Combined experimental and computational study of the pressure dependence of the vibrational spectrum of solid picene C${}_{22}$H${}_{14}$

We present high-quality optical data and density functional perturbation theory calculations for the vibrational spectrum of solid picene (C${}_{22}$H${}_{14}$) under pressure up to 8 GPa. First-principles calculations reproduce with a remarkable accuracy the pressure effects on both frequency and intensities of the observed phonon peaks. We use the projection on molecular eigenmodes to unambiguously fit the experimental spectra, resolving complicated spectral structures, in a system with hundreds of phonon modes. With these projections, we can also quantify the loss of molecular character under pressure. Our results indicate that picene, despite a $\sim 20\%$ compression of the unit cell, remains substantially a molecular solid up to 8 GPa, with phonon modes displaying a smooth and uniform hardening with pressure, without any evidence of structural phase transitions. The Grüneisen parameter of the 1380 cm${}^{-1}$ $a_1$ Raman peak (${\gamma }_p=0.1$) is much lower than the effective value (${\gamma }_d=0.8$) due to K doping. Therefore, doping and pressure have very different effects and it can be argued that softening of the 1380 cm${}^{-1}$ mode is probably due to coupling with electronic states in K-doped solid picene.

Figure 1

Crystal structure of solid picene. (a) Unit cell, comprising two molecules. (b) Definition of distance and angle $\alpha$ between the molecules. (c) Top view of a single picene molecule (C${}_{22}$H${}_{14}$) and definition of the intramolecular distances. Carbon and hydrogen atoms are shown in red and white, respectively.

Figure 2

Experimental (upper panel) and theoretical (lower panel) IR spectra within the range of 400–1700 cm${}^{-1}$ at selected pressures. We make a convolution of the computed DFT spectra with a Lorentzian profile with 10 cm${}^{-1}$ linewidth to ease comparison with experiment. Notice that experimental peaks close to 800 cm${}^{-1}$ show saturation effects (look at the dotted lines).

Figure 3

Experimental (upper panel) and theoretical (lower panel) Raman spectra within the range 200–1600 cm${}^{-1}$ at selected pressures. We make a convolution of the computed DFT spectra with a Lorentzian profile with 10 cm${}^{-1}$ linewidth to ease comparison with experiment. The shaded region around 1350 cm${}^{-1}$ in the experimental spectra is where the Raman peaks of diamond appear.

Figure 4

Equation of state of solid picene under pressure, from DFT calculations. (a) Energy vs volume relation. Total energies from density functional theory (symbols), fitted with Birch-Murnaghan equation of state (line). The inset shows an enlargement of the region around the energy minimum. (b) Corresponding $p$ vs $V$ relation. (c) Evolution of the intermolecular angle $\alpha$; (d) intramolecular long and short distances $ld$ and $sd$ divided by their equilibrium value—for definitions, see Fig. 1; (e) distance between the geometric centres of the two molecules, as a function of the unit-cell volume.

Figure 5

Decomposition of the theoretical Raman (top) and IR (bottom) spectra into crystalline and molecular modes (see text). The irreducible representation of the corresponding molecular modes is indicated in correspondence of the peaks; greek letters indicate peaks that result from the superposition of more than one mode (see Table ). The red dotted lines are guidelines for the eyes for modes which are both IR and Raman active.

Figure 6

(a) The mean of the largest projections $\overline{A_{\Pi }}$ vs pressure. (b)–(d) Relative frequency of the molecular basis states $F_{\mathrm{mol}}$ needed to reconstruct the crystal phonon mode with an accuracy of at least 0.9 for $p=(0,3,6)$ GPa.

Figure 7

The Raman modes of picene around 1380 cm${}^{-1}$ at different external pressures. The experimental data are presented in panel (a). The computed spectra presented in panel (b) are obtained through a convolution of the DFT cross sections with a Lorentzian function to mimic the experimental broadening; see panels (c)–(e). Examples of the spectral deconvolution at two pressures are shown in panels (f) and (g). Panel (h) shows the pressure dependence of the frequency of the component which has the highest intensity in experiment (blue) and theory (red).

Figure 8

The IR modes of picene around 415 cm${}^{-1}$ at different external pressures. Panels are organized according to the same scheme as in Fig. 7. In panels (c)–(e), we indicate the symmetry of the main molecular modes for the most intense calculated peaks. With $+/-$ we indicate the two components of a Davydov pair.

Figure 9

Hinton plot for the matrix elements ${\Pi }_{mn}^{\alpha }$ of crystal phonon eigenstates $|{\Psi }_m\rangle$ on molecular vibrational eigenstates $|{\psi }_n^{\alpha }\rangle$. The area of the colored square is proportional to the square of the absolute value of the respective scalar product (see text for details); red and blue indicate a positive or negative sign of the scalar product ($+/-$).

Figure 10

Pressure evolution of the frequencies of modes forming a Davydov pair, according to Eq. (3) for two different energy ranges: (a) 520 to $575{\mathrm{cm}}^{-1}$ and from (b) 1390 to $1450{\mathrm{cm}}^{-1}$. Davydov pairs are plotted with the same color/symbol (blue/diamond, red/hexagon, green/circle). The symbols are calculated points and the dashed lines are guidelines for the eyes.

Figure 11

Raman modes of crystalline picene around 650 cm${}^{-1}$ at different external pressures. The experimental data are presented in panel (a). The computed spectra are presented in panel (b) are obtained by convolving the DFT cross sections [see panels (c)–(e)] with a Lorentzian function to mimic the experimental broadening. Examples of the spectral deconvolution at two pressures are shown in panels (f) and (g). Panel (h) shows the pressure dependence of the frequency of the component which has the highest intensity in experiment (blue) and theory (red). For the major calculated peaks, the symmetry of the main molecular modes are given [see panels (c)–(e)]. Linear combinations are shortened as, e.g., $a_{121}{b}_{12}=a_1+a_2+a_1+b_1+b_2$, where the order is descending according to their contribution.

Figure 12

The IR modes of picene around 1440 cm${}^{-1}$ at different external pressures. Panels are organized according to the same scheme as in Fig. 11.