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Quantum dynamics study of the competing ultrafast intersystem crossing and internal conversion in the “channel 3” region of benzene
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10.1063/1.4767054
/content/aip/journal/jcp/137/20/10.1063/1.4767054
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/20/10.1063/1.4767054

Figures

Image of FIG. 1.
FIG. 1.

A cut through the potential energy surfaces for benzene along the prefulvene mode. The singlet states are in black and triplet in red. Note the near degeneracy of the potential energy leading to the CI, with the lines for S1 and a triplet state superimposed. In addition we have labelled either side of the barrier ( and ) according to the diabatic character of the S1 state. This is important for the discussion of the experimental results shown in Sec. III.

Image of FIG. 2.
FIG. 2.

Cuts along the normal modes through the triplet potential energy surface for benzene. In order of energy at Q = 0 these states are T1 (B1u ) and T2 (E1u ). (a) ν1 (1a1g ), the breathing mode, (b) ν4 (1b2g ), the chair mode, (c) ν6a (1e2g ), the quinoid mode, (d) ν16a (1e2u ), the boat mode, (e) ν9a (4e1g ), and (f) the prefulvene combination mode (ν4,16a ). The solid black dots are the ab initio points for the triplet states, the open circles are the S1 state, and the black line is the fit to the triplet states.

Image of FIG. 3.
FIG. 3.

Photoelectron spectra of benzene from the continuous (a) and pulsed (b) expansion, following excitation with a 243 nm pump pulse and a 235 nm probe pulse as a function of pump-probe delay.

Image of FIG. 4.
FIG. 4.

Photoelectron signal as a function of the pump-probe delay from the continuous expansion: (a) total integrated photoelectron signal, (b) 0.34–0.37 eV, (c) 0.65–1.0 eV, and (d) 1.11–1.46 eV. Experimental data (open circles) and fit (bold solid line) together with the contributions from the decays, τ1 ∼ 233 fs (widely spaced dots), τ2 ∼ 1.8 ps (closely spaced dots), τ3 ∼ ∞ (dashes), and the cosinusoidal oscillation (solid line) obtained using the global fitting procedure described in the text.

Image of FIG. 5.
FIG. 5.

Photoelectron signal as a function of the pump-probe delay from the continuous expansion: (a) total integrated photoelectron signal, (b) 0.34–0.37 eV, (c) 0.65–1.0 eV, and (d) 1.11–1.46 eV. Experimental data (open circles) and fit (bold solid line) together with the contributions from the decays, τ1 ∼ 256 fs (widely spaced dots) and τ3 ∼ ∞ (dashes) obtained using the global fitting procedure described in the text.

Image of FIG. 6.
FIG. 6.

State populations following excitation to the Franck-Condon point on with (a) (red) and S1 (black) using the 2-state Hamiltonian with . The blue line is for a cold simulation for which ν16 was not initially excited. (b) (red) and S1 plus triplets (black) using the 4-state ISC Hamiltonian with . (c) (red) and S1 plus triplets (black) using the 4-state ISC Hamiltonian with . (d) (red) and S1 plus triplets (black) using the 4-state ISC Hamiltonian with no hot band, . In (a) and (b) the purple lines correspond to the double exponential fit of the decay curves. In (b)–(d) the green line is the sum of the triplet populations. (e) The population of the T 1 (red), T 2 (blue), and total triplet population (green) for simulation (c). (f) The population of the T 1 (red), T 2 (blue), and total triplet population (green) for simulation (d).

Image of FIG. 7.
FIG. 7.

Expectation values of the position of the wavepacket during propagations for first 2000 fs using the 2-state Hamiltonian. (a) ⟨q⟩ of ν4 (blue) and ν16a (green) on S0. (b) ⟨q⟩ of ν1 (red) and ν6a (black) on S0. (c) ⟨q⟩ of ν4 and ν16a on S1. (d) ⟨q⟩ of ν1 and ν6a on S1.

Image of FIG. 8.
FIG. 8.

Expectation values of the position of the wavepacket in the triplet states during propagations for first 2000 fs using the 4-state ISC Hamiltonian. (a) ⟨q⟩ of ν4 (blue) and ν16a (green) on T1. (b) ⟨q⟩ of ν1 (red) and ν6a (black) on T1. (c) ⟨q⟩ of ν4 and ν16a on T2, x . (d) ⟨q⟩ of ν1 and ν6a on T2,x .

Tables

Generic image for table
Table I.

Computational details for the quantum dynamics simulations. N i ,N j are the number of primitive Harmonic oscillator discrete variable representation (DVR) basis functions used to describe each mode.26 n i are the number of single-particle functions used for the wavepacket on each state. (A) 2-state singlet model. (B) 4-state intersystem crossing model.

Generic image for table
Table II.

Mode symmetry and vibration energies in eV for all the normal modes of benzene, using Wilson numbering. Calculated using a CAS(6,6) active space and 6-31g* basis set.

Generic image for table
Table III.

Vertical excitation energies (in eV) of the lowest four singlet and lowest four triplet states of benzene relative to the benzene singlet ground state, calculated at the equilibrium geometry. The SA-CAS(6,6) used a 6-31g* basis and are averaged over the four states. The CASPT2(6,6) and CASPT2(6,10) calculations use a MOLPRO specific Roos(3s2p1d/2s) basis.

Generic image for table
Table IV.

On-diagonal κ and off-diagonal, λ, linear coupling constants, (in eV) for the important normal modes of benzene in the triplet manifold obtained by fitting a vibronic coupling Hamiltonian to the adiabatic potential energy surfaces at the CASPT2(6,6) level. Superscript shows the state and subscript the normal mode(s) associated with the parameter. States 1,2,3 refer to and respectively.

Generic image for table
Table V.

First (λ) and second (γ) order vibrational spin orbit coupling terms (in cm−1). Calculations performed with (6,6) active space and MOLPRO specific Roos(3s2p1d/2s) basis. The subscript shows the normal mode(s) associated with the parameter.

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/content/aip/journal/jcp/137/20/10.1063/1.4767054
2012-11-28
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quantum dynamics study of the competing ultrafast intersystem crossing and internal conversion in the “channel 3” region of benzene
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/20/10.1063/1.4767054
10.1063/1.4767054
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