) Zhao, G.-J.; Han, K.-L. Time-Dependent Density Functional Theory Study on Hydrogen-Bonded Intramolecular Charge-Transfer Excited State of 4-DimethylaminoBenzonitrile in Methanol.

J. Comput. Chem.

2008, 29, 20102017.

(42) Yang, D.; Yang, G.; Zhao, J.; Zheng, R.; Wang, Y. A Competitive Excited State Dynamical Process for the 2,20 -((1e,10 E)-((3,30 -Dimethyl-[1,10 -Biphenyl]-4,40 Diyl)-Bis(Azanylylidene))Bis(Methanylylidene))-Diphenol System.

RSC Adv.

2017, 7,

12991304. (43) Runge, E.; Gross, E. Density-Functional Theory for Time-Dependent Systems. Rev. Lett.

Phys.

1984, 52, 9971000.

(44) Liu, W.; Settels, V.; Harbach, P.; Dreuw, A.; Fink, R.; Engels, B. Assessment of TDDFT- and TD-HF-Based Approaches for the Prediction of Exciton Coupling Parameters, Potential Energy Curves, and Electronic Characters of Electronically Excited Aggregates.

J. Comput. Chem.

2011, 32, 19711981.

(45) Komoto, K.; Kowalczyk, T. How Parallel Are Excited State Potential Energy Surfaces from Time-Independent and Time-Dependent DFT? A BODIPY Dye Case Study. Phys. Chem. A

2016, 120, 81608168. 20


J.

Page 21 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(46) Becke, A. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior.

Phys. Rev. A

1988, 38, 30983100.

(47) Perdew, J. Density-Functional Approximation for the Correlation Energy of the Inhomogeneous Electron Gas.

Phys. Rev. B

1986, 33, 88228824.

(48) Becke, A. Density-Functional Thermochemistry. III. The Role of Exact Exchange. Chem. Phys.

J.

1993, 98, 56485652.

(49) Stephens, P.; Devlin, F.; Chabalowski, C.; Frisch, M. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields.

J. Phys. Chem.

1994, 98, 1162311627.

(50) Casida, M.; Jamorski, C.; Casida, K.; Salahub, D. Molecular Excitation Energies to High-Lying Bound States from Time-Dependent Density-Functional Response Theory: Characterization and Correction of The Time-Dependent Local Density Approximation Ionization Threshold.

J. Chem. Phys.

1998, 108, 44394449.

(51) Grimme, S.; Parac, M. Substantial Errors from Time-Dependent Density Functional Theory for the Calculation of Excited States of Large Systems. ChemPhysChem 2003, , 292295.

4

(52) Wang, Y.-L.; Wu, G.-S. Improving the TDDFT Calculation of Low-Lying Excited States for Polycyclic Aromatic Hydrocarbons Using the Tamm-Danco Approximation.

Int. J. Quantum Chem.

2008, 108, 430439.

(53) Huix-Rotllant, M.; Nikiforov, A.; Thiel, W.; Filatov, M. sections with Density Functional Methods

Description of Conical Inter-

; Springer, 2015; pp 445476.

(54) Li, Z.; Madjet, M.-A.; Vendrell, O.; Santra, R. Core-Level Transient Absorption Spectroscopy as a Probe of Electron Hole Relaxation in Photoionized H + (H2 O)n . Discuss.

2014, 171, 457470. 21


Faraday


Page 22 of 25

(55) Madjet, M.-A.; Vendrell, O.; Santra, R. Ultrafast Dynamics of Photoionized Acetylene. Phys. Rev. Lett.

2011, 107, 263002263006.

(56) Tully, J. Molecular Dynamics with Electronic Transitions.

J. Chem. Phys.

1990,

,

93

10611071. (57) Aquilante, F.; De Vico, L.; Ferré, N.; Ghigo, G.; Malmqvist, P.-a.; Neogrády, P.; Pedersen, T. B.; Pito nák, M.; Reiher, M.; Roos, B. O. et al. MOLCAS 7: The Next Generation.

J. Comput. Chem.

2010, 31, 224247.

(58) Li, Z.; Madjet, M.-A.; Vendrell, O. Non-Born-Oppenheimer Dynamics of the Photoionized Zundel Cation: A Quantum Wavepacket and Surface-Hopping Study. Phys.

J. Chem.

2013, 138, 094313094311.

(59) Hase, W. L.; Buckowski, D. G. Monte Carlo Sampling of a Microcanonical Ensemble of Classical Harmonic Oscillators.

Chem. Phys. Lett.

1980, 74, 284 287.

(60) Swope, W.; Andersen, H.; Berens, P.; Wilson, K. A Computer Simulation Method for the Calculation of Equilibrium Constants for the Formation of Physical Clusters of Molecules: Application to Small Water Clusters.

J. Chem. Phys.

1982, 76, 637649.

(61) Deleuze, M.; Tromov, A.; Cederbaum, L. Valence One-Electron and Shake-Up Ionization Bands of Polycyclic Aromatic Hydrocarbons. I. Benzene, Naphthalene, Anthracene, Naphthacene, and Pentacene.

J. Chem. Phys.

2001, 115, 58595882.

(62) Bâldea, I.; Köppel, H. Multistate Multimode Vibronic Dynamics: Entanglement of Electronic and Vibrational Degrees of Freedom in the Benzene Radical Cation. J. Chem. Phys.

2006, 124, 064101.

(63) Boechat-Roberty, H. M.; Neves, R.; Pilling, S.; Lago, A. F.; De Souza, G. G. B. Dissociation of the Benzene Molecule by Ultraviolet and Soft X-Rays in Circumstellar Environment.

Mon. Notices Royal Astron. Soc.

22

2009, 394, 810.


Page 23 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(64) Holland, D.; Shaw, D.; Sumner, I.; Bowler, M.; Mackie, R.; Shpinkova, L.; Cooper, L.; Rennie, E.; Parker, J.; Johnson, C. A Time-of-Flight Mass Spectrometry Study of the Fragmentation of Valence Shell Ionised Benzene.

Int. J. Mass Spectrom.

2002,

,

220

3151. (65) Galbraith, M.; Smeenk, C.; Reitsma, G.; Marciniak, A.; Despré, V.; Mikosch, J.; Zhavoronkov, N.; Vrakking, M.; Kornilov, O.; Lépine, F. XUV-Induced Reactions in Benzene on Sub-10 Fs Timescale: Nonadiabatic Relaxation and Proton Migration. Chem. Chem. Phys.

Phys.

2017, 19, 1982219828.

(66) Kühlewind, H.; Kiermeier, A.; Neusser, H. Multiphoton Ionization in a Reectron Timeof-Flight Mass Spectrometer: Individual Rates of Competing Dissociation Channels in Energy-Selected Benzene Cations.

J. Chem. Phys.

1986, 85, 44274435.

(67) Baer, T.; Willett, G.; Smith, D.; Sanford Phillips, J. The Dissociation Dynamics of Internal Energy Selected C6 H6+ .

J. Chem. Phys.

1979, 70, 40764085.

(68) Köppel, H. New Ultrafast Nonradiative Decay Mechanism in the Benzene Radical Cation.

Chem. Phys. Lett.

1993, 205, 361370.

(69) Sardar, S.; Paul, A. K.; Sharma, R.; Adhikari, S. A Classical Trajectory Driven Nuclear Dynamics by a Parallelized Quantum-Classical Approach to a Realistic Model Hamiltonian of Benzene Radical Cation. Int. J. Quantum Chem. 2011, 111, 27412759. (70) Köppel, H.; Döscher, M.; Bâldea, I.; Meyer, H.-D.; Szalay, P. G. Multistate Vibronic Interactions in the Benzene Radical Cation. II. Quantum Dynamical Simulations. Chem. Phys.

J.

2002, 117, 26572671.

(71) Braitbart, O.; Castellucci, E.; Dujardin, G.; Leach, S. Radiationless Transitions in Excited Electronic States of the Benzene Cation in the Gas Phase.

1983, 87, 47994804. 23


J. Phys. Chem.


(72) Kim, M.; Kwon, C.; Choe, J. Discovery of Benzene Cation in a Very Long-Lived Excited Electronic State.

J. Chem. Phys.

2000, 113, 95329539.

24


Page 24 of 25

Page 25 of 25

Graphical TOC Entry electronic state

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


J I H G F E D C B X

XUV + 0

50

100

150

200

250

time / fs

25


300

Challenges in XUV Photochemistry Simulations: A Case Study on

Recommend Documents