Vibrationally resolved N $1s$ absorption spectra of the acrylonitrile molecule

Besides two strong ${\pi }_{\perp 1}^{*}$ and ${\pi }_{\parallel }^{*}$ resonances in the 398- to 400-eV energy range, N 1$s$ near edge x-ray absorption fine structure spectra of acrylonitrile molecules have a less intense 401- to 403-eV doublet. The two components correspond to the N 1$s$ $\to$ ${\pi }_{\perp 2}^{*}$ and N 1$s$ $\to$ $D_{\parallel }^{*}$ transitions, where $D_{\parallel }^{*}$ is a diffuse state with strong Rydberg character. The vibrational analysis shows that in the $D_{\parallel }^{*}$ excited state, two low-energy $\mathit{out}$-$\mathit{of}$-$\mathit{plane}$ normal modes are strongly excited. The ${\pi }_{\perp 2}^{*}$ excitation triggers a set of $\mathit{\text{in}}$-$\mathit{plane}$ vibrations, in particular, two C=C–C$\equiv$N bendings of the molecule.

Figure 1

N$\equiv$C$-$CH$=$CH${}_2$, acrylonitrile molecule.

Figure 2

The entire experimental N 1$s$ NEXAFS spectrum (black points) of the acrylonitrile molecule compared to calculations including vibrational analysis (red line). The spectra show two strong low-energy structures (${\pi }_{\perp 1}^{*}$ and ${\pi }_{\parallel }^{*}$), a $D_{\parallel }^{*}$–${\pi }_{\perp 2}^{*}$ doublet and a small $D_{\perp }^{*}$ structure close to the ionization potential. Experimental details are given in Ref. [17].

Figure 3

Ground [(a) and (c)] and excited [(b) and (d)] state forms of $D_{\parallel }^{*}$ and ${\pi }_{\perp 2}^{*}$ orbitals. The $D_{\parallel }^{*}$ orbital changes strongly in the excited state: The small bag close to the C${}_1$ atom in the ground state (a) surrounds the C${}_1$ atom like a crescent moon in the excited state (b). On the other hand, the ${\pi }_{\perp 2}^{*}$ orbital changes much less when accommodating the supplementary electron [(c) and (d)]: There is a slight transfer of one part of the N states to the H–C=C–H${}_2$ part of the molecule.

Figure 4

Ground state (black solid line), $D_{\left|\right|}^{*}$ excited state (orange) potential surface of its most excited, C–C$\equiv$N out-of-plane bending vibrational mode ($m=14$). Corresponding wave functions (solid lines) and eigenvalues (dashed lines) are drawn for each potential. The arrow indicates a vertical transition (at $q=0$) between ${\psi }_0$ and ${\psi }_0^{\prime }$. The probability of the excitation of the three most important quantum states is indicated at the right side of the excited potential.

Figure 5

Ground state (black), ${\pi }_{\perp }^{*}$ excited state (orange) potential surface projected to its second most excited, out-of-plane C=C–C bending vibrational mode ($m=13$). Wave functions and eigenvalues are indicated. The probability of the excitation to the three states with most important Franck-Condon factors is indicated at the right side of the excited potential.

Figure 6

Calculation of the 401.5- to 402.5-eV doublet compared to the experiment. It is composed of vibrational progressions of the $D_{\parallel }^{*}$ excited state (orange line, maximum at 401.9 eV) and the ${\pi }_{\perp 2}^{*}$ excited state (green line, centered at 402.35 eV). Addition of these two structures (black line) matches experimental spectra well.