Transient-Absorption Pump-Probe Spectra as Information-Rich Observables: Case Study of Fulvene

Abstract

Conical intersections (CIs) are the most efficient channels of photodeactivation and energy transfer, while femtosecond spectroscopy is the main experimental tool delivering information on molecular CI-driven photoinduced processes. In this work, we undertake a comprehensive ab initio investigation of the CI-mediated internal conversion in fulvene by simulating evolutions of electronic populations, bond lengths and angles, and time-resolved transient absorption (TA) pump-probe (PP) spectra. TA PP spectra are evaluated on the fly by combining the symmetrical quasiclassical/Meyer-Miller-Stock-Thoss (SQC/MMST) dynamics and the doorway-window representation of spectroscopic signals. We show that the simulated time-resolved TA PP spectra reveal not only the population dynamics but also the key nuclear motions as well as mode-mode couplings. We also demonstrate that TA PP signals are not only experimental observables: They can also be considered as information-rich purely theoretical observables, which deliver more information on the CI-driven dynamics than conventional electronic populations. This information can be extracted by the appropriate theoretical analyses of time-resolved TA PP signals.

Keywords: conical intersections; doorway window approximation; symmetrical quasiclassical/Meyer–Miller–Stock–Thoss; transient absorption pump-probe spectroscopy.

Figure 6

Fourier transforms of the normalized TA PP spectra of fulvene with respect to the population time $\tau$: $I_{int}^{SE}(\Omega ,{\omega }_{pr})$ (a,c) and $I_{int}^{ESA}(\Omega ,{\omega }_{pr})$ (b,d). The upper spectra are computed by integrating from 0 to 600 fs, while the lower spectra are evaluated by integrating from 10 to 600 fs. In addition, the tiny black curves in the inset of (a) show the splitting of the board peaks.

Figure A1

Normalized (a) SE signal and (b) GSB signal of fulvene versus the delay time $\tau$ and the probe signal ${\omega }_{pr}$ obtained at the SA2-CASSCF(6,6) level of electronic structure theory. The pump-pulse frequency ${\omega }_{pu}=4.39$ eV is resonant with the $S_1$ state.

Figure A2

Normalized SE (a), ESA (b), GSB (c), and total (d) integral TA PP spectra of fulvene vs. pump-probe delay $\tau$ and the probe carrier frequency ${\omega }_{pr}$ evaluated up to 600 fs. The carrier frequency of the pump pulse, ${\omega }_{pu}=4.39$ eV, is in resonance with the $S_1$ state.

Figure A3

Fourier transforms of the normalized cold (a,c) and hot (b,d) GSB spectra of fulvene. The upper spectra are computed by integrating from 0 to 600 fs, while the lower spectra are evaluated by integrating from 10 to 600 fs.

Figure A4

Normalized time-dependent distributions of C4–C5 stretch (a,d), C1–C2, and C1–C3 asymmetric stretches (b,e), and C2–C4 and C3–C5 asymmetric stretches (c,f). The upper panels are evaluated for the first excited state $S_1$, while the lower panels are evaluated for $S_0$.

Figure A5

Normalized Fourier transform of (a) C1–C6, (b) C1–C2/C1–C3, (c) C2–C4/C3–C5, (d) C4–C5, and (e) C2–C1–C3 bending.

Figure 1

Optimized equilibrium structures of fulvene in (a) $S_0$, (b) $S_1$, and (c) CI.

Figure 2

Time-dependent populations of the $S_0$ and $S_1$ states of fulvene.

Figure 3

Normalized SE (a), ESA (b), GSB (c), and total (d) integral TA PP spectra of fulvene vs. pump-probe delay $\tau$ and the probe carrier frequency ${\omega }_{pr}$. The carrier frequency of the pump pulse, ${\omega }_{pu}=4.39$ eV, is in resonance with the $S_1$ state.

Figure 4

(a) Linear interpolated PESs of $S_0$ and $S_1$ between $S_0$ minimum and $S_0/S_1$ CI obtained at SA2-CASSCF(6,6)/6-31G(d) and SA6-CASSCF(6,6)/6-31G(d) levels. (b) Linear interpolated TDMs from $S_0$ to $S_1$ between $S_0$ minimum and $S_0/S_1$ CI obtained at SA2-CASSCF(6,6)/6-31G(d) and SA6-CASSCF(6,6)/6-31G(d) levels. (c) Linear interpolated PESs from $S_0$ to $S_5$ between $S_0$ minimum and $S_0/S_1$ CI. (d) Linear interpolated TDMs from $S_1$ to $S_2-S_5$ between $S_0$ minimum and $S_0/S_1$ CI.

Figure 5

Normalized time-dependent distributions of C1–C6 bond lengths (a,e), C1–C2 and C1–C3 symmetric stretches (b,f), C2–C4 and C3–C5 symmetric stretches (c,g), and C2–C1–C3 bendings (d,h). The upper panels are evaluated for the first excited state $S_1$, while the lower panels are evaluated for $S_0$.