ARTICLE pubs.acs.org/JPCA
Ab Initio Based Surface-Hopping Dynamics Study on Ultrafast Internal Conversion in Cyclopropanone Ganglong Cui and Weihai Fang* College of Chemistry, Beijing Normal University, Beijing 100875, P. R. China ABSTRACT: Cyclopropanone exhibits an intriguing phenomenon that the fluorescence from the S1 state disappears below 365 nm. This is ascribed to the ultrafast S1 f S0 internal conversion process via conical intersection, which deprives opportunity of the fluorescence emission. In this work, we have used ab initio based surface hopping dynamics method to study vibrationalmode-dependent S1 f S0 internal conversion of cyclopropanone. A new conical intersection between the S1 and S0 states is determined by the state-averaged CASSCF/cc-pVDZ calculations, which is confirmed to play a critical role in the ultrafast S1 f S0 internal conversion by the nonadiabatic dynamics simulations. It is found that the internal conversion occurs more efficiently when the initial kinetic energies are distributed in the four vibrational modes related to the CdO group, especially in the C-O stretching and the O-C-C-C out-of-plane torsional modes. Meanwhile, the S1 lifetime and the time scale of the S1 f S0 internal conversion are estimated by the ab initio based dynamics simulations, which is consistent with the ultrafast S1 f S0 internal conversion and provides further evidence that the ultrafast internal conversion is responsible for the fluorescence disappearance of cyclopropanone.
I. INTRODUCTION Control and design of photophysical and photochemical processes in polyatomic molecules is one dream of chemical and physical scientists; to arrive at this aim, however, we should first understand the mechanisms of photophysics and photochemistry of these polyatomic molecules both correctly and accurately.1-18 In the past decades, substantial progress in understanding the photodissociation dynamics of the smalland medium-sized polyatomic molecules has been achieved experimentally and theoretically. Now we are striding ahead in unraveling the mechanistic photophysics and photochemistry of large systems in biology and material.2,6,8,19-31 Carbonyl compounds as one representative of medium size polyatomic molecules have been systematically and extensively studied due to their importances in organic photochemistry.32-43 In comparison with aliphatic and aromatic carbonyl compounds, the cyclic carbonyl compounds gain few attention, especially for their photodissociation dynamics. Cyclic carbonyl compounds have a unique characteristic—strong ring tension—that could cause the ring-opening reaction to occur fast, even ultrafast, in the excited states or the ground state. This ultrafast process may remarkably change our understanding of the mechanistic photodissociation in the common aliphatic and aromatic carbonyl compounds. For this reason, it is significant to explore the photodissociation dynamics of cyclopropanone. Cyclopropanone, the simplest cyclic carbonyl compound, was first synthesized by Deboer et al. in the 1960s.44 After this early study, Pochan et al. studied its ground-state structures using the microwave spectroscopy techniques and found that it has a C2v spatial symmetry in the ground state.45,46 Later, Thomas et al. r 2011 American Chemical Society
explored cyclopropanone photodissociation dynamics in the gas phase in the wavelength range of 292-365 nm.47 They observed that carbon monoxide (CO) and ethylene (C2H4) were the exclusive photoproducts, and their quantum yields increased with the decreased irradiation wavelength. The electronically first excited singlet state (S1) was assigned to a n f π* transition whose band origin was estimated to be about 395 nm. In addition, because of the appearance of the diffuse vibrational spectroscopy in cyclopropanone irradiated at 292 nm, Thomas and co-workers suggested that the photochemical reactions might proceed at this wavelength. More interestingly, the S1 fluorescence disappeared when the irradiation wavelength was below 365 nm, implying that certain ultrafast photophysical or photochemical routes are opened at this wavelength. As the S1 state lifetime of cyclopropanone was predicted to be much shorter than the time required for the intersystem crossing (ISC) process, the S1 decay to the T1 state can be ruled out. What kind of ultrafast process is responsible for the fluorescence disappearance is still not illuminated until recently.17 By using the high-level electronic structure calculations and the ab initio diabatic surface hopping method, we have uncovered the mechanism of fluorescence disappearance in cyclopropanone below 365 nm that the ultrafast S1 f S0 internal conversion process, via conical intersections, deprives the opportunity of the fluorescence emission.17 However, the diabatic surface hopping method uses an approximate, Landau-Zener-based switch Received: November 7, 2010 Revised: January 8, 2011 Published: February 14, 2011 1547
dx.doi.org/10.1021/jp110632g | J. Phys. Chem. A 2011, 115, 1547–1555
The Journal of Physical Chemistry A
ARTICLE
function to control the nonadiabatic transition. This criterion only allows hopping at the conical intersection seam, and thus, this strict diabatic hopping criterion could lead to an underestimation of the S1 f S0 population transfer probability because a surface hop from the regions with strong nonadiabatic coupling, which could be far from the conical intersection regions, is prohibited. Furthermore, the weak nonadiabatic coupling regions are also completely ignored in the diabatic surface hopping method because the hopping can occur only if a diabatic crossing occurs.6,48 Nevertheless, one also should note that the weak coupling regions could play a significant role in spite of the low hopping probability. Finally, in the previous work, only the effect of the CdO stretching vibrational mode on the ultrafast internal conversion process has been explored, without considering the other key vibrational modes in cyclopropanone. The different but important vibrational modes might have a distinct impact on the S1 state lifetime and the ultrafast internal conversion process. In this work, we use more rigorous fewest switches surface hopping method, which considers both strong and weak nonadiabatic coupling regions, and reinvestigate the photodissociation dynamics of cyclopropanone.1,3,49,50 Moreover, we also explore the effect of the different vibrational modes on the S1 state lifetime and the ultrafast internal conversion process. The paper is divided into several sections: section II briefly presents the trajectory fewest switches surface hopping method and simulation details; section III is the results and discussion; section IV is our conclusions.
II. METHODS Trajectory Surface Hopping Method. In this subsection, we give a short description of the standard classical trajectory surface hopping procedure that we have used in this study. For more details, we recommend the literature.1-5,49 In adiabatic representation, we can express the time-dependent electronic wave function of a system by the adiabatically electronic-state wave function as below s X ci ðtÞΦi ðr, RðtÞÞ ð1Þ Ψðr, R, tÞ ¼ i¼1
v(t) is the velocity vector of nuclei and the derivative coupling vector is * + D ð4Þ dRji i ðRðtÞÞ ¼ Φj ðr, RðtÞÞ Φi ðr, RðtÞÞ DR i In this expression, Ri(t) is the nuclear coordinate vector of the ith atom in a system at time t and the integration is carried out over the electronic degrees of freedom. On the other hand, the motion of the βth atom in a system on the electronic state i at the time t is _ = propagated according to the classical Newton equation, MβV(t) -ÆΦi(t)|∂/(∂Rβ)|Φi(t)æ. The time evolution of the nuclear degrees of freedom is propagated by the velocity Verlet algorithm; while the fourth-order Adams-Bashforth-Moulton predictor-corrector scheme are employed to propagate the quantum amplitudes, eq 2. To improve the numerical integration of the electronic timedependent Schrodinger equation, a smaller time step δt0 = δt/ms is used, with the relevant quantities are linearly interpolated. The accurate evaluation of transition probability from one state to another one is rather important for nonadiabatic surface hopping method.6,11,17,48-54 In the Tully's fewest-switches-surface-hopping algorithm, the transition probability from the ith state to the jth state is defined as " # bij ð5Þ pij ¼ max 0, δt aii where there are the below relations, aij = ci*cj and bij = 2Re(aijv 3 dij); and δt is time step.51 Later, Hammes-Schiffer and Tully proposed another modified fewest-switches-surface-hopping algorithm, where the transition probability is written as52 2 R 3 t þ δt 2t dt Reðaij Þv 3 dij 5 ð6Þ pij ¼ max 40, aii In order to determine to which state a switch occurs, a uniform random number 0 < ξ < 1 is selected at each time step and a hop from state i to state j is performed if j X
from which the propagation of the time-dependent Schrodinger equation can be transformed into s X ci ðtÞΛji ðtÞ ð2Þ i_cj ðtÞ ¼ - ip-1 cj ðtÞEj ðtÞ i
In eq 2, r and R(t) are the coordinate vector of electrons and nuclei in a system; Ej(t) is the eigenenergy of the jth adiabatic electronic state at time t; and * + D ð3Þ Λji ðtÞ ¼ Φj ðr, RðtÞÞ Φi ðr, RðtÞÞ Dt is the nonadiabatic coupling term between the electronic states j and i. This nonadiabatic coupling term, based on the time derivative of Φi ðr, RðtÞÞjΦj ðr, RðtÞÞ ¼ δij
k
pki < ξ
