The effective isotropy of the hydrogen local potential in biphenyl and other hydrocarbons

Abstract

We present an experimental investigation of the hydrogen nuclear momentum distribution in biphenyl using deep inelastic neutron scattering. Our experimental results suggest that the local potential affecting hydrogen is both harmonic and isotropic within experimental uncertainties. This feature is interpreted as a consequence of the central limit theorem, whereby the three-dimensional momentum distribution is expected to become a purely Gaussian function as the number of independent vibrational modes in a system increases. We also performed ab initio phonon calculations on biphenyl and other saturated hydrocarbons, from methane to decane. From the results of the simulations, one can observe that the nuclear momentum distribution becomes more isotropic as the number of atoms and normal modes in the molecule increases. Moreover, the predicted theoretical anisotropy in biphenyl is clearly larger than in the experiment. The reason is that the total number of normal modes necessary to reproduce the experimental results is much larger than the number of normal modes encompassed by a single unit cell due to the presence of structural disorder and intermolecular interactions in the real crystal, as well as coupling of different normal modes. Finally, experimental data were collected, over a subset of detectors on the VESUVIO spectrometer at ISIS, with a novel setup to increase the count rate and signal-to-background ratio. We envision that such an optimized experimental setup can provide faster measurements and more stringent constraints for phonon calculations.

The correction of Inelastic Neutron Scattering data of organic samples using the Average Functional Group Approximation

“…While we could not find an experimental value to compare this result with, we note that in the case of biphenyl investigated in Ref. [32] at room temperature, the relative difference between the calculated and experimental MSDs was found lower than 20%, and the difference should decrease significantly at base temperatures. Similarly, as anticipated, the total scattering cross section, σ(E) for triptindane per formula unit was calculated using the AFGA approximation included within the NCrystal module [34], and it is reported in Figure 3 for sample temperatures of both 20 K, similar to the one used for experiments on TOSCA, and 300 K. The lowtemperature cross section is a clear example of how such function changes drastically as a function of the incident neutron energy, moving from the sum of free scattering cross sections, of hydrogens and carbons in the molecule, at epithermal neutron energies, to the (approximate) sum of bound scattering cross sections, of the same elements, in the cold-neutron energy limit.…”

Nuclear quantum dynamics in Hexamethylenetetramine and its deuterated counterpart: a DFT-augmented neutron study

“…Figure 13 clearly shows that the HLD approximation accounts very well for the experimental NMD widths of carbon and nitrogen in HMT, whereas it fails to properly account for the figures 15 and 16). Overall, the vanishing value of c 4 in the signal's isotropic harmonic local binding potential [112], and thus carbon and nitrogen in HMT and DHMT are, within the experimental accuracy, described very well by isotropic and harmonic potentials. Thus, we limit our discussion to the nuclear quantum dynamics of protons (deuterons) in HMT (DHMT).…”

Thermal neutron cross sections of amino acids from average contributions of functional groups

“…Finally, u v, j is the related atomic displacement, expressed as the difference of the time-dependent and mean nuclear positions. Additional details regarding the calculation of eigenvectors and eigenfrequencies were reported in references [85,86].…”