Theoretical and Experimental Study of the CâH Stretching Overtones

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Theoretical and Experimental Study of the C-H Stretching Overtones of 2,4,6,8,10,12-hexanitro- 2,4,6,8,10,12 hexaazaisowurtzitane (CL20) Jerry B Cabalo, and Rosario C. Sausa J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp403778a • Publication Date (Web): 19 Aug 2013 Downloaded from http://pubs.acs.org on August 22, 2013

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The Journal of Physical Chemistry

To be submitted to the Journal of Physical Chemistry

Theoretical and Experimental Study of the C-H Stretching Overtones of 2,4,6,8,10,12hexanitro-2,4,6,8,10,12 hexaazaisowurtzitane (CL20)

J. Cabalo* Edgewood Chemical Biological Engineering Center RDCB-DRI-I 5183 Blackhawk Rd, E5951 Aberdeen Proving Ground, MD 21010 and R. Sausa US Army Research Laboratory RDRL-WML-B Aberdeen Proving Ground, MD 21005

*Corresponding Author

ACS Paragon Plus Environment


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ABSTRACT An understanding of how molecular environment and structure are reflected in optical absorption spectra offers a number of advantages, such as improved detection of materials or providing an easy means of distinguishing crystal polymorphs of the same molecular solid. This study advances this understanding by comparing near IR laser photoacoustic absorption measurements of the first C-H stretch overtones around 5975 cm-1 of beta 2,4,6,8,10,12hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL20) to simulated spectra using density functional calculations and the local mode model of C-H stretches. It was found that accounting for movement of charge throughout the model crystal unit cell with a pure quantum mechanical method in the calculation of the transition dipole moment was critical to matching the experimental data. Vibrational modes in a given molecule induced movement of charge in neighboring molecules, such that calculation of the transition dipole moment had to include the entire crystal unit cell. Movement of charge across the periodic boundary conditions (PBC) of the model had to be accounted for in order to calculate a spectrum validated by the experimental measurement. The Hirshfeld population analysis minimized discontinuities for movement of charge across the PBC.

Key words: 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazatetracyclododecane, 2,4,6,8,10,12hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane, CL20, laser photoacoustic overtone spectroscopy, C-H stretching vibrations, Harmonically Coupled Anharmonic Oscillators, Hirshfeld and Mulliken population analyses, and electron density analysis


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INTRODUCTION Intermolecular interactions play critical roles in the mechanical and chemical properties of molecular crystalline materials.1-4 Physical measurement is critical to the understanding of these interactions in solid materials. To that end, this study furthers the understanding of how molecular structure and intermolecular interactions are reflected in the overtone near IR absorption spectra of solid energetic materials. Such an understanding offers two potential advantages. First, overtone absorption transitions should experience greater changes in absorption frequencies and intensities than the corresponding fundamental transitions. The overtones involve the higher vibrational states where the average bond lengths are greater, and the effective molecular volume is greater. As a result, the interactions between a molecule and its surroundings for these vibrational states should be greater in magnitude than the ground and first vibrational states. Thus, an understanding of how intermolecular interactions are reflected in the overtone vibrational spectrum can permit inference of crystal structure or the nature of molecule-surface interactions.1, 3 Second, the overtone spectrum of a molecule presents a spectral fingerprint that can be used for identification, and knowledge of how the spectral fingerprint is perturbed by molecular interactions can enable use of the near-IR absorption signature. While mid-IR spectroscopy using the fundamental vibrations of a molecule is already a powerful analytic tool, an understanding of the overtone spectra in the near IR enables exploitation of existing solid state laser sources at these wavelengths. In addition, light transducers at the mid IR wavelengths require cryogenic cooling. In contrast, powerful solid state light sources and sensitive detectors operating in the near IR wavelengths are readily



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available, and these could balance the weaker oscillator strengths of the overtone absorptions. Thus, instrumentation working in the near IR wavelengths can readily operate outside the laboratory. Previously, we performed a combined theoretical and experimental study on the first overtone spectra of 1,3,5-trinitrotoluene (TNT) as well as a TNT film on a fumed silica surface.5 The study attempted to model solid state TNT as a single molecule treated quantum mechanically, and intermolecular interactions as classical fixed partial atomic charges. The study showed that each molecule in the crystal unit cell contributed to the many features in the experimental spectrum, and that a single molecule could not account for all the features in the measurement. However, this previous study made two assumptions. First, that the intermolecular interactions are dominated by electrostatic interactions and that the van der Waals interactions can be neglected. Second, the charges on the molecules surrounding the molecule undergoing Harmonically Coupled Anharmonic Oscillators (HCAO) analysis6-9 remain static along the C-H stretching coordinate. This study will show that a completely quantum mechanical model is necessary to fully account for the forces which arise from movement of charge on the surrounding molecules. As a follow on study, a fully quantum mechanical treatment is used with density functional theory and periodic boundary conditions. We use the energetic material 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL20) as the focus of the study for three reasons. First, CL20 has a simpler crystal structure with four molecules per unit cell,10-12 in contrast to the eight molecules in the TNT unit cell.13 This simpler system could be more easily treated quantum mechanically, facilitating the connection between crystal structure and the measured spectrum. Second, because the rigid cage structure of CL20 would most likely have minimal coupling between C-H


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stretches, it would be a reasonable assumption to neglect coupling between modes. We use the local mode model for simulating the overtone spectra and generating overtone transition absorption intensities rather than the full HCAO. This assumption cuts computational cost and facilitates calculations of large, purely quantum mechanical models by avoiding the calculation of two dimensional potential energy surfaces generated from pairwise scans. These scans are necessary for determination of the interaction potential between C-H modes in the full HCAO treatment. Third, an easy method for identifying the crystal polymorphs of CL20 is highly desirable due to the different properties between forms. While CL20 is potentially a next generation energetic material thanks to its high energy content, shock sensitivity has prevented the exploitation of the material. Sensitivity and other properties are highly dependent on the crystal structure, and the control of the selection of the crystal polymorph is essential to successful formulations of CL20 that have limited shock sensitivity while possessing high energy content.14-15 In this paper, we report on the laser photoacoustic overtone spectroscopy and quantum mechanical calculations with density functional theory and periodic boundary conditions of CL20 in the region of the first overtone C-H stretches near 5975 cm-1. We performed the calculations both on a single molecule and unit crystal cell treating the C-H stretches as local modes. The utilization of a purely quantum mechanical model predicts more accurate spectra than a dual quantum/classical (QM:MM) model because it allows movement of charge in surrounding molecules in response to movement along the C-H stretch coordinate within a particular molecule, and this study focuses on that treatment of charge. Because the focus is on the movement of charge in response to vibrational motion rather than dispersion effects, we do not use a dispersion corrected functional, and thus the effect of dispersion or van der Waals



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forces will be underestimated.16 Transition dipole moments are calculated from Hirshfeld and Mulliken population analyses and electron density analysis. These analyses are compared and contrasted as they influence the calculated absorptions intensities.

EXPERIMENTAL METHODS CL20 is an energetic material with a rigid molecular structure, consisting of four crystal polymorphs, the α, β, ε, and ζ forms.10 Each of the four conformers involves bond angles of only the nitro functional groups, and the positions of the hydrocarbon portion of the molecule are unaffected. The experimental setup for the measurement of the first overtone absorption spectrum of the C-H stretches of CL20 has been described in detail previously.5, 17 Briefly, the experiments are performed using an absorption photoacoustic cell (MTEC Photoacoustics, PAC 300) containing about 20 mg of β-CL20 and tunable laser radiation. The experimental spectrum is obtained using the photoacoustic cell containing β-CL20 with an argon flow rate of ~3 cm3/s to eliminate interference from water vapor. The rapid local heating and cooling of the sample and its surrounding gas by the pulsed laser causes a change in pressure and results in acoustic waves. The acoustic waves are detected with a microphone. The signal amplitude depends linearly on the energy absorbed by the sample, its thermal diffusivity, and the interface coupling between the sample surface and its surrounding gas. An optical parametric oscillator (Continuum Sunlite EX) pumped by the 355-nm output of a 10-Hz pulsed Nd:YAG laser (Continuum Powerlite® Precision II) provides the tunable laser radiation in the range of 5500 to 6500 cm-1 with pulses of about 5 ns duration and approximately 0.08 cm-1 linewidth. Typical pulse energies are about 0.4 mJ/pulse and are focused with a 200-mm lens onto the cell’s sample cup. We amplify the photoacoustic signal using the cell’s onboard amplifier and direct it to both a


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boxcar integrator (Stanford Research Systems, SR250), set to a gate and delay of 0.03 µs and 10 µs, respectively, and an oscilloscope (LeCroy 9400). The spectra are recorded with 10-shot averaging using a personal computer interfaced to the boxcar and commercial software supplied by Stanford Research Systems. The photoacoustic spectra are obtained by monitoring the signal while scanning the laser radiation over the spectral region of interest and correcting them for laser energy fluctuation with wavelength and background noise.

THEORETICAL METHODS We invoke a local mode treatment similar to that used in the previous study.5 The C-H stretch overtones are assumed to be nearly independent of the other motions of the molecule, and are thus treated separately from the rest of the molecule as if they were a collection of diatomic anharmonic oscillators. We use the local mode model rather than the full HCAO treatment and neglect coupling between C-H oscillators because the CL20 cage is rigid and the hydrogen atoms do not share carbon atoms. The Morse potential function was assumed to describe the potential energy surface (PES) along the C-H stretching coordinate, so that the local mode vibrational Hamiltonian for optical absorption into the ith mode without coupling corrections can be described as:

|〉 |〉 |〉 |〉

| 〉 |0〉 | 〉 |0〉

(1)

is the where ωe is the harmonic vibrational constant, ωexe is the anharmonicity constant, Hamiltonian operator for the C-H stretch,| 〉 is the Morse oscillator wavefunction of the absorbing C-H stretch with v the number of vibrational quanta absorbed, and |0〉 are the Morse



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oscillator wavefunctions of oscillators not involved in the absorption. To calculate the potential energy surface as a function of displacement q from the equilibrium bond length, a potential energy scan is recorded for q in increments of 0.05 Å for a total of +0.30 Å. The PES is treated as a Taylor series expansion and a fourth order polynomial is least squares fitted to the calculated PES as a function of C-H stretch displacement. The second and third order force constants are obtained from the coefficients of the Taylor series expansion and used in the equations of Kjaergaard7 to obtain the harmonic and anharmonic constants. At the same time, Mulliken18 and Hirshfeld19 population analyses are performed at each step of the PES scan to obtain partial atomic charges that are used to calculate the transition dipole matrix elements and the absorption intensities. To explore the effect of the intermolecular interactions on the PES, one scan is carried further for 40 steps in 0.1 Å increments, out to 3.5 Å from the equilibrium position. For each position along the PES scan, both Gaussian 200920 and DMOL321-22 output the total electron density over the volume of the crystal unit cell. The results are discrete absorption frequencies for each C-H stretch mode and a matching oscillator strength. In order to generate spectra for comparison to experiment, the Lorentzian lineshape is used for each transition with a full width half maximum (FWHM) of 10 cm-1. For each transition, the height of the peak is determined from the result of the intensity calculation, then all the Lorentzian lineshapes are summed to produce the final spectrum that is compared to experiment. For the quantum mechanical treatment, both Gaussian 2009 version B.02 and DMOL3 are used on a ~10,000 core SGI Altix cluster as well as a 200 core POGO/Linux cluster. DMOL3 is used primarily for both single molecule models and crystal unit cell models with periodic boundary conditions (PBC) using the gradient corrected Perdew-Burke-Enzerhof


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(GGA-PBE) and Perdew-Wang (PW91) functionals with the double zeta numerical basis set plus polarization functions. To reduce the computational cost of a purely quantum mechanical model of 144 atoms, we neglect dispersion correction which consists of pairwise 1/r6 potentials, and focus on the movement of charge in response to displacement along the C-H stretch. Calculations were also attempted in Gaussian 2009 using PBC and the PBE/3-21G method, but it was found that with the β-CL20 system, calculations even with the 3-21G basis set were computationally expensive. In constructing the crystal unit cell models of β and ε CL20, the results of Ou, et al. and Xu et al.12, 23 are used as an initial structure and reoptimized within DMOL3 using the “fine” convergence criteria to ensure a global energy minimum was maintained. The unit cell model has 4 CL20 molecules, and thus a total of 24 C-H oscillators. The transient dipole moment is calculated either using the resulting partial atomic charges from the population analyses, or directly from the total electron charge density. For the calculation from partial charges, the outputs of the population analyses that assign partial charge to the atomic locations were used to calculate the dipole moment using the standard definition in Cartesian space:

∑

! !̂

(2)

where µ is the electric dipole moment, qi is the partial charge of the atom located at the Cartesian point (xi,yi,zi). For calculating the dipole moment using the total electron density, the total density from DMOL3 was read from the GRD file output. Equation 2 is still used, except that the sum of the volume elements of charge times their location is added to the sum of the nuclear



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charges times the location of the atomic nuclei. The crystal unit cell boundaries are left in place during the calculation, although when atoms traversed the PBC boundary, it could either be reflected to the opposite side of the unit cell, or permitted to move into the adjacent unit cell image. For moments calculated from the electron density, the transient dipole moment induced by motion along the C-H coordinate was calculated from the entire unit cell because segregating total electron charge to each molecule would have required a complex code. For dipole moments calculated from the partial atomic charges, the dynamic dipole moment could be calculated from the entire unit cell or from individual molecules. The results for all three methods of calculation are the dipole moment calculated at each displacement step along the PES scan. Again, the dipole moment as a function of displacement is treated as a fourth order Taylor series and a fourth order polynomial is fitted to the results with least squares. The constant component of the polynomial is removed and the transition dipole moment component is calculated as shown in Equation 3. | | 〈$| 〈0| % |0〉 |0〉

(3)

where |µe| is the transition dipole matrix element that is proportional to the absorption oscillator strength, j are the Morse wavefunctions of the local modes not involved in the absorption that remain in the ground vibrational state. To reduce the computational cost, truncated models are investigated as an alternative means to obtain dipole moments. For C-H stretches undergoing analysis, two to three of the nearest neighbor molecules are retained in the calculation, and molecules on the opposite side were neglected. On account of very poor agreement with the experimental spectrum, this


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approach is not continued. To check that the unit cell for the periodic boundary conditions is sufficiently large so that mirror images of a given C-H oscillator do not affect calculations, three additional calculations are performed where one model consisted of a unit cell doubled along the a crystal axis, a second model was doubled along the b crystal axis, and a third was doubled along the c crystal axis. The local mode vibrational analysis was performed on all three models. Disagreement was small between these three models and the single unit cell model, so we conclude the unit cell is sufficiently large to limit a molecule’s image from affecting itself. RESULTS Figure 1A and 1C shows the single molecule model of the β and ε polymorphs of CL20 showing each C-H oscillator, respectively, with its appropriate label. The β and ε crystal unit cells are shown in Figure 1B and 1D, respectively, with each molecular position labeled. The model lattice constants from the β conformer model, a= 9.999 Å, b=12.028 Å, c=13.778 Å,

α=90.99o, β=89.84o, and γ=89.86o, compare well with those reported in the literature from X-ray diffraction measurements, a=9.670Å, b=11.62Å, c=13.03Å, and α=β=γ=90o. The β-CL20 model roughly maintains the Pca21 space group symmetry as found in the literature, although the geometry optimization is performed with no constraints. The model lattice constants from the ε conformer shown in Figure 1D are calculated to be a=14.174 Å, b=13.214 Å, c=9.207 Å,

α=94.69o, β=107.58o, and γ=89.27o. The corresponding X-ray diffraction data are a=13.696 Å, b=12.554 Å, c=8.833 Å, and α=90.00o, β=113.05o, and γ=90.00o, reported in Xu.12 Xu et al. obtained smaller differences between calculated structure and the x-ray diffraction (XRD) measurements on ε-CL20 using a plane-wave basis set in the CASTEP code with the PBE functional. We do not impose tighter convergence criteria in this study because the difference in the lattice constants and the XRD measurements are relatively small. We obtain more accurate



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values for the lattice constants of β-CL20 using the PBE/DNP method rather than the PW91/DNP method. As a result, we perform subsequent calculations on periodic models using the PBE/DNP method.

Figure 1: Single molecule structure of the β-CL20 conformer, and the labeling scheme for the C-H oscillators and nitro functional groups (A), the unit cell structure of the β-CL20 crystal, including the designating labels for each molecule in the unit cell (B), single molecule structure for the ε-CL20 conformer and the


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labeling scheme for the C-H oscillators and nitro functional groups (C), and the unit cell structure for the ε-CL20 crystal (D).

Figure 2A shows the experimental first overtone absorption spectrum of β-CL20 compared to spectra predicted from an all DFT model, as well as a single molecule model. Figure 2B is the resulting spectrum when the Hirshfeld population analysis is used and the transition dipole moment is calculated from the entire crystal unit cell in the model. Figure 2C is the resulting spectrum when only the molecule containing a particular C-H oscillator is used in the calculation of transition dipole moment, and the surrounding molecules are treated with static charges. Figure 2D is the predicted spectrum from a single β-CL20 molecule. All theoretical spectral frequencies have been scaled by 1.0405, which brings the frequencies of 2B into agreement with experiment, and the theoretical spectra are on the same height scale. Because this local mode approach uses the anharmonic Morse potential and a correction is added to account for anharmonicity, the frequency scaling factor is greater than one.



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Figure 2: A comparison of the experimental 1st C-H stretch overtone of A) βCL20 to B) the model spectrum (Lorentzian lineshape with 10 cm-1 FWHM and stick spectrum) predicted with periodic boundary conditions (PBC), and the Hirshfeld population analysis over the entire crystal unit cell. C) shows the predicted overtone spectrum when the contribution of molecules surrounding the molecule with the C-H oscillator to the transition dipole moment is neglected. D) shows the predicted spectrum from a single, isolated β-CL20 molecule.

The differences between Figures 2B and 2C illustrate the importance of the motion of charge to correctly calculating the transient dipole moment. For the spectrum in 2C, when calculating the transition dipole moment along a particular C-H stretch coordinate, only the molecule containing the particular C-H oscillator is used to calculate the transition dipole moment. This approach makes the assumption that the dipole moment of the surrounding molecules remains static and do not respond to the motion of charge in the molecule containing the C-H oscillator. On the other hand, the spectrum in Figure 2B results when the transition


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dipole moment is calculated from the entire crystal unit cell. This calculation allows the charge from both the molecule containing the C-H oscillator and the surrounding molecules to respond to the motion along the C-H coordinate. Of the spectra calculated by varying methods of getting the transition dipole moment, Figure 2B best agrees with experiment. This result shows that a transient dipole moment can be induced in surrounding molecules that do not contain the motion coordinate, and that it is significant enough to affect the absorption spectrum.

The predicted

spectrum from the single molecule model in Figure 2D does not account for the features observed in the experiment, and demonstrates that a single molecule model is insufficient to simulate the spectrum from the solid state. Calculations that include the surrounding molecules generally tend to reduce the transition dipole moment. This result can be observed in a comparison of the intensities in the stick spectra of Figure 2B and 2C, where the intensities in Figure 2B tend to be weaker than in 2C. This can be understood by the fact that CL20 is a dielectric material. As a dielectric tends to counteract an electric field, the dipole moments of surrounding molecules also tend to counteract the transient dipole moment of the molecule containing the C-H oscillator. The three groups of transition frequency wavenumbers around 5900 cm-1, 5935 cm-1 and 5995 cm-1 that appear strong in Figure 2C are much reduced in intensity in Figure 2B. The transitions that remain observable appear as shoulders in the experimental spectrum. However, for several peaks, at 5964 cm-1, 5972 cm-1 (2 peaks), 5992 cm-1, 5938 cm-1, and 5965 cm-1, there is enhancement. Clearly, the geometry of the crystal is such that for some cases, the induced dipoles in the different molecules are additive. For the spectra in Figures 2B and 2C, the frequency wavenumbers are identical, suggesting that the changes in intensities are due to the calculation of dipole moment.



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We also examined the predicted spectra for the fundamental transition in order to understand how the contribution of surrounding molecules to the transition dipole moment changes as a function of the amplitude of vibrational displacement. Figure 3A shows the spectrum resulting from transition dipole moments calculated from the entire crystal unit cell, and Figure 3B shows the result when the transition dipole moment is calculated when assuming the dipole moments of the surrounding molecules are static. Figure 3 shows that even for the fundamental transitions, there can be significant differences in predicted spectra when making the assumption of static charge in the surroundings. The results show that intermolecular interactions are reflected in both the overtone and fundamental absorption spectra.

Figure 3: Predicted fundamental absorptions from β-CL20. A) Theoretical spectrum resulting from dipole moments calculated from the entire unit cell, and B) spectrum resulting from dipole moments localized to the molecule containing the C-H oscillator.


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Figures 4 and 5 show the differences in spectra depending on how the PBCs are handled. Figure 4 shows the resulting spectra when allowing atomic charges to move into neighboring unit cells. The spectra in Figure 5 result when the atomic charges are confined within the unit cell in the calculation of dipole moment so that when an atomic nucleus crosses a PBC, it reappears on the opposite side of the unit cell. Both figures contain spectra using the Hirshfeld population analysis, the total electron density, and the Mulliken population analysis to calculate the dipole moment. For both figures, the intensity scale is relative to facilitate comparison between spectra.

Figure 4: A comparison of spectra calculated from dipole moments from the Hirshfeld population analysis, directly from the total electron density and the location and charge of the atomic nuclei, and the Mulliken population analysis. The charges on the nuclei are permitted to move into adjacent crystal unit cells.



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Figure 5: A comparison of spectra from the same models as in Figure 4, except when atomic charges cross the boundary of the crystal unit cell, they reappear on the opposite side of the crystal unit cell.

As stated above, the Hirshfeld population analysis is necessary to predict a spectrum in agreement with experiment. The comparison of spectra generated from the Hirshfeld and Mulliken population analyses and from electron densities shows significant differences in the intensity pattern as well as absolute intensities. To normalize the 3 spectra within Figure 4, the Hirshfeld spectrum had to be scaled by 270, the electron density spectrum had to be scaled by 40, and the Mulliken spectrum was not normalized at all. We hypothesize these differences arise from the sensitivity to the PBCs for each method of calculating the dipole moment. The Hirshfeld population analysis uses the deformation density, which is the difference between the density around a free atom and the density around the atom within the molecule. We would expect the deformation density to be small far away from the atom, so that only regions close to


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the atomic nuclei would contribute significantly to the calculation of partial atomic charge. Thus, the Hirshfeld population analysis should be the least sensitive to the PBC. Although the spectrum from the electron density has a smaller scaling factor than the spectrum from the Mulliken population analysis, the pattern of intensity from the Mulliken spectrum more closely resembles the data. This is most likely due to the fact the electron density is still confined within the PBC, resulting in some exaggeration of the dipole moment when charge crosses the PBC and is reflected to the other side of the unit cell. Dipole moments calculated from the Mulliken analysis were large and peaks close to 5910 cm-1 were exaggerated. We expect the assignment of partial charge by the Mulliken population analysis to be very sensitive to the PBCs. It is known that the Mulliken analysis is very sensitive to the selection of basis sets, and that portions of the wavefunction far from the molecule can have a significant impact on the resulting charges. Movement of wavefunction density across PBC boundaries could thus have an impact on the calculated partial atomic charge. The handling of the PBCs has the largest effect on the predicted absorption intensity. When confining movement of atomic nuclei to the unit cell, such that as an atom moves across the PBC it reappears on the opposite side of the unit cell, a discontinuity in the calculated dipole moment results. The discontinuity is dependent on the location of the PBC and not the physics of the system, so that the approach causes overestimation of the transition dipole moment for modes that move atoms across the PBC. This is seen in the spectrum calculated from electron density in Figure 5, where all transition frequencies are dwarfed in absorption intensities by a single frequency. The dipole moments calculated from Hirshfeld or Mulliken population analyses do not exhibit the same extreme discontinuities. In the calculation of dipole moment



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from electron density, the full nuclear charge is assigned to the atom centers, and when an atom nucleus crosses the PBC, there is a large change in dipole moment. When using partial charges, when an atom crosses the PBC, the effect is less extreme; however, the problem still persists. The problem exhibits itself because the calculations grossly exaggerate the dipole moment changes for some of the C-H stretches, and because the resulting predicted spectra do not agree with experiment. Unwrapping the PBC by allowing the nuclear charges to move into adjacent images of the unit cell solves this problem for the Hirshfeld and Mulliken population analyses. The dipole moment calculation is more independent of the PBC location, causing the extreme discontinuities to disappear. This approach does not completely solve the problem for calculating the dipole moment directly from the electron density. The movement of the electron “gas” across the PBC cannot be as readily tracked as the atom nuclei and the PBC is not easily unwrapped as for the atomic nuclei. Table 1 compares C-H stretch frequency data from a single free molecule to the four molecules in the β−CL20 crystal unit cell. The C-H oscillators in each molecule were named as in Figure 1, C-H 1 through C-H 6, so that the location of the C-H oscillators within each individual molecule was kept consistent. The first overtone vibrational frequencies, the harmonic constants ωe, the anharmonicities ωeχe, and the frequency shifts between a molecule in the unit cell versus the free molecule are included in the table to show how the intermolecular interactions in the crystal affect the observed overtone absorption spectrum. For the free molecule, C-H (5) and C-H (6) are on the “bridge” over the ring structure. The intramolecular interaction of these oscillators is minimal with the nitro functional groups in the molecule, and thus they have the highest vibrational frequencies. On the other hand, the dihedral angle between the respective nitro groups N(1) through N(4) and the C-H oscillators C-


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H (1) through C-H (4) does not lead to greater than 10 cm-1 differences in the vibrational overtone frequency. However, when the molecule is embedded in a crystal matrix, much larger shifts in C-H stretch frequencies, on the order of 50 cm-1, are observed. For all of the C-H (5) and C-H (6) oscillators in the unit cell, intermolecular interactions within the crystal cause red shifts in the absorption frequencies. For the C-H (1) through C-H (4) oscillators, the intermolecular interactions cause alternating blue and red shifts in the frequency. The geometric arrangement of the CL20 molecules causes the pattern of red and blue shifts. For molecules M1 and M3, the dihedral angles between C-H (1) and N(1), and C-H (4) and N(4) are less than 5o and the dihedral angles between C-H (2) and N(2), and C-H (3) and N(3) are about 70o. However, this pattern is reversed for molecules M2 and M4. This pattern is reflected in the frequency shifts, where small dihedral angles with the nitro group result in a blue shift in frequency, and the larger dihedral angles cause red shifts in frequency. While the dihedral angle doesn’t have a large effect in the free molecule, it does affect the arrangement of surrounding molecules, which in turn affects the vibrational wavenumbers. Figure 6 shows the perturbation to the PES of C-H (1) induced by intermolecular interactions with a comparison of the unperturbed free molecule and molecule M1 in the crystal matrix. The perturbation is most obvious at long distance.



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Figure 6: Comparison of C-H stretch PES in free molecule vs. a molecule in a crystal

Finally, in order to explore differences between the near-IR absorption spectra of the different polymorphs, the spectrum of ε-CL20 is also calculated, using the same approach and frequency scaling factor. Figure 7 shows a comparison between the two predicted spectra and they are clearly different. It is reasonable to expect that the two polymorphs could be distinguished with near IR spectroscopy.


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Figure 7: Comparison of predicted spectra from the β-conformer and the εconformer. Given the significant difference between spectra, it should be possible to distinguish the crystal polymorphs with simple near-IR absorption measurements.

CONCLUSIONS

The first overtone C-H stretch spectrum of β-CL20 has been experimentally measured and simulated using a local mode model with Mulliken and Hirshfeld population and electron density analyses. The calculation of the transition dipole moment is critical to correctly simulating the overtone absorption spectrum, as it influences the calculation of absorption intensities. Although the crystal unit cell of β-CL20 has four individual molecules, movement along the C-H stretch coordinates in one molecule induces charge shifts in the surrounding molecules. As a result, the transition dipole involves the entire unit cell rather than just the molecule where the C-H stretch coordinate is localized. The movement of charge in surrounding



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molecules is shown in the all quantum DFT model, and the spectrum calculated from the model best agrees with the experiment when the entire unit cell is used in calculating the transition dipole moment. Also critical to calculating the transition dipole moment is the method of handling the periodic boundary conditions. When the C-H stretch coordinate traverses a boundary of the unit cell, large discontinuities in the calculated dipole moment result as the charge is reflected to the opposite side of the crystal unit cell. These discontinuities are mitigated by allowing charge to move beyond the boundary of the unit cell. Progress has been made in developing the method for calculating overtone absorptions within crystals and future work refining this method is planned. The absorption spectrum for the ε-CL20 polymorph were also performed, and differences between the predicted spectra for the β and ε forms suggest near IR absorption spectroscopy could be used to differentiate between polymorphs.

ACKNOWLEDGEMENTS We thank Dr. Rose Pesce-Rodriguez of the US Army Research laboratory for providing us with the CL20 sample and the use of her photoacoustic cell. We also thank the ARL DoD Supercomputing Resource Center for providing access to high performance computing resources. Support from both the ARL and the ECBC In-house Laboratory Independent Research Program administered by Dr. A. W. Fountain is greatly appreciated.


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Table 1: Calculated first overtone wavenumbers, harmonic and anharmonic constants of both single molecule and crystal unit cell of β-CL20 in the C-H oscillator region. Single C-H 1 C-H 2 C-H 3 C-H 4 C-H 5 C-H 6

Overtone -1 Wavenumber (cm ) 5721.93 5728.49 5725.87 5715.72 5767.82 5776.71

ω (cm-1)

ωeχe (cm-1)

3083.16 3084.66 3085.95 3077.21 3100.44 3109.16

88.88 88.17 89.21 87.74 86.61 88.32

-1 a

∆ (cm )

M1 C-H 1 C-H 2 C-H 3 C-H 4 C-H 5 C-H 6

5732.79 5711.16 5757.79 5682.62 5749.70 5740.30

3083.52 3074.84 3099.36 3064.08 3089.60 3091.90

86.85 87.70 88.18 89.11 85.90 88.70

10.86 -17.33 31.93 -33.10 -18.12 -36.41

M2 C-H 1 C-H 2 C-H 3 C-H 4 C-H 5 C-H 6

5713.34 5739.90 5682.47 5759.69 5753.47 5735.76

3081.82 3088.41 3060.78 3101.59 3092.77 3086.30

90.06 87.39 87.82 88.70 86.41 87.37

-8.59 11.40 -43.39 43.97 -14.35 -40.95

M3 C-H 1 C-H 2 C-H 3 C-H 4 C-H 5 C-H 6

5739.18 5707.28 5766.23 5680.87 5755.01 5746.30

3087.17 3076.94 3105.00 3059.12 3093.47 3092.93

87.03 89.32 88.75 87.47 86.39 87.91

17.24 -21.21 40.37 -34.85 -12.81 -30.41

M4 C-H 1 C-H 2 C-H 3 C-H 4 C-H 5 C-H 6

5760.00 5678.41 5732.89 5710.50 5743.04 5753.84

3098.68 3059.96 3083.70 3075.54 3090.74 3092.46

87.47 88.30 86.90 88.12 87.69 86.22

38.07 -50.08 7.03 -5.23 -24.78 -22.87

a

∆ is the wavenumber difference between a particular C-H oscillator in an isolated molecule and the same corresponding C-H oscillator in a given molecule within the crystal unit cell.



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LIST OF FIGURES: Figure 1: Single molecule structure of the β-CL20 conformer, and the labeling scheme for the CH oscillators and nitro functional groups (A), the unit cell structure of the β-CL20 crystal, including the designating labels for each molecule in the unit cell (B), single molecule structure for the ε-CL20 conformer and the labeling scheme for the C-H oscillators and nitro functional groups (C), and the unit cell structure for the ε-CL20 crystal (D). Figure 2: A comparison of the experimental 1st C-H stretch overtone of A) β-CL20 to B) the model spectrum (Lorentzian lineshape with 10 cm-1 FWHM and stick spectrum) predicted with periodic boundary conditions (PBC), and the Hirshfeld population analysis over the entire crystal unit cell. C) shows the predicted overtone spectrum when the contribution of molecules surrounding the molecule with the C-H oscillator to the transition dipole moment is neglected. D) shows the predicted spectrum from a single, isolated β-CL20 molecule. Figure 3: Predicted fundamental absorptions from β-CL20. A) Theoretical spectrum resulting from dipole moments calculated from the entire unit cell, and B) spectrum resulting from dipole moments localized to the molecule containing the C-H oscillator. Figure 4: A comparison of spectra calculated from dipole moments from the Hirshfeld population analysis, directly from the total electron density and the location and charge of the atomic nuclei, and the Mulliken population analysis. The charges on the nuclei are permitted to move into adjacent crystal unit cells. Figure 5: A comparison of spectra from the same models as in Figure 4, except when atomic charges cross the boundary of the crystal unit cell, they reappear on the opposite side of the crystal unit cell. Figure 6: Comparison of C-H stretch PES in free molecule vs. a molecule in a crystal. Figure 7: Comparison of predicted overtone absorption spectrum from the β and the ε crystal polymorphs.


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REFERENCES (1) Suttiwijitpukdee, N.; Sato, H.; Unger, M.; Ozaki, Y., Effects of Hydrogen Bond Intermolecular Interactions on the Crystal Spherulite of Poly(3-hydroxybutyrate) and Cellulose Acetate Butyrate Blends: Studied by FT-IR and FT-NIR Imaging Spectroscopy, Macromolecules 2012, 46 (6), 2738-2748. (2) Delattre, S., et al., Experimental and Theoretical Study of the Vibrational Properties of Diaspore (Alpha-AlOOH), Phys. Chem. Miner. 2012, 39 (2), 93-102. (3) Paulson, L. O.; Anderson, D. T.; Lundell, J.; Marushkevich, K.; Melavuori, M.; Khriachtchev, L., Conformation Resolved Induced Infrared Activity: trans- and cis- Formic Acid Isolated in Solid Molecular Hydrogen J. Phys. Chem. A 2011, 115 (46), 13346-13355. (4) Frost, R. L.; Reddy, B. J.; Palmer, S. J.; Keeffe, E. C., Structure of Selected Basic Zinc/Copper (II) Phosphate Minerals Based Upon Near-infrared Spectroscopy - Implications for hydrogen bonding Spectrochim. Acta A 2011, 73 (3), 996-1003. (5) Cabalo, J.; Sausa, R., Experimental and Theortical Investigation of the First Overtone Spectrum of 1,3,5-Trinitrotoluene, J. Phys. Chem. A 2011, 115, 9139-9150. (6) Child, M. S.; Lawton, R. T., Local and Normal Vibrational States: a Harmonically Coupled Anharmonicoscillator Model, Faraday Discuss. 1981, 71, 273-285. (7) Kjaergaard, H. G.; Henry, B. R., The Relative Intensity Contributions of Axial and Equatorial CH Bonds in the Local Mode Overtone Spectra of Cyclohexane, J. Chem. Phys. 1992, 96 (7), 4841-4851. (8) Petryk, M. W. P.; Henry, B. R., CH Stretching Vibrational Overtone Spectra of tert-Butylbenzene, tertButyl Chloride, and tert-Butyl Iodide, J. Phys. Chem. A 2005, 109 (18), 4081-4091. (9) Zhu, C.; Kjaergaard, H. G.; Henry, B. R., CH-stretching Overtone Spectra and Internal Methyl Rotation in 2,6-difluorotoluene, J. Chem. Phy. 1997, 107 (3), 691-701. (10) Kholod, Y.; Okovytyy, S.; Kuramshina, G.; Qasim, M.; Gorb, L.; Leszczynski, J., An Analysis of Stable Forms of CL-20: A DFT Study of Conformational Transitions, Infrared and Raman spectra, J. Mol. Struct. 2007, 843, 14-25. (11) XiaoJuan, X.; Jijun, X.; Hui, H.; JinShan, L.; HeMing, X., Molecular Dynamics Simulations on the Structures and Properties of epsilon-CL-20-based PBXs, Sci. China Ser. B 2007, 50 (6), 737-745. (12) Xu, X. J.; Zhu, W. H.; Xiao, H. M., DFT studies on the four polymorphs of crystalline CL-20 and the influences of hydrostatic pressure on epsilon-CL-20 crystal, J. Phys. Chem. B 2007, 111 (8), 2090-2097. (13) Carper, W. R.; Davis, L. P.; Extine, M. W., Molecular Structure of 2,4,6-Trinitrotoluene, J. Phys. Chem. 1982, 86 (4), 459-462. (14) Meents, A.; Dittrich, B.; Johnas, S. K. J.; Thome, V.; Weckert, E. F., Charge-density Studies of Energetic Materials: CL-20 and FOX-7, Acta Crystall. Sec. B 2008, 64, 42-49. (15) Ghule, V. D.; Jadhav, P. M.; Patil, R. S.; Radhakrishnan, S.; Soman, T., Quantum-Chemical Studies on Hexaazaisowurtzitanes, J. Phys. Chem. A 2010, 114 (1), 498-503. (16) Klimes, J.; Michaelides, A., Perspective: Advances and Challenges in Treating van der Waals Dispersion Forces in Density Functional Theory, J. Chem. Phys. 2012, 137, 120901. (17) Sausa, R. C.; Cabalo, J. B., The Detection of Energetic Materials by Laser Photoacoustic Overtone Spectroscopy, Appl. Spect. 2012, 66 (9), 993-998. (18) Mulliken, R. S., Electronic Population Analysis on LCAO-MO Molecular Wave Functions. I, J. Chem. Phys. 1955, 23, 1833-1831. (19) Davidson, E. R.; Chakravorty, S., A test of the Hirshfeld definition of atomic charges and moments, Theor. Chim. Acta 1992, 83, 319-329. (20) Frisch, M. J., et al. Gaussian 2009, Revision B.02, Gaussian, Inc.: Wallingford CT, 2009. (21) Delley, B., From Molecules to Solids with the DMOL(3) Approach, J. Chem. Phys. 2000, 113 (18), 7756-7764.



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(22) Delley, B., AN ALL-ELECTRON NUMERICAL-METHOD FOR SOLVING THE LOCAL DENSITY FUNCTIONAL FOR POLYATOMIC-MOLECULES, J. Chem. Phys. 1990, 92 (1), 508-517. (23) Ou, Y. X.; Huiping, J.; Xu, Y.; Chen, B.; Guangyu, F.; Liu, L.; Zheng, F.; Pan, Z.; Wang, C., Synthesis and Crystal Structure of β-hexanitrohexaazaisowurtzitane, Sci. China Ser. B 1999, 42 (2), 217-224.


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Table of Contents (TOC) Graphic



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C-H 1 C-H 5

C-H 2

N1 N2

N5

N6

N3 N4 C-H 6 C-H 4

C-H 3

A


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M2 M3 M4

M1

B



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

C-H 1

N1

C-H 2 C-H 5

N5 N3

N2 N6

C-H 6 N4 C-H 3 C-H 4

C


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M2 M1

M3 M4

D


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Intensity (arb. Units)


A B C

D 5875

5925 5975 6025 -1 Wavenumber (cm )


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Signal (arb. Units)

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A B

2850

2900 Wavenumber (cm-1)


2950

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Relative Signal (arb. units)


Hirshfeld

Electron density

Mulliken

5870

5920

5970

6020

Wavenumber (cm-1)


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Relative Signal (arb. units)

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Hirshfeld

Electron density

Mulliken

5870

5920

5970

6020

Wavenumber (cm-1)



0.3

Energy (Hartrees)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

0.25 0.2 0.15

Free Molecule

0.1

b-CL20 b-CL20 Crystal

0.05 0

-2

0

2

4

C-H displacement (Å)


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b-CL20 conformer Signal (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58


5850

e-CL20 conformer

5900

5950

Wavenumber

6000 (cm-1)


6050


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Overtone Spectrum

Inter-molecular interactions

-1

PES

4

5875

5975

Wavenumber (cm-1)


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