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MOLECULAR SOLIDS. DETONATION THEORY IN A CRYSTAL : LIMITS
A. Karo, J. Hardy
To cite this version:
A. Karo, J. Hardy. ENERGY TRANSFER PROCESSES IN CONDENSED MOLECULAR SOLIDS.
DETONATION THEORY IN A CRYSTAL : LIMITS. Journal de Physique Colloques, 1987, 48 (C4), pp.C4-235-C4-251. �10.1051/jphyscol:1987417�. �jpa-00226649�
JOURNAL D E PHYSIQUE
Colloque ~ 4 , supplbment au n'g, Tome 48, septembre 1987
ENERGY TRANSFER PROCESSES IN CONDENSED MOLECULAR SOLIDS.
DETONATION THEORY IN A CRYSTAL : LIMITS*
A.M. KARO and J . R . HARDY'
Lawrence Ltvermore National Laboratory, Livermore, CA 94550, U.S.A.
'BehZen Laboratory of Physics, University of Nebraska, Lincotn, Nebraska 68588, U.S. A.
R6sum6
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On pr6sente ici une revue de la diversit6 des simulations numeriques par ordinateur en dynamique mol6culaire de complexit6 croissante, qui ont btb rdalis6es ces dernieres ann6es sur la propagation d'un choc dans des systemes condens6s. Commenqant par les simulations de chocs les plus simples dans des syst2.mes ordonnds mono et di-atomiques, nous considbrons l'influence des h6t6rogbnbit6s, telles les dbfauts (point et ligne), cavitbs, parois de grains et surfaces, sur la structure et la stabiliti: du front de choc. Nous discutons nos rgcents travaux sur les processus de transfert dt6nergie induit par choc dans des r6seaux contenant des fragments moldculaires ou des radicaux, repr6sentant les especes d'intdrst dans la d6composition des mat6riaux 6nerg6tiques. Les r6sultats indiquent que l'excitation des liaisons intra-moli.culaires prbsente un caractere spectral 6tendu avec des temps de mont6e de l'bnergie essentiellement identiques pour tous les domaines de frbquence.Abstract
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We present a review of the variety of computer molecular dynamics simulations of gradually increasing complexity that have been carried out in recent years on shock propagation in condensed systems.Beginning with the simplest simulations of shocks in ordered monoatomic and diatomic systems, we consider the influence of heterogeneities such as point and line defects, voids, grain boundaries, and surfaces on the structure and stability of the shock front. We discuss our recent work on shock-induced energy transfer processes occurring in lattices containing molecular fragments or radicals, representing species of interest in the decomposition of energetic materials. The results indicate that the excitation of the intra-molecular bonds is of broad spectral character with energy rise times essentially identical for all frequency ranges.
Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract number W-7405-ENG- 48; one of us (AMK) also would like t o acknowledge the addl tional support of the Off Ice of Naval Research under contract NO00 1 4-86-F-0086.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987417
A shock disturbance can be supported by a variety of media, e.g., solids, liquids, gases, and plasmas. However, a chemically reactive medium presents a situation different from the others, since shocks i n such media can induce chemical reactions which not only become self-sustaining, but f o r energetic materials can also proceed from steady burn t o detonation. A conventional continuum hydrodynamics model f o r understanding t h i s behavior, based on the onset of initiation by "hot spots" of compressed entrapped gas [ 1
I,
i s f a r from satisfactory, since it i s apparent that the initiation mechanism, whatever i t is, has t o begin by a breaking of bonds such as C=N, C=C, C-H, and C-0, a l l of which are quite strong and mechanically s t i f f . It would seem that neitherconventional Arrhenius rate theory nor the local lzation of mechanical PdV work i n hot spot regions of the material can o f f e r a fully satisfactory description of the initiation process or of the chemical reactions occurring w i t h i n and behind the shock front.
In 1955 a fresh approach t o the problem began t o appear, based on a new understanding of shocked nonlinear systems, when the capabilities of high- speed digital computers were utilized by Ferml, Pasta, and Ulam [21 i n
numerlcal studies of the dynamics of nonl lnear systems. Their calculations on a one-dimensional anharmonic chain given some i n i t i a l excitation, explored on a mlCr0SCOpl~ scale the dynamics of the approach to equipartl tion and
thermalization. However, they found an unexpected recurrence of energy local ization i n the normal modes, indicating an apparent lack of randomization.
An explanation of t h i s behavior was given by Ford [31 i n terms of a resonant mode behavlor peculiar t o the speclf i c cases examined by Fermi, Pasta, and Ulam. Results such as these led Zabusky and Kruskal [41 t o a more fundamental explanation of intermode energy transfer by showing the relationshlp of the discrete lattice difference- differential equatlons t o a nonllnear partlal differential form transformable t o the Korteweg-deVries continuum equation [51. Solutions of t h i s equatlon are described as solitary propagating waves, or solitons, w i t h time-invariant properties. Subsequently, Toda [61 demonstrated analytically that f o r an Interparticle nonllnear force depending exponentially on the relative displacements of first-neighbor atoms, a one-dimensional chain of masses w i l l support stable, intrinsically nonlinear excttatlons.
Our early work [7-91, which coincided w i t h the beginning of today's immense range of studies on nonlinear systems, was stimulated by the suggestion of Walker and Wasley [ 101 that shocks could break chemical bonds mechanically and athermally, and appears t o have been the f i r s t i n which the consequences of t h i s "soliton-like" behavior were discussed as belng important f o r a f u l l understanding of the mechanisms underlying the shock-induced
Initiation of 'energetic materials. We considered whether or not the analytical results obtained f o r solitons i n the Toda l a t t i c e depended c r i t i c a l l y on the assumption of a specific force law. From our numerical studies on both
quiescent, i.e., no i n i t i a l random particle motion, and thermal one-dimensional anharmonic lattices, ranging from monatomic t o complex structures, we clearly demonstrated that the effect of shock loading was t o generate sequences of pulse-like disturbances showing rapid and drastic variation on the atomic scale which were highly stable - i n fact had a l l the attributes of "solitons." Since the lattice difference equations of motion are not s t r i c t l y integrable f o r realistic potentials, these are not true l a t t i c e solitons i n sense of being infinitely long-lived and completely decoupled. However, it can be shown that formal expansion to lowest order i n both displacement gradient and
anharmonicity leads t o a Korteweg-deVries equation w i t h stable soliton solutions i n one-dimension. The stability which occurs thus appears t o be general and dependent on t w o factors: 1 ) the distribution of the mass of the system i n a periodic array of discrete points, and 2) a reasonably strong nonlinearity i n the dependence of the interatomic forces on interatomic
separation. The conclusion i s that any one-dimensional anharmonic l a t t i c e w i l l , therefore, have a natural tendency t o repond t o impulsive shock loading by developing patterns of "quasi-solitons." This i s found t o be the case
irrespective of whether or not the l a t t i c e i s l n l t i a l l y quiescent or has a ftntte temperature.
Thus we have found that it i s always possible t o match the steepening effect of anharmonicity against the retarding effect of l a t t i c e dispersion i n order to obtain a stable propagating pulse or pulses, w i t h some dissipation introduced by higher-order terms and by higher dimensionality. In nonlinear systems a strong propagating front steepens u n t i l the width becomes comparable w i t h the spacing between the tndividual elements of which the system i s composed. In the absence of surfaces or imperfections, there i s every evidence that shock pulses can maintain their integrity over 100 t o 1000 interplanar distances. Thts i s most true when there 1s no random thermal motion, but even i n the presence of thermal agitation whlch i s close t o melting the lattice, the i n i t i a l shock, though blurred, i s preserved over comparable distances. Regardless of the presence of solitary motion i n highly-idealized, quiescent three-dimensional lattices, i n more realistic situations where l a t t i c e imperfections and irregularities are present, rapid exponentiation of l a t t i c e soliton instability i s expected t o occur.
Historically, one-dimensional computer calculations on shock propagation i n simple monatomic latt4ces were carried out some years ago by Manvi, Duvall, and Lowell [ 1 1
I,
by Tsai and Beckett [ 121, and by Tasi [ 131. Early calculations on l a t t i c e thermal conductivity were reported by Payton, Rich, and Visscher1
1 41 and by Jackson, Pasta, and Waters [ I 51. Over the past twenty years extensive calculations on planar shocks i n semi-infinite three-dimensional monatomic and diatomic crystals have been carr'ied out by Tsai and co-workers [ I 61. A summary of their work on monatomic crystals i s found i n a review by MacDonald and Tsai [ 171. More recent work on simple one-, two-, and three-dimensional systems has been reported by Holian and Straub [ 181, by Batteh and Powell [ 191,by Dremin and Klimenko [201, and by Karo, Hardy, and Walker E2 1-23]. In a l l of this work simple pair potentials of the type represented by the Lennard-Jones or Morse form were used t o represent the interaction between pairs of atoms.
Potentials which can give rise to net energy release were f i r s t studied by Karo and Hardy [7,91 i n the simulation of an exothermic chemical reaction i n the vicinity of the surface of a lattice, and later by Tsai and Trevino 1241 and by Peyrard et al. [251 as model potentials describing a condition of pre-
dissociation that could lead to a detonation wave following shock impact.
I I
-
JHF l NTFRACTlON OF SHOCKS WITH DFFFCTSAn understanding of the dynamics and microscopic mechanisms underlying energy transfer between a propagating shock front and various defects within a condensed energetic material (and subsequently from these defect structures to the surrounding medium) i s of prime importance for a realistic description of "hot spot" formation and explosives inltiatton. By understanding such microscopic processes i n the initiation of high explosives, these processes might be altered or controlled to provide improved and novel high explosives and munitions. The goal of any theoretical computer molecular dynamlcs modeling effort w i l l then be to obtain a fundamental understanding of the deposition of energy i n and around various types of defects during high rate processes (e.g., shock or photolytic stimulation) and the relation of such mechanisms to initiation and propagation of chemical energy release i n energetic materlals.
We have developed very general molecular dynamics codes that permit us to investigate shock-induced processes i n complex, heterogeneous systems. In these codes local variables, such as the energy or kinetic temperature, can be monitored as a function of time for any selected region of the system. This region can be a Portion or a l l of a specific defect or general heterogeneity, or a region of interest lying near such a discontinuity. In this way we can observe the manner i n which energy flows into and out of the "tagged" area and, i n the case of a polyatomic unit, the energy flux between different degrees of freedom.
Then, by enlarglng the area, we can progressively monl tor increasingly less local conditions i f this appears desirable. In addition, i n order t o address the specific question of the rate and amount of energy flux into and out of the region, our calculations also can continuously monitor the center-of-mass energy for the regfon, i t s rotational energy about the center-of-mass, i t s total vibrational energy, as well as the kinetic and potential components of the vibrational energy, and the total energy of the region. With reference t o the potential energy of the reglon, as illustrated i n Ftg. 1, It i s posslb!e to consider only those bonds between atoms within the region or t o include not only a l l
interactions o f atoms w i t h i n the region, but also those w l t h atoms outside the region
-
these exterior atoms forming the so-called l a t t i c e "cage." I n this way we can observe the manner i n whlch energy f l o w s into and out of the defect and nearby regions. Compacting of the flux data has often been found t o be desirable and can be accomplished by computing the temporal Fourier transforms f o r varying time intervals. Thus, we can obtain the frequency fingerprints f o r a given region before, during, and after transit of the shock front.The simplest nontrivial defect that can be considered would be a point imperfection
-
a substitutional or i n t e r s t i t i a l atom of differing mass or binding energy or a vacancy. A series of calculations carried out f o r point defects w i t h wide variations i n mass and force constants showed that energy i s readily transferred from a propagating pulse t o such imperfections placed w i t h i n the lattice 1231. It was found that a heavy impurity picks up more energy from the shock front as it passes, but the resonant vibration that develops i s rapidly damped; on the other hand a light impurity picks up somewhat less energy, but the vibrattonal motfon which such a defect develops persists and remains localized w i t h subsequent conslderable local distortion and damage. This corresponds t o the usual situation i n which a local mode developing w e l l above the band of bulk modes decays slowly. When the defects are placed near oneFig. 1. Schematic illustration of the partitioning of motion for a molecular unit treated either as tsolated or as tnteractlng with the lattice cage.
another, energy i s rapidly removed from the shock, and l a t t i c e destruction i s extensive. These results are Illustrated i n Fig. 2 where i t can be easily seen that coupling of shock energy to defects occurs readily, yet even f o r these imperfect lattices, shock coherence and stability remain clearly evident. When defects are located near the surface, severe distortion occurs, w i t h possible spa11 from the surface [231.
Grain boundaries or line defects have been simulated by the type of situation shown i n Fig. 3. Here the line defect i s represented by a column of heavy substitutional atoms. In t h i s case the line defect acts both t o shelter the region on the farther side from the incoming shock and a t the same time takes up considerable energy from the shock itself. The energy flux has been
monitored for various regions sheltered by such a line defect and compared w i t h the situation found i n a perfect lattice (261. The protected region does not see
Fig.
2. Multlple plate Impacts on a lattice contatning (a) ltght mass defects at the filled circle positions shown at t = 15 time units and (b) heavy mass defects placed at the same positions. The early onset of severe lattice disruption for shock interactlon with heavy impurities, compared with light impurities, i s very apparent, (ref. 23).Fig. 3. Initial configuration for the simulation of a lattice containing a line defect of heavy atoms, about to be shock-loaded by the impact of a "flying plate."
the same strong athermal movement that otherwise would take place as the shock front passes, and therefore the mechanism by means of which molecular bonds are sharply excited i s repressed. The line of heavy masses has also taken up a large amount of energy from the shock front and has reflected most of the remaining energy; we would expect that thermal effects emanating from t h i s region of heavy masses w i l l undoubtedly be significant.
A number of simulations of shock interactions w i t h voids show that as a strong shock front passes by a vold, material i s ejected from the interior surface f i r s t reached by the shock [21,271. This material i s rapidly moving and possesses a large amount of internal kinetic energy. As i t strikes the opposite wall, damage and atomic rearrangement can be extensive. Typical results from an early simulation are shown i n Fig. 4. We see that, although local kinetic temperatures may be very large, we are not required t o assume that shock energy must f i r s t degrade t o thermal energy before some i n i t a l reaction can begin. In t h i s particular case, the formation of a "hot spot," via shock-void interaction, can be seen t o be a rather complex process of Interrelated spall, disruption, and localization of large kinetic temperatures, i n which the whole process i s i n i t i a l l y f a r from equilibrium. Such a mechanism f o r hot spot formation, developing i n picoseconds, can be seen t o be an important stage, occurring before a possible void collapse, the l a t t e r usually found from
continuum calculations to require a period of time of the order of nanoseconds.
Distance
-
natural unitsFig. 4. Configurations of an impact-loaded model void, initially at zero temperature. As in Fig. 2, times are measured i n reduced units, equal to the transit time of a disturbance across one inter-row spacing.
(ref. 2 1 1.
1 1 1 - SHOCK-INDUCFD ENFRGY FI UX IN MOI FCUl AR BONDS
As an introduction t o f u l l sirnulattons on molecular crystals, we have studied shock transport i n diatomlc lattices. These systems are important i n their own right as representing the f i r s t step toward the truly polyatomic systems exemplified by organic explosives and binders [281. Figure 5
illustrates the i n i t i a l configuration for one of the calculations. Various pairs of diatoms were tagged and the energy flux and partittoning monitored during shock transit. Even I n these simple simulations i t was found that, I n contrast t o thermal excitation, any pair of diatomic units i n a shocked solld i s subjected t o sudden coherent excitation over i t s entire extent; i.e., the forces on the different atoms of the pair have a definite phase relationship conditioned by the geometry of the molecule w i t h i n the lattice, the geometry of the surrounding host cage, and similar factors. From analyzing the Fourier transforms, again it i s easily seen that high-frequency Intramolecular motions are excited on a Picosecond time scale and i n a strongly athermal manner.
In our most recent work we have made a detailed examination of the energy transfer processes occurring i n lattices containing molecular fragments or radicals representing species of interest i n the decomposition of energetic materials. The f i r s t calculations in this area were f o r single diatomic
molecules embedded i n monatomic host lattices [29,301. The basic concern was to answer the question as to-what, i n fact, i s the "rise time" of a shock as it transits a molecular group; i.e., what time i s required f o r a major component of the shock energy to be converted into internal energy of the molecule, as w e l l as t o answer the related question w i t h regard t o whether or not there I s ever a signi f icant conversion of shock energy into internal energy. The results demonstrated that moderate t o strong shock fronts, because of their sharpness on an atomic scale, can transmit t o the internal motton of molecular groups
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surprisingly large amounts of translational energy. The transfer occurs rapidly (in picoseconds), and the resulting internal energy i s several orders of
magnitude larger than the thermal energy of the host l a t t i c e after the shock front has passed.
The results obtained from the series of calculations involving diatomic fragments weakly bonded i n host matrices were highly suggestive of the ease w i t h which energy i s transferred from the shock front t o the internal motion of the diatoms i n spite of the so-called "impedance m i s m a t c h between the low- frequency, weakly-bonded l a t t i c e structure, the low-frequency host-fragment modes, and the strongly-bonded fragment. In order t o study i n more detail the ability of shock loading to Impart sufficient energy t o the s t i f f and strong intra- molecular bonds i n a real explosive, where the inter-molecular bonds are weak and soft, we carried out a calculation for a simple, yet realistic, model of a nitromethane molecule embedded i n a heavy, loosely-bound host [3 1
I.
To retain the essential physics of the situation but to avoid unneeded complexity we used a two-dimensional simulation of a planar nitromethyl radical, bonded internally w i t h potentials that give realistic frequencies, i.e., comparable to those of related fragments. As indicated i n Fig. 6 the molecule has been placed i n a favorable position to be part of the spalled material as the shock reaches the far end of the lattice. Table I l i s t s the Morse potential parameters f o r the strong intra-molecular bonds along w i t h the parameters for the host-host and host-molecule interactions. The mass of the host and i t s interaction w i t h the molecule and w i t h other host particles can be thought of as a simulation of a f u l l nitromethene lattice, Including a detailed probe of the energy fluxassociated w i t h one of the molecular units. I n addition t o calculations i n which the flux of energy into and out of the complete molecule was monitored, the energy flux was also monitored f o r each bond making up the molecule, and the
Fig. 6. Initial configuration for a nitromethly radical placed near the surface of a host lattice. Impact from the plate will produce a shock disturbance leading to an extremely "hot" spalled cluster containing the radical.
(ref. 3 1 1.
Table I. Parameters f o r the Morse potentials used i n the nltromethene simulation: V(r) = ~ ~ [ e - 2 f i ( r - r 0 ) - 2e-D(r-ro)l. The
host-host and host-molecule interactions are a t equilibrium for NN and NNN separations.
N-C 7.888 2.5389 2.633 2068.6 6.4622
C-H 3.640 1.9589 3.723 2858.5 0.9297
M-M 0.250 2.0000 2.633 134.6 30.0000
3.723
M-H 0.250 2.0000 2.633 743.6 0.9836
3.723
M-C 0.250 2.0000 2.633 233.2 10.0000 3.723
M-N 0.250 2.0000 2.633 21 8.9 1 1.35 14 3.723
Fourier transforms were computed. In Fig. 7 we show the total energies found i n each bond as a function of time, obtained by integrating the transforms over the f u l l frequency range and adding i n the average bond energy. In Figure 8 we show the spectral decomposition of the energy flux f o r the C-N bond.
From these results i t can be seen that f o r polyatomic systems the uptake of energy per bond i s of the same magnitude as that obtained for the simple diatomlc fragments i n the earlier studies. I t appears that large molecules may readily and rapldly be excited above their dissociation energies by moderate t o strong shock loading. However, f o r dissociation t o occur it would appear necessary f o r them t o escape from thelr host environment; otherwise, the energy rapidly galned can be lost equally rapidly [3 1
I.
The presence of defects such as surfaces, interfaces, or voids provldes such an escape mechanism. I nFig. 7. Total energles for each bond as a function of tlme for the simulation described i n Fig. 6.
Flg. 8. The spectral decomposition as a functlon of tlme for the C-N bond i n the nltromethly radical for the simulation described i n Flg. 6.
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t h i s way, free radicals can be produced that, i n the case of a shock-loaded explosive, could serve t o i n i t i a t e exothermic reactions leading t o detonation.
To repeat: the t i m e scale f o r energy transfer from the shock front correlates w i t h the shock velocity on an atomic scale and occurs i n a few tenths of picoseconds.
One of the most interesting results from the Fourier analysis of each of the bond energies i s that a l l frequency ranges are immediately excited and closely track the total bond energies I3 1
I.
The rate of energy uptake into the high-frequency modes from the low-frequency host-molecule forces would seem a t f i r s t glance surprising. However, from a careful inspection of the dynamics i t can be seen that the i n i t i a l l y soft host-molecule spring i s quickly compressed i n bringing the heavy host atom t o rest. Consequently, the host- molecule spring s t i f f e n s rapidly and i s much closer to being i n resonance w i t h the intramolecular vibrations, and consequently equipartition of energy between the t w o can readily take place.In
t h i s paper we have presented a review of the application of computer molecular dynamics to shock processes i n condensed systems. Earlycalculations of shock propagation i n simple monatomic chains and two- and three-dimensional lattices demonstrated that events occur as the consequence of a sequence of atomic or molecular processes occurring i n sub-nanosecond t o sub-picosecond times over dimensions of angstroms. These early studies also demonstrated the crucial role played by free surfaces i n converting shock energy into individual particle kinetic energy by bond rupture. These relatively simple models also were appliedto lattices containing point and line defects, voids, and graln boundartes and led to a quail t a t ive understanding of the manner
i n which the energy localized i n the shock front can dissipate by interaction w i t h such imperfections, as well as the role of various types of defects i n focusing the energy transferred from the shock front into microscopic regions w i t h resulting very high kinetic temperatures.
Following these early studies, much more general and flexible computer codes were developed that are capable of handling arbitrary atomic
arrangements and rearrangements by generalized neighborhood look-up
procedures. These codes were also designed t o monitor selectively and detail the energy flux into and out of any specific region of the lattice. Compactfng of the flux data was often found to be desirable and i s accornpllshed by computing the temporal Fourier transforms f o r varying time intervals. Studies were then carried out f o r various diatomic units embedded i n host matrices and most recently f o r a simulated planar nitromethene molecule embedded i n a host l a t t i c e having many of the attributes of a nitromethene molecular crystal.
Results from our most recent simulations are a l l i n agreement w i t h our earlier results, which showed that i n a shocked medium conditions in the atomically sharp front produced stongly athermal behavior. I n particular, the strong intramolecular bonds, which must be broken by some means before a propagating reaction can be initiated, are loaded in a sudden and violent manner which can pump into the molecule electron v o l t s of energy over t l m e scales of picoseconds. The excitation of the intra-molecular bonds i s of a broad spectral character w i t h the uptake times essentially identical f o r a l l frequency ranges, a1 though the amount of energy in a sampled spectral range i s a strong function of the frequency a t which that sample I s taken. Persistence of a significant amount of locallzed energy in the molecule depends on whether or not the molecule becomes a t least somewhat free of the l a t t i c e cage, as would be the case i f it were part of surface spall. I f the molecule remains confined w i t h i n the host lattice, de-excitation occurs more rapidly a f t e r the shock has passed.
It i s from an understanding of the microscopic processes involved i n the shock-Initiation of high explosives that a more complete picture of the path or paths t o explosive decomposition from mechanical shock loading w i l l be obtained.
The authors are indebted t o Mr. Thomas DeBoni and Mr. Marc Mehlman f o r invaluable programming assistance during the development and the applicatton o f the codes t o the simulations reported here.
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Q u e s t i o n - J . P . R I T C H I B
Can you g i v e me an i d e a o f how much energy ( t o t a l a b s o l u t e ) i s i n p u t t o t h e c a l c u l a t i o n by t h e f l y i n g p l a t e , i .e. what i s t h e p l a t e shock v e l o c i t y . Also, o f t h i s energy, what i s t h e maximum amount t h a t i s " l o c a l i z e d " o r absorbed by t h e CH2N02 m o l e c u l e ?
I n t h e s i m u l a t i o n s r e p o r t e d h e r e t h e shock p r e s s u r e i s moderate and w i l l be of t h e o r d e r o f 50 t o 60 Kbar. As t h e shock f r o n t passes t h e n i t r o m e t h y l r a d i c a l , t h e m o l e c u l e as a whole t a k e s up around 1.1 eV o f v i b r a t i o n a l energy w i t h i n a t i m e p e r i o d o f 0.2 ps. T h i s w i l l i n c r e a s e t o more t h a n 2 eV a b o u t 2 ps l a t e r , l o n g a f t e r spa11 has developed. I t s h o u l d be p o i n t e d o u t t h a t t h e t o t a l energy absorbed by t h e m o l e c u l e i n t h i s s i m u l a t i o n w i l l i n f a c t r e a c h a l m o s t 1 4 eV when we i n c l u d e t h e center-of-mass t r a n s l a t i o n a l energy and t h e r o t a t i o n a l energy about t h e center-of-mass. I f we i n c l u d e t h e s t o r e d p o t e n t i a l energy between t h e m o l e c u l a r u n i t and t h e s u r r o u n d i n g cage of l a t t i c e atoms, t h e t o t a l a v a i l a b l e energy w i l l be s i g n i f i c a n t l y g r e a t e r .
