4.4 Methods
119
Electronic band structures were calculated in CRYSTAL17 [42] using localised
basis sets, available from the CRYSTAL17 database and selected due to previous
success with similar materials and DFT functionals (H- H_pob_TZVP_2012 [43]; CC_m-6-311G(d)_Heyd_2005 [44]; N- N_m-6-311G(d)_Heyd_2005 [44]; O–O_m6-311G(2d)_Heyd_2005 [44]. To ensure closest reproduction of experimental results,
all calculations were performed on the experimental geometries. The band structures
were calculated using the HSE06 [44], B3PW91 [45] and PBE [46] functionals. For
all materials, the tolerances (TOLINTEG) were set at 7 7 7 9 30 (as recommended
for use with these basis sets [44]). The electronic structure was sampled across a
regular grid of points, with ca. 120 points sampled in each material.
Inelastic Neutron Scattering Spectroscopy. All INS spectra were collected using
the TOSCA spectrometer at the ISIS Neutron and Muon source [47, 48]. Samples (ca.
1.5 g) were placed in aluminium sample holders. Samples were cooled to ca. 10 K
and collected for a total of ca. 400 μAh. The sample temperature was subsequently
heated in steps of 50 K to a maximum of 200 K for β-HMX and TATB, and 150 K
for α-FOX-7. Data were collected at each 50 K interval. Both forward and backscattered data were summed and corrected for scattering from the sample holder
and background. All data processing was done using Mantid [49]. Simulated INS
spectra were generated using ABINS [50], as implemented in Mantid. Only first
order quantum events (i.e. the fundamentals) are considered in the simulation of INS
spectra.
Density of States. All g(ω) are inherently normalized to 3N . Consistent with the
‘indirect’ up-pumping model (i.e. where up-pumped energy thermalises across the
internal vibrational manifold), the two-phonon density of states,
(2) is normalized
by
(g(ω)). This follows the procedure suggested previously for the treatment of
molecular materials [19, 23].
4.5 Results and Discussion
4.5.1 Electronic Structure
For large systems, the use of high level functionals such as HSE06 are computationally demanding. It has been shown that the hybrid GGA functional B3PW91
is somewhat cheaper, and offers excellent agreement with experimental results for
electronic band gap (E g ) prediction across a broad range of inorganic materials [51,
52]. It was therefore of interest to consider these two methods for application to
molecular materials, and compare to a standard GGA functional, PBE. Only limited
experimental data is available for E g for the materials studied here. Experimental
UV-Vis spectra have been documented for β-HMX [53]. While the fundamental
band gap (i.e. the difference between the ionization potential and electron affinities)
is in principles different to the optical band gap (which is stabilized by electron-hole
interactions), the discrepancy is often small in solid state materials [54], and hence
119
Electronic band structures were calculated in CRYSTAL17 [42] using localised
basis sets, available from the CRYSTAL17 database and selected due to previous
success with similar materials and DFT functionals (H- H_pob_TZVP_2012 [43]; CC_m-6-311G(d)_Heyd_2005 [44]; N- N_m-6-311G(d)_Heyd_2005 [44]; O–O_m6-311G(2d)_Heyd_2005 [44]. To ensure closest reproduction of experimental results,
all calculations were performed on the experimental geometries. The band structures
were calculated using the HSE06 [44], B3PW91 [45] and PBE [46] functionals. For
all materials, the tolerances (TOLINTEG) were set at 7 7 7 9 30 (as recommended
for use with these basis sets [44]). The electronic structure was sampled across a
regular grid of points, with ca. 120 points sampled in each material.
Inelastic Neutron Scattering Spectroscopy. All INS spectra were collected using
the TOSCA spectrometer at the ISIS Neutron and Muon source [47, 48]. Samples (ca.
1.5 g) were placed in aluminium sample holders. Samples were cooled to ca. 10 K
and collected for a total of ca. 400 μAh. The sample temperature was subsequently
heated in steps of 50 K to a maximum of 200 K for β-HMX and TATB, and 150 K
for α-FOX-7. Data were collected at each 50 K interval. Both forward and backscattered data were summed and corrected for scattering from the sample holder
and background. All data processing was done using Mantid [49]. Simulated INS
spectra were generated using ABINS [50], as implemented in Mantid. Only first
order quantum events (i.e. the fundamentals) are considered in the simulation of INS
spectra.
Density of States. All g(ω) are inherently normalized to 3N . Consistent with the
‘indirect’ up-pumping model (i.e. where up-pumped energy thermalises across the
internal vibrational manifold), the two-phonon density of states,
(2) is normalized
by
(g(ω)). This follows the procedure suggested previously for the treatment of
molecular materials [19, 23].
4.5 Results and Discussion
4.5.1 Electronic Structure
For large systems, the use of high level functionals such as HSE06 are computationally demanding. It has been shown that the hybrid GGA functional B3PW91
is somewhat cheaper, and offers excellent agreement with experimental results for
electronic band gap (E g ) prediction across a broad range of inorganic materials [51,
52]. It was therefore of interest to consider these two methods for application to
molecular materials, and compare to a standard GGA functional, PBE. Only limited
experimental data is available for E g for the materials studied here. Experimental
UV-Vis spectra have been documented for β-HMX [53]. While the fundamental
band gap (i.e. the difference between the ionization potential and electron affinities)
is in principles different to the optical band gap (which is stabilized by electron-hole
interactions), the discrepancy is often small in solid state materials [54], and hence