Computing inelastic neutron scattering spectra from molecular dynamics trajectories

Abstract

Inelastic neutron scattering (INS) provides a weighted density of phonon modes. Currently, INS spectra can only be interpreted for perfectly crystalline materials because of high computational cost for electronic simulations. INS has the potential to provide detailed morphological information if sufficiently large volumes and appropriate structural variety are simulated. Here, we propose a method that allows direct comparison between INS data with molecular dynamics simulations, a simulation method that is frequently used to simulate semicrystalline/amorphous materials. We illustrate the technique by analyzing spectra of a well-studied conjugated polymer, poly(3-hexylthiophene-2,5-diyl) (P3HT) and conclude that our technique provides improved volume and structural variety, but that the classical force field requires improvement before the morphology can be accurately interpreted.

Figure 1

(a,b) Schematic depicting neutron scattering off a prolate anisotropic oscillator (oval wireframe object) in two different orientations demonstrating how molecular orientation changes the available scattering processes. In (a) the momentum transfer is directed solely along the short axis of the oscillator, creating vibrationally excitations along that axis. In (b) the oscillator is rotated such that the momentum transfer is directed along the long axis of the oscillator, which has smaller spacing between energy levels. (c) Potential energy surface for a harmonic oscillator. The quantum mechanical levels are represented by grey dashed lines, and the rough red line represents a trajectory of a classical simulation.

Figure 2

Comparison between experimental INS spectrum for crystalline P3HT (defined as the difference between the semicrystalline spectrum and 55% of the amorphous spectrum) and a simulated spectrum from molecular dynamics. The spectral contributions for individual overtones are also shown. The MD spectrum was convolved by a variable width Gaussian with $\sigma =$ 0.01E, where E is the energy transfer given by the values on the horizontal axis of the plot.

Figure 3

(a) Comparison between experimental INS spectrum, DFT simulated spectrum, and MD simulated spectrum. The MD spectrum was convolved by a Gaussian of width 0.01E, where E is the energy transfer. (b) The INS spectrum calculated from the normal modes of a supercell of the DFT structure using the MD forcefield is also plotted.

Figure 4

Comparison between MD simulated spectra for crystalline and amorphous P3HT materials. (a) Comparison between the MD simulated spectra of the crystalline and amorphous phases. (b) Comparison between experimental INS spectrum for regiorandom (RRa) P3HT, and the amorphous MD simulated spectrum. (c) Radial distribution functions comparing crystalline and amorphous regions of P3HT; the inset is the same plot expanded at low probability densities to demonstrate the differences between the two distributions. The MD spectrum was convolved by a Gaussian of width 0.01E, where E is the energy transfer.