Intermolecular potentials for some crystals of hetrocyclic compounds ccontaining nitogen

Volume

69, number

CHEMICAL

3

INTERMOLECULAR POTENTIALS CONTAINING NITROGEN 2. GAMBA and H. BONADEO

PHYSICS LETTERS

FOR SOME CRYSTALS

OF HETEROCYCLIC

1 Februzy

1980

COMPOUNDS

l

Dwmdn Finca de1 Sdlrdo. Comlsidn National de Enetgib Atdmim. Buenos Aues 1429. Argentrna Received

8 October

Atom-atom

1979,

potential

in f~l

form 9 November

parameters

1979

for N-N.

N-C and N-H wth evpenrnent to be Important.

contanungmtrogen are refined. The agreement actlons

is consIdered,

and shown

In the last few years, a number of papers considering potential functions, mostly of the atom-atom type, for crystals of heterocyclic compounds containmg nitrogen have been published. Reynolds [l] calculated the latticedynamic propertles of pyranne fittmg an atom-atom potential plus a rutrogen lone-pair dipole-CH bond dlpoIe term. Besnainou and Cummings [2] refined atom-atom parameters for solid pyrazine and lmldazole, the last one being hydrogen bonded. Covers [3] refined atom-atom parameters on the static propertIes of six crystals containing nitrogen; these were found by Luty and van der Avoird [4] to yield poor resuks in the calculation of lattice frequencies of tetracyanoethylene. They also refined some of the parameters to give a good agreement with existing static and dynamic data. Bougeard et al. [5,6] calculated the lattice frequencies of 1,2,4tnazole and of purine, two crystals with strong hydrogen bonds. This large amount of information, however, is quite heterog’eneous: some of the crystals considered are largely hydrogen bonded, some are ring compounds, some possess dipole moment; most refmements are based on one particular crystal and the transferabdity of the parameters is not certain. Atom-atom potential parameters for a series of chlorlnated benzene crystals [7], and for brommated benzene crystals [8] have been refiied in our laboratory.

l

Fellow of the Consejo Clentificas y TCcmcas.

Naclonal

de Investigacrones

mteractlons m a series of crystals of heterocyclic compounds is not very satisfactory. The addrtion of electrostatic inter-

In both cases, static and dynamic properties of the crystals were very well reproduced, and later the parameters were found to be transferable to other caystals not included in the fit [9]; the molecules considered were nonpolar, since it has been found that the simple atom-atom approach is not adequate when large dipoles are present [lo] _ In view of the success of these calculations it seemed logical to perform a reTmement on heterocyclic ring compounds which a priori could be predlcted to show a consistent behaviour. We have chosen a group of five crystals: pyrazinc, s-tetrazme, pyridazino-(4,Sd)pyndazme and the two known phases of s-triazme, which contain nonpolar molecules and are thought not to have hydrogen bonds, in order to clear the calculation of possl%Ie side complications. The calculation is essentially simdar to that of Bonadeo and D’Alessio [7], and the rigrd body model is used throughout. The force constants are given by:

where Qsvmare the E&art mass-weighted displace-

ment coordinates of the tih molecule in the j&h Unix cell in the mth mode, and V$$is the pairwise inreraction. In the atom-atom model, one term of the second

Volume 69, number 3

CHEhlICAL

PHYSICS LETTERS

I February 1980

unpolanzed Raman and far-infrared bands of 01and F .r-triazine [20,21 J and pyrazine [22];(c) the heats of sub~atlon of o s-triazine [23] and pyrazme (quoted m ref. 13-5), and the heat of transrtion of s-triaz.me 1243 _ There are a few problems with some available data. The published far-mfrared spectrum of s-trrazme [ZOJ is rather inconclusive: five bands are reported for the p phase, for whrch only three are predicted by sym-

sum is wrnten as.

metry, and therefore the informatzon IS not taken mto account, only the strong band at 84 cm-l of the Q

(1) where V,$ = V,!${ 1s the pan-wise mteractron between the ith atom in the wth molecule and the jth atom m the wit molecule, ‘;I IS the interatomic &stance and _x~, 1s the nh cartesan component of the atomic posrt1on x*. The thud term m (I), not included m our previous

calcuiatrons, rs discussed by Neto et al. [12]. It was found that at the startmg pomt of the refmement, the part of the force constant depending on this term has a very large contrrbutron, which is drastically reduced when the potentrais are near their eqmhbrium value, the mclusion of the term from the beginning causes some in&rally calculated frequencres to turn Imaginary, comph~t~g unnecessarrfy the con~pntatlons. Therefore the first refinement cycles were performed ormttmg the term, whrch was added at a later stage. Bonadeo et al. 2131 have shown that the entropy contrrbutrons to the heat of sub-hmatron are considerable, and have to be added to the calculated crystal packmg energy for comparison wrth experiment; they also showed that the Debye-Emstem ap~ro~matlon gives a good estunate of thermodynamrc propertiesIn order to rnctude this effect, we have made a rough estimate of the entropy contrrbutions usmg the calculated frequencres, since we lack a complete set of observed frequencies_ Alt~ou~ these frequencies obviously change during the re~nement, thts difference rs reflected only very weakly m the caiculated contnbutrons to the heat of subhmatron. The data included m the refinement are the following: (a) the crystal structures of Q s-tnazine at 300 K [14j,@s-trrazmeat ISOK[i3,IS],pyrazme [16], s-tetrazme [l”rf , and py~daz~o-(4,Sd~py~dazine [18j, (b) the polarized Raman bands of pyrazme [19 J, the 526

phase far-infrared spectrum 1s included in the refmement. We have used atom-atom potentrals of the Buckmgham form5 = - A r$j + B e.xp f- C rr,). The C-C, C-II, and H-H parameters were fmed at the vahres given by Williams [25], which were used wrth success for the calculation of dynamical propert&esof benzene [26,27] and halogenated benzene crystals 17.81. The parameters corresponding to N-N, N-C and N-II interactions were refmed. As in prevtous calculations, the parameters S and C were found to be highly interdependent, and the parameter C for all interactrons was kept futed, We used the parameters of Covers [3], Besnainou and Cummings f2], and WrUiams [25] as starting points; m the last case we consrdered the nitrogen atoms to have initially the same parameters as the carbon atoms; thrs approach was used wrth sucess by Elliot and IqbaI 1211 to calculate the lattrce frequencies of (Ystriazme. All three sets give several imaginary frequencres when the third term of eq. (1) is mcluded. The refinement presented here was performed starting from W~rams’ parameters, but no appreciable difference ISobserved wrth respect to other startmg points. TabIe 1 shows. together with the experimental data, the results of the calculation with the imtial and refined parameters, whrch are shown m table 2. In our previous refinements, the convergence proceeded smoothIy and rapidly, and the fial error was quote small; m this case, however, the differences between experiments and calculatrons are quite hrgh, and the refmement procedure was hindered by some problems, one of the most important of which was the tendency of some frequenctes to become cabal. It can be seen that there are several results which are in contradiction with experiment, mainly: (a) the packmg

Table 1 Evperunental

data and properties calculated using WdBams’ [25 1 and refuted parameters. Lhtits: A&b. Repack:kglfmob; Y: cm-t ; the equthbrmrn condittons are the differences between observed and calcrdated equiBJrinrn structures in degrees for molecuhrr rotattons and A for molecuJar translations

Experimental

0

s-tnazine AHsub Epack Mt. freq

lo.3W -11.3

c)

A2g A2ll 2 g

%I

914d) 67 54 84

e)

Parameter

ExperimentaJ

set

bunal a)

refiied

10 0 -110

11.5 -125 100 64 43 80 69 85

108 53 82 103 70 96

ht&-@

wrazrne %ub Epack Jatt freq.

8.7 -94 110 59

Ag

42 %

104

d)

79

d)

B” eq cond.h)

Ty Ry

158 130 77 64 42 121 73 -0 05 -5.7

9.0 -9.7 86 60 95 123 75 59 50 108 42 -0.03 -21

Au B Ill f32u

Ag BJg Brg

p s-trlazuie AHsub Epack latt. freq

Parameter set

%

12.8 D -14.53) 75

k)

52

k)

::: 77 47 ($’

:: 1) B u”

eq. cond.mJ Rx s-tetrazme eq. cond. n) R, 5 pY’ndaamo-I4,SdJpyridazine eq.cond.0) Rx 22

refined

-9.9 141 67 70 113 123 67 JO 113 36i 4.2

8.2

143 -16.0 JO5 68 59 E07 118 68 52 83 3 t-0

4.1 -16 3.1

3-L -4.5 6.5

2.6 -2.6 -S-O

0.3 -2.8 -7.0

rms total error

b, Ref. [23J,at 253 K. a) Calculated propertres without including the thud term in eq. (1). d, Ref. I21 J_ e, Ref. (20]_ f) Est hated c, Estimated at 300 K using ref 1131 and calculated lattice frequencres. g) Estnnated at 150 K, usmg ref. [I3 ] and cafcuhted lattice frequencies. iJ Quoted rn red [‘_I_ h, z axis perpendtcular to molecular pi3ne.y avls mrnndes with the Cs crystal axis. J) Estnnated at 180 K, using ref. [ 13 ] and calculated lattice frequencres.

4.2

at 150 K_

k, Lmear interpolatton between the values reported m ref. [22] at 77 K and 290 K. JJ Ref. 1161. m, z &USperpendmular to molecular plane;x axis throngh the nitrogen atoms.

*lx ayls pPrpendrc&u to molecular plane;y axis through carbon atoms. O) x axs perpendrcular to molecular plane; z axes between mtrogen atomr Table 2 Potentrals parameters before and after refiiement. A and B in

kcal/mole, C m A Parameter

Parameterset untlal[25 I

refined

c A

83630.0 36 568 0

76699.0 36 467.0

N-N

B C A

83630.0 3.6 568 0

26997.0 36 -798.0

N--H

B C A

N-C

B

8766.0 3.67 125.0

13824 0 3.67 590 0

of the high temperature phase of s-triazine is larger than that of the low temperature phase; (b) the pattern of the Raman Frequencies of fi.s-triazine is incorrectly reproduced; (c) the separation of the infrared bands of pyrazine is calculated as much too small. These effects do not depend on the particular PMBReters used, but on the structure of the atom-atom potentml, unIess there is some mistake in the experimental data. Since some of the confktiqg results stem from the p s-t-e, this crystaf was removed from the refmement; in spite of this, the rest of the data showed no significant improvement. Therefore the mode1 should be improved to take into account the physical reasons behind the dkcrepanties. Firstly we considered the possr%ility of the exisenergy

Volume69, number3

CHEhlICAL

PHYSICS

tence of weak hydrogen bonding m pyrazme and pyridazmo~4,5d)pyridazine, which have some nonbonded N-H drstances of about 2.5 A. These close contacts were consrdered and refined separately. However, again no substantral rmprovement in the fit was observed. Recently, Righim et al. [X3] showed that multipole-multrpole mteractions may give sizable contributions to calculated frequencres, 111the partrcular case of naphthalene [29], the ordering of the highest A8 and B, modes was gwen correctly first when the quadrupole-quadrupole interaction was included. Smce the molecules of the crystals under consideration are all nonpolar, qyadrupolar mteractions must be the leadmg electrosfatrc term. Unfortunately, the quadrupoles of these molecules are not known accurately; a gross estimatron of the quadrupole moments was made, using the bond population moments calculated by Palmer et al. [30] and adding to this a dipole moment associated to the nitrogen lone pair The calculated values are shown m table 3. Given the roughness of the estimate and the fact that the atom-atom potential parameters were refined wrthout including the effect of the quadrupole term, no good agreement can be expected; however, it can be seen that the effect of the quadrupolar term is very large, and that It affects the different frequencies m different ways, pushmg some up, some down, and leavmg some unchanged_ At this stage, it is not possible to refine the atomatom parameters together wrth the quadrupoie moments, smce too many unknowns are introduced, the possibrhty of re-refmmg the atom-atom parameters alone, leaving the quadrupole moments fured, as has been done for other compounds 1291 is also rejected because the quadrupole moments are too poorly determined. But, m any case, it seems to be very probable that for the system under consideration, the mclusion of the appropriate electrostatic interactrons may correct the uncommonly large discrepancies between atom-atom calculations and expenment. There are two approaches to the refinement of potential parameters- to take one crystal and adjust Its properties accurately, or to take a series of similar crystals and try a more crude general adjustment; both have their advantages and drawbacks_ In our case, aIthough inlvrdual crystals may be adjusted well with the atom-atom model, because drfferent effects are

1 February

LETTERS

Table 3 Calculated properties usmg refmed parameter Molecular axes as mdicated in table I

Q

set. Q is m e A*.

Atom-Atom

Atom-atom quadrupole mteraction

-12.5 100 64

-10.0 114 64 43

s-tnazme

Qz=087 Epack latt freq.

43

80 69 85

70 33 81

p s-triaune Qz = 0.87

-9 7 86 60 95 123 75 59 50 108 42 003 -2.2

Epack Mt. freq.

eq. cond.

-7.4 76 23 91 135 62 40 31 105 43 004 -128

pyrazine

QX = -Q,. = -3.0; Q, = 0.0 Epack -16.0 tatt. freq. 105 AU Bill 68 %l 59 Ag 107 *3g *tg *% eq mnd

Rx

s-tetrazme Qx=1.75;QY=28;Qz=455 eq. mnd. Rx RY R, pyrldazmo-(4,Sd)pyrxlazine Q, = 2.55; QY = -0.17;Qz eq. mnd. %

118 68 52 83 3 1 .o

3.1 4.5

6.5 = -2.38 03 -2.8 -7.0

1980

-15.2 91 86 60 129 I41 81 881 24 891 4.8 1.9 4.8 18.4

3.5 -105.0 -53.0

plus

Volume 69, number 3

CHEMXCAL PHYSICS LETTERS

subsumed mto It, we learn more from the collective refiiement about the shortcomings of the approach_ A more detailed study of the effect of different types of electrostatic

interactions

is in progress_

References 111PAA.Reynolds, J. Chem. Phys. 59 (1973) 2777, 121S. Bemamou and D.L. Cummmgs, J. Mol. Strud 34

(1976) 131. I31 H AJ. Covers, Acta Cryst. A31 (1975) 380. 141 T. Luty and A van der Avoird. Chem. Phys. Letters 61 (1979) 10. VI D. Bougeard, A Lautie and A. Novak, 3. Raman Spectty. 6(1977)81.

f61 D. Bougeard, N. Ie Calve. B. Samr Roth and A. Novak,

J_Chem Phys 64 (J976) 5152. I71 H. Bonadeo and E. D’Alessro, Chem Phys. Letters 19 (1973) 117; Prooaedmgs of the internatronal School of Physrcs Enrico Fermi, Course 55 (Academrc Press, New York, 1972) p. I36 181 E. Burgos and H. Bonadeo, Chem. Phys Letters 49 0977) 475. [91 E. D’Alesso and H Bonadeo, Chem. Phys. Letters 22 (1973) 559. IJOI E. Burgos and H. Bonadeo, Chem. Phys. Letters 57 (1978) 125 1111 E. Burgos, E D’ALesno and H. Bouadeo, J. Chem. Phys 66 (1977) 347

1 February E980

[ 121 N. Neto, G. Taddei, S. Cabfano and SK Wabusfey, NoL Phys. 31 (1976) 457. 1131 H. Bonadeo. E. D’Alessro, E. Hatac and E. Burgos, I. Chem. Pbys. 68 C1978) 4714. 1141 P. Coppens, Science I58 (1967) 1577. flSl J&L Smith and kLM_ Rae. 3. Phys. Cl 1 (f97B) 1761. [I61 G. de Wrth, Acta Cryst. B32 (1976) 3178. [ 17 1 F. Berttnotti, G. GiacomeBo and A.M. Liquor& Acta Cryst. 9 (1956) 510. [IS) C. SabeL, P. Tangocci and P-F. Zanazzi, Acta Cry-r&EL5 (1969) 223I. [ 191 R H. Larkin and HD Strdham. Spectmchun. Acta A29 (1973) 78X. [20] S.J. Daunt, H.F. Shurvell and L. Pazdemik, J. Raman Spectry. 4(1975) 105. [21 I G-R Elliot and Z. Iqbal, 3. Chem. Phys 63 (1975) 1914_ 1221 X. Gerbaux and A. Hadni, J. Chem. Phys- 49 (1968)955_ [23] R. Mason and A LM. Rae, Proc. Roy. Sot A304 <1968) 501. 1241 J.H. Smith and A.I.M. Rae, J. Phys. Cl 1 (1978) 1773. D.E. Williams, J. Chem. Phys 47 (1967) 4680. G. Taddei, H. Bonadeo, M_P_Marzocchi and S_ Calithao, J. Chem. Phys. 58 (1973) 966_ BM_ Powett, G. DoBurg and H. Bonadeo, J. Chem. Hiys69 (I 978) 2428. R. Rrghini. N. Neto, S. Califano and SH. Wahnsley, Chem. Phys. 33 (1978) 345. S. Cabfano, R. Righmi and S.H. Walmsley, to be pubIished_ kf.H_ Palmer, R H. Fmdlay and AJ. GaskeB, I. Chem. Sot. Perhn Trans. H(1974) 425.