doi.org/10.26434/chemrxiv.5362630.v2

Relaxed structure of typical nitro explosives in the excited state:observation, implication and applicationGenbai Chu, Zuhua Yang, Tao Xi, Jianting Xin, Yongqiang Zhao, Weihua He, Min Shui, Yuqiu Gu, YingXiong, Tao Xu

Submitted date: 13/11/2017 • Posted date: 13/11/2017Licence: CC BY-NC-ND 4.0Citation information: Chu, Genbai; Yang, Zuhua; Xi, Tao; Xin, Jianting; Zhao, Yongqiang; He, Weihua; et al.(2017): Relaxed structure of typical nitro explosives in the excited state: observation, implication andapplication. ChemRxiv. Preprint.

Understanding the structural, geometrical and chemical changes that occur after electronic excitation isessential to unraveling the inherent mechanism of nitro explosives. In this work, relaxed structures of typicalnitro explosives in the excited state are investigated by time-dependent density functional theory. During theexcitation process, nitro group becomes activated and then relaxes, leading to a relaxed structure. All five nitroexplosives exhibit a similar behavior, and impact sensitivity is related to excitation energy of relaxed structure.High sensitivity d-HMX has a lower excitation energy for relaxed structure than b-HMX. This work offers anovel insight into energetic material.

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Relaxed structure of typical nitro explosives in the excited state:

observation, implication and application

Genbai Chu1, Zuhua Yang1, Tao Xi1, Jianting Xin1, Yongqiang Zhao1, Weihua He1,

Min Shui1*, Yuqiu Gu1*, Ying Xiong2, Tao Xu2

1Science and Technology on Plasma Physics Laboratory, Research Center of Laser Fusion, China

Academy of Engineering Physics, Mianyang 621900, P. R. China

2Institute of Chemical Materials, China Academy of Engineering Physics, Mianyang 621900, P. R.

China

Corresponding authors: shm@caep.cn, yqgu@caep.cn

Relaxed structure of typical nitro explosives in the excited state:

observation, implication and application

Abstract: Understanding the structural, geometrical and chemical changes that occur after

electronic excitation is essential to unraveling the inherent mechanism of nitro explosives. In this

work, relaxed structures of typical nitro explosives in the excited state are investigated by time-

dependent density functional theory. During the excitation process, nitro group becomes activated

and then relaxes, leading to a relaxed structure. All five nitro explosives exhibit a similar behavior,

and impact sensitivity is related to excitation energy of relaxed structure. High sensitivity -HMX

has a lower excitation energy for relaxed structure than -HMX. This work offers a novel insight

into energetic material.

1. Introduction

Electronic excitation and electron transfer processes play important roles in photo-initiated

reactions [1-4]. Excited states have also been recognized as having vital roles in the conversion of

energy in energetic materials (EMs) [5-7], that are used widely in many fields. However, the

excitation processes of these materials, at the molecular level, are largely unknown. Exploring the

structural, geometrical and chemical changes after electronic excitation is essential to unraveling

the inherent physical and chemical mechanisms [8]. Until now, the majority of EMs are nitro

explosives [7,9-12]. Nitro group is the most important functional group, which has been established

to evaluate molecular stability, impact sensitivity, and nitrating reaction [11,13]. It is known that the

π-anti-bonding orbital of nitro group (NO2 π* orbital) is a large, conjugated and unoccupied orbital

of relatively low energy. During excitation processes, an electron is promoted mainly into NO2 π*

orbital for nitro-containing species. Hence, nitro group affects significantly photo-physical behavior

of molecules [14-21].

From a practical perspective, understanding the sensitivity of energetic materials also serves to

improve reliability and safety, which has been an area of research focus [11,22,23]. A number of

theoretical methods have been established to show that there is correlation between molecular

properties and sensitivity, while not feasible in some cases. It is a long one of the challenges in

understanding the significant difference between -HMX (1,3,5,7-tetranitro-1,3,5,7-tetraza-

cycloctane) boat structure and -HMX chair structure [24-26]. It is also found that the molecular

decomposition process of -HMX from its ground state hardly differs from -HMX. On this

situation, polarization-induced charge ions of -HMX has been proposed to explain the different

sensitivity [27,28] . New insight into the molecular conformation is severely required, to unravel

the high sensitivity of -HMX and identify whether the intra-molecular interaction contributes to

the sensitivity.

In this work, we present an investigation into the excitation and relaxation processes of some

typical nitro explosives, including RDX (1,3,5-trinitro-1,3,5-triazacyclohexane), -HMX, CL-20

(2,4,6,8,10,12-hexanitrohexaazaisowurtzitane), PETN (pentaerythritol tetranitrate) and LLM-105

(1-oxide-2,6-diamino-3,5-dinitropyrazine), using quantum chemical calculations. Electrons are

vertically excited to the low-lying excited states, which leads to the population of N-NO2 π* orbital.

The excited molecule then relaxes through vibrational cooling of an active nitro group. The

excitation energy of the relaxed structure is then calculated and the relationship with the impact

sensitivity is established. Furthermore, a study on relaxed structure of -HMX shows that its

excitation energy is 1.45 eV and the sensitivity is predicted to be 0.15m. The relaxed structure in

the excited state offers a new insight into the molecular conformation of HMX and inhibits potential

application in energetic materials.

2. Quantum chemical calculation methods

Time-dependent density functional theory (TD-DFT) is a moderate and reliable method for

excited-state calculations that has been utilized in many papers [29-31]. Herein, TD-DFT was

employed to study the excitation and relaxation processes of six typical nitro explosives: RDX, -

HMX, -HMX, CL-20, PETN, and LLM-105. The structures of the ground state (S0 state) and the

first singlet excited-state (S1 state) were optimized by TD-DFT methods at the B3LYP/6-311++g(d,p)

level. Vertical excitation energies were calculated at the same level, as were the Kohn-Sham orbitals,

orbital energies, and excitation energies. All calculations were performed using Gaussian 09

software [32]. Molecular information, orbitals, electron distributions and electronic excitation

analyses were obtained by wave function analyzer (Multi-wfn) [33]. The highest occupied

molecular orbitals (HOMOs) are labeled from HOMO-5 to HOMO-1, in increasing orbital energy,

while the lowest-unoccupied molecular orbitals (LUMOs) are labeled from LUMO+1 to LUMO+4.

3. Results

The initial geometrical structures, relaxed structures in the S1 states, orbitals, electron and hole

distributions of RDX and LLM-105 are presented in Fig. 1 and Fig. 2, respectively, while other nitro

explosives in Fig. S2-7 and Fig. S9. The excitation energies of the relaxed structures are presented

to explore the relationship with impact sensitivity.

There are five processes in the proposed mechanisms in Fig. 3, listed as following: 1. Photo-

excitation, 2. Relaxation in the excited state, 3. Radiative or non-radiative transition, 4. External

stimulation from the ground state, and 5. Excitation of relaxed structure. All explosives are shown

to perform similar ways and exhibit an inherent relationship between excitation energy and impact

sensitivity.

3.1 RDX, HMX, CL-20 and PETN

The vertical excitation and optical absorption processes of RDX have been studied previously

[34-36]. Herein, we briefly discuss the orbital energies and electron distributions of the frontier

orbitals to illustrate the application of this work. The low-lying excited states of RDX mainly arise

from the contributions of frontier MO pairs to the transition dipole moment, which corresponds to

nπ* transitions [34,36]. The relaxation process of RDX0 in the S1 state (vertical excitation of the

RDX0) proceeds via the nuclear motions of the active nitro groups, which become elongated due to

N-NO2 π* orbital. The relaxed S1 state of RDX (RDX1) exhibits two elongated bonds, N(7)-O(12)

and N(7)-O(13), at 1.294 and 1.296 Å, 0.073 and 0.076 Å longer than the analogous bonds in RDX0,

respectively. In addition, the N(4)-N(7) bond is found to be slightly elongated, from 1.431 Å in

RDX0 to 1.440 Å in RDX1. The electron in the LUMO+1 orbital is distributed mostly in one N-NO2

π* orbital. The orbital energy of LUMO+1 is reduced by 1.67 eV, compared to that of RDX0, while

the energies of other LUMOs are largely unaltered.

The electrons in HOMO-1 of RDX1 are mainly distributed as the lone pairs on O(12) and O(13).

The elongation of the two N(7)-O(12,13) bonds of RDX1, when transposed to the S0 state, increases

the energy of RDX0 by 1.86 eV (Table 2). The low-lying electronic excitation of RDX1 involves

major contributions from the HOMO-1 LUMO+1 pair. The orbitals involved in the transition,

which correspond to the excited electron and the hole, overlap with each other in the relaxed nitro

group. This transition is attributed to local excitation and the excitation energy for this transition is

calculated to be 1.53 eV, much lower than that of RDX0. Consequently, RDX1 exhibits an optical

absorption band at 800 nm, as shown in Fig. 4, which is different from that of RDX0.

-HMX0, CL-200 and PETN0 have a similar structures to RDX0 [7,9-11,35,37]. The detailed

relaxation processes are given in supplementary information. Herein, the excitation energies of

relaxed structures are calculated to be 1.60, 1.63 and 1.52 eV for -HMX1, CL-201 and PETN1,

respectively. New absorption bands are shown in the optical absorption spectra in Fig. 4.

3.2 LLM-105

LLM-105 is a new molecule with performance and sensitivity lying somewhere between HMX

and TATB [11]. HOMO-1 of LLM-1050 corresponds to an extended pseudo-π* system across the

entire molecule. The distribution of LUMO+1 corresponds to an N-NO2 π* orbital involving two

nitro groups and the central N atom. The low-lying excited state involves a major contribution from

the HOMO-1LUMO+1 transition dipole moment, which can be assigned to be a charge transfer

process.

The relaxation process of excited LLM-1050 proceeds via elongation of the two nitro groups. The

excitation energy of LLM-1051 is calculated to be 2.41 eV. It leads to a new absorption band in the

optical absorption spectrum in Fig. 4.

3.3 Relationship between excitation energy and impact sensitivity

The low-lying excited states of the relaxed structures involve major contribution from HOMO-1

LUMO+1 pairs. The hole and electron orbitals overlap with each other in the relaxed nitro group

of RDX1, -HMX1, CL-201 and PETN1. These transitions are attributed to local excitations, with

low excitation energies of 1.53, 1.60, 1.63 and 1.52 eV for RDX1, HMX1, CL-201 and PETN1,

respectively. The excitation energy of LLM-1051 is determined to be 2.41 eV, higher than the four

other explosives in this study, but lower than the value of 3.02 eV for TATB. These excitation

energies are consistent with the impact sensitivities of these molecules.

The excitation energy of an explosive is recognized to be an important factor in assessing the

transition probability of electronic excitation to a low-lying excited state. In this sense, we propose

that the excitation energy (EE) of relaxed structure is related to its impact sensitivity (H50) [11], in

Fig. 5. This relationship is a positive correlation and fitted with the expression very well.

3.4 Predication of high sensitivity of -HMX

The relaxed process of -HMX is similar to -HMX, while there is some differences in energy,

as shown in Fig. 6. The energy of -HMX is 0.09 eV higher than that of -HMX in the ground state,

and 0.08 eV higher in the excited state. After relaxation, the energy of -HMX1 is nearly the same

to -HMX1 in the excited state, while is 0.18 eV higher in the ground state.

The excitation energy of -HMX1 is determined to be 1.45eV, which is 0.15eV lower than that of

-HMX1. The value is in well agreement with the energy difference of 0.18 eV in the ground state.

It indicates that the energy between the relaxed conformers in the ground state leads to a decrease

in the excitation energy. In addition, the decrease in excitation energy of relaxed structure leads to

an increase in the sensitivity, as shown in Fig. 5. The impact sensitivity of -HMX is exhibited to

be 0.15m.

4. Discussion

It is of particular importance to discuss the insight provided by this information into the inherent

excitation/de-excitation mechanisms of these nitro-based explosives.

4.1 Experimental evidence for the relaxed structure

The photo-excitation process (process 1) is a widely studied process, and the excitation energy is

clearly seen in the steady optical absorption spectra [34,36,37]. The nitro group exhibits special

behavior owing to a large conjugated NO2 π* orbital [10,15,16,18,19,30], which has been shown to

be an energy pitfall for nitro explosives [15,16,18-20]. In this work, the electron is promoted to the

NO2 π* orbital upon excitation; this excitation energy is then trapped by active nitro groups that

relax, leading to a relaxed structure. The relaxation process (process 2) can be investigated by

transient absorption spectroscopy [4,21] and coherent anti-Stokes Raman spectroscopy [38]. The

excited state dynamics of TATB shows one absorption peak at 600 nm disappears and another peak

shifts from 470 to 450 nm, which indicates electron transfer into an activated nitro group. The

process happens in a time scale of 0.64 ps [39]. The Raman spectra show a clear vibrational cooling

dynamics of CH3NO2, while the authors suggest the phenomena is attributed to NO2 moiety [38].

This motion also favors ultrafast intersystem crossing to the triplet state of these nitro-substituted

species [15,16,18-21,30,31,39,40]. There is a distinct absorption band for triplet state of

2,2’,4,4’,6,6’-hexanitrostilbene (HNS), which is primarily populated from the minimal intersystem

crossing of the S1 state in 6 ps [21].

In addition, the radiative or non-radiative transition from the excited state (process 3) is evidenced

from the fluorescence spectrum. The new bands of these relaxed structures that appear in the visible

region correspond to experimentally radiative emission bands. With regard to the low fluorescence

quantum yields, it is unfortunate that, to the best of our knowledge, there are no reports on the

fluorescence bands of these explosives. But it is noticed that the emission spectra from shock-

induced RDX experiments show an emission band at 800 nm [41,42]. It can be referred as an

experimental evidence for process 3, since emissions usually happen at a relaxed excited state.

The re-investigation of the relaxed structures of nitro explosives in their ground states is essential.

External stimuli leads to a relaxed structure in the ground state (process 4). It is clear that the

elongation of the N-O bonds in the relaxed structures lead to electron transfer into nitro groups, in

particular the O n states of RDX, HMX, CL-20 and PETN; it also leads to obvious increase in energy

of ~2 eV in the ground state. To support the viewpoint, the intramolecular vibrational redistribution

show that the electron transfer and energy concentration into N-O bond of RDX under multi-photon

up-pumping condition, which have been observed by multiplex coherent anti-Stokes Raman

spectroscopy [43]. In this sense, the energy gap between HOMO-1 and LUMO+1 is distinctly

reduced as a result of this elongation. In addition, the orbitals corresponding to the excited electron

and remaining hole strongly overlap, facilitating electronic transition of relaxed structure (process

5). It is evidenced from the absorption peaks of RDX, which is close to the absorption spectra via

shock loaded RDX. In the experiment, a broad and featureless band in the visible spectral region

around 800 nm has been observed [44]. The broad and featureless band is ascribed to other

vibrational modes simultaneously excited in the shock-inducing RDX. But it is in fair agreement

with the absorption peaks of relaxed RDX in this work. From processes 3 and 5, the new bands of

relaxed structure facilitate the excitation/de-excitation process, when the nitro explosive under

extreme condition.

In general, the five processes have been evidenced from different experimental results. It is

feasible to understand the phenomena with the concept of relaxed structure.

4.2 Implication for energetic material in extreme condition

It should be pointed out the direct excitation of initial structure has been investigated via photons,

while energetic materials are initiated without photons or not transparent for photons. How it is

applied to the non-photon cases? It is essential to investigate the relaxed structure in the ground

state.

The excitation energy of relaxed structure is much smaller than that of direct excitation of initial

structure. For example, RDX, -HMX, PETN and CL-20 have much lower excitation energies of

~1.67 eV than the initial structure of ~4 eV. And the electron on the orbitals corresponding to the

excited electron and remaining hole strongly overlapped, facilitating electronic transition. When the

temperature is high, the thermal electronic transition is distinct via the relaxed structure. The thermal

excitation is different from that photo-initiated excitation, but feasible at present case via the relaxed

structure. Consequently, a large quantity of molecular explosives can be thermally excited, leading

to the induction of ultrafast reactions in the excited states.

The absorption and emission spectra from shock-induced RDX experiments show absorption and

emission bands under high pressure [41,42,44]. The bands at wavelength of 800 nm are close in

wavelength to the absorption bands of the relaxed structures calculated in this work. In addition, a

study on charge transfer in HMX and TATB under high temperatures and pressures, by molecular

simulation, has been reported [13]. From the distributions of the frontier orbitals of HMX, the HMX

molecule undergoes electron transfer into a nitro group at high temperature. The energy gap is also

reduced as a result of this electron transfer. This phenomenon also serves as evidence for the

explanation provided in this work.

The relaxed structure of the nitro group is important to nitro explosives, which is due to electronic

excitation and de-excitation transition probabilities are greatly increased as a result of the relaxed

structure. Whether or not similar characteristics exist in other EMs, such as metal azides [23] and

energetic polynitrogen compounds [45], among others, needs to be determined.

4.3 Application in high sensitivity of -HMX

The relaxed structure of -HMX behaves similarly to the -HMX, and the energies of the two in

the excited state are close to each other. But owing to the conformational change, there is a little

energy difference in the ground state and then it leads to a different excitation energy. In this sense,

the intra-molecular interaction contributes to a different excitation energy of relaxed structure and

results in a consequent impact sensitivity change. The high sensitivity of -HMX serves as an

example for the sensitivity of the two materials [27,28] .

This work offers a new insight into the high sensitivity -HMX, and a method to potentially assess

impact sensitivity for different conformations of EMs.

Conclusions

In the work, the TD-DFT method has been used to investigate the excitation and relaxation of

some nitro explosives, including RDX, -HMX, CL20, PETN and LLM-105. In the initial structures,

the low-lying excitations of the five explosives involve major nπ* transitions. The excitation

energy is transferred into the nitro groups, which relax through vibrational cooling leading to relaxed,

excited-state structures in which the N-O bonds of the nitro groups are elongated.

The electron is transferred into the relaxed nitro group through O n orbitals in the S0 state, which

overlaps with the NO2 π* orbital of the S1 state upon excitation. Hence, the accumulation of electron

density in the nitro group tends to decrease the excitation energy while greatly increasing the

transition probability. This work has shown that the excitation energy of the relaxed structure

correlates with the impact sensitivity of the nitro compound.

High sensitivity -HMX is revealed to the fact, which has a lower excitation energy of relaxed

structure than that of -HMX. This provides a novel and efficient method of potentially unraveling

the essence of energetic materials.

5. Acknowledgement

This work is supported by the National Natural Science Foundation of China (Grant

No.11504349).

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Figure captions

Figure 1. Initial structure (RDX0) and relaxed structure (RDX1) of RDX (top); and HOMO-1 and

LUMO+1 of RDX1 (bottom left and right), with electron (green) and hole (blue) distributions of

the S1 state in the middle.

Figure 2. Initial structure (LLM-1050) and relaxed structure (LLM-1051) of LLM-105 (top); and

HOMO-1 and LUMO+1 of LLM-105-S1 (bottom left and right), with electron (green) and hole

(blue) distributions of the S1 state in the middle.

Figure 3. Schematic of process 1-5 in the proposed mechanism.

Figure 4. Steady-state absorption spectra of the relaxed structures of five nitro explosives, which

shows new bands compared to those of the initial structures.

Figure 5. Relationship between impact sensitivity (H50, m) and the excitation energy (EE, eV) of

the relaxed structures.

Figure 6. Potential energy surface for key points of -HMX and -HMX in the S0 and S1 state.

Table captions

Table 1. Selected orbital energies (eV) of initial structures (-0) and relaxed structures (-1) of the five

nitro explosives in this work.

Table 2. Excitation energies (eV) to the S1 states of the initial structures (-0) and relaxed structures

(-1), and energy differences (eV) between the two structures in the S0 state.

Energy RDX -HMX CL20 PETN LLM-

105 TATB

Excitation

Energy

-0 4.46 4.62 4.60 4.83 3.05 3.67

-1 1.53 1.60 1.63 1.52 2.41 3.02

Energy

difference S0 1.86 1.93 1.86 1.98 0.33 0.40

Orbital RDX -HMX CL-20 PETN LLM-105

-0 -1 -0 -1 -0 -1 -0 -1 -0 -1

LUMO

+4 -0.98 -1.08 -2.55 -2.53 -3.26 -3.35 -2.76 -2.81 -0.84 -0.90

+3 -2.58 -2.76 -2.59 -2.56 -3.27 -3.38 -2.79 -2.89 -1.98 -2.00

+2 -2.72 -2.85 -3.22 -2.94 -3.36 -3.48 -2.84 -3.01 -3.10 -3.34

+1 -2.96 -4.63 -3.52 -4.90 -3.39 -5.23 -3.00 -5.23 -3.74 -4.16

HOMO

-1 -8.90 -7.97 -8.85 -8.28 -9.13 -8.65 -9.50 -8.61 -7.26 -7.06

-2 -8.90 -8.81 -8.96 -8.88 -9.42 -9.27 -9.60 -9.27 -7.89 -8.00

-3 -9.18 -9.08 -9.10 -8.94 -9.48 -9.46 -9.66 -9.65 -8.62 -8.54

-4 -9.22 -9.14 -9.32 -9.20 -9.66 -9.59 -9.70 -9.67 -8.90 -8.95

-5 -9.24 -9.35 -9.33 -9.22 -9.78 -9.64 -9.78 -9.73 -9.12 -9.15

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Graphical abstract:

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Supplementary information for the manuscript

Relaxed structure of typical nitro explosives in the excited state:

observation, implication and application

Genbai Chu1, Zuhua Yang1, Tao Xi1, Jianting Xin1, Yongqiang Zhao1, Weihua He1,

Min Shui1*, Yuqiu Gu1*, Ying Xiong2, Tao Xu2

1Science and Technology on Plasma Physics Laboratory, Research Center of Laser Fusion, China

Academy of Engineering Physics, Mianyang 621900, P. R. China

2Institute of Chemical Materials, China Academy of Engineering Physics, Mianyang 621900, P. R.

China

Corresponding authors: shm@caep.cn, yqgu@caep.cn

1. Quantum chemical calculation method Time-dependent density functional theory (TD-DFT) is a moderate and reliable method for

excited-state calculations that has been utilized in many papers. Although the TD-DFT method is

not as accurate as multi-configuration methods such as the complete-active-space self-consistent

field (CASSCF) method, it was utilized for the following reasons. Firstly, it is suitable for large

molecules and is inexpensive compared to the CASSCF method; and secondly, reliable results can

be obtained for related states of molecules [1,2]. In the end, results obtained at this level in this

work are representative.

2. Results

2.1 RDX

In the ground state, the RDX molecule (RDX0) possesses C3V symmetry [3-8]. The high-lying

HOMOs correspond to the lone pairs (n orbitals) that are mainly located on O atoms, in Fig. S1.

As shown in Table 1, the five HOMOs are relatively close to each other in energy, at around –9 eV.

The low-lying LUMOs are distributed mainly over the nitro groups and correspond to N-NO2 π*

orbitals. The first three LUMOs have similar energies of –2.96, –2.72 and –2.58 eV. The

HOMO-LUMO splitting in RDX0 is 5.94 eV, consistent with previous reports [9]. The low-lying

excited states of RDX mainly arise from the contributions of frontier MO pairs to the transition

dipole moment, which correspond to nπ* transitions [7,8]. The orbitals corresponding to the

hole and the excited electron associated with this transition are both displayed in Fig. S1. The

excitation process involves a major contribution from LUMO+1, which means that the excitation

energy is transferred into the nitro groups and activates them.

Figure S1. Orbital energiess of initial structure, HOMO-1, and LUMO+1 of initial structure

(RDX0), with electron (green) and hole (blue) distributions for the transition in the middle.

2.2 -HMX, CL-20 and PETN

-HMX0, CL-200 and PETN0 have a similar structures to RDX0 (Fig. S2–7) [3-5,10-12]. Owing

to the greater number of nitro groups, the orbital structures around the HOMOs of these three

explosives are predicted to be more complex than that of RDX0. They mostly correspond to

non-bonding electron; the n states on the oxygen and nitrogen atoms. The five HOMOs of

-HMX0 have orbital energies close to each other, as do those of CL-200 and PETN0. The LUMOs

simply correspond to N-NO2 π* orbitals, similar to that observed for RDX0. Two LUMOs in each

case also have energies close to each other. The low-lying excited states of -HMX0 involve

contributions of frontier MO pairs to the transition dipole moment. Likewise, the low-lying

excited states of -HMX0, CL-200 and PETN0 correspond to nπ* transitions, and the excitation

energy is transferred into two nitro groups in each molecule.

The relaxation process of each active nitro group, once again, proceeds via nuclear motion,

leading to relaxed structures. The two N(17)-O(21,22) bonds of -HMX1 are elongated by 0.086

and 0.075Å over those of -HMX0. Similarly, the two N(21)-O(29,30) bonds of CL-201 are

elongated by 0.081 and 0.083Å. There are also obvious elongations of the N(15)-O(16,17) bonds

in PETN1, by 0.078 and 0.070Å. As a consequence of structural relaxation, the energies of

-HMX1, CL-201 and PETN1 in the S1 state are reduced by 1.09, 1.13 and 1.34 eV over the initial,

vertically excited, S0 structures, respectively. The relaxation processes can, once again, be

attributed to vibrational cooling of the relevant nitro groups. Following cooling, the electron

distributions and excitation energies are transferred into the relaxed nitro groups, in particular, the

LUMO+1 orbitals of the relaxed structures.

On the contrary, elongations of the N-O bonds of the S0 structures lead to increases in energy of

the S0 states. The energies of -HMX1, CL-201 and PETN1 are 1.93, 1.86 and 1.98 eV higher than

those of -HMX0, CL-200 and PETN0 in their S0 states, respectively. It is interesting to note that

the energies of the HOMO-1 and LUMO+1 orbitals of -HMX1, CL-201 and PETN1 have

significantly changed when compared to those of -HMX0, CL-200 and PETN0, while other

orbital energies have not (Table 1). The energies of the HOMO-1s increase to –8.28, –8.65 and

–8.61 eV, in -HMX1, CL-201 and PETN1, respectively, which are 0.60, 0.62 and 0.66 eV higher

than the energies of the corresponding HOMO-2s. The distributions of the various HOMO-1s

mostly correspond to O n states. At the same time, the orbital energies of the LUMO+1s decrease

to –4.90, –5.23 and –5.23 eV, respectively, which are 1.96, 1.75 and 2.22 eV lower than those of

LUMO+2. The LUMO+1 distributions are predominately made up of N-NO2 π* orbitals. The

low-lying electronic excitations of -HMX1, CL-201 and PETN1 involve major contributions from

HOMO-1LUMO+1 pairs, as was observed for RDX1. The orbitals corresponding to the various

holes and excited electrons associated with these transitions overlap with each other in the relaxed

nitro groups. The excitation energies for these transitions are calculated to be 1.60, 1.63 and 1.52

eV for -HMX1, CL-201 and PETN1, respectively, much lower than that of -HMX0, CL-200 and

PETN0. This indicates that the S1 states of -HMX1, CL-201 and PETN1 are Franck-Condon

accessible from the corresponding S0 states, with the transition probabilities greatly increased by

local excitation. New absorption bands are shown in the optical absorption spectra in Fig. 4.

Figure S2. HOMO-1, HOMO-5 and LUMO+1 of initial structure (-HMX0), with electron (green)

and hole (blue) distributions for the transition in the middle.

Figure S3. Initial structure (-HMX0) and relaxed structure (-HMX1) of -HMX (top); and

HOMO-1 and LUMO+1 of -HMX1 (bottom left and right), with electron (green) and hole (blue)

distributions of the S1 state in the middle.

Figure S4. HOMO-1, HOMO-4 and LUMO+1 of initial structure (CL-200), with electron (green)

and hole (blue) distributions for the transition in the middle.

Figure S5. Initial structure (CL-200) and relaxed structure (CL-201) of CL-20 (top); and HOMO-1

and LUMO+1 of CL-201 (bottom left and right), with electron (green) and hole (blue)

distributions of the S1 state in the middle.

Figure S6. HOMO-1, LUMO+1 and LUMO+4 of initial structure (PETN0), with electron (green)

and hole (blue) distributions for the transition in the middle.

Figure S7. Initial structure (PETN0) and relaxed structure (PETN1) of PETN (top); and HOMO-1

and LUMO+1 of PETN1 (bottom left and right), with electron (green) and hole (blue) distributions

of the S1 state in the middle.

Figure S8. Steady-state absorption spectra of the initial structure and relaxed structures of five

nitro explosives.

2.3 LLM-105

LLM-105 is a new molecule with performance and sensitivity lying somewhere between HMX

and TATB [5]. It has a ring structure, which is different to RDX, HMX, CL-20 and PETN. The

HOMO-1 of LLM-1050 corresponds to an extended pseudo-π* system across the entire molecule

(Fig. S9), with an energy of –7.26 eV, 0.63 eV higher than that of HOMO-2. The distribution of

LUMO+1 also corresponds to an N-NO2 π* orbital involving two nitro groups and the central N

atom. It is a larger, more conjugated π* orbital than those of RDX, HMX and CL-20. The

LUMO+1 has an energy of –3.74 eV, which is 0.64 eV lower than that of LUMO+2. The

low-lying excited state involves a major contribution from the HOMO-1LUMO+1 transition

dipole moment. The excitation process can be assigned to be a charge transfer process, as shown

by the electron and hole orbitals that correspond to this transition. The excitation energy is

distributed equally over the two NO2 groups.

Figure S9. HOMO-1, LUMO+1 and LUMO+4 of initial structure (LLM-1050), with electron

(green) and hole (blue) distributions for the transition in the middle.

2.4 Predication of high sensitivity of -HMX

The initial and relaxed structures of -HMX are shown in Figure S10. The obvious differences

located at one nitro group and labeled in the figure. The N(18)-O(25) and N(18)-O(26) bonds are

elongated from 1.217Å to 1.297Å. It indicates the relaxation process proceed via vibrational

cooling. HOMO and LUMO of -HMX show that the electron and hole are overlapped in the

relaxed nitro group, which indicates local excitation.

An absorption band appears in the energy range from 500-1200nm, with a peak centered at 857

nm. It is slightly different from that of -HMX in Fig. S11.

Figure S10. Initial structure (-HMX0) and relaxed structure (-HMX1) of -HMX (top); and

HOMO-1 and LUMO+1 of -HMX1 (bottom left and right), with electron (green) and hole (blue)

distributions of the S1 state in the middle.

Figure S11. Steady-state absorption spectra of the relaxed structures of -HMX1 and -HMX1.

3.1 Comparisons with PET and NGCM

In this work, the excitation energies of the relaxed structures of six typical nitro explosives were

shown to be consistent with the impact sensitivities of these explosives. Establishing an

understanding of the underlying principles that govern this relationship relies on an investigation

of excited state dynamics and electron transfer processes [13]. This provides a novel and efficient

method for potentially unraveling the essence of energetic materials.

The method in this work somewhat resemble PET [14] and NGCM [5]. PET relies on the band

gap of the initial structure. It is clear that PET is suitable for crystalline phases of nitro explosives,

but is limited to similar structures or similar thermal decomposition mechanisms. It is recognized

that the transition of the initial structure is direct excitation following Fermi’s Golden rule, while

the excitation energy is several eVs and the probability is very low. The method in this work

suggests that relaxed structure performs as an intermediate and the excitation energy is much

lower than that of initial structure. The excitation energy corresponds to the impact sensitivity, at

least quantitatively in the present work. As discussed above, the relaxed structure of similar

structures has a close energy in the excited state, but a little different excitation energy from each

other. For different structures, the excitation energy of the relaxed structure is different and related

to its impact sensitivity. Thus, the method in this work may be applicable to more structures, while

it still needs much more work to verify this assumption.

The method used in this work is clearly different from NGCM [5] as they are based on different

principles. The method in this work uses excited states, which are recognized as being important

in the inherent detonation mechanism. The excited-state dynamics has been unraveled by ultrafast

pump-probe techniques and quantum chemical calculations. NCGM is based on Pauling

electronegativities, which are only applicable to molecules in their ground states. In addition, the

excitation energy method takes into consideration much more information about the energetic

material, such as initial structure, excited-state relaxed structure, Kohn-Sham orbitals, electronic

excitation, oscillator strength transition, and the relaxation process. The electronic excitation and

relaxation process, and the overlap of the hole and excited-electron orbitals can be clearly

visualized. The method is much more complex than NCGM, but is credible. In the end, the

method described in this work is not only suitable to nitro explosives, but is also potentially

applicable to other energetic materials and cases under extreme conditions, while NGCM is

limited to charges on nitro groups.

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