Vibrations of acrylonitrile in N $1s$ excited states

The N $1s$ near edge x-ray absorption fine structure spectra of acrylonitrile gas are accurately reproduced by a complete ab initio multidimensional vibrational analysis. The role of ${\pi }^{\ast }$-orbital localization and hybridization on vibrations accompanying core excitation is discussed. Transition to the ${\pi }_{\perp }^{\ast }\left(\text{C}=\text{C}-\text{C}\equiv \text{N}\right)$ delocalized orbital excites mostly stretching vibrations of the whole spinal column of the molecule. Promoting a core electron to the localized ${\pi }_{\parallel }^{\ast }\left(\text{C}\equiv \text{N}\right)$ produces $\text{C}\equiv \text{N}$ stretching vibration combined with two strong bending modes of the $\text{C}-\text{C}\equiv \text{N}$ end of the molecule, related to the change of carbon hybridization.

Figure 1

(Color online) ${\text{H}}_2\text{C}=\text{CHC}\equiv \text{N}$, acrylonitrile molecule.

Figure 2

(Color online) ${\pi }_{\perp }^{\ast }$ (left-hand side) and ${\pi }_{\parallel }^{\ast }$ (right-hand side) orbitals in the ground state (upper), ${\pi }_{\perp }^{\ast }$-excited state (middle), and the ${\pi }_{\parallel }^{\ast }$ (lower) state.

Figure 3

Experimental N $K$-edge NEXAFS spectrum of acrylonitrile molecule.

Figure 4

(Color online) Potential leading to the optimized geometry in the ${\pi }_{\perp }^{\ast }$-excited state, from the vertically attained (at $q=0$) ${\pi }_{\perp }^{\ast }$-excited state, shown along a direct path and in terms of normal coordinate distance between the two states. The molecule with relaxed geometry in the excited state is shown in the minimum of the potential. The ${\text{CH}}_2\text{CHCO}$ molecule of similar geometry is shown in the inset.

Figure 5

(Color online) Ground state (full black line), ${\pi }_{\perp }^{\ast }$-excited-state [full gray (red) line] potential, and corresponding wave functions, for the second most excited, C–C stretching, vibrational mode $\left(a=11\right)$. The ground-state energy scale is on the right-hand side, and the excited state at the left-hand vertical axis. Horizontal dashed lines indicate corresponding eigenvalues. The arrow indicates a vertical transition (at $q=0$) between ${\psi }_0$ and ${\psi }_0^{\prime }$. Probabilities of transitions to the first three vibrational states are indicated. Wave functions with higher excitation probability are drawn by a thicker line.

Figure 6

Vibrational progression in the ${\pi }_{\perp }^{\ast }$-excited state calculated directly (full line) and using the LC model (dashed line). Black intensity bars correspond to the direct calculation (DC). Gray full line direct calculation with displacement (DCd) and intensity bars correspond to calculation including a shift of $\Delta q=+0.15$ of the $a=11$ potential, corresponding to C–C stretching. For the DCd simulation the character of the most important intensity (gray) bars is indicated.

Figure 7

(Color online) Potential leading to the optimized geometry in the ${\pi }_{\parallel }^{\ast }$-excited state, in the function of the normal coordinate distance between the ${\pi }_{\parallel }^{\ast }$-excited with ground-state molecular shape and relaxed geometry ${\pi }_{\parallel }^{\ast }$-excited state. The optimized geometry corresponds to the deeper minimum of the potential, and it has 1.13 eV lower energy than the vertically attained (at $q=0$) ${\pi }_{\parallel }^{\ast }$-excited state. Compared to the ground-state geometry, which has $\text{C}-\text{C}\equiv \text{N}$ linear, it has $50°$ bending of the $\text{C}-\text{C}\equiv \text{N}$ angle. A similar geometry, that of the acrylonitrile cycloadded to a dimer of a silicon (100) surface, represented here by a ${\text{Si}}_9{\text{H}}_{12}$ cluster, is shown in the inset.

Figure 8

(Color online) $\text{O}={\text{C}}_1-{\text{C}}_2={\text{C}}_3$ spinal column of the acrylaldehyde molecule has similar shape as the $\text{N}={\text{C}}_1-{\text{C}}_2={\text{C}}_3$ column of ${\pi }_{\parallel }^{\ast }$-excited acrylonitrile.

Figure 9

(Color online) Ground state (black full line), ${\pi }_{\parallel }^{\ast }$-excited-state [gray (red) full line] potential, and corresponding wave functions, for the most excited, $\text{C}=\text{C}-\text{C}$ bending, vibrational mode $\left(a=13\right)$. Horizontal dashed lines indicate corresponding eigenvalues. The arrow indicates a vertical transition (at $q=0$) between ${\psi }_0$ and ${\psi }_0^{\prime }$. The probability of the excitation of the most important quantum states is indicated, and these wave functions are drawn by a thicker line.

Figure 10

Vibrational progression in the ${\pi }_{\parallel }^{\ast }$-excited state calculated directly (full line) and using the LC model (dashed line). Intensity bars higher than ${10}^{-3}$ are shown for direct calculation. Excitation character of the most important intensity bars is indicated: There is a group of bars at about 399.8 eV with different combinations of $a=13,15$ bimodal excitations, and a group at about 400.1 eV concerning $a=4,13,15$ trimodal excitations.

Figure 11

Best simulations of two N $1s\to {\pi }^{\ast }$ excitations added and compared to the experiment.