highlighted in red, those without in black. Up-pumping is
considered into the region 200–700 cm
−1 with
X max ¼ 200 cm
−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Fig. 4.9
Integration of X
2
ð Þ generated from overtone pathways from
N = 2–6. Materials with explosophoric –NO 2 moieties are
highlighted red, those without in black. Up-pumping is
considered into the region 200–700 cm
−1
with X max ¼ 200 cm
−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Fig. 4.10 Integration of X
2
ð Þ generated from the overtone pathways for
N = 2–3. The –NO 2 containing materials are highlighted in
red, those without in black. No restrictions are placed on X max
or the upper frequency bound for the doorway modes . . . . . . . . 132
Fig. 4.11 X
2
ð Þ for the molecular energetic materials. X
2
ð Þ for NTO is
given for (black) X
NTO
ð
Þ
max
¼ 200 cm
−1 and (green) X
NTO
ð
Þ
max
¼
240 cm
−1 . Plots are generated according to Eq. 4.1 and under
restriction of x 1 \2X max and x 2 \X max . Vertical dotted lines
indicate X max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Fig. 4.12 The full X
2
ð Þ for ABT (black), alongside the single phonon
DOS g(xÞ (orange) and the projection of X
2
ð Þ onto the DOS,
P(X
2
ð Þ ) (blue). Figure from Ref. [64], https://doi.org/10.1039/
C9TA06209B. Copyright CC-BY . . . . . . . . . . . . . . . . . . . . . . . . 135
Fig. 4.13 Integration of X
2
ð Þ from combination pathways. Compounds
containing –NO 2 explosophores are highlighted in red. Note
that X
2
ð Þ is restricted to a maximum of 3 X max given the
restrictions of x 1 \2X max and x 2 \X max . . . . . . . . . . . . . . . . . . 135
Fig. 4.14 Construction of the two-layered approach for vibrational
up-pumping for a-FOX-7. (Top) The phonon density of states
(blue) is shown, along with the first overtone density of states
(green). (Bottom) Recasting the overtone populations onto the
phonon density of states in the region X max \x\2X max
(highlighted by red box) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Fig. 4.15 Relative up-pumping rates according to the two-layered model.
Note that X
2
ð Þ is restricted to a maximum of 3 X max given the
restrictions of x 1 \2X max and x 2 \X max . Compounds
containing –NO 2 explosophores are highlighted in red . . . . . . . . 138
Fig. 4.16 Relative up-pumping rates according to the two-layered model.
Only the up-pumping contribution to 2X max \x\3X max is
considered here . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Fig. 4.17 Bose-Einstein populations as a function of frequency at (blue)
300 K, (red) 500 K and (green) 1000 K . . . . . . . . . . . . . . . . . . . 140
xxiv
List of Figures
considered into the region 200–700 cm
−1 with
X max ¼ 200 cm
−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Fig. 4.9
Integration of X
2
ð Þ generated from overtone pathways from
N = 2–6. Materials with explosophoric –NO 2 moieties are
highlighted red, those without in black. Up-pumping is
considered into the region 200–700 cm
−1
with X max ¼ 200 cm
−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Fig. 4.10 Integration of X
2
ð Þ generated from the overtone pathways for
N = 2–3. The –NO 2 containing materials are highlighted in
red, those without in black. No restrictions are placed on X max
or the upper frequency bound for the doorway modes . . . . . . . . 132
Fig. 4.11 X
2
ð Þ for the molecular energetic materials. X
2
ð Þ for NTO is
given for (black) X
NTO
ð
Þ
max
¼ 200 cm
−1 and (green) X
NTO
ð
Þ
max
¼
240 cm
−1 . Plots are generated according to Eq. 4.1 and under
restriction of x 1 \2X max and x 2 \X max . Vertical dotted lines
indicate X max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Fig. 4.12 The full X
2
ð Þ for ABT (black), alongside the single phonon
DOS g(xÞ (orange) and the projection of X
2
ð Þ onto the DOS,
P(X
2
ð Þ ) (blue). Figure from Ref. [64], https://doi.org/10.1039/
C9TA06209B. Copyright CC-BY . . . . . . . . . . . . . . . . . . . . . . . . 135
Fig. 4.13 Integration of X
2
ð Þ from combination pathways. Compounds
containing –NO 2 explosophores are highlighted in red. Note
that X
2
ð Þ is restricted to a maximum of 3 X max given the
restrictions of x 1 \2X max and x 2 \X max . . . . . . . . . . . . . . . . . . 135
Fig. 4.14 Construction of the two-layered approach for vibrational
up-pumping for a-FOX-7. (Top) The phonon density of states
(blue) is shown, along with the first overtone density of states
(green). (Bottom) Recasting the overtone populations onto the
phonon density of states in the region X max \x\2X max
(highlighted by red box) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Fig. 4.15 Relative up-pumping rates according to the two-layered model.
Note that X
2
ð Þ is restricted to a maximum of 3 X max given the
restrictions of x 1 \2X max and x 2 \X max . Compounds
containing –NO 2 explosophores are highlighted in red . . . . . . . . 138
Fig. 4.16 Relative up-pumping rates according to the two-layered model.
Only the up-pumping contribution to 2X max \x\3X max is
considered here . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Fig. 4.17 Bose-Einstein populations as a function of frequency at (blue)
300 K, (red) 500 K and (green) 1000 K . . . . . . . . . . . . . . . . . . . 140
xxiv
List of Figures