Nonadiabatic Effect in Photodissociation Dynamics of Thiophenol via

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Nonadiabatic Effect in Photodissociation Dynamics of Thiophenol via the ##* State 1

Guang-Shuang-Mu Lin, Changjian Xie, and Daiqian Xie J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b03460 • Publication Date (Web): 01 Jun 2018 Downloaded from http://pubs.acs.org on June 1, 2018

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The Journal of Physical Chemistry

Nonadiabatic Effect in Photodissociation Dynamics of Thiophenol via the 1ππ* State Guang-Shuang-Mu Lin,† Changjian Xie,*,¶ and Daiqian Xie*,†

†

Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, China

¶

Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, NM 87131, USA

1

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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 Nonadiabatic photodissociation dynamics of thiophenol (PhSH) and deuterated thiophenol (PhSD) via the 1ππ* state was investigated by a reduced three-dimensional (3D) quantum model based on the associated 3D diabatic potential energy surfaces constructed at the explicitly correlated multireference configuration interaction (MRCI-F12) level with the cc-pVTZ-F12 basis. The lifetimes of the low-lying vibronic S1 states for PhSH and PhSD were calculated using a low-storage filter diagonalization method and in reasonably good agreement with the available experimental results. The nonadiabatic effect was further examined in the photodissociation process by comparing the results in diabatic and adiabatic models. It was found that the adiabatic lifetimes are about 2~4 times shorter than the exact ones in diabatic model for both PhSH and PhSD. More importantly, the exact ground wavefunction including geometric phase (GP) possesses a node along the C-C-S-H/C-C-S-D torsional coordinate, while the node is absent when GP is not included in adiabatic model. The node structure of the wavefunction is a hallmark of GP, which sheds light on the nonadiabatic photodissociation dynamics facilitated by the conical intersections.

2


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1. Introduction Nonadiabatic dynamics facilitated by the conical intersections (CIs) has received increasing attentions, because of its important role for understanding the radiationless relaxation mechanisms in many heteroaromatic molecules, such as phenols, pyrroles, and indoles.1-13 The ultraviolet (UV) absorptions of the heteroaromatic molecules dominated by the S1←S0 transitions are the key in photoprotection for humans on the earth.14-15 It is well known that the first and second excited states (S1 and S2) of phenol are coupled in the Franck-Condon (FC) region by the S1/S2 CI,16-17 which is responsible for the 1πσ*-mediated photodissociation ascribed to the nature that the 1

ππ* state has the characteristic of the bound state and the 1πσ* is repulsive along the

O-H dissociation coordinate. The nonadiabatically predissociative nature of the 1ππ* state allows to determine its lifetime, which differs from the case of resonances in complex-forming reactions.18-19 Compared to phenol system, the characteristics of the excited electronic states of thiophenol are quite similar due to S and O atoms with identical number of valence electrons. There are multi-states coupled in the dissociation pathways to the products of H and thiophenoxyl radicals. Apart from the S1/S2 CI in FC region, there is another CI formed between the 1πσ* state and the ground state 1ππ at longer S-H distance (see Fig. 1). It is clarified throughout this paper that 1ππ, 1ππ*, and 1πσ* denote the diabatic states, and S0, S1, and S2 are for the adiabatic labels. There have been many experimental studies on the photodissociation dynamics of thiophenol (PhSH) and deuterated thiophenol (PhSD), including the low bands of the 3



absorption spectra,20-21 lifetimes of the S1 vibronic states,20-22 and the product branching ratios (X/A) between the ground and first electronic excited states of the C6H5S radical.21 Particularly, the kinetic energy distributions for the ground and excited states of the products were measured at several wavelengths as well,17, 20, 23 and the dominant product vibrational states in the distributions were found to be an odd number of quanta in aʹʹ C-C twist mode v16a.17 This mode specificity in the product state distributions were attributed to the geometric phase (GP) effect in the nonadiabatic photodissociation facilitated by the CIs.24 The GP is associated with the sign change (eiπ = -1) of the electronic wavefunction when the system encircles the CI in a close loop, which makes the wavefunction double-valued.25-28 The recent theoretical study demonstrated that the size of the nonadiabatic effect in the tunneling-facilitated photodissociation of phenol (S1) was extremely large, the adiabatic predicted lifetimes were about two orders of magnitude shorter than the exact ones.29 More importantly, the adiabatic wavefunctions without GP have been shown to be significantly different from the exact wavefunctions (implicitly including GP),29-32 which suggested that the neglect of GP would lead to incorrect results in describing the dynamics near the CIs. Compared to phenol, the lifetimes of the S1(1ππ*) state of thiophenol were found to be shorter and in femtosecond by several experimental groups.20-22 As discussed above, the nonadiabatic effect had been found to have significant impact on the lifetimes of phenol (S1), but for the nonadiabatic photodissociation of thiophenol S1 state, the nonadiabatic effect is still unclear. The size of the nonadiabatic effect in the photodissociation dynamics can be taken into 4


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account by comparing the results in diabatic (exact) and adiabatic (on a single surface) models. The adiabatic treatment on a single surface ignores the couplings with other states and the derivative couplings (including GP and diagonal Born-Oppenheimer corrections33). It should be noted that the GP effect is in quantum community and thus cannot be treated by classical approach. The diabatic potential energy surfaces (PESs) are the cornerstone in nonadiabatic quantum dynamical calculations, a deep understanding of the photodissociation dynamics can be achieved by the state-to-state quantum dynamical calculations on the available diabatic PES, such as in the cases of H2O and NH3.34-47 It is still a challenging to construct the full dimensional diabatic PESs for polyatomic systems. In the past few years, the full dimensional diabatic PESs of phenol have been constructed based on the ab initio energy gradients and derivative couplings.48-50 While for the thiophenol, there were only two-dimensional (2D) diabatic PESs available

at

low

computational

level.51-52

Recently,

we

constructed

a

three-dimensional(3D) diabatic PESs with multi-reference configuration interaction method with explicitly correction (MRCI-F12) based on the linear-vibronic coupling method.53 The vibronic energy levels of S1 states of PhSH and PhSD calculated by a reduced 3D quantum dynamical model were in good agreement with the available experimental results, which validates the PESs and reduce dynamical model are reasonably accurate.53 In this work, the lifetimes of PhSH and PhSD were calculated in a reduced 3D model, and the nonadiabatic effect in the photodissociation of PhSH and PhSD was 5



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further investigated. The theoretical results are in reasonably good agreement with the available experimental values. This paper is organized as follows, section 2 presents the description of PESs and the wave packet propagation method. Results and discussions are given in section 3, and a brief summary is presented in section 4. 2. Theory In order to investigate the photodissociation dynamics of thiophenol, the adiabatic PESs are taken from our recent work,53 and the construction of the diabatic PESs were achieved by the linear-vibronic coupling method.54-55 The reduced 3D PESs include three degrees of freedom, S-H stretch, C-S-H bend, and C-C-S-H torsion, in which the CIs are one-dimensional (1D). As shown in Fig. 2, the energy of the CI seam is sensitively dependent on the C-S-H bending coordinate. At the planar geometry (φ=0), the 1ππ, 1ππ*, and 1πσ* states are of Aʹ, Aʹ, and Aʹʹ symmetries, respectively, whereas at φ=90 deg, the states have Aʹ, Aʹʹ, and Aʹ symmetries, respectively. In this work, in order to constrain the correct symmetry changes for the C-C-S-H torsional angle varying from 0 to 90 deg, we instead used the expressions for the non-diagonal elements,

W12 = λ sin ϕ ,

(1)

and

W23 =

λ 2

sin 2ϕ ,

(2) in which the symbols 1, 2, and 3 denote the 1ππ, 1πσ*, and 1ππ* states, respectively. It is clear that W12 and W23 in Eqs. (1) and (2) satisfy the linear-vibronic coupling 6


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conditions as well. It should be noted that the new treatment for the non-diagonal elements in diabatic PESs would not qualitatively change the photodissociation dynamics near the FC region, as discussed below. The nonadiabatic coupling parameters λ were determined in the high-symmetry Cs planar subspace with numerical differentiation of the following equation54-55 12

 1 ∂ 2 (V1 − V2 ) 2  λ= ,  ∂ϕ 2 8  R ,θ ,ϕ =0 (3) where Vi are the adiabatic potential energies. The final diabatic PESs were fitted by the cubic spline method.56-57 Fig. 3 shows the 3D plots of the diabatic and adiabatic PESs. Following our recent work,53 the reduced 3D quantum dynamical model was used to study the photodissociation dynamics of thiophenol. The nuclear Hamiltonian in the diabatic representation is given as follows

 1 0 0  V11 V12 V13    Hˆ = Tˆ  0 1 0  + V21 V22 V23  ,      0 0 1 V31 V32 V33  d

(4) in which Tˆ is the kinetic operator,

ˆj 2 h2 ∂2 , Tˆ = − + 2 µ R ∂R 2 2 µ R R 2 (5)

where

µR

is reduced mass µ R =

m H m C 6 H 5S m H + mC 6 H 5S

, j is the angular momentum operator of

7



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thiophenoxyl, and the total angular moment is set to zero. The total wavefunction is expressed as a vector,

ψ 1    Ψ = ψ 2  , ψ 3    (6) in which three components are the wavefunctions for the 1ππ, 1πσ*, and 1ππ* states, respectively. Each nuclear wavefunction is expanded in a direct-product basis in a mixed representation:34

ψ i = ∑ Cαi jm α jm , α jm

(7) i in which Cα jm are the expansion coefficients, α denotes the DVR (discrete variable

representation58) grid index for radial coordinates R. Specifically, the Fourier bases eimφ (m=0, ±1, …) were used to represent the wavefunctions of the whole nonadiabatic system, which allows both the odd and even reflection symmetries.

jm

imϕ

is the spherical harmonics Ne Pj (θ ) , where Pj (θ ) is the associated m

m

Legendre polynomial, and N is the normalized factor. The photodissociation on the S1 state was simulated assuming a Condon excitation, in which the initial wave packet is a vibrational eigenfunction of the S0 state of thiophenol placed vertically on the first singlet excited 1ππ* (S1) state. The wave packet is propagated using the Chebyshev propagator59

Ψk = 2DHsΨk−1 − D2Ψk −2 , k ≥ 2 ,

(8) 8


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with

Ψ1 = DHsΨ0

(9)

and

0  Ψ0 =  0  Ψ   i

,

(10)

where

Ψi is the S0 vibrational eigenfunction, which is obtained by the iterative

Lanczos algorithm.60 The Hamiltonian is scaled to the spectral range of (-1,1) via

Ηs = (Η − H+I)/ H− , (11) +

in which the spectral medium ( H = (Hmax + Hmin )/ 2 ) and half width −

( H = (Hmax − Hmin )/ 2 ) were determined by the spectral extrema,

Hmax and Hmin ,

which can be readily estimated. To avoid reflection, the damping functions (D) were used at the edge of the radial grids. For the S1 vibronic resonances, we have also determined their complex energies (E-iГ/2) using a low-storage filter diagonalization method.60 The Chebyshev correlation function was used to build an energy-localized Hamiltonian matrix, from which the complex energy of the resonance is obtained by diagonalization. The numerical parameters used in wave packet calculations are listed in Table 1.

9



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3. Results and discussions Table 2 lists the energy levels of S1 vibronic states of thiophenol (PhSH) and deuterated thiophenol (PhSD) calculated on the new diabatic PESs. In particular, the calculated vibrational frequency for the C-S-D bend state is 41015.8-40418.5=597.3 cm-1, which is close to the experimental value (608 cm-1)21 and that on our previous PES.53 It can be readily seen that the energies of PhSD vibronic states are lower than those of the PhSH ones, due to the isotope effect. The comparison between diabatic and adiabatic energies is discussed below. Due to the nonadiabatic coupling between the bound state 1ππ* and repulsive state πσ*, the S1 state is non-stable and has a lifetime in femtosecond range.20-22 This lifetime is shorter than that of phenol, due apparently to the energy barrier caused by the S1/S2 CI much lower than that of the phenol PESs. Table 3 lists the full-width at half maximum (FWHM) and lifetimes of three low-lying vibronic states of S1 state for PhSD and PhSH along with the available experimental data21 for comparison. It is clear that the lifetimes are mode specific and isotope dependent, which is consistent with previous quantum dynamical calculations in phenol.

29, 61-64

The lifetimes of

these low-lying vibronic states are ranging from 10-40 fs, which is consistent with the observed lifetime in femtosecond range for S1 state in experiment. 20-22 In particular, it can be readily seen that the predicted widths of the ground vibronic state 00 of PhSD and PhSH are 143.9 and 186.7 cm-1, respectively, which are in good agreement with the experimental data (190 and 195 cm-1). On the other hand, the lifetimes of PhSD vibronic states were found to slightly (3.5 with   R − Rend   =1, otherwise Chebyshev steps: 10,000

16


Rend = 6.0 ;

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Table 2. Energies (in cm-1) of S1 state relative to ground state minimum on PES for PhSH/PhSD in adiabatic and diabatic models. m and n in the label mn denote the vibrations (2 and 3 represent the CSH/CSD bending and CCSH/CCSD torsion modes, respectively) and quantum numbers. Diabatic 0

0

2

1

31

Adiabatic

PhSH

PhSD

PhSH

PhSD

40957.2 41889.9 40999.7

40418.5 41015.8 40430.2

40854.9 41740.9 40872.6

40357.2 40936.3 40358.7

17



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Table 3. Full-width at half maximum (FWHM, in cm-1) and lifetime (in fs) of the low-lying vibronic S1 state PhSD and PhSH. Experimental results were taken from Refs 20 and 21.

FWHM 00 Lifetime FWHM 31 Lifetime FWHM 21 Lifetime

Adiabatic

Diabatic

Exp.

PhSD

428.7

143.9

190

PhSH

834.7

186.7

195

PhSD

12.3

36.6

27.7

PhSH

6.3

28.2

27.0

PhSD

474.5

181.9

PhSH

967.1

284.2

PhSD

11.1

29.0

PhSH

5.4

18.5

PhSD

564.7

285.5

PhSH

1108

413.2

PhSD

9.3

18.4

PhSH

4.8

12.7

18


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Figure captions: Figure 1. The 1D adiabatic and diabatic PES as a function of S-H stretch at several C-C-S-H torsion angles (the C-S-H bend angle was fixed at the ground state equilibrium geometry). Figure 2. The energy of CI seam as function of C-S-H bend angle. Figure 3. The 3D adiabatic (left panel) and diabatic (right panel) PESs as functions of S-H stretch and C-C-S-H torsion (the C-S-H bend angle was fixed at the ground state equilibrium geometry). Figure 4. Moduli of the wavefunction of 00 for the S1 PhSD (upper panel) and PhSH (lower panel) from the diabatic(left) and adiabatic(right) calculations. The angle θ fixed at 97.4 and 94.5 deg for PhSH and PhSD, respectively. Red dot denotes the CI. Figure 5. Moduli of the wavefunction of 31 for the S1 PhSD (upper panel) and PhSH (lower panel) from the diabatic(left) and adiabatic(right) calculations. The angle θ fixed at 97.4 and 94.5 deg for PhSH and PhSD, respectively. Red dot denotes the CI.

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Fig. 1

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Fig. 2

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Fig. 3

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Fig. 4

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Fig. 5

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Nonadiabatic Effect in Photodissociation Dynamics of Thiophenol via

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