Light-induced nonadiabatic photodissociation of the NaH molecule including electron-rotation coupling

Abstract

It is well established that electronic conical intersections (CIs) in molecular systems can be induced by laser light, even in diatomic molecules. The emergence of these light-induced degeneracies leads to strong coupling among electronic, vibrational, and photonic modes, which significantly influences ultrafast nuclear dynamics. In this work, we perform pump-probe numerical simulations on the NaH molecule, considering the first three singlet electronic states- (X1Σ+(X), A1Σ+(A) and B1Π(B)) -and including several light- induced degeneracies in the theoretical model. To elucidate the ultrafast molecular dynamics, the combined effects of multiple light-induced nonadiabatic couplings and rotational motion of the nuclei, together with the situation when the electronic angular momentum projected onto the diatomic axis couples with the angular momentum of the nuclei has been studied. We then calculate key dynamical observables such as dissociation probabilities, kinetic energy release spectra, and angular distributions of the photofragments within and above the linear regime.

Figures (11)

• Figure 1: (a) Lowest three adiabatic potential energy curves of the $\mathrm{NaH}$ molecule. (b) Permanent dipole moment (PDM) functions of the three adiabatic electronic states. (c) Transition dipole moment (TDM) functions between the different adiabatic electronic states.
• Figure 2: Vector diagram of the electron-rotation coupling conforming to Hund's case (a). $\Lambda$ and $\Sigma$ are the projections of the electronic orbital $\mathbf{L}$ and spin $\mathbf{S}$ angular momenta onto the molecular axis, i.e. the $z$ axis of the molecule-fixed (MF) frame. $\mathbf{K}$ is the nuclear rotational angular momentum, and $\mathbf{J}$ is the total angular momentum with $\mathrm{M}$ being its projection onto the space fixed (SF) $Z$ axis. $\varphi$ and $\chi$ are the Euler angles representing rotations around the SF $Z$ and MF $z$ axes, while $\theta$ is the angle between these two.
• Figure 3: (a) The three lowest-lying singlet adiabatic potential energy curves of the $\mathrm{NaH}$ molecule. The corresponding light-dressed states are denoted by dashed lines. The position of the light-induced conical intersections ($\mathrm{LICI}_{1}^{(BA)}$, $\mathrm{LICI}_{2}^{(BA)}$, $\mathrm{LICI}_{1}^{(XA)}$ and $\mathrm{LICI}_{2}^{(XA)}$) are also marked. (b) Magnification of the region highlighted on panel (a) with the light-induced conical intersections.
• Figure 4: (a) Vibrational motion of the nuclear wave packet on the A state after excitation by the pump pulse, and the expectation value of the $R$ coordinate (magenta curve). The horizontal lines show the LICI positions, while the markers indicate when the $R$-expectation curve crosses them: $\mathrm{LICI}_{1}^{(BA)}$ continuous line / blue circles; $\mathrm{LICI}_{2}^{(BA)}$ dotted line / blue plus signs; $\mathrm{LICI}_{1}^{(XA)}$ dashed line / red squares; and $\mathrm{LICI}_{2}^{(XA)}$ dash-dotted line / red $\times$ signs. Panels (b) and (c) zoom in the two investigated delay time windows, and show the $R$-expectation curve and LICI position indicators as on panel (a), along the TDM weighted sums of the nuclear wavepacket density at $\mathrm{LICI}_{1+2}^{(BA)}$ with dashed blue line, and $\mathrm{LICI}_{1+2}^{(XA)}$ with continuous red line.
• Figure 5: Dissociation probabilities corresponding to the individual adiabatic electronic states ($\mathrm{X}$ - red with circles, $\mathrm{A}$ - green with squares, $\mathrm{B}$ - blue with triangles) as a function of delay time between the pump and the probe pulses. The $\mathrm{A}$ state dissociation probability is scaled for better visibility, with the scaling factor $\mathrm{f_{sc}}$ indicated on each panel. The dashed, continuous and dotted lines correspond to results obtained with the 1D, 2D and 3D models, respectively. Panels (a) and (b) show our results for $I_{pr}=1\times10^{11}$$\mathrm{W/cm^2}$, while (c) and (d) for $I_{pr}=1\times10^{12}$$\mathrm{W/cm^2}$