On the interpretation of molecular photoexcitation with long and ultrashort laser pulses

Abstract

Photoexcitation is an inherent part of any photochemical or spectroscopic experiment, yet its impact on the excited-state dynamics is often overlooked. However, it is the excited molecular state, built upon photoexcitation and shaped by the characteristics of the light source, that determines the fate of the excited molecule and its subsequent photochemical reactions. In this work, we investigate how excited molecular states are built by different laser pulses, leveraging two representations of the molecular wave function: Born-Huang expansion and exact factorization. We explore the generation of two limiting cases: a stationary molecular state with a long laser pulse and an electronic wave packet by an ultrashort (attosecond) laser pulse. The standard concepts of population transfer between electronic states, resonance condition, or sudden vertical excitation, inherent to the Born-Huang representation and used by chemists to approximate the impact of photoexcitation on molecular systems, are challenged by the exact factorization.

Figures (5)

• Figure 1: A: Potential energy curves of the OH radical model with the relevant vibrational eigenstates of the lowest two diabatic states. The diabatic state labels ($\mathrm{X}^2\Pi$, $\mathrm{A}^2\Sigma^+$, $\mathrm{1}^2\Sigma^-$, $1^2\Delta$) are depicted together with adiabatic state labels ($D_1$, $D_2$, $D_3$, $D_4$). The inset portrays the molecule and a schematic depiction of the dipole and transition dipole moments. B: Zoom on the region of the absorption spectrum of the OH radical concerned with the $\mathrm{X}^2\Pi \rightarrow \mathrm{A}^2\Sigma^+$ electronic transition, depicted together with the spectral intensity of the 100-fs laser pulse used in our model (the pulse is shown in the inset). The grey dashed lines highlight the different vibronic transitions, demonstrating that only the 0--2 transition is resonant with the laser pulse employed in the present model. C: The normalized absorption spectra for the three excited states considered in the OH model are depicted together with the spectral intensity of the 1-fs laser pulse used in our model (the pulse is shown in the inset). The pulse spectral intensity targets all three excited states.
• Figure 2: Snapshots of the OH photoexcitation with the 100-fs laser pulse in the BH (top row) and EF (bottom row) representations at four different time snapshots: 0, 35, 50, and 138 fs. The initial molecular state before the laser pulse interaction is observed at time 0 fs (first column), the final stationary molecular state is observed for $t > 100$ fs -- the snapshot at 138 fs (last column) in this figure. Top panel: the BH nuclear densities for the adiabatic states ($|\chi_I|^2$) and their corresponding adiabatic potential energy curves (black) are represented. Lower panel: the total nuclear density ($|\chi|^2$) and the TDPES ($\varepsilon$) are depicted. The insets contain the electric-field component of the laser pulse [$\vec{E}(t)$] up to the given time of the snapshot. An animated version of the plot is available using the following https://github.com/JanosJiri/Photoexcitation-From-Different-Perspectives/blob/main/100-fs pulse/BH_vs_EF_A0.gif.movierepo
• Figure 3: Populations of the $|D_1,v=0\rangle$ (purple) and $|D_2,v=2\rangle$ (green) states for simulations with a truncated expansion of the vibronic states: A two vibronic states, B seven vibronic states. The vibrational eigenstates used in the expansion are depicted in the right panels.
• Figure 4: A: Populations of the vibrational states belonging to electronic state $D_2$ during the photoexcitation process. The legend uses a simplified notation where $|D_2,v=n\rangle$ is denoted as $|v=n\rangle$. The inset focuses on the off-resonant vibrational states between 10 and 75 fs. B: Normalized (time-dependent) nuclear density on $D_2$ ($|\chi_2|^2/\langle\chi_2|\chi_2\rangle$) for selected times of 1, 15, 25, and 40 fs. The dashed lines depict the normalized (stationary) nuclear densities of the initial $|D_1,v=0\rangle$ state (grey) and final $|D_2,v=2\rangle$ state (black).
• Figure 5: Snapshots of the photoexcitation of OH with a 1-fs laser pulse in the BH (top panel) and the EF (bottom panel) representations at four times: 0, 1.1, 3.5, and 5.5 fs. For the BH representation, we plot the BH nuclear densities for the adiabatic states ($|\chi_I|^2$) and their corresponding adiabatic potential energy curves (black). For the EF representation, we plot the total nuclear density ($|\chi|^2$) and the TDPES ($\varepsilon$). The transparent lines in the lower panel depict TDPES at other snapshot times. The insets contain the laser pulse electric field $\vec{E}(t)$ up to the given time of the snapshot. Animated version of the plot is available using the following https://github.com/JanosJiri/Photoexcitation-From-Different-Perspectives/blob/main/1-fs pulse/BH_vs_EF_A0.gif.movierepo