Vibrational Dynamics of Crystalline 4-Phenylbenzaldehyde from INS Spectra and Periodic DFT Calculations

Abstract

The present work emphasizes the value of periodic density functional theory (DFT) calculations in the assessment of the vibrational spectra of molecular crystals. Periodic calculations provide a nearly one-to-one match between the calculated and observed bands in the inelastic neutron scattering (INS) spectrum of crystalline 4-phenylbenzaldehyde, thus validating their assignment and correcting previous reports based on single molecule calculations. The calculations allow the unambiguous assignment of the phenyl torsional mode at ca. 118-128 cm^-1, from which a phenyl torsional barrier of ca. 4000 cm^-1 is derived, and the identification of the collective mode involving the antitranslational motion of CH···O bonded pairs, a hallmark vibrational mode of systems where C-H···O contacts are an important feature.

Keywords: C-H···O hydrogen bonds; density functional theory; inelastic neutron scattering; molecular crystal; torsional potential; vibrational assignment.

Figure 1

Representation of 4-phenylbenzaldehyde, with the atom labeling used throughout the text (left) and fragment of the crystal structure, evidencing the two types of dimer present in the crystal (right) [21].

Figure 2

The inelastic neutron scattering (INS) spectra of 4-phenylbenzadhyde in the 25–1800 cm⁻¹ range: experimental (top), simulated from periodic calculations (middle) and from single molecule discrete calculations (bottom).

Figure 3

Atomic displacements of the normal mode at ca. 832 cm⁻¹, assigned to a νC-C stretching mode of the benzaldehyde ring.

Figure 4

Vibrational spectra of 4-phenylbenzaldehyde in the spectral region below 450 cm⁻¹. From top to bottom: INS spectra (experimental, calculated), far-infrared spectra (experimental, calculated) and Raman spectrum (experimental).

Figure 5

Potential curves for internal rotation of –CHO (top) and C₆H₅– (bottom) groups in 4-phenylbenzaldehyde. Dashed lines from single molecule calculations (G09, energy vs. dihedral angle), solid lines from experimental wavenumber in the crystal (Barrier [26]). The G09 potential curve for phenyl internal rotation (blue dashed line) is described by the terms V₂ = −241 cm⁻¹, V₄ = 743 cm⁻¹, V₆ = 126 cm⁻¹ and V₈ = 51 cm⁻¹.

Figure 6

Schematic representation of atomic displacements for the external modes at 45 cm⁻¹, 70 cm⁻¹ (translations), 86 cm⁻¹ and 101 cm⁻¹ (librations). For better readability, only the total displacement of the molecules is shown for translations and only the displacements of heavy atoms are shown for librations.