Density functional theory calculations of nuclear quadrupole coupling constants with calibrated 1 4 ~ quadrupole moments

E. SICILIA'. G. DE LUCA', S. CHIODO? N. RCJSSO'*, P CALAMINICI~,', A. M. KOSTER~ %and K. JUG?.

' Dipartimc.nto di Chimica. Universita della Calabria, 87037 Arcavacata di Kcnde (CS). Italy

'Theoretische Chemie. LlniversitSt Hannovcr. Am Kleinen Felde 30, 30167 Hannover, Germany

%cpartamallo de Quimica, CINVESTAV, Av. Institute Politecnico Nacional 2508, A.P. 14-740 Mexico D.F. 07000. Mexico

Density functional c:tlculations of the electric field gradient tensor at the nitrogen nucleus in 13 test molecules. containing 14 nilrogen sites, have been performed using the linear combina~ion ofciaussian-tyy*: orbital Kohn-Sham density functiond theory (LCGTO-KSDFT) approxch. Local and gradient corrected functional.; were used for all-electron calculations. All the inol- ecular structurts were optimized at their respective levels of theory with extentled basis sets. Calibrated 14N nuclear quadrupole monlents were chtained through a fitting procedull: between calculated electric lield gradients and experi~nen~al nuclear quadrupok: coupling constants of the test set of ~nolecules for each basis set and funclional considered. With these calibrated I4N nuclear quadrupok moment^ tllz nuclear quadrupok coupling constants o r the fillowing selecttxl systems were derem-niined: Huoron~ethylisonitrile, pyridine, pyrrole, inladazole. pyrazole. 1.8-bis(dime1 hy1-amino)n;1phrhde1~. cyclo ie~rmethyle~le~et r r~ni t ra~nin~ . .

cocaine and heroin.

1. Introduction Developments in density Suunctional theory (DFT)

during the last decade have provided a new and increas- ingly powerful loo1 for the calculation of lnolecular properties. Attenlion has been focused recently on elec- trostatic properties [14] and nuclear quadrupolc. coup- ling constants [SS] (NQCCs) and nuclear quadrupole resonance (NQR) frequencies [9]. The NQCCs can be obtained experinlentally by microwave spectroscopy [10-121. Usually. accurate values for NQCCs can be found in the literature only for ma l l molecules. A theor- etical contribution is therefore highly desirable to close this gap and to extend thc applicability of NQR spectro- scopy. A step in this direction was given by the works of Ludwig cJt NI., who suggested and performed calcu- lations [ l j , 141 with a generalized scheme for the prcdic- tion of NQCCs at the Hartree-Fock and highly correlated levels of theory. We adopted their scheme of DFT calc~~lations and demonstrated that there is a greater variability due to the choice ~ ~ o t only of difTerent basis sets but also of diiTerent f~mctionals. The success of this work on "0 compounds [15] ~notivated us to extend

* A u ~ h o r ihr correspondence e-mail: nrusso@$unicd.it

the work to the quadrupole moment calibration ol' L 4 ~ .

For this nucleus the most recently determined value [16] of the nuclear quadrupole mon~enl is 2.044(3) fm'. Very reccntly Bailey [8] investigated thc efficacy of DFT nlcthods for the calculation of '% coupling constants using several exchange-correlation f~mctionals and basis sets and employing, Tor the calibration procedure, the experimental gecmetries of the target molecules.

As a lirst step in our work we describe the calibralion results for the test lnolecules NF,, N2, HCN, CF;CN, HCCCN, FCCCN, CH;CN. NH3, CNCN. IJF2.NH2, FCN, HCCNC, and CF3NC, for which accurate experi- nlental NQCCs are available. For all the n~olecules con- sidered? f ~ d l geometry optimization has been perftmned. Baed on the results we then apply the method for the NQCCs calculation to other nlediunl and large size nitrogen containing compounds, including aromatic (pyridine, pyrrole, irnidazole, pyrazole, 1.8-bis(di- methyl-an1ino)ilaphthalene) and other ring systems (cyclotetrar~~etl~yleneteI~a~~itramiie , cocaine, heroin).

2. Computational details All the calculations have been performed using the

density Sunctional program Allchenl [17] in which both

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the linear conlbination of Gaussian-type orbital local spin density (LCGTO-LSD) and the corresponding generalized gradient approximation (LCGTO-GGA) methods are imple~nented. For the local spin density calculations the exchange correlation functional pro- posed by Vosko er d. [18] (VWN) has been used. The gradient corrected density f~~nctionals chosen are those oT Perdew and Wang [19] and Pcrdew [20] (PW86-P86). of Becke [21] and Perdew (B88-P86) and Becke and Lee et (11. [22. 231 (B88-LYP). The orbital basis sets enlployed were the TZVP [24], EPR-111 [25? 261 and A N 0 [27]. For fitting the density the auxiliary fuiunction set A2 [24] was used.

All molecular structures werc fully optimized using analytical energy gradients and the Berny qmsi- Newton update [2S].

The theoretical evaluation 01' NQCCs requires the calculation of thc electric field gradient (EFG) tensor at a nucleus. Indeed, the largest absolute conlponent of the Waceless EFG tensor Y,, in its principal axis system is related to the corresponding nuclear quadru- pole coupling constant by

2 Q TL, x ( M H ~ ) = -= 2.3496Qiin fin') TJ,,(in au), ( 1) h

whcre the factor 2.3496 includes all thc constants and takes care 01' thc units. T o obtain a unique orientation of the principal axis system at 1he nucleus we used the convention:

For the calculalion of the EFG tensor colnponenls a1 the m~cleus of interest. lhe following expression is used PI :

where the first tern1 on the right of equation (3) repre- sents the contribution to the EFG tensor conlponents from the electrons, whereas the second term represents the contribution from nuclei A with charge Z. The nota- tion ( p l A ( ~ , + I3))v) is used Tor the electric field gradient integrals over contracted Gaussian-type orbitals. P,,,, are elen~ents of the density matrix and the summation over A refers to all atoms of the molecules except that for which the calculation is performed. For the calc~rlation of these integrals a newly developed algorithm based on that of Obara and Saika [29] and of McMurchie and Davidson [30] was used. After obtaining lhese EFG components the traceless tensor

V is diagonal~zed to obtam 11s principal components chosen according to the convention oT equation (2).

The eigenvalues of the EFG tensor. C ' , , , I;,) and TTzI. and the cal~brated ''N quadrupolc inolnent Q haw bcen used to calculate NQCCs and rl throush equation (1) and

3. Calculation of I4N nuclear quadrupole moments In order to calibrate the "N ~~uc lea r quadrupole

moment, the n~olecular structures oT the target ~nol- ecules were optimized by using local and gradient cor- rected Tunctionals and diflerent extended basis sets. A co~nparison between optimized molecular structures and available experin~ental ones [-71--77], from table I, shows that better general agreement is obtained by using the V WN l'unctional.

T o derive the calibrated DFT 1 4 ~ nuclear quadrupolt. nmnlent a least-squares linear regression analysis of the calculated T',, (table 2) versus the corresponding experi- mental NQCCs [38-491, was employed. In tablc 3 the calibrated DFT "N nuclear quadrupole moments Q and the corresponding correlation coefficients, Tor dill-ere111 functionals and basis sets, are listed. The best correla- tion coeficient is obtained by using the local VWN func- tional, as expected due to the agreement between theoretical and experimental geometries. and the EPKlIlIA2 basis set. It is worth noting that the correla- tion coeflicient obtained at the same level of theory with the relalively small TZVI'IA2 basis and auxillary func- tion sets is allnost identical. This result indicates that the relatively small and co~l~pulationally less expensive TZVPIA3 basis is appropriate for highly accurate NQCC calculations. In this last case the good ayeemen1 can be ascribed to lhe fact the basis set is oplimized fix local DFT calculations, and we may conclude that DFT optimized basis set may be used to conqxnsate for some failures in the functionals.

A graphical display of the derived calibrated quadru- pole monlents against the diiTeren1 functionals is given in figure 1 for all the basis sets used. For a given basis set the corresponding Q show a non-negligible dependence on lhe functional. The calibrated values of Q for the VWN Tunctional are. generally, larger than the GGA values. Althougli it is not the goal of this work to obtain an accurate Q value for ' 4 ~ 7 the values obtained are all close to the rccomnlended experimental value 01' 2.044 fin2 reported in [I_(]. This value corresponds lo a scale factor oT 0.975. 11 is noteworthy that our best calibrated value (I.!M2 lin2) agrees with that (1 .!MI (2) f l ' ) obtained by Bailey [8 ] at B3PW9116-311+ G(df,pd) level using for the calibration 39 lnolecules at experi-

Table 1. Bond lzngths ( in A) and angles (in cleg) for optimird molecular structures

Molecule Bdsis Slructure VWN PW86-P86 B88-P86 B88-L'r-P Exp .

N F I TZVPIA?

EPR-IIIIAZ

AN OIA2

N2 TZVPIA2 EPR-IIIIAZ .4N 0 1 A2

HCN TZVPIA2

EPR-IIl1.U

AN OIA?

C'F3 CN TZVPlA2

HCC'CN TZVPIA2 CN CC CC HC

EPR-I II1.U

FCCCN TZVPIA2 CN C7C c:c FC

EPR-IIIIA1

CN CC HC HCC

N F FNF

NN

CN HC

CN CC FC FCC

Table 1. l i~nt i r~t led

Molecule Basis Structure W N PW86-PS6 B88-P86 B88-L'rT Esp .

NH.7

CNCN

BF2NH2

EP R-1 IIIA2

AN 0 1 A2

TZVPlA2

EPR-IlII.42

.4N 01.42

TZVPIA?

EPR-IIIIAZ

ANOlA2

TZVPIA7

EPR-IIIIA2

NH HNH

CN NC C'N

BF BN NH FBF HNB

FCN TZVPIA7 CN FC

EPR-I I I1.U

HC'CNC TZVPIA2 NC CN CC HC

EPR-IIIIA2

Molecule Basis Structure W N PW86-P86 B88-P86 B88-LkT Esp .

1 .075 1.068 1 .07 1 1.068 C'CFINC TZVPlA2 CN 1.395 1.410 1.409 1.413 1.407*

NC 1.181 1.189 1.185 1.188 1.171" FC 1.333 1.359 1.347 1.359 1.324" FCN 109.2 109.1 109.3 109.2 108.8'

EPR-1 IIIM 1.398 1.413 1.41 3 1.416 1.174 1.182 1.183 1.187- 1 .326 1.353 1.345 1.354

109.3 109.2 109.1 109.1 AN OIA2 1.393 1.393 1.409 1.416

1.178 1.178 1.186 1.183 1.328 1.328 1.348 1.354

109.3 109.3 109.1 109.3

"Refirzncx [31]. k~rference [32]. 'Refzrzncx [33]. "~efzrznw [MI. 'Rzfennce [35]. '~eference [36]. Rzference [37].

mental geometries. By using the calibsated DFT "N quadrupole moment, NQCCs for the target molecules have been calculated with the aid of equation (1). They are listed in table 4 together with thc experitncntal values. The correlalion between calculated and experi- ment NQCCs is plotted in figure 3. Both table 4 and figure 7 reveal that the local VWN values are closer to the experiment, the ~naximunl error being 0.13, 0.33 and 0.65 MHz for the TZVP. EI'KIII m d A N 0 basis sets, respectively. The corresponding average errors are 0.13 MHz for TZVPlA2, 0.13, MHz for EPRIIIlA2 and 0.23 MHz for ANOIA2. We underline again that the cali- brated 1 4 ~ VWNITZVP value of quadrupole moment is accurate enough for reliable prediciioris o l "N NQCCs.

Figure 3 presents the calculated NQCCs (N) using experimental structure parameters at VWN/EI'K-I11 level of theory in conjunction to the "N recommended value [15] or Q = 7.044 fm2. The deviations in these calculated NQCCs with respect to the experinlental ones is reduced by using both experimental structure (0) and optimized paramelers (0) coupled with the calibraied "N nuclear quadrupole moment at the same level of theory.

4. Application to aromatic and other ring systems In order to prove the uscfulncss of the prcsenl

approach, we hake carried out thc conlputation of the EFG tensor con~ponents, f r o n ~ which thc NQCC and the asynmctry parameter 71 can be obtaincd. for s o n ~ c aromatic and non-aromatic compound\. On the basis of the results of the calibration of the "N quadrupole moment. the EPRIllIA2 basis in conjunction with the VWN functional were used for these computations. The n~olecular structu~ es (31 all the selected compounds were l ~ ~ l l y optimi~ed at t h ~ s lewl of theory.

4.1. Aromatic sysrsns Nuclear quadrupole constants and anisotropy par-

ameters, calculated using the procedure just discussed, of the selected aro~natic system are listed in table 5 along will] cspcrimental values.

Coupling constants have derived from microwave spectra for pyridine [50. 511, pyrrolc [52], imidazole [53] , and pyrazole [53]. The agreement between expcri- mental and theorelical values for these four hctcrocyclic conlpounds is good. with a larger deviation being found in the case of i~niclaiole. The differences with rcspect to a recent theoretical evaluation 1161 of NQCCs for thc same molecules rcfect thc differences in the approach used in the calibralion procedure.

The aromatic diamine 118-bis(di~nethyla~nino)- naphlhalcne (DMAN) has already attracted consider- able attention for iis structure :und properties. The crystal and molecular structure of DMAN have been determined by X-ray drffraction [54]. It has been shown that the molecule is strained, wilh a large dcvi- ation of the naphthalene skeleton from planarity. The central CC bond is twisted so that the N(CH3)? groups are on dnerent sides of the naphthalene plane. On the basis of a previous uh inito and fluorescence study [55] the optimization of the geometry for two difTerent con- formations of the molecule has been performed. The structure of the most stable conformer is depicted in figure 4 and the corresponding most relevant geome- trical parameters are reported in table 6 and compared will1 those obtained in the crystallographic studies. Results o l calculations coniirm that the n~olecule is markedly non-planar and has C symme~ry in the absence of any crystal packing forces. The values of the largest conlaoncuts of the EFGs for the nitrogen atoms in DMAN have been determined by Wozniak cr crl. with "N NQR spectroscopy a i room temperature

E. Sicilia cl 01.

Table 2. Calculated principal components Vr, ( i n au) of the clec~ric lield gradient tensor for difTerent excl~ange~orrc la ion fut~ctionals and basis sels using optimizd nmolecular structures.

Molecule Basis VWN PWP86-P86 B88-P86 B88-LYP

NF;

N2

HC'N

CF;CN

H CCCN

FCCCN

CHlCN

NH?

CNCN#

BF2NH2

FCN

HC'CNC

CF;NC

C N K N

TZVPI A? EPR-IIIlA2 ANOlA2 TZVPIA2 EPR-IIIlA2 ANOIA2 TZVPI A2 EPR-IIIIA2 .WO/A2 TZVPIA2 EPR-IIIIA? ANOIA? TZVPI A2 EPR-IIIIA2 ANOlA2 TZVPIA? EPR-I IlIA3 ANOIA2 TZVPlA2 EPR-IIIIA2 .AN OlA2 TZVPI A? EPR-IlIIA3 ANOIA? T N P I A 2 EPR-IIIlA2 AN OIA? TZVPI A? EPR-IIIIA? ANOlA2 TZVPIA2 EPR-I IIIA? ANOIA1 TZVPI A? EPR-IIIIA2 .WO/A2 TZVPIAZ EPR-I IIIA? ANOIA? TZVPI A2 EPR-IIIIA2 .WO/A2

[56] and at 77 K [57]. Thc authors, assuming a value of the moleculc at low tcmpcraturcs, whik thc discrepancy 2.02 lin' for "N nuclear quadrupole constant [58] and in the anisotropy paramcter rcflccts thc crystallographic measuring the components of the EFG tcnsor, have environment. obtained the corresponding nuclear quadrupolc coup- ling constants for thc two non-cquivalent nitrogns 4 .2 . Otlwr riirg s,v.stc~rns reported in table 5. It is evident that the good agreement The calculated coupling constants and asymmetry of the calculated values with the experimental ones paramenters for the selected other ring conlpounds are obtained at 77 K is due to the increase of sylnnletry of collected in table 7 together with the experimental

Table 3. Cklibraretl nuclear quadrupole nom me nts Q (in fm'). for the density funcctiond methods considered obtaitml by using the correlation berrveen the calculated V z , (table 2) and the experimental nuclear quadrupok coupling constants y. The correspond- ing correlation codficients are reportal in parentheses.

Basis VWN PW86-P86 BS8-P86 BSR-LYP

TZVPI A? 2.0162 1.0750 2.0037 1.9773 (0 9974) (0.9891) (0.9918) (0.9898)

EPRl IUA2 1.9922. 1.9711 1.9976 1.962.3 (0 9979) (0.9921 ) (0.9041 ) (0.99 1 7)

ANOIA', 2.011 1 2.Wl I 2.020 1 1 .987 1 (0.9969) (0.989 1) (0.9920) (0.9893)

Figure 1. Dependenct: of the calibrated ''N nuclear qudrupole molnent (in fin2) on the excl~ailge-corl~I~~tic>n functional and basis ser .

results. The choice of lhese liloleculcs is due to consider- able dlim made in recent years to use '%. Lhrougli NQR spectroscopy, as a sensor for the detection or colnpounds with physiological or energetic interest.

The o p t i m i d structure of Lhe cyclotetranietliylei~ete- tranitramine (0-HMX) is reported in figure 5. In tliis molecule there are four peripheral and Tour ring nitrogen atoms. but because of the C2 type rotational symmetry about the line joining the atoms N(2) and N(6). the nitrogen atoms can be grouped in four pairs. two in tlie ring and two in the peripheral NO, groups, each pair containing two equivalent "N nuclei. Experi-

nientally nuclear quadrupole interaction parameters (1 and TI) have been measured for ring nitrogens by the conventional NQR teclinique [59] and tl~rougli the use or special double-resonance techniques [MI for tlic two pairs or equivalent nuclei in Lhe NO2 groups. For tlie two sets or ring nuclei, termed equatorial and axial. the measured coristaiits and anisotropy parameters have been assigned on h e basis of he temperature depen- dance of h e NQR frequencies. On the other hand. no assiglin~ents of the nuclear quadrulmlc interaction par- ameters has been made experinlentally for the peripheral nitrogen nuclei. We have calculated the coupling

1046

1 NF,

N2

3 HCN 4 CF3CN

5 HCCCN 6 FCCCN 7 CH,CN

NH3 9 CNCN# 10 BF2NH2

11 FCN 12 HCCNC

E. Sicilia cl 01.

Exp. NQCC (MHz)

B88-P86

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2

Exp. NQCC (MHz)

Exp. NQCC (MHz)

-8 -7 -6 -5 -4 -3 -2 -1 0 1

BP. NQCC W )

Figure 2. Cwnparison between calculated and measured nuclear quadrupole coupling constants (in MHz).

constants and the asymmetry parameter for ' 4 ~ nuclei hotli in the ring and in peripheral NO, groups, attempting in the latter case an assignment of the observed values. Analysing the results reported in table 7, it appears ihat there is excelleni agreement hetween theory and experiment, the larpest deviation being lound in the values of ihe asynmetr y paranieier for the ring nitrogen atoms.

Experiinental information on the ''N nuclear quadru- pole interaction of cocainc and heroin molecules is avail- able [61, 631. In both n~olecules, see figures 6 and 7, there is one ' 4 ~ nucleus, and then only one set 01 nuclear quadrupole interaction parameless, 2 and 17, has been observed experimenta.11~ by NQR spectroscopy in poly- crystalline samples. The agreement beiween theoretical

and experinlent NQCC \dues is satisfactory (see table 7), hut poorer than for the previously considered co111- pounds not. included in the calibration. The source of the existing discrepancies can be the use of the ophlizcd geometrical structures in conjunction with the calibraied Q va.lues. Indeed, this coupling, as shown in iipure 3 for the NF, molrtcule. could be a rough choice for the com- ~uta t ion of NQCCs. Moreover, the influence of the environnleni would also not be neglected.

5. Conclusion Wc have repr ied thc values of the nuclear quadru-

pole moments of ''N obiaincd through a calibration procedure in ihe lraniework o l density lu~ictional theory. The calibration involved ihe optimization o l

Table 4. Calculatecl nuclear quadrupole coupling constanis x (in MHz) using optimized nmolec~~lar structures ;md calibrated nuclear quadruple moments.

Molecule Basis VWN PWP86-P86 B88-P86 B88-LYI' Exp.

NF:

N2

HCN

C'FqCN

HCC'CN

FC'CC'N

CH;C'N

NH;

CNCN#

BF2NH2

FCN

HCC'NC

C'FqNC

CN E N

T Z W I A2 EPR-IIIIA2 AN01 A2 TZVP1.42 EPR-IIIlA2 AN01 A2 TZWlA2 EPR-IIIIA? AN01 A? TZVP/,4? EPR-IIIIA2 ANOIA2 T Z W I A2 EPR-IIIIA? ANOlA2 TZVPIA2 EPR-IIIIAZ ANOIA2 TZVPI A2 EPR-IIIIA? ANOIA? TZVPI A2 EPR-IIIIA2 AN01 A2 TZVPIA? EPR-IIIlA2 ANOIA? TZVPIAZ EPR-IIIIA2 ANO1.42 TZVPIA? EPR-IIIlA2 ANOIA:! TZWIA2 EI'R-IIIlA2 ANO1.42 TZVPI A3 EPR-IIIlA2 ANOIA2 TZWIA2 EPR-IIIIA? ANOIA?

"Reference [3X]. "~eference [39]. ' Reference [MI. "~eference [41]. "Referenw [42]. '~eference [43]. 'Rel'erence [MI. '~eference [45]. i Rel'erence [46]. . i~e~el-ence 1471. "~eference 1481. '~eferencc: [49].

peolnetrical paranlelers and the calculation uf the EFG scopy. This nlipht help in obtaining nlore reliable knowl- tensors at several levels of theory for a chosen set of cdgc of many i~npurtant classes of cu~npouild for which molecules. Since cxperinlcntal structural data are not experimental information is not available or has to be enlployed, the techniclue used can greatly expand the interpreted. By using the nuclear cluadrupole nlornents range of the theoretical description of NQR spectro- obtained, highly accurate NQCCs were calculated for

2 Geom. ExpJQ

ref 0 Geom. ExpJQcaI

-6 -4 -2 0

Exp. NQCC (MHz)

Figure 3. Comparison brtwzen nleasured and VWNIEPR-I11 calculated. by using diferent approaches, nuclear quadrupole coupling consrants (in MHz).

Table 5. ' 4 ~ I I L L C ~ I T qundrupok coupling constr1ni.s y (in MHL) and a sqlnmetl) paranlerer 7, for aronlaric systelns.

Y 'I

Molecule Nucleus Tl~eory Exy. Theory Exp.

Pyndine - 5.07 1 -4.87 f 0.01" 0.394 0.43" - 4.908~

Pq rrole - 2.691 - 2.704' 0.101 0.04' Imidazole N o ) - 2.501 - 2.537" 0.149 0.18"

N(3) - 4.104 - 4.032" 0.083 0.12" Pyra~ole N(1) - 3.053 - 3.03 0 503 0.523" d

N(2) - 4.53 1 - 4 . 4 ~ ~ 0.673 0.647" DMAN N(11) 5.541 5.5541 ' : 5.6315 ' 0.0 18 0.0419': 0.0302'

N(13) 5.563 5.6033"; 5.6975' 0.014 0.0439': 0.0385 !

"Referencv [%I. "~ei'erence [51]. 'Relkrence [51]. "~eferencv [53]. 'Reference [57]. ' ~ e l r e n c t : [%I.

medium and large size systems. The best correlated the VWNIEPR-Ill. Then, the corresponding value of Q value of the nuclear quadrupole momcnt was obtained is highly recommended for studying medium and large by using the VWN lunctional in conjunction with the s i ~ e systenls to obtain reliable results. Work is in pro- cxtended EPKIlllA2 basis and auxiliary sets. Finally. grcss in our laboratories to extend the same calibralion the value of the correlation coeficient for Q calibration, method to the density functional evaluation of nuclear obtained using the same furlcfional and the less compu- quadrupole inornents for other nuclei of chemical talional expensive TZVP basis s e ~ , is allnost identical to interest.

n. '.,5 Figure 5. Nu~nbering scheme and alomic arrangement of 3-

Figure 1. Numbering scheme and atomic arrangement of HMX molecule. DMAN molecule.

Table 6. Selecrecl ~eomerrical parameters (in A. deg) of DMAN.

Parameter VWNIEPRIII up."

C(1)-C(6) 1.419 1.425 C(5)-C(6) 1.434, 1.135 1.429. 1.408 CI(4)-C(5) 1.383, 1.385 1.383. 1.353 C(3)-C(4) 1.392, 1.395 1.387. 1.410 C(S'kN(1 I) 1.389. 1.391 1.395, 1.399 N( 1 1)-C( 12) 1.441. 1.MO 1.465, 1.165 C(4)-C(5)-C(h) 11Y.l. 119.0 119.4 118.6 C(3)-c'(4)-C(5) 122.1. 121.8 121.4: 121.4 C(6)-C(5]-N(1 I ) 120.9, 170.7 120.8. 120.1 C( 5)-N( 1 1)-C( 12) 117.5, 117.4 118.5 118.0 CI( 5)-N( I 1)-C( 1 5) 116.0, 116.3 117.1. 117.2 C(Z)-C(3)-C(4)-C(S) 3.3, 3.1 3.0, 3.0 C(1)-C(6)-C'(5j-N( 11) 166.4, 1fh.O 168.5, 167.9 C(6)-C(5)-N(l l)-C'( 12) - 56. I . - 6 . 6 - 59.4, -60.6 C(6)-C(5)-N(l I)-C(15) 167.8. 167.5 162.7: 160.9

"Reference [.j4]. For double entries the first refe~s to the parameter denoted in the lirst columq while the second entry refers the o t h a half of the naphthalene system.

This work was partially supported by the VlGONl exchange program. Finailcia1 support fiom thc Univer- sit5 clegli Studi Calacria and MURST is gatefully acknowledged.

References [l] DUFFY. P.. CHONG D . P.. ;md Dnrurs, M., 1095.

J . chum.. P/Qx, 102, 3312. [2] K ~ S T E K , -4. M.. LEBOIJF, M.: and SALAHUB, D . R.. 1996,

T/worcticd m ~ d C'an~pirtirio?ui/ C:/~etni.rtr)*. Vol. 3, edited by .I.S. Murray and K . Sen (Amslerdan~: Elsevier).

,;

Figure 6. A~omic arrangelnent of cocaine molecule.

Figure 7. Atomic arrangement of heroin ~nolecule.

Table 7. "N nuclex yuxlrupok coupling constants 1 (in MHz) and asymmetry parameter 1 ) for other ring systems.

X ' I

Molec~ilz Nucleus Theor Exp. Thzory Exp.

8-H MX N(10). N(13) 0.840 0.810" 0.005 0.42" N(9). N(11) 0.703 0.806" 0.02 3 0.4gR N(2). N(6) (7.098 5.791" 0.445 (1.4977~ N(4). N(8) 6.175 6.025~ 0.378 0.51 80"

Cocaine 5.753 5.02YL 0.074 0.395" Heroin 5.955 5.3136" 0.017 0.028~

"Reference [(d)]. "~zference [SO]. 'Reference [(,I]. "~ei~erence [(,?I

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