Correlation of impact sensitivity with electronic ... - ACS Publications

The effective coupling constant k'sbb =* 55t$ cm"1 2corresponds to a strong coupling in agreement with our earlier estimate (75. ± 30 cm'1), but with...
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J. Phys. Chem. 1991, 95. 1209-1213 4. Conclusions (i) The vibrational overtone absorption spectrum of bromoform (CHBr3) is dominated by bands arising from the Fermi-resonance-coupled C H stretching ( u I ) and bending ( u 4 ) modes, with very few and weak additional combinations with the CBr3 stretching vibrations ut and us. (ii) The tridiagonal effective Hamiltonian provides an accurate description for the assignment of band positions and intensities. The effective coupling constant k’&b 55:;; cm-’ corresponds to a strong coupling in agreement with our earlier estimate (75 f 30 cm-I), but with more adequate error bounds estimated mostly from the easily measured intensity distribution in the highest polyads ( 5 to 6). (iii) The tridiagonal Fermi resonance Hamiltonian is quantitatively equivalent to variational Hamiltonians both in polar normal coordinates and curvilinear internal coordinates as shown by similarity transformations. This equivalence holds to better than experimental accuracy. Whereas the anharmonic force constants in polar normal coordinates are moderately well determined, the anharmonic constants Fsbb and Fssbb are strongly correlated and individually undetermined even with respect to sign. This finding is similar to our earlier finding in (I), in spite of the increased size of the data set. The internal coordinate force field can be transformed to the normal-coordinate system but leads then to a very rough approximation of the accurate potential. (iv) The possibility of pure kinetic energy coupling (Fsbb = Fsbb = 0) in curvilinear coordinates can be definitely ruled out for CHBr3 on the basis of the present data set, whereas the previous, smaller data set would have been consistent with such an assumption.s These findings for bromoform are in agreement with the findings for other CHX3 m~lecules.’~

(v) Rough estimates of band strengths and dipole functions for the CH chromophore are consistent with a systematic trend in the position of the maximum in the effective one-dimensional bond dipole moment as a function of bond extension in the series CHF3, CHCI3,and CHBr3, but our present results are insufficient to prove this. I 9 i 3 ’ (vi) Vibrational redistribution is found to be mode selective and very fast (=100 fs) within the C H stretching-bending system in bromoform, but of modest amplitude even at high excitations corresponding to 6 quanta of C H stretching. Decay of the local excitation to the remaining low-frequency modes is at least an order of magnitude slower. Our spectroscopic results may also be helpful in future interpretations of vibrational relaxation of CHBr3 in the liquid on the picosecond time scale.33 At the highest excitations there may be some interplay with chemical reaction, because the N = 6 polyad is above the thermodynamic threshold for the reaction CHBr3 CBr2 HBr, for which a rough estimate is around 15 000 cm-I, opening up possibilities of overtone-induced chemistry.

-

+

Acknowledgment. Help from Marius Lewerenz and correspondence with K. Kuchitsu is gratefully acknowledged. Our work is supported financially by the Schweizerischer Schulrat and the Schweizerischer Nationalfonds and by the U S . National Science Foundation under (in part) the US.-Switzerland cooperative projects. J.D. received part of his support from the Swedish Natural Research Council. (33) Graener, H.; Dohlus, R.; Lauberau, A. Chem. Phys. Leff.1987,140, 306. Graener, H. Chem. Phys. Left. 1990,165, 110. (34) D’Ans-Lax. Taschenbuch fur Physiker und Chemiker; Springer: Berlin, 1970; Band 3.

Correlation of Impact Sensitivity with Electronic Levels and Structure of Molecules J. Sharma,t B. C. Beard,**+and M. Chaykovskyt Materials Evaluation Branch and Synthesis and Formulations Branch, Naval Surface Warfare Center, 10901 New Hampshire Ave., Silver Spring, Maryland 20903-5000 (Received: January 30, 1990; In Final Form: July 26, 1990)

Explosive impact sensitivity among the homologous series of compounds, TNB to TATB, has been found to demonstrate a linear correlation with shake-up promotion energy. The shake-up transition observed in the N( Is) and O( Is) X-ray photoemission spectra is a direct probe of the energy separation between valence molecular orbitals at the ionized atom. Conversion of the impact energy to thermal initiation is assumed equivalent among this series of compounds due to their structural similarity, thus making the chemical reactivity the determiner of relative explosive sensitivity. TAT9 analogue compounds demonstrate a shake-up energy/impact sensitivity correlation with a different slope. The change in the slope is attributed to alteration in the physical coupling of impact energy due to differing structure of the analogue compounds.

introduction

Polynitro aromatic compounds trinitrotoluene (TNT), triaminotrinitrobenzene (TATB), and hexanitrostilbene (HNS) are among the most common and most stable explosives. TATB in particular represents one of the most stable high-performance explosives known. One feature well documented for polynitro aminobenzene is the presence of shake-up structure in the X-ray induced photoelectron spectra (XPS).’-’ A correlation has been found between the shake-up satellite peak separation from the main photoelectron line and the impact sensitivity of the compound. [This result is highly significant, demonstrating the critical role valence electronic states have in establishing macroscopic sensitivity.] In addition, this is the first report of an experimentally

’‘Synthesis Materials Evaluation Branch and Formulations Branch.

measured parameter that directly correlates electronic character to energetic materials sensitivity. The first observation of a systematic variation in XPS satellite structure in the TNB/TATB family was noted a number of years ago.4 At this time the relation to impact sensitivity was not explicitly stated, rather only the coincident variation of satellite separation with the number of electron-donating amine groups on the benzene ring. Subsequent works by ow en^^.^ and Politzer’ ( I ) Pignataro, S.; Distefano, G. J. Elecfron. Specfrosc. Relat. Phenom. 1973,2, 17 1. ( 2 ) qignataro, S.; Distefano, G. Z . Nafurforsch. 1975,Ma, 815. (3) Jianqi, Wang; Wenhui, Wu;Minxiu, Zeng; and Hengyuan, Lang, J .

Electron Spectrosc. Relat. Pbenom. 1988, 46, 363. (4) Sharma, J.; Garrett, W. L.; Owens, F. J.; Vogel, J. L. J. Phys. Chem. 1982,86, 1455. ( 5 ) Owens, F. J. J. Mol. Srrucr. (THEOCHEM) 1985,121, 213.

This article not subject to US. Copyright. Published 1991 by the American Chemical Society

Sharma et al.

1210 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 TABLE I: Comdhtion of Data on the TATB Family of Compounds compd TNB . picramide DATB TATB 1

8 9

IO 11 12 13 14

drop hgt hm, cm 72' 12:' 215' 345'

OB

drop hgt" hs0, eV

AE(N(ls)), eV

AE(O(ls)), eV

-1,s

0.0

0.0

-2.1 -2.3

0.8 2. I 2.7

1.4 3.0 3.6

TATB Derivatives from Ref 8 -2.1 169 2.1 >320 -2.3 196 2.4 46.6 -1.5 1.9 187 -3.3 2.4 112 -2.6 2.3 118 -3.7 2.1 55.4 -3.7 0.9 30.8 -2.5 2.4

2.7 2.8 2.7 2.9 2.3 1.9 2.4 2.6

-1.8

From Kamlet/AdolphZ3sensitivity-oxygen balance relation, corrected to scale from ref 8. 'Corrected value from Kamlet'O (TNT = 160 cm) to Chaykovskye impact scale where TNT = I IO cm. From Storm:' TATB = 520 cm on Kamlet'O scale, 345 cm on Chaykovskys scale.

have discussed the electronic level consequences of donor groups. Calculations of charge density and bond strength at the C-N02 bond demonstrate good correlations to impact sensitivity. Owens5 placed these calculational results on a stronger footing by relating N MR shifts to calculated charge density and measured sensitivity. However, attempts to correlate sensitivity with calculated values such as midpoint -C-NO, bond energy have met with failure for the general case of a trinitroaromatic energetic molecule. We report shake-up satellite energy splittings from both the N( Is) and O(Is) core level photoelectron spectra for TATB and several TATB analogues as well as for diaminotrinitrobenzene (DATB), monoaminotrinitrobenzene or picramide and trinitrobenzene (TNB). Correlation of the observed valence level transitions is made with published impact sensitivity values for these molecules. The role of physical and chemical properties in establishing an ignition threshold is discussed in light of the observed results. A subsequent publication will more closely examine the physical nature of the shake-up process and discuss possible relations to high-pressure effects in energetic materials.

Experimental Section Samples of TATB, DATB, picramide, and TNB were of the highest purity available. The TATB analogue compounds were synthesized, purified, and recrystallized as described elsewhere.8 Each material was ground to expose fresh surface and mounted to nitrogen-free tape for analysis. Spectra were collected at room temperature with a Kratos ES300 photoelectron spectrometer described previo~sly.~The TATB analogue (numbers, names, and structures) included in this work from ref 8 are listed in Chart 1. Impact sensitivity values (Table I) were obtained from the work of Chaykovsky et aL8 and Kamlet.Io Values from the two scales were corrected to a common scale by values for TNT, RDX, and Comp A-3, as described in the Appendix. X-ray photoelectron spectroscopy (XPS) is a technique providing semiquantitative elemental and chemical information. Soft X-ray photons (typically AI Ka, 1486.7 eV or Mg Ka, 1253.6 eV) excite core level electrons from atoms in the near-surface region. Energy analysis of the emitted photoelectrons produces a spectrum from which the elemental composition of the surface is determined. Shifts in the energy position of these peaks indicate the specific oxidation state and/or bonding environment of the element. By comparison of the quantities of the various elements (6) Owens, F. J.; Jayasuriya, Abrahmsen, L.; Politzer, P. Chem. Phys. Ler. 1985. / / 6 ( 5 ) . 434. (7) Politzer, P. Air Force Armament Laboratory, Eglin Air Force Base, FL, AFATL-88-107, Sept. 1988. (8) Chaykovsky, M.; Adolph, H . G. NSWC TR 83-22, Naval Surface Weapons Center, Silver Spring, MD, March 1983. (9) Sharma, J . Proceedings of the International Symposium on the Analysis and Detection of Explosives, FBI Academy, March 29-31, 1983; p 181.

(IO) Kamlct, M. J.; Adolph, H. G . Propellants Explos. 1979, 4, 30.

415

410

4m

400

3 1

3w

BINDINQ ENERQY, *V

Figure 1 . N( Is) photoelectron spectrum of TATB. The two major peaks arise from the nitro and amine nitrogen chemistries as indicated. The low-intensity peak is due to a shake-up energy loss ( A eV) process of photoelectrons emitted from the nitro nitrogen.

Shake-up Satellb

ElNDlNQ ENERQY, eV

Figure 2. O(Is) photoelectron spectrum of TATB. The low-intensity peak is due to a shake-up energy loss ( A eV) process of photoelectrons from the oxygen.

in specific chemical states, a good picture of the average molecular makeup can be made. The source of the shake-up structure is an energy loss event, where the outgoing photoelectron provides energy to promote a valence electron to a higher unoccupied molecular orbital.'1J2 For nitroanilines the electronic levels involved in the valence electron promotion are the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). In the model compound p-nitroaniline the LUMO is associated with the nitro group whereas the HOMO is associated with the amine and benzene ring.13 Upon core hole formation the orbitals associated with the atom decrease in energy in response to the uncompensated charge present in the nucleus. Lowering in energy is particularly acute in the LUMO, decreasing the net HOMO/LUMO energy difference and hence increasing the probability of shake-up promotion. Separation and intensity of the shake-up feature relative to the photoelectron peak depend upon the orbital overlap, electron donor-acceptor strengths, and substitutional positioning on the aromatic ring.'-3J3-'4 Nonaromatic energetic materials in general do not show shake-up structure in their spectra. In the nitroaniline-like compounds studied here, shake-up satellites appear only from the nitro N( Is) peak. The nitro group is the charge acceptor while the amine group is the charge donor. The amine has a net excess of electron density (from the amine nitrogen lone pair) which is donaied into the ring, delocalizing the HOMO across the amine and the ring. When a core hole is formed on the nitro group by photoemission, the electron deficiency pulls more charge from the ring, resulting in a closer overlap of ( I I ) Brundle, C. R., Baker, A. D., Eds. Electron Spectroscopy: Theory, Techniques and Applications; Academic Press: London, 1977; Vol. 1, p 48. ( I 2) Carlson, T. A. Photoelecrron and Auger Specfroscopy;Plenum Press: New York, 1975; p 241. (13) Bigelow, R. W.; Freund, H . J . Chem. Phys. Lett. 1981, 77(2), 261. (14) Nakagaki, R.; Frost, D. C.; McDowell, C. A. J . Electron Specfrosc. Relat. Phenom. 1982, 27, 69.

Impact Sensitivity of Polynitro Compounds

The Journal of Physical Chemistry, Vol. 95, No. 3, I991

1211

CHART I NHCHO

-

t 7 N-Formyltrinitro-1,3,5-benzenetriamine

x

P

HNC-NH2

-

#8 Ureidotrinitro-l,3,-benzenediamine

-

t 9 5-(2-Nitroguanidino)-trinitro-l,3,-benzenediamine

HzN,

-

t10 1,2-Bis-(3,5-Diaminotrinitroanilino)-ethane

7 0

X-C/

C‘

HzN\

-NH-CHz-CHrNH- C

/

>c-c

X-C

\,c-c HZN

2-

0



X

X

‘NH~

/”

H /“-”\0 C-N-C-N I

t11 3,5-Bis-(3,5-Diaminotrinitroanilino)-l,2,4-triazole

NHZ

‘c-c

\X

HZN

-

X )-C’

c-c

/

\x

‘’

NHz

\c -c’

C II

N I1

“ - C / O

I

H

>C-X

\

,C-C,

X

NH2

-

#12 3-(3,5-Diaminotrinitroanilino)-1,2,4-triazolr

t13 ~4-(3,5-Diaminotrinitroanilino)-l,2,4-triazole

HzN

‘c-c. X-c /

0

-

614 5-(3,5-Diaminotrinitroanilino)-1,2,4-tetrazole

\C-C

H~N‘

the HOMO and LUMO. This response is within the time frame of the photoelectronic event, resulting in the finite probability of the shake-up electron promotion satellite. Core hole formation by photoemission from the amine N( Is) results in the withdrawing of charge from the ring back toward the amine. The HOMO/ LUMO orbitals become spatially separated, reducing the promotion probability due to the amine N(ls) photoelectron essentially to zero.

Results Figures 1 and 2 demonstrate the N( Is) and O(Is) spectra from TATB. Shake-up peaks appear on the low kinetic energy (high binding energy) side of the photoelectron peak in these spectra. The two major peaks in the N(ls) spectrum are from the nitro and amine chemistries present in the TATB molecule. The intensity of the nitro peak is reduced relative to the amine due to loss of intensity to the shake-up process. Separation between the

7 ‘C-NH-C/

/N-N

/

‘N--U



H‘

X

photoelectron peak and the shake-up peak is illustrated in Figure 1.

Summarized in Table I are the data used for the shake-up/ impact sensitivity relationship. Impact sensitivity values have been corrected to the scale present in ref 8. The correlation procedure is demonstrated in the Appendix. The impact sensitivity of TATB analogue 7 was not available and therefore was calculated by using Kamlet’s oxygen balance (OB) relation.I0 The shake-up separation from the main photoelectron line for oxygen and nitrogen satellites for each of the considered molecules is tabulated in Table 1. Errors in the shake-up satellite separation are f O . l eV. Uncertainties in the impact values have been suggested as *1O%.Io Calculations by Bigelow et. al.Is on p-nitroaniline have demonstrated the orbital relaxation following o(1 s) photoemission (15) Bigelow, R. W.; Weagley, R. J.; Freund, H.J . Chem. Phys. Lett. 1981, 82(2), 305.

Sharma et al.

I212 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991

NB

0

I

!

,

I

,

r

,

1

,

I

I

I

I

I I t I l

100

10

1000

Impact Sensltlvlty, h, (em)

Figure 3. Plot of log impact sensitivity versus N ( Is) shake-up promotion energy ( A cV) for the TNB/TATB family and the TATB analogue

compounds. 41

,,/

TATB

X9 A A X14

A X13 X11

X12

Plcramlds

TNB

convolution of chemical (in this study probed by electron spectroscopy) and physical factors. The impact phenomena itself involves the conversion of mechanically input energy into thermal energy to initiate chemistry. Crystalline nature, defined by defect density," crystal ~ i z e , ' *and ~ ' ~ molecular structure,*O has been shown to manifest alterations of the observed impact sensitivity. In general, it has been found that the impact sensitivity can be "adjusted" by altering the size or quality of the crystal^.'^*'^ TNB does not demonstrate shake-up structure; however, the fact that its impact sensitivity falls onto the same line in Figures 3 and 4 as TATB, DATB, and picramide is highly significant. Each of these compounds is H-bonded to its neighbors, aromatic, planar, and forms a planar crystal lattice (or nearly so). The impact sensitivity dependence on molecular structure demonstrated by Storm et al.I9 illustrates the critical role structure plays in the energy conversion within the molecular solid. The observed trend in the TNB/TATB family, therefore, indicates that, when the physical structures are similar, chemistry accounts for the impact sensitivity difference between compounds. Kamlet has illustrated good correlation of impact sensitivity to the oxygen balance for groups of molecules that possess common chemical structures.I0 The trendlines observed by Kamlet were explained by suggesting various reaction mechanisms in response to the chemical structure of the molecule. Noting the various structures of the analogues, Kamlet's assertion is supported and seen as the reason for the sensitivity differences among these compounds despite their similar electronic nature. Changes in the crystal structure between the TNB/TATB family and the TATB analogues are manifested by a change in the slope between the two lines in Figure 3. Change in the slope mirrors the new coupling behavior between physical concentrators and chemical reaction in these structurally different groups of molecules. The crystal structure of the analogue compounds has not been determined, but to a first approximation their structure would be expected to be significantly different than that of the TNB/TATB family. In Figure 3 the variation in the A eV between the analogue compounds is seen to be very small despite their large variation in impact sensitivity. The analogue compounds themselves differ only by the exchange of one group on the aromatic ring. These compounds can be looked on as DATB with various groups placed on the ring instead of the hydrogen. Recent work by Datta and Singh2' evaluates the total electronegativity of various organic groupings. As a result of this analysis they have found that groups which maintain the same connecting atom but vary the remainder of the group show essentially identical electronegativity at the site of connection. As an example, the total group electronegativity for -CHO, -COCH3, -COC6Hs, and CH@H varies by at most 3.3%. Therefore, the small differences in the shake-up energy is not starting from the group substitutions that account for the differences among the analogue compounds. The significant differences in sensitivity among the analogue compounds, therefore, are attributed to their structural differences. Conclusions

I n this work we have experimentally demonstrated the importance of both the physical and chemical nature of an explosive material in determining the impact sensitivity. When explosive materials are very similar in physical structure, impact sensitivity differences reflect chemical reactivity differences between the materials. The HOMO/LUMO valence electron promotion energy as measured by the shake-up feature in photoelectron (17) Dick, J . J . Appl. Phys. 1982, 53(9), 6161-6167. (18) Bahl, K . L.; Bloom, G.; Erickson, L. M.; Lee, R. S.;Tarver, C. M.; VonHolle, W. G.; Weingart, W. C. Proceedings of the Eighth Symposium (International) On Detonation; Naval Surface Warfare Center: White Oak, Silver Spring, M D 20903; MP-194, p 1045. (19) Moulard, H.; Kury, J. W.; Delclos, A. Proceedings of the Eighth

(16) Delpuech, A.; Cherville, V. Propellants Explos. 1978, 3, 169.

Symposium (International) on Detonation; Naval Surface Warfare Center: White Oak, Silver Spring, MD 20903; NSWC MP-194, p 902. (20) Storm, C. B.; Ryan, R. R.; Ritchie, J. P.; Hall, J. H.; Bachrach, S. M. J . Phys. Chem. 1989, 93, 1000. (21) Datta, D.; Singh, S.N. J . Phys. Chem. 1990, 94, 2187.

J. Phys. Chem. 1991, 95, 1213-1220

TABLE 11: Correcting Impact Sensitivity Values to a Common Scale hm, cm TR 83-22 Kamlet'O I IO I60

explosive TNT Comp A-3 100

65 23

47.9 24.2

RDX

4

Slope Intr. Corr.

A

L E

B

60

ii

Linear Regreinion Result8

S

C

D I F F E

diff 50 17.1 1.2

--

0.35

-

-6.5 0.99

Ai ii

i

50 40

I

C

E 10

AII

,0-40

II

0

calculational efforts to correlate C-NO2 bond strength or polarity with ~ensitivity.~-'**~ Shake-up structure does not appear in the XPS spectra of all energetic materials. It is limited to donor-acceptor compounds such as TATB where nitro and amino groups are both present on an aromatic backbone. For the examination of other energetic materials such as nitramines or aliphatic nitro compounds other approaches such as ultraviolet photoelectron spectroscopy or UV-vis spectrophotometry may be valuable. Clearly the full explanation of a molecule's explosive sensitivity continues to be a mystery. Careful analysis of the many factors (chemical stability, structural triggers, and crystalline quality) must continue to bring our understanding closer to the long-sought fundamental coherent description of sensitivity. We believe the work outlined here will add significantly to this process.

Acknowledgment. We express our gratitude to Dorn Carlson of NSWC and Dr.Carl Storm of Los Alamos National Laboratory for their helpful comments.

4

E N

1213

_*

i

20

Appendix

/ II

40

n

60

I U U

u

80

II

100

n

120

I,

II

II

II

n

'I

140 160 180

IMPACT SENSITIVITY1o hso (cm)

Figure 5. Plot used for the correction of impact sensitivity values.

spectroscopy has been found to correlate very well with the impact sensitivity. The fortuitous combination of charge-transfer shake-up satellites and similarity of physical structure in the TNB/TATB family has provided a means of demonstrating the separate roles of physical energy concentrators and chemical sensitivity. The correlation between promotion energy and impact sensitivity provides for the first time experimental verification of

The plot shown in Figure 5 and the values in Table I1 were used for the correction of impact sensitivity values from the Kamlet scale to the TR 83-22 scale. The difference between the two scales is plotted verses the Kamlet scale. Compounds listed in ref 6 then can be corrected to the T R 83-22 scale bv determinina the difference from the plot. Linear regression analysis of the thee data pairs demonstrated a very good linear relation as illustrated by the correlation coefficient. (22) Mullay, J. Propellants, Explos., Pyrotech. 1987, 12, 121. (23) Kamlet, M.J. Proceedings of the Sixih Symposium (International) on Detonalion; Office of Naval Research, Department of the Navy: Washington*DC: 1976; p 312. (24) Storm, C. Proceedings of the NATO Advanced Study Institute on Chemistry and Physics of the Molecular Processes in Energetic Materials, Altavilla Milicia, Silicly, Italy, Sept 4-1 5, 1989.

Theoretical Analysis of Nonconventional Hydrogen-Bonded Structures in Ion-Molecule Complexes E. M. Evleth,*.t Z. D. Hamou-Tahra,' and E. Kassab*qt Dynamique des Interactions MolPculaires, E.R. 271, Tour 22, UniversitC Pierre et Marie Curie, 4, Place Jussieu, 75230 Paris, France, and Facult; des Sciences, UniversitC Mohamed V,Rabat, Morroco (Received: April 24, 1990)

A computional analysis of the importance of nonconventional hydrogen-bonded structures in ion-molecule isotopic fractionation reactions is presented. Although it is usually thought that single-site complex structures, S , are the global minima in hydrogen-containing ion-molecule systems, the calculations presented here demonstrate exceptional behavior for phosphonium complexes in forming trifurcated (type T2) configurations. This feature was missed in all previous theoretical work and may have important experimental ramifications in both gas- and condensed-phase dynamical behavior of phosphonium derivatives. In the other structures, the mechanistic importance of the B2 and T2 structures is discussed, and recommendationsare made with regard to particularly interesting candidate systems for dynamical studies.

Introduction

The work here was undertaken for two main reasons, First of all, essentially all previous a b initio studies of the ionmolecule structure dealt with in this paper have been technically oriented. We felt that some attention should now be given to the ramifications of these kinds of theoretical studies with regard to *Towhom inquiries should be addressed.

'Universit€ Pierre et Marie Curie. 'UniversitC Mohamed V.

0022-3654/91/2095-1213%02.50/0

recommending candidate systems for future experimental and dynamical modeling studies. Second, as a result of discussions' on the differences encountered between semiempirical and ab initio methods in estimating the binding energies and structures of ion-molecule hydrogen-bonded complexes, we reviewed the reliability of the AMI2 semiempirical parametrization. This method does yield sufficiently reasonable neutral and ion-molecule hydrogen-bonded binding e n t h a l p i e ~ ~that - ~ it will be used in the ( I ) Dannenberg, J. J., private communication.

0 1991 American Chemical Society