Energies of Electronic Transitions of Pentaerythritol Tetranitrate

Article pubs.acs.org/JPCC

Energies of Electronic Transitions of Pentaerythritol Tetranitrate Molecules and Crystals Roman V. Tsyshevsky, Onise Sharia, and Maija M. Kuklja* Materials Science and Engineering Department, University of Maryland, College Park, Maryland 20910, United States ABSTRACT: Despite significant effort in research on energetic nitrocompounds coupled with a great interest in these materials for a range of technological and medical applications, the electronic structure of condensed energetic materials is barely studied. In this research aimed at a better understanding of the low energy absorption in the optical spectrum of nitro-compounds, the electronic structure and vertical electronic transitions of a gas-phase pentaerythritol tetranitrate (PETN) molecule and an ideal PETN crystal were explored by means of density functional theory based calculations. In accordance with most experimental observations, the optical absorption spectrum of PETN has a well-resolved intense band above 6 eV that is accompanied by a few low intensity broad bands at lower energies. Our modeling suggests that the high intensity band corresponds to a series of strong singlet−singlet transitions, while the lower energy bands are attributed to the formation of tightly bound singlet and triplet excitons. All transitions are well-localized on O−NO2 groups of PETN. We also systematically analyze low energy excitations in other nitro-compounds, which exhibit similar patterns in the spectra even though the experimental data are incomplete at the moment. We predict that tightly bound excitons and charge transfer excitons should exist in PETN and both would trigger the nitrate decomposition, which allows for precise control of the initiation process.

I. INTRODUCTION Photosensitivity and selectivity of nanostructures,1,2 organic molecules,3 metal−organic frameworks,4 and polymers5−8 among other systems have been long explored for sensing9,10 and detecting11−13 high explosives to prevent threats to human security, locate buried land mines, and aid environmental protection efforts. The working principles of optical sensors or detectors are usually based on known interactions between explosive molecules and the sensitive media. Through variation in luminescence or fluorescence the optical sensor can detect the presence of explosives.14,15 In a similar way, it is possible to detect a wide variety of chemical and biological entities including organic and inorganic compounds, proteins, chemical warfare toxins, biological agents and viruses, narcotics, and groundwater contaminants. In principle, a single laser and detector can be used to illuminate and detect the signals from a dozen or more sensing channels. Although the engineering field of sensing and detecting is rapidly progressing, fundamental optical properties of realistic explosive materials (rather than simply isolated molecules) are far from completely known or understood, and the details of the electronic structure and optical transitions in most energetic materials have yet to be established. This knowledge would enhance and accelerate the development of efficient and economical sensors and detectors. Unlike luminescence, which is the central property for detecting and hence is being extensively studied, much less is known about the optical absorption of explosive samples. In the meantime, a propensity to absorb light (for example, from laser © 2014 American Chemical Society

irradiation) can be also used for initiating a chemical decomposition reaction in explosives.16−18 For our study, we selected pentaerythritol tetranitrate (PETN) as an ideal model system with a wealth of experimental and theoretical data and, at the same time, with relevant and specific outstanding questions. PETN, an important high explosive and pharmaceutical, belongs to the nitrate ester class of organic compounds.19 Vibrational properties of PETN have been explored using theoretical and experimental techniques.20 Intra- and intermolecular bonding in the PETN crystal were analyzed by the experimental electron density obtained from X-ray diffraction data at 100 K and theoretical calculations.21The electrostatic potential and population analysis of PETN and sila-explosive molecules suggests that the observed colossal sensitivity of Si-PETN to shock and friction22 is likely due to the greater tendency to form Si−O bonds in Si-PETN, compared to the formation of C−O bonds in PETN.23 The UV absorption spectrum of PETN reported in experimental literature varies in both the number and intensity of peaks. For example, the absorption of PETN measured in acetonitrile consists of three broad bands: a strong electronic transition at or below 193.5 nm (>6.41 eV)24−27 and two weak transitions at 260 nm (4.77 eV)24,25 and 290 nm (4.27 eV).24 The corresponding excitations were suggested to be localized Received: January 1, 2014 Revised: April 11, 2014 Published: April 15, 2014 9324

dx.doi.org/10.1021/jp500011a | J. Phys. Chem. C 2014, 118, 9324−9335

The Journal of Physical Chemistry C

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Figure 1. Structure of (a) an ethyl nitrate molecule, (b) a PETN molecule, and (c) a PETN unit cell.

on the -NO2 groups of PETN and have been assigned to π → π*, n → π*, and n → π* transitions, respectively.24 Unlike the earlier study,24 the recently reported UV absorption of PETN registered only two maxima, 6.5 and 4.8 eV.25 With many published reports describing the structure of PETN along with its explosive properties, experimental studies of the optical spectra are surprisingly scarce,24−26,28−30 and theoretical works on the electronic properties of PETN are nearly nonexistent.30−34 This lack of a systematic theoretical analysis is in sharp contrast with the need for understanding the electronic structure for many technological and medical applications. Interest in nitro-esters is growing due to recently synthesized nitrate ester-functionalized electroactive tetrazines,35 which promise to be capable of on/off fluorescence switching through reversible oxidation/reduction chemistry. In this work, aimed at advancing our understanding of the electronic structure and the optical spectrum of PETN and other relevant nitro-compounds, we performed detailed quantum-chemical calculations of the electronic structure and vertical electronic transitions of a model molecule of ethyl nitrate, an PETN molecule in the gas phase, and a PETN crystal. Our results suggest a consistent interpretation of available experimental data.24−26,29,30 We also systematize low energy excitations in other nitro-compounds and contribute to unraveling the long-standing puzzle about the nature of the lowest optical excitations in organic materials.

Vertical excitation energies for the lowest singlet (S) and triplet (T) states were computed using time-dependent DFT (TD B3LYP and TD PBE0) methods.44,45 In addition, singlet− triplet (S0→T1) excitation energies were obtained by means of the ΔSCF method (SCF = self-consistent field) based on differences of total energies in accordance with the Franck− Condon principle: E(S0 → T) 1 = E1(T) 1 − E0(S0 )

(1)

where E(S0→T1) is the energy of the vertical S0→T1 excitation, E0(S0) is the total energy of the ground state equilibrium PETN, and E1(T1) is the total energy of PETN in its triplet state, with the geometry of the structure corresponding to the ground state equilibrium molecule. For periodic solid state calculations we used DFT in the generalized gradient approximation (GGA) with the PBE functional and its hybrid modifications PBE0 and HSE06 as implemented in the VASP code.46−48 Projector augmented wave (PAW) pseudopotentials49 were employed. In simulating an ideal PETN crystal using the PBE functional, we used 2 × 2 × 2 Monkhorst−Pack k-point mesh with a kinetic energy cutoff of 520 eV, whereas hybrid functional calculations were performed with a k-point at the Γ-point only. Atomic coordinates and lattice constants were allowed to simultaneously relax without any symmetry constraints. The convergence criterion for electronic steps was set to 10−4 eV, and the maximum force acting on any atom was set not to exceed 0.02 eV/Å. Energies of the lowest S0→T1 transition in the periodic calculations were obtained from eq 1. The triplet state was simulated by specifying the difference between the numbers of electrons with up and down spin components equal to 2. For consistency, we also performed test calculations with PBE method within the GAUSSIAN and calculations of a single PETN molecule placed in the center of a large periodic box with the cell parameters a = b = c = 15 Å using the VASP code (also with the PBE method). Both of these calculations served as additional validation and reference points, which helped with interpreting the obtained results and conclusions.

II. DETAILS OF CALCULATIONS All molecular calculations in our study were carried out within the GAUSSIAN36 program suite. Equilibrium ground state structures and energies of the highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) gap were obtained using the density functional theory37,38 (DFT)-based exchange gradient-corrected correlation functional of Perdew, Burke, and Ernzerhof (PBE).39 We used its hybrid versions PBE040 and HSE06,41 together with B3LYP, which includes Becke’s three parameter42 and the Lee− Yang−Parr correlation43 functionals. We performed test calculations using a series of basis sets, 6-31G(d), 6-31+G(d), 6-31+G(d,p), 6-311+G(df,p), 6-311+G(2df,p), and 6-311+G(3df,p), which showed that 6-31+G(d,p) basis is sufficient to reliably reproduce the geometry structures of the ethyl nitrate (EN) and PETN molecules. An increase of the basis set beyond 6-31+G(d,p) does not bring any improvements in obtaining physical observables while requiring significant computational resources. Hence, the split-valence double-ζ basis set 631+G(d,p) was employed for all molecular calculations.

III. ETHYL NITRATE AS A MODEL MOLECULE We start our study with careful modeling of a relatively simple ethyl nitrate molecule. Ethyl nitrate (EN, H3C−CH2NO3) can be considered a model molecule of PETN (C−[CH2NO3]4) as it has one O−NO2 group, one C−C bond, and one C−H2 group (Figure 1) versus four similar functional groups in a PETN molecule. In addition, there are plenty of experimental and theoretical data reported and validated for EN as it is an 9325



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Table 1. Structural Parameters of an EN Molecule (Bond Distances, Å; Valence Angles, Degrees) method parameter

B3LYP

ε (%)

PBE0

ε (%)

HSE06

ε (%)

expt53

C1−C2 C2−O1 O1−N1 N1−O2 N1−O3 ∠C1−C2−O1 ∠C2−O1−N1 ∠O1−N1−O2 ∠O1−N1−O3 ∠O2−N1−O3

1.518 1.455 1.410 1.208 1.217 105.5 114.4 113.0 117.6 129.3

0.1 0.8 0.4 0.3 0.7 0.5 1.2 0.7 0.5 0.2

1.510 1.442 1.385 1.201 1.209 105.5 114.4 113.2 117.6 129.2

0.6 0.1 1.4 0.2 0.0 0.5 1.2 0.9 0.5 0.3

1.510 1.443 1.387 1.200 1.209 105.5 114.3 113.2 117.6 129.2

0.6 0.0 1.3 0.3 0.0 0.5 1.2 0.9 0.5 0.3

1.519 1.443 1.405 1.204 1.209 106.0 113.0 112.2 118.2 129.6

The calculated characteristics of low energy singlet and triplet optical transitions along with the oscillator strength magnitudes of EN are displayed in Table 2. There is not a single set of commonly accepted rules in designation of molecular orbitals for nitro-compounds, which often makes comparison of results, presented by different authors, quite difficult. With all excitations considered in this work occurring from a nonbinding occupied orbital to a π-type unoccupied orbital, assignments of each optical transition were made based on an analysis of molecular functions (Figure 2) that have been included in the CI procedure to create each of the exited states. In particular, nO indicates HOMO states and π* stands for LUMO states (Figure 2). The electronic state is assigned nπtype if it is mainly formed by 2pz atomic orbitals of oxygen atoms and the two nonbonding orbitals possess the symmetry of a π orbital (Figure 2). The nσ electronic state is assigned to nonbonding orbitals possessing the symmetry of a σ orbital and formed by a large contribution of 2py and a relatively small contribution of 2px and 2pz functions of oxygen atoms (see Figure 2). The reported experimental studies of the UV spectrum of ethyl nitrate vary in the number of peaks and their intensity. We collected most of the available data in Table 2. In accordance with most authors, the experimental spectrum is characterized by an intense π→π* absorption band centered around 6.52 eV55,56 and a series of relatively weak bands at lower energies. For example, n→π* absorption bands were observed at 5.63 eV55 and at 4.96 eV,55 and another one appearing as a shoulder at ∼4.77 eV.50,55,57−59 UV absorption cross-sections reported for EN,50 (see also discussion in ref 58 and references therein) show that EN also absorbs light in the range of atmospheric interests with the energy smaller than 4.27 eV and wavelengths longer than 290 nm, which is likely to be associated with photolysis.52 Our calculations performed with two different TD DFT methods (B3LYP and PBE0; see Table 2) are in excellent agreement with each other and allow us to interpret the experimental spectrum by attributing specific transitions to those measurements. According to our B3LYP calculations, two lowest optical excitations of EN correspond to spin-forbidden singlet−triplet transitions, S0→T1 (nπ→π*) at 3.88 eV and S0→T2 (nO→π*) at 4.12 eV, with the energies very similar to the experimental results of 3.9652 and 4.0250 eV (Table 2). Comparable energies of 3.94 and 4.25 eV are obtained with PBE0. The breadth of the absorption peak registered in experiments50,52 and the close values of the two calculated excitation energies suggest that the two transitions overlap and are therefore not distinguished in optical measurements.

organic nitrate (R−NO3), secondary pollutants formed from photochemical reactions involving hydrocarbons and oxides of nitrogen (NOx = NO + NO2) that play an important role in the atmospheric chemistry of NOx. Organic nitrates are important during atmospheric cycles of nitrogen and organic carbon; they also affect the tropospheric distribution of total reactive nitrogen (NOy), and hence their photochemistry has been extensively studied over the years.50,51 In particular, the three photolysis pathways for the photodissociation of EN were proposed52 to produce NO2 and HONO as major products with the dominating NO2 loss reaction (see, for example, refs 50, 52, and 51). These products are similar to the initial products of PETN decomposition as well. Therefore, ethyl nitrate can serve as a good prototype molecule for a comprehensive study of PETN. The calculated structural parameters of an EN molecule with the C1 point symmetry group (Figure 1) are collected in Table 1. As expected, the bond distances and valence angles calculated with hybrid DFT methods, B3LYP, PBE0, and HSE06 are consistent with each other and are found to be in good agreement with gas-phase electron diffraction experiments.53 The error in calculated bond lengths does not exceed 0.8% for B3LYP (which overestimates the C2−O1 bond) or 1.4% for PBE0 and 1.3% for HSE06 (both of which underestimate the O1−N1 bond) and 1.2% for bond angles (which are similarly overestimated by all three methods). The resulting structure of the EN molecule is very similar in PBE0 and HSE06 methods. The HOMO of EN (Figure 2) is a nonbonding orbital formed by oxygen 2px and 2py atomic orbitals and is usually

Figure 2. Molecular orbitals of EN involved in the configuration interaction procedure to simulate excited states.

assigned as the nO orbital.25,54 The LUMO is a π* antibonding orbital, with a large contribution of 2pz atomic orbitals of oxygen and nitrogen atoms from the nitro-group and a relatively small contribution of 2pz atomic orbitals from the ester oxygen atom (Figure 2). 9326



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Table 2. Vertical Electronic Transitions of the EN Molecule Calculated by TD DFT Methods TD B3LYP transition

absorption spectrum peak (eV)a

E (eV)

f

E (eV)

f

→ → → → → → →

3.88 4.12 4.69 5.15 5.23 5.62 6.20

0 0 ∼10−7 0 0 ∼10−4 0.0696

3.94 4.25 4.86 5.37 5.52 5.88 6.57

0 0 ∼10−7 0 0 ∼10−4 0.0866

S0→T1 S0→T2 S0→S1 S0→T3 S0→T4 S0→S2 S0→S3 a

TD PBE0

transition type nπ nO nO nσ nπ nσ nπ

π* π* π* π* π* π* π*

3.96,52 4.0250 4.67,55 4.7750,57−59 4.9655 5.6355 6.5255,56

Optical absorption of gas-phase ethyl nitrate was measured in refs 50, 52, 56, 58, and 59 and in solution of heptane, in refs 55 and 56.

forbidden transition 3 orders of magnitude from 10−7 to 2 × 10−4, which is consistent with the experimentally observed value of 3 × 10−4 (see ref 60). The second vibration was modeled by changing the dihedral angle O1−O2−O3−N1 (see Figure 1a) in the equilibrium structure by ∼9°. The distortion requires 1.9 kcal/mol and increases the oscillator strength from 10−7 to 10−5. Next, the calculated energies show two close singlet−triplet transitions, S0→T3 (nσ→π*) at 5.15 eV and S0→T4 (nπ→π*) at 5.23 eV (Table 2). These slow spin-forbidden excitations are likely to overlap and to be associated with the distinct low intensity broad peak at 4.96 eV resolved in UV spectra of EN.55 The next series of transitions includes one low intensity S0→ S2 (nσ→π*) transition with the energy of 5.62 eV and one wellresolved high intensity S0→S3 (nπ→π*) transition at 6.20 eV, which agree well with the experimental peaks centered at 5.6355 and 6.52 eV,55,56 respectively (Table 2). Variations in the energies of optical transitions calculated from PBE0 and B3LYP are small and correlate well with the predicted geometric structures of the EN molecule. TD PBE0 systematically overestimates the excitation energies by ∼0.2− 0.3 eV relative to TD B3LYP (Table 2), which is consistent with the PBE0 trend to slightly underestimate the N−O bond distance in EN. Hence, as the B3LYP predicts a structure for the gas-phase molecule that is closer to experimental values as compared to PBE0, the spectrum obtained by B3LYP should also be considered as closer to experiment as compared to PBE0. However, the noted discrepancies are still very small. These calculations reveal two immediate observations. First, our modeling of electronic excitations of an isolated ethyl nitrate molecule yields the electronic transitions in good agreement with experimentally registered spectra and provides a consistent interpretation of the spectra. Second, all of the low energy optical transitions are strongly localized on nitro-groups,

Interestingly, experiments indicate that the excitations at 313 nm (3.96 eV)52 and 308 nm (4.02 eV)50 cause bond breaking in the ethyl nitrate molecule through a photodecomposition mechanism. The first singlet−singlet S0→S1 transition is of the nO→π* type with an energy of 4.69 eV and is in agreement with the experimental peaks of 4.6755−4.77 eV.50,57−59 The low magnitude of the oscillator strength points to the low intensity of this transition (Table 2), which is consistent with experimental observations. We note that the calculated oscillator strength of this symmetry-forbidden excitation is too small to make the transition observable. Hence, we explored whether vibronic coupling (the interaction between electronic and nuclear vibrational motion), which may lift the restriction, has any effect on the probability of the transition. We identified two potentially relevant vibrations, a twisting of the nitro-group about the O−NO2 bond and an out-of-plane wagging of the nitrogen atom, shown in Figure 3. To simulate

Figure 3. Two select vibrational modes of a EN molecule: (a) twisting of the nitro-group and (b) nitrogen out-of-plane wagging.

the effect of the first vibration, we changed the torsion angle C2−O1−N1−O2 in the EN equilibrium structure by 15° (Figure 3a) and repeated calculations of the optical transitions in the slightly distorted molecule using TD PBE0 method. Our calculation showed that such a distortion requires only 1.2 kcal/ mol in energy and increases the oscillator strength of the S0→S1

Table 3. Structural Parameters of the PETN Molecule in the Gas Phase and in the Crystal gas-phase molecule

crystal-phase molecule

PETN param

B3LYP

δ (%)

HSE06

δ (%)

PBE0

δ (%)

PBE

δ (%)

HSE06

ε (%)

PBE0

ε (%)

PBE

ε (%)

expt61

C1−C2 C2−O1 O1−N1 N1−O2 N1−O3 ∠C1−C2−O1 ∠C2−O1−N1 ∠O1−N1−O2 ∠O1−N1−O3 ∠O2−N1−O3

1.544 1.446 1.429 1.204 1.212 106.3 114.0 112.4 117.0 130.5

0.5 0.8 2.3 0.2 0.8 1.1 1.6 0.8 0.7 1.3

1.534 1.434 1.404 1.196 1.204 106.1 114.0 112.6 117.0 130.4

0.1 0.0 0.5 0.9 1.5 1.3 1.6 0.6 0.7 1.2

1.534 1.433 1.402 1.196 1.204 106.3 114.0 112.4 117.0 130.5

0.1 0.1 0.4 0.9 1.5 1.1 1.7 0.8 0.7 1.3

1.547 1.445 1.476 1.211 1.218 106.5 112.9 111.7 116.6 131.6

0.7 0.8 5.7 0.3 0.3 0.9 2.6 1.4 1.0 2.2

1.528 1.437 1.384 1.205 1.203 107.5 113.6 112.8 117.9 129.3

0.5 0.2 0.9 0.2 1.6 0.0 2.0 0.4 0.1 0.4

1.530 1.438 1.382 1.205 1.203 107.3 113.7 112.9 117.8 129.3

0.4 0.3 1.1 0.2 1.6 0.2 1.9 0.4 0.0 0.4

1.543 1.449 1.451 1.217 1.215 107.3 113.1 111.8 117.5 130.6

0.5 1.0 3.9 0.8 0.6 0.2 2.4 1.3 0.3 1.4

1.536 1.434 1.397 1.207 1.222 107.5 115.9 113.3 117.8 128.8

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predominantly by pairs of px−py, px−pz, and py−pz functions of oxygen atoms from nitro-groups (Figure 4). The degenerate

which carries implications for photochemistry of nitrocompounds and also implies that similar trends should be expected for PETN and, likely, for other nitro-molecules.

IV. PENTAERYTHRITOL TETRANITRATE a. Structure of PETN. The structures of the PETN molecule and the crystal are shown in Figure 1b,c. As determined by X-ray diffraction measurements,19 the space group of the PETN crystal is P4̅21c. In the P4̅21c group, one molecule is the mirror image of the other, displaced by c/2. The central atom in the molecule lays at the corners and at the center of the unit cell, i.e., at (0; 0; 0) and (1/2; 1/2; 1/2). These atoms are symmetrically related by an n glade plane or (equivalently) by a c glade or (still the same) by 21 axes normal to the −4 axis. The molecules may rotate freely around their −4 axes, with all atoms other than the central one being in general positions (Figure 1c). The calculated geometry parameters of the gas-phase and crystalline PETN molecules are collected in Table 3 and found to be fairly consistent. The parameter ε measures the accuracy of the DFT methods in reproducing the experimental molecular configuration, and δ illustrates the difference between the gas-phase and crystal-phase structures. The calculated lattice constants (Table 4) are also in agreement

Figure 4. Molecular orbitals of PETN involved in the configuration interaction procedure to simulate excited states.

HOMO-1 and HOMO-2 are also nonbonding orbitals of similar nature and lie only 0.06 eV lower than the HOMO. Another nO orbital, HOMO-3, lies 0.11 eV below HOMO. Hence, the S4 symmetry characteristic of the PETN crystal,19 which would ordinarily bring a 4-fold degeneracy of molecular orbitals, is not preserved in the gas phase. The full relaxation of the isolated PETN molecule causes the four -O−NO2 tails to have slightly different bond lengths and torsion angles, which is reflected in the splitting of the four occupied molecular orbitals. The LUMO is an antibonding π* molecular orbital (Figure 4) with a large contribution of pairs of px−py and px−pz functions of nitrogen and oxygen atoms. Similar to the occupied orbitals, LUMO is followed by two degenerate LUMO+1 and LUMO+2 with an energy of only 0.02 eV higher than LUMO. LUMO+3 lays 0.05 eV above LUMO, and it has the same nature as the LUMO while differing only in sign and the coefficients of the contributing functions. The nature of frontier molecular orbitals calculated with PBE, PBE0, and HSE06 functionals is similar to that obtained with B3LYP. Periodic calculations also give consistent results. The top of the valence band of crystalline PETN is formed by a combination of 2p states of oxygen atoms, and the bottom of the conduction band is predominantly made of 2p states of oxygen and nitrogen atoms from nitro-groups, as shown in Figure 5c,d. Isosurfaces of the top of the valence band and the bottom of the conduction band of an ideal PETN crystal (Figure 5c,d) resemble the corresponding HOMO and LUMO isosurfaces of a single PETN molecule (Figure 5a,b). This indeed should be expected from the nature of molecular crystals in which molecules seek to preserve their “identities” in a crystal field arrangement and all electronic density is welllocalized on the molecules. c. Vertical Electronic Excitations in the PETN Molecule. The calculated energies and the oscillator strengths of a series of lowest optical electronic transitions in the PETN molecule are collected in Table 5 and are accompanied by the matching absorption peaks found in experimental reports. In accordance with the calculations, all optical transitions of PETN molecule observed in the experimental range of 3.18− 6.79 eV24 (Table 5) are localized on ONO2 fragments, which is

Table 4. Lattice Parameters of the PETN Crystal

a

method

a (Å)

ε (%)

b (Å)

ε (%)

c (Å)

ε (%)

PBE PBE0 HSE06 expta

9.64 9.37 9.51 9.38

2.8 0.1 1.4

9.64 9.38 9.51 9.38

2.8 0.0 1.4

6.82 6.79 6.70 6.71

1.6 1.2 0.1

Data from ref 61.

with experimental data a = b = 9.38 Å, c = 6.71 Å,61 and earlier theoretical estimates.31 Among the three DFT methods used, PBE shows the worst performance, overestimating the O1−N1 bond length in the molecule by 3.9% and underestimating the ∠C2−O1−N1 by 2.4% for the crystalline PETN molecule. The HSE06 and PBE0 yield fairly similar PETN structures, slightly underestimating the N−O distance and the ∠C2−O1−N1 angle in the molecule (Table 3). As expected, the crystalline field causes some contraction of most bond lengths. For example, all of the methods used here indicate that the N−O bond is shorter in the solid state phase molecule relative to the isolated molecule. Specifically, B3LYP elongates the gas-phase N−O distance by 2.3% (as compared to the bulk crystal distance), PBE by 5.7%, and PBE0 and HSE06 by 0.5% (while both approximations underestimate the distance in bulk). The a and b vectors are reproduced by PBE within 2.8% and the c vector is within 1.6%. Hybrid functionals produce better results with accuracy of ∼1%. A small difference however is noted in performance of PBE0 and HSE06. The a (9.37 Å) and b (9.38 Å) lattice constants, although numerically nearly identical to experiment (9.38 Å), do not stay the same within PBE0 approximation, which causes a slight distortion of the crystalline unit cell symmetry; the c constant (6.79 Å) is 1% larger than that of the experiment (6.71 Å). HSE0 gives c (6.70 Å) 1% smaller than experiment and a = b vectors 1.2% larger than experiment, and preserves the original symmetry. b. Nature of PETN Molecular and Crystalline Orbitals. In accordance with molecular calculations with B3LYP, the PETN HOMO is found to be a nonbonding nO orbital formed 9328



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Figure 5. (a) HOMO and (b) LUMO isosurfaces of the PETN molecule; (c) decomposed charge density of the top of the valence band; and (d) the bottom of the conduction band of the PETN crystal.

Table 5. Vertical Electronic Transitions of the PETN Molecule Calculated with TD DFT Methods TD B3LYP

a

TD PBE0

transition

transition type

E (eV)

f

E (eV)

f

S0→T1 S0→T2 S0→S1 S0→T3 S0→T4 S0→S2 S0→S3 S0→S4 S0→S5

→ → → → → → → → →

3.88 4.18 4.76 5.20 5.32 5.66 6.07 6.21 6.44

0.0000 0.0000 ∼10−6 0.0000 0.0000 5 × 10−4 0.1181 0.0027 0.0290

3.92 4.30 4.92 5.40 5.65 5.92 6.51 6.75 6.98

0 0 ∼10−6 0 0 7 × 10−4 0.1710 0.0021 0.0222

nπ nO nO nσ nπ nσ nπ nO nπ

π* π* π* π* π* π* π* π* π*

a

absorption spectrum peakb (eV) 4.2724 4.77;24 4.825 ≥5.2825,26

>6.41;24 >6.50;25 >6.5226,27

Isosurfaces of molecular orbitals are depicted in Figure 4. bAuthors of refs 24−26 register the UV spectrum of PETN solution in acetonitrile.

experimental estimate of 4.27 eV.24 The magnitude of the oscillator strength indicates a low intensity transition, which is consistent with the nature of a spin-forbidden singlet−triplet excitation, and the broad band in UV absorption spectra of PETN may be explained by an overlap of these two transitions. Unlike one-electron energies that are strongly dependent on the method used and may produce large deviations as observed for the band gaps (see Table 7), ΔSCF takes differences between the total energies of the system in different electronic states and that is why it does not suffer from this dependence

quite similar to the ethyl nitrate case. The only difference is that an analysis of optical transitions of PETN and their assignments is somewhat more complicated, as compared to EN molecule, due to 4-fold quasi-degeneracy of molecular orbitals which is caused by the presence of four -O−NO2 fragments. As a result, each excited state displayed in Table 5 represents a series of degenerate excitations. Two lowest optical transitions in a PETN molecule correspond to the singlet−triplet excitations S0→T1 and S0→ T2 with energies of 3.88 and 4.18 eV, which are close to the 9329



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Table 6. Energies of Singlet and Triplet Excitons in EN EN molecule method

EHOMO−LUMO

PBE PBE0 HSE06 B3LYP expt

4.38 7.35 6.54 6.66 −

E(S1)a

SBEb

4.86

2.49

4.69 −4.67e; 4.77f

1.97 −

E(T1)c/EΔSCF(T1)d

TBEb

−/4.26 3.94/4.29 −/4.29 3.88/4.17 3.96g, 4.02h

−/0.12 3.41/3.06 2.25 2.78/2.49 −

a E(S1) is the singlet exciton formation energy. bSBE (TBE) stands for the singlet (triplet) exciton binding energy. cE(T1) is the triplet exciton formation energy obtained by TD DFT (for PBE0 and B3LYP approximations). dThe triplet exciton formation energy obtained by ΔSCF method. e From ref 55. fFrom ref 50. gFrom ref 52. hFrom ref 50.

Table 7. Energies of Singlet and Triplet Excitons in PETN PETN molecule

PETN crystal

method

EHOMO−LUMO

E(S1)a

SBEb

E(T1)c/EΔSCF(T1)d

TBEb

Egap

EΔSCF(T1)

TBEb

PBE PBE0 HSE06 B3LYP expt

4.35 7.32 6.51 6.64 −

4.92 4.41 4.76 4.77e; 4.80f

2.40 2.10 1.88 n/a

−/4.31 3.92/5.95 −/4.33 3.88/4.22 4.27e

−/0.04 3.40/1.37 −/2.18 2.76/2.42 n/a

4.09 7.07 6.04 − −

4.26 4.32 4.29 −

− 2.75 1.74 n/a

a

E(S1) is the singlet exciton formation energy. bSBE (TBE) stands for the singlet (triplet) exciton binding energy. cE(T1) is the triplet exciton formation energy obtained by TD DFT (for PBE0 and B3LYP approximations). dThe triplet exciton formation energy obtained by ΔSCF method. e From ref 24. fFrom ref 25.

lends some additional support to the interpretation of these excitations. The next calculated excitation is a singlet−singlet S0→S3 (nπ→π*) transition with an energy of 6.07 eV and a pronounced oscillator strength of f = 0.1181, indicating a high intensity absorption maximum and nicely fitting the experimental result of a broad, strong absorption peak at or above ∼6.41−6.52 eV.24−27 This high intensity S 0 →S 3 transition is followed by two singlet−singlet, S0→S4 (nO→ π*) and S0→S5 (nπ→π*), transitions at 6.21 and 6.44 eV, respectively. Their oscillator strengths (0.0027 and 0.0290) define relatively intense transitions that are likely to contribute to the breadth of the main absorption maximum. An analysis of the calculated optical transitions of PETN and EN allows us to make important conclusions: (1) the experimental absorption spectrum of both molecules is accurately reproduced, refined, and interpreted in our simulations; the spectrum is characterized by a strong, broad absorption maximum at ∼6.5 eV that is accompanied by a series of lower energy excitonic features. (2) All low energy optical transitions observed in the UV spectrum of both EN and PETN are strongly localized on O−NO2 fragments of the molecules, which defines the parallels in the energies, the nature of the optical transitions, and the corresponding values of oscillator strength. These calculations provide a solid ground to expect that representatives of other subclasses of nitrocompounds will exhibit similar optical properties. d. Band Gap and Exciton Energies. The energies relevant to the exciton formation in EN and PETN are collected in Tables 6 and 7, respectively. Table 7 shows that the calculated HOMO−LUMO gap of the PETN molecule, 6.64 eV, produced with B3LYP is a little bit higher than the earlier estimate of 6.47 eV obtained with B3LYP and a small 6-21G basis set.32 As expected, other functionals produce comparable HOMO−LUMO gap values, 6.51 eV (HSE06, close to B3LYP), 7.32 eV (PBE0, visibly higher than B3LYP), and the underestimated 4.35 eV (PBE, more than 2.5 eV lower than

(disadvantage). As a result, the energies of the lowest singlet− triplet S0→T1 excitation (Table 5) evaluated in accordance with ΔSCF as described by eq 1 are in close agreement with each other and the energy of the lowest absorption band (4.27 eV) observed in the UV spectrum of PETN.24 The lowest singlet−singlet S0→S1 (nσ→π*) excitation with the energy of 4.76 eV matches up with the second absorption peak at 4.7724−4.8 eV.25 On one hand, a low oscillator strength would be expected for a symmetry-forbidden transition, resulting in a low intensity of the peak. The calculated magnitude of f ∼ 10−6 however appears too low to register this transition in the actual spectrum, which seemingly contradicts the experiment.24 On the other hand, PETN has four vibrational modes relevant to out-of-plane wagging of the nitrogen atom with the frequencies of 784.44, 784.44, 785.08, and 786.75 cm−1, as was calculated using PBE0/6-31+G(d,p). Once the vibronic coupling is taken into account, the oscillator strength increases from 10−6 to 10−4 and removes the symmetry-imposed restriction, making the excitation measurable. This bears a notable resemblance to the ethyl nitrate case. Further, our calculations predict that the singlet−singlet S0→ S1 transition is followed by a pair of spin-forbidden S0→T3 (5.20 eV) and S0→T4 (5.32 eV) transitions assigned as nσ→π* and nπ→π*. We note that neither those two singlet−triplet transitions nor the next singlet−singlet excitation (also obtained theoretically) appear as well-resolved individual peaks in the reported experiments. Nevertheless, the close energy (5.66 eV) of the next transition, S0→S2, and the small nonzero oscillator strength (5 × 10−4) indicate a low intensity transition and possible overlap with the adjacent maxima, consistent with the most recent measurements26 which show that PETN exhibits absorption at the energies somewhat higher than 5.28 eV. According to recent laser-irradiation experiments,25 gas-phase PETN can be excited by absorption of a single UV photon at wavelengths of 236 (5.25 eV) and 226 nm (5.48 eV). A similarity with the pattern in the EN spectrum 9330



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components of the singlet exctons are well-localized on the O− NO2 groups.

B3LYP). Our calculations also show that the HOMO−LUMO gap, 4.35 eV, obtained from PBE by GAUSSIAN practically coincides with 4.36 eV, computed by PBE from VASP. PETN band gaps obtained from the periodic calculations, shown in Table 7, follow the same trend as the molecular HOMO−LUMO energies but are systematically and consistently lower by 0.25−0.5 eV, as should be expected due to weak intermolecular interactions in molecular crystals. In particular, the band gap of 6.04 eV (HSE06) is very close to 5.96 eV (B3LYP)32 and comparable to 7.07 eV (PBE0), which is somewhat higher. The lowest gap of 4.09 eV (PBE) agrees well with previous calculations (4.2 eV)31 and is 30−40% lower than those obtained using hybrid functionals. The observed trends in the obtained energy gaps (that is, the discrepancy of the results generated by different functionals: PBE and hybrid functionals B3LYP, PBE0, and HSE06) are anticipated and consistent with the well-established problem of Kohn−Sham formalism of DFT, which does not accurately predict the excitation energies.62,63 Arising from the derivative discontinuity problem,64 the single-particle Kohn−Sham eigenvalues cannot be attributed a direct physical meaning of quasi-particle energies. Hence a simple difference of the occupied and unoccupied ground-state DFT eigenvalues should not give the correct gap for an insulating molecular crystal. For insulators and semiconductors, local and gradient-corrected functionals underestimate the optical gap by 30%−100%.65 Hybrid functionals generally improve the values for excitation energies in DFT, and B3LYP was specifically adjusted using empirical parameters to fit data on molecular systems.42,66 Interestingly, the S0→S1 transition, obtained by all methods used, has an appreciably lower energy (about 2 eV lower) than the band gap (see Tables 6 and 7), which is a strong indication of a tightly bound singlet exciton. It is commonly believed that, due to the weak intermolecular interactions in organic molecular crystals, the electron−hole (e−h) pairs are confined to single molecules resulting in large exciton binding energies. For anthracene, which is a prime example of an organic molecular crystal, it was found that its photophysics are determined by tightly bound excitons and that the molecular exciton theory67 is able to correctly describe the lowest energy optical absorption processes.68 By solving the Bethe−Salpeter equation for the electron−hole Green function for crystalline anthracene, it was relatively recently established that the lowest absorption peak may be generated by strongly bound excitons or by a free electron−hole pair, depending on the polarization direction being parallel to the short or the long molecular axis.69 Anthracene binding energies of singlet and triplet excitons reported in those studies were 0.64 and 1.86 eV, respectively.69 Binding energies of 1.0−1.5 eV for singlet exitons and 2.4−2.8 eV for triplet excitons in oligoacene series were found to depend on the linear size of molecular units in the crystals.70 Our results demonstrate that the calculated binding energies of PETN excitons are large (1.88−2.40 eV, depending on the method, for the singlet exciton and 1.74− 3.40 eV for the triplet exciton, see Table 7) and consistent with the tightly bound exciton model. PBE0 overestimates the binding energies due to overestimated band gaps. In comparison, B3LYP and HSE06 give smaller and likely more realistic binding energies. As expected, similar trends are also characteristic of EN (Table 6). The electron and hole components of the singlet exciton in PETN and EN are illustrated in Figure 6, which shows that both electron and hole

Figure 6. Hole and electron components of the singlet exciton configuration in PETN and EN.

We predict that tightly bound excitons exist in PETN and that their presence defines the physics of the optical absorption spectrum as well as the photochemistry of initiation reactions. Intriguingly, this fact is critically important for understanding PETN properties and for particular applications, such as initiation of explosive decomposition, explosive sensing and detection, and the use of nitrate-based medications.

V. COMPARISON TO OTHER NITRO-COMPOUNDS Noting that the low energy electronic excitations of PETN are all associated with the nitro-groups, we argue that the optical spectra of most nitro-compounds should exhibit similar features, carrying implications for design of sensors and detectors and other applications (as previously mentioned). In Table 8, we compiled experimentally and theoretically obtained energies of optical transitions for various nitrocompounds reported in the literature. We sorted the data by energy intervals and added both experimental and theoretical results as much as available. It is unsurprising that the table appears incomplete since the optical studies of most nitrocompounds are still insufficient and therefore many of the articles that we have chosen to collect the data from were intended for other purposes than to study the optical absorption spectra. Nevertheless, it is apparent that nitrocompounds absorb light in four main regions with the most intense transition above 6 eV and a few transitions at lower energies. By using the results obtained for PETN, we will make an attempt to interpret (or predict) the optical properties of relevant nitro-compounds. The first region is associated with the energy range of ∼3.4− 4.3 eV. We suggest that the low intensity broad peaks correspond to two overlapping, spin-forbidden singlet−triplet transitions. The second region, ∼4.3−5.0 eV, with the most common peaks at 4.4−4.8 eV, also shows up in the spectra as a broad low intensity band. This band can be attributed to the lowest singlet−singlet (S0→ S1) transition. Both low energy bands are related to the formation of tightly bound excitons, well-localized on nitro-group atoms. It would be appealing to analyze in great detail how the exciton binding energy depends on the structure of the molecules and their crystalline 9331



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Table 8. Energies of Optical Transitions in Nitro-compounds Available in Literature energies of optical transitions (eV) E < 4.2

4.3 < E < 5.0

3.8 3.74; 3.81; 4.07; 4.15

4.45 4.35 4.36−4.59 ∼4.59

substance (state) nitromethane (gas) C1−C8 nitroalkanes (solution) C4−C9 alkyl nitrates (solution) simple nitrate esters methyl nitrate (solution) n-propyl nitrate (solution) isopropyl nitrate (solution) n-butyl nitrate (solution) tert-butyl nitrate (solution) nitramines RDX (solid) RDX (solution) RDX (gas)

HMX (solid) HMX (solution) HMX (gas) DMNA (gas) TNT (solution) TNT (gas) imidazole series (gas) 1,4-dinitroimidazole

4.86 4.86 4.59 4.40; 4.76 4.59 3.39

5.0 < E < 6.0

E > 6.0 6.23 6.23 >6.2

5.39; 5.90 5.39 5.50; 5.63 5.39, 5.63 5.39; 5.63

6.39

6.18; 6.25 6.09; 6.13

expt: Marinkas74,75 theory: Kuklja34,76 expt: Cooper26 expt: Bernstein77 theory: Bernstein78 theory: Cooper25 expt: Marinkas74 expt: Cooper26 theory: Cooper26 expt: Bernstein79 theory: Bernstein79 expt: Cooper26 theory: Cooper26 expt: Bernstein80 theory: Bernstein80 expt.: Bernstein80 theory: Bernstein80 expt: Bernstein80

of available functionals (PBE, PBE0, B3LYP, and HSE06) and time-dependent approximations. We started with a careful simulation and analysis of an ethyl nitrate molecule as it is wellstudied experimentally in the gas phase and therefore allows for a multilayered validation of our computational approach. The geometric configuration and electronic excitations in ethyl nitrate were explored, and performance of the applied DFT approximations was examined. This simple molecule was then used as a model system to study PETN electronic transitions in the gas phase and to provide an interpretation to the experimental optical absorption spectrum, which clarified some contradictory (or rather incomplete) experimental data. Further, we expanded our modeling to include periodic PETN calculations. Finally, we applied the obtained results and conclusions to systematize, complete, and interpret the optical spectra of the entire class of nitro-compounds. We were also able to predict several important photodissociation and excitonic features that have immediate implications for understanding explosive decomposition mechanisms, the design of sensors and detectors, and the use of nitrates in medications. In accordance with most experimental observations, the optical absorption spectrum of PETN (and other nitrocompounds) has a well-resolved intense band above 6 eV that is accompanied by a few low intensity broad bands at lower energies. Our modeling suggests that the high intensity band corresponds to a series of strong singlet−singlet transitions,

arrangements in nitro-compounds. The difference (if any) may be relevant to the stability of molecules and/or crystals. The third region with the energy range of 5.0−6.0 eV yields a series of absorption peaks in most experiments. In accordance with our calculations, this region in the spectra represents the next two singlet−triplet transitions overlapping with the following singlet−singlet transition. Finally, the fourth region at the energies above 6.0 eV reflects to most intense absorption bands, corresponding to a series of well-resolved singlet−singlet excitations. Curiously, according to experimental studies nitramine explosives tend to decompose after absorbing light. For example, RDX and HMX as well as their model compound DMNA were observed to initiate decomposition due to laser irradiation with the energies of 5.0, 5.26, and 5.5 eV.25,77,79 These observations coupled with our simulations suggest that the dissociation of most nitro-compounds can also be initiated with lower energies due to the formation (and following dissociation) of excitons. This proposition lends strong support to the excitonic mechanism of detonation initiation that was originally proposed some 15 years ago.76

VI. SUMMARY AND CONCLUSION We performed a state-of-the-art theoretical study to explore the nature of optical absorption in PETN and possibly in other relevant nitro-compounds. Our electronic structure calculations were executed by using DFT-based methodology with a variety 9332



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(7) Germain, M. E.; Knapp, M. J. Discrimination of Nitroaromatics and Explosives Mimics by a Fluorescent Zn(salicylaldimine) Sensor Array. J. Am. Chem. Soc. 2008, 130, 5422−5423. (8) Li, Z.; Ding, J.; Song, N.; Lu, J.; Tao, Y. Development of a New sTetrazine-Based Copolymer for Efficient Solar Cells. J. Am. Chem. Soc. 2010, 132, 13160−13161. (9) Pinnaduwage, L. A.; Gehl, A.; Hedden, D. L.; Muralidharan, G.; Thundat, T.; Lareau, R. T.; Sulchek, T.; Manning, L.; Rogers, B.; Jones, M.; et al. Explosives: A Microsensor for Trinitrotoluene Vapour. Nature 2003, 425, 474. (10) Moore, D. S. Recent Advances in Trace Explosives Detection Instrumentation. Sens. Imaging 2007, 8, 9−38. (11) Rose, A.; Zhu, Z.; Madigan, C. F.; Swager, T. M.; Bulovic, V. Sensitivity Gains in Chemosensing by Lasing Action in Organic Polymers. Nature 2005, 434, 876−879. (12) Andrew, T. L.; Swager, T. M. A Fluorescence Turn-On Mechanism to Detect High Explosives RDX and PETN. J. Am. Chem. Soc. 2007, 129, 7254−7255. (13) Germain, M. N.; Arechederra, R. L.; Minteer, S. D. Nitroaromatic Actuation of Mitochondrial Bioelectrocatalysis for Self-Powered Explosive Sensors. J. Am. Chem. Soc. 2008, 130, 15272−15273. (14) Malashikhin, S.; Finney, N. S. Fluorescent Signaling Based on Sulfoxide Profluorophores: Application to the Visual Detection of the Explosive TATP. J. Am. Chem. Soc. 2008, 130, 12846−12847. (15) Zhang, K.; Zhou, H.; Mei, Q.; Wang, S.; Guan, G.; Liu, R.; Zhang, J.; Zhang, Z. Instant Visual Detection of Trinitrotoluene Particulates on Various Surfaces by Ratiometric Fluorescence of DualEmission Quantum Dots Hybrid. J. Am. Chem. Soc. 2011, 133, 8424− 8427. (16) Evans, B. L.; Yoffe, A. D. Structure and Stability of Inorganic Azides. II. Some Physical and Optical Properties, and the Fast Decomposition of Solid Monovalent Inorganic Azides. Proc. R. Soc. London, Ser. A 1959, 250, 346−366. (17) Bernstein, E. R. In Overviews of Recent Research on Energetic Materials; Shaw, R., Brill, T., Thompson, D., Eds.; World Scientific: Singapore, 2004; pp 161−190. (18) Kunz, A. B.; Kuklja, M. M.; Botcher, T. R.; Russel, T. P. Initiation of Chemistry in Molecular Solids by Processes Involving Electronic Excited States. Thermochim. Acta 2002, 384, 279−284. (19) Kitaigorodskii, A. I. Organic Chemical Crystallography; Consultants Bureau: New York, 1958; pp 120−124, 216−217, and 263−264. (20) Gruzdkov, Y. A.; Gupta, Y. M. Vibrational Properties and Structure of Pentaerythritol Tetranitrate. J. Phys. Chem. A 2001, 105, 6197−6202. (21) Zhurova, E. A.; Stash, A. I.; Tsirelson, V. G.; Zhurov, V. V.; Bartashevich, E. V.; Potemkin, V. A.; Pinkerton, A. A. Atoms-inMolecules Study of Intra- and Intermolecular Bonding in the Pentaerythritol Tetranitrate Crystal. J. Am. Chem. Soc. 2006, 128, 14728−14734. (22) Klapötke, T. M.; Krumm, B.; Ilg, R.; Troegel, D.; Tacke, R. The Sila-Explosives Si(CH2N3)4 and Si(CH2ONO2)4: Silicon Analogues of the Common Explosives Pentaerythrityl Tetraazide, C(CH2N3)4, and Pentaerythritol Tetranitrate, C(CH2ONO2)4. J. Am. Chem. Soc. 2007, 129, 6908−6915. (23) Liu, W.-G.; Zybin, S. V.; Dasgupta, S.; Klapötke, T. M.; Goddard, W. A., III. Explanation of the Colossal Detonation Sensitivity of Silicon Pentaerythritol Tetranitrate (Si-PETN) Explosive. J. Am. Chem. Soc. 2009, 131, 7490−7491. (24) Mullen, P. A.; Orloff, M. K. Ultraviolet Absorption Spectrum of Pentaerythritol Tetranitrate. J. Phys. Chem. 1973, 77, 910−911. (25) Yu, Z.; Bernstein, E. R. Decomposition of Pentaerythritol Tetranitrate [C(CH2ONO2)4] Following Electronic Excitation. J. Chem. Phys. 2011, 135, 154305-1−154305-10. (26) Cooper, J. K.; Grant, C. D.; Zhang, J. Z. Experimental and TDDFT Study of Optical Absorption of Six Explosive Molecules: RDX, HMX, PETN, TNT, TATP, and HMTD. J. Phys. Chem. A 2013, 117, 6043−6051.

while the lower energy bands are attributed to the formation of tightly bound singlet and triplet excitons. In particular, the lowest optical absorption peak, which appears in UV−visible spectra of condensed PETN as a weak broad band with the maximum at 4.27 eV, is due to two overlapping singlet−triplet excitations S0→T1 and S0→T2. The next broad peak at 4.8 eV comes from a weak singlet−singlet excitation S0→S1. The third weak broad band at above 5.28 eV represents a mixture of two singlet−triplet excitations S0→T3 and S0→T4 followed by a singlet−singlet S0→S2 transition. Finally, the forth high intensity broad peak at 6.5 eV is attributed to the strong singlet−singlet transition S0→S3 with an admixture of two closely positioned S0→S4 and S0→S5 excitations. All low energy excitations in PETN are well-localized on the nitro-groups. Similar patterns are recognized in the spectra of other relevant nitro-compounds even though the experimental data are somewhat incomplete at the moment. We predict that laser irradiation with the energies of 3.88− 4.30 eV and possibly even slightly lower should initiate the chemical decomposition of PETN and likely of other explosives containing nitro-groups. In addition, we speculate that charge transfer excitons may be induced in PETN by adding impurities, such as oxide particles, what can trigger the nitrate decomposition at a significantly lower energy and, at the same time, allow for the precision control of the initiation process.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: (703)-292-4940. E-mail: [email protected] and mkukla@ umd.edu. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research is supported in part by ONR (Grant N00014-121-0529) and NSF. Most of our calculations were performed with NSF XSEDE resources (Grant TG-DMR130077), using the Stampede supercomputing system at TACC/UT Austin (funded by NSF Award OCI-1134872) and DOE NERSC resources (Contract DE-AC02-05CH11231). M.M.K. is grateful to the Office of the Director of NSF for support under the IRD program.

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Energies of Electronic Transitions of Pentaerythritol Tetranitrate

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