^{1,2}, Leonardus W. Jenneskens

^{1}and Joop H. van Lenthe

^{2,a)}

### Abstract

The molecular geometry and the normal modes properties of coronene are investigated by means of DFT(B3LYP) and restricted/Hartree–Fock calculations utilizing basis sets of triple quality. The interpretation of the infrared and Raman spectra of coronene, especially in solid state, is critically revised. The phantom bands in the solid state, previously not understood, are readily assigned after considering a minute out-of-plane molecular distortion from to .

The authors gratefully acknowledge financial support from NCF and NWO for the use of supercomputer time on HUYGENS, SARA (The Netherlands, Project No. SH-028).

I. INTRODUCTION

II. COMPUTATIONAL APPROACH

A. Density functional theory calculations

B. Restricted Hartree–Fock calculations: Basis set or geometry

III. VIBRATIONAL SPECTROSCOPY

A. Infrared spectroscopy

B. Raman spectroscopy

IV. MOLECULAR GEOMETRY

V. POTENTIAL ENERGY SURFACE

VI. CONCLUSIONS

### Key Topics

- Normal modes
- 19.0
- Infrared spectra
- 18.0
- Raman spectra
- 16.0
- Density functional theory
- 14.0
- Crystal structure
- 7.0

## Figures

A short movie that visualizes one period of the imaginary normal mode ( symmetrical stationary point) calculated at the level (enhanced online). [URL: http://dx.doi.org/10.1063/1.3282331.1]10.1063/1.3282331.1

A short movie that visualizes one period of the imaginary normal mode ( symmetrical stationary point) calculated at the level (enhanced online). [URL: http://dx.doi.org/10.1063/1.3282331.1]10.1063/1.3282331.1

A short movie that visualizes one period of the real normal mode ( symmetrical stationary point) calculated at the level (enhanced online). [URL: http://dx.doi.org/10.1063/1.3282331.2]10.1063/1.3282331.2

A short movie that visualizes one period of the real normal mode ( symmetrical stationary point) calculated at the level (enhanced online). [URL: http://dx.doi.org/10.1063/1.3282331.2]10.1063/1.3282331.2

Illustration of two of the most distinguishing features of the solid-state infrared spectrum of coronene (b) [derived from Table II, Figs. 2a and 2g in Ref. 8] compared with the gas-phase infrared spectrum (a) [derived from Table II, Figs. 2a and 2g in Ref. 8] and its infrared spectrum in low temperature Ne Matrix (c) [derived from Table II, Figs. 2a and 2g in Ref. 8]. The bands’ positions are exactly as presented in Ref. 8. The shapes of the bands are qualitatively modeled with Gaussian functions to match the experimentally observed bands (Ref. 8) as closely as possible. The band at approximately represents four-frequency absorptions in the solid state, whereas in the gas-phase and the low temperature Ne matrix spectrum this band represents a one-frequency absorption. The band at approximately is present only in the solid-state spectrum and represent a two-frequency absorption. See Table IV for the exact band positions.

Illustration of two of the most distinguishing features of the solid-state infrared spectrum of coronene (b) [derived from Table II, Figs. 2a and 2g in Ref. 8] compared with the gas-phase infrared spectrum (a) [derived from Table II, Figs. 2a and 2g in Ref. 8] and its infrared spectrum in low temperature Ne Matrix (c) [derived from Table II, Figs. 2a and 2g in Ref. 8]. The bands’ positions are exactly as presented in Ref. 8. The shapes of the bands are qualitatively modeled with Gaussian functions to match the experimentally observed bands (Ref. 8) as closely as possible. The band at approximately represents four-frequency absorptions in the solid state, whereas in the gas-phase and the low temperature Ne matrix spectrum this band represents a one-frequency absorption. The band at approximately is present only in the solid-state spectrum and represent a two-frequency absorption. See Table IV for the exact band positions.

Illustration of two of the most distinguishing features of solid- state Raman spectrum of coronene (b) (see Table I in Ref. 9; also included in Table V) compared with the calculated spectrum at the symmetrical stationary point (a) (see also Table V) and the calculated spectrum at the symmetrical stationary point (c) (see Table V). The shapes of the bands are qualitatively modeled with Gaussian functions. The experimental band at approximately as present in the experimental Raman spectrum of crystalline coronene is only visible in the calculated spectrum but it is not visible in the calculated spectrum. The strong experimental line at approximately as present in the crystalline coronene spectrum is visible only in the calculated spectrum but is absent from the calculated spectrum.

Illustration of two of the most distinguishing features of solid- state Raman spectrum of coronene (b) (see Table I in Ref. 9; also included in Table V) compared with the calculated spectrum at the symmetrical stationary point (a) (see also Table V) and the calculated spectrum at the symmetrical stationary point (c) (see Table V). The shapes of the bands are qualitatively modeled with Gaussian functions. The experimental band at approximately as present in the experimental Raman spectrum of crystalline coronene is only visible in the calculated spectrum but it is not visible in the calculated spectrum. The strong experimental line at approximately as present in the crystalline coronene spectrum is visible only in the calculated spectrum but is absent from the calculated spectrum.

X-ray measured (Ref. 11) carbon-carbon bond distances (in angstroms).

X-ray measured (Ref. 11) carbon-carbon bond distances (in angstroms).

Carbon-carbon bond distances (in angstroms) for the and optimized neutral coronene restricted to either or symmetry.

Carbon-carbon bond distances (in angstroms) for the and optimized neutral coronene restricted to either or symmetry.

Coordinate system, carbon and hydrogen labels used to present the Cartesian coordinates in Tables VI and VII.

Coordinate system, carbon and hydrogen labels used to present the Cartesian coordinates in Tables VI and VII.

## Tables

Harmonic frequencies (, ) calculated at and level of theory that deviate more than upon change of basis set. Both calculations used the symmetry (constrained) molecular geometry optimized at the corresponding level of theory.

Harmonic frequencies (, ) calculated at and level of theory that deviate more than upon change of basis set. Both calculations used the symmetry (constrained) molecular geometry optimized at the corresponding level of theory.

All and harmonic frequencies (, ), infrared (I, km/mole), and Raman (Raman, ) intensities calculated at level compared with the corresponding and paired , normal modes properties calculated at . The table is a numerical illustration of how the calculated and normal modes defer in frequency and/or intensity upon symmetry reduction.

All and harmonic frequencies (, ), infrared (I, km/mole), and Raman (Raman, ) intensities calculated at level compared with the corresponding and paired , normal modes properties calculated at . The table is a numerical illustration of how the calculated and normal modes defer in frequency and/or intensity upon symmetry reduction.

Harmonic frequencies ( in ) and Raman intensities (Raman in ) of the two normal modes that depended on the basis set: or . Both calculations were conducted at the symmetrical minimum obtained at level of theory.

Harmonic frequencies ( in ) and Raman intensities (Raman in ) of the two normal modes that depended on the basis set: or . Both calculations were conducted at the symmetrical minimum obtained at level of theory.

Experimental (fundamental) wave numbers ( in ), theoretical (harmonic) frequencies ( in ) and the corresponding experimental/calculated infrared intensities (I in km/mole).

Experimental (fundamental) wave numbers ( in ), theoretical (harmonic) frequencies ( in ) and the corresponding experimental/calculated infrared intensities (I in km/mole).

Experimental (fundamental) wave numbers ( in ) in solid state, theoretical (harmonic) frequencies ( in ), and their corresponding experimental/calculated Raman intensities (Raman in ).

Experimental (fundamental) wave numbers ( in ) in solid state, theoretical (harmonic) frequencies ( in ), and their corresponding experimental/calculated Raman intensities (Raman in ).

Cartesian coordinates (angstrom) ( symmetry unique atoms) of neutral coronene from Ref. 11 (coordinates of the hydrogen atoms not published). The choice of the coordinate system and the nuclei labels are depicted in Fig. 7.

Cartesian coordinates (angstrom) ( symmetry unique atoms) of neutral coronene from Ref. 11 (coordinates of the hydrogen atoms not published). The choice of the coordinate system and the nuclei labels are depicted in Fig. 7.

Cartesian coordinates (angstrom) ( symmetry unique atoms) of the optimized coronene for comparison to the x-ray data (Table VI). The coordinate system and the nuclei labels are depicted on Fig. 7.

Cartesian coordinates (angstrom) ( symmetry unique atoms) of the optimized coronene for comparison to the x-ray data (Table VI). The coordinate system and the nuclei labels are depicted on Fig. 7.

Mulliken gross population of atomic orbitals condensed to the implied core, -bonding, -bonding, polarization and total electron density on each atom of coronene. The raw data is extracted from a calculation conducted with GAMESS-UK (Ref. 13) at the stationary point. The coordinate system and the nuclei labels are depicted on Fig. 7.

Mulliken gross population of atomic orbitals condensed to the implied core, -bonding, -bonding, polarization and total electron density on each atom of coronene. The raw data is extracted from a calculation conducted with GAMESS-UK (Ref. 13) at the stationary point. The coordinate system and the nuclei labels are depicted on Fig. 7.

Mulliken gross population of atomic orbitals condensed to the implied core, -bonding, -bonding, polarization, and total electron density on each atom of coronene. The raw data is extracted from a calculation conducted with GAMESS-UK (Ref. 13) at the stationary point. The coordinate system and the nuclei labels are depicted on Fig. 7.

Mulliken gross population of atomic orbitals condensed to the implied core, -bonding, -bonding, polarization, and total electron density on each atom of coronene. The raw data is extracted from a calculation conducted with GAMESS-UK (Ref. 13) at the stationary point. The coordinate system and the nuclei labels are depicted on Fig. 7.

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