Density functional theory calculations of nuclear ...

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Density functional theory calculations of nuclear quadrupole coupling constants with calibrated quadrupole moments a

a

E. SICILIA , G. DE LUCA , S. CHIODO JUG

a b

a

, N. RUSSO , P. CALAMINICI

b c

14

N

, A. M. KOSTER

b c

& K.

b

a

Dipartimento di Chimica, Università della Calabria, 87037, Arcavacata di Rende (CS), Italy

b

Theoretische Chemie, Universität Hannover, Am Kleinen Felde 30, 30167, Hannover, Germany

c

Departamento de Quimica, CINVESTAV, Av. Instituto Politecnico Nacional 2508, A.P. 14-740, Mexico D.F., 07000, Mexico Published online: 16 Nov 2009.

To cite this article: E. SICILIA , G. DE LUCA , S. CHIODO , N. RUSSO , P. CALAMINICI , A. M. KOSTER & K. JUG (2001): Density 14

functional theory calculations of nuclear quadrupole coupling constants with calibrated N quadrupole moments, Molecular Physics: An International Journal at the Interface Between Chemistry and Physics, 99:12, 1039-1051 To link to this article: http://dx.doi.org/10.1080/00268970110042820

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MOLECULAR PHYSICS, 2001, VOL.99, No. 12, 1039-1051

Density functional theory calculations of nuclear quadrupole coupling constants with calibrated 14N quadrupole moments

Downloaded by [Univ Studi Della Calabria] at 00:39 03 May 2013

E. SICILIA', G. DE LUCA', s. C H I O D O ~ N. ~ ~ ,RUSSO~*, P. CALAMINIC12>3,A. M. KOSTER2s3and K. JUG2 Dipartimento di Chimica, Universita della Calabria, 87037 Arcavacata di Rende (CS), Italy Theoretische Chemie, Universitat Hannover, Am Kleinen Felde 30, 30167 Hannover, Germany Departamento de Quimica, CINVESTAV, Av. Instituto Politecnico Nacional 2508, A.P. 14-740 Mexico D.F. 07000, Mexico (Received 23 January 2001; accepted 6 February 2001)

Density functional calculations of the electric field gradient tensor at the nitrogen nucleus in 13 test molecules, containing 14 nitrogen sites, have been performed using the linear combination of Gaussian-type orbital Kohn-Sham density functional theory (LCGTO-KSDFT) approach. Local and gradient corrected functionals were used for all-electron calculations. All the molecular structures were optimized at their respective levels of theory with extended basis sets. Calibrated I4N nuclear quadrupole moments were obtained through a fitting procedure between calculated electric field gradients and experimental nuclear quadrupole coupling constants of the test set of molecules for each basis set and functional considered. With these calibrated 14Nnuclear quadrupole moments, the nuclear quadrupole coupling constants of the following selected systems were determined: fluoromethylisonitrile, pyridine, pyrrole, cyclotetramethylenetetranitramine, imadazole, pyrazole, 1,8-bis(dimethyI-amino)naphthalene, cocaine and heroin.

1. Introduction Developments in density functional theory (DFT) during the last decade have provided a new and increasingly powerful tool for the calculation of molecular properties. Attention has been focused recently on electrostatic properties [ 1 4 1 and nuclear quadrupole coupling constants [5-81 (NQCCs) and nuclear quadrupole resonance (NQR) frequencies [9]. The NQCCs can be obtained experimentally by microwave spectroscopy [lo-121. Usually, accurate values for NQCCs can be found in the literature only for small molecules. A theoretical contribution is therefore highly desirable to close this gap and to extend the applicability of NQR spectroscopy. A step in this direction was given by the works of Ludwig et al., who suggested and performed calculations [13, 141 with a generalized scheme for the prediction of NQCCs at the Hartree-Fock and highly correlated levels of theory. We adopted their scheme of DFT calculations and demonstrated that there is a greater variability due to the choice not only of different basis sets but also of different functionals. The success of this work on 170compounds [ 151motivated us to extend

* Author for correspondence. e-mail: [email protected]

the work to the quadrupole moment calibration of I4N. For this nucleus the most recently determined value [ 161 of the nuclear quadrupole moment is 2.044(3) fm2. Very recently Bailey [8] investigated the efficacy of DFT methods for the calculation of I4N coupling constants using several exchangexorrelation functionals and basis sets and employing, for the calibration procedure, the experimental geometries of the target molecules. As a first step in our work we describe the calibration results for the test molecules NF3, N2, HCN, CF3CN, HCCCN, FCCCN, CH,CN, NH3, CNCN, BF2,NH2, FCN, HCCNC, and CF3NC, for which accurate experimental NQCCs are available. For all the molecules considered, full geometry optimization has been performed. Based on the results we then apply the method for the NQCCs calculation to other medium and large size nitrogen containing compounds, including aromatic (pyridine, pyrrole, imidazole, pyrazole, 1,S-bis(dimethyl-amin0)naphthalene) and other ring systems (cyclotetramethylenetetranitramine,cocaine, heroin).

2. Computational details All the calculations have been performed using the density functional program Allchem [ 171 in which both

Molecular Physics ISSN 00268976 print/ISSN 1362-3028 online

02001 Taylor & Francis Ltd

http://www.tandf.co.uk/journals DOI: 10.1080/00268970110042820


I040

E. Sicilia et al.

the linear combination of Gaussian-type orbital local spin density (LCGTO-LSD) and the corresponding generalized gradient approximation (LCGTO-GGA) methods are implemented. For the local spin density calculations the exchange correlation functional proposed by Vosko et al. [18] (VWN) has been used. The gradient corrected density functionals chosen are those of Perdew and Wang [19] and Perdew [20] (PW86-P86), of Becke [21] and Perdew (B88-P86) and Becke and Lee et ai. [22, 231 (B88-LYP). The orbital basis sets employed were the TZVP [24], EPR-I11 [25, 261 and A N 0 [27]. For fitting the density the auxiliary function set A2 [24] was used. All molecular structures were fully optimized using analytical energy gradients and the Berny quasiNewton update [28]. The theoretical evaluation of NQCCs requires the calculation of the electric field gradient (EFG) tensor at a nucleus. Indeed, the largest absolute component of the traceless EFG tensor V z , in its principal axis system is related to the corresponding nuclear quadrupole coupling constant by ~ ( M H z= ) e2QVzz = 2.3496Q(in fm2)V,,(in au), (1) h where the factor 2.3496 includes all the constants and takes care of the units. To obtain a unique orientation of the principal axis system at the nucleus we used the convention: ~

For the calculation of the EFG tensor components at the nucleus of interest, the following expression is used PI: UadR)=

c

qIu(Fl&L

+I d l 4

A”

(3) where the first term on the right of equation (3) represents the contribution to the EFG tensor components from the electrons, whereas the second term represents the contribution from nuclei A with charge 2. The notation ( p l A ( I u 1p)lv) is used for the electric field gradient integrals over contracted Gaussian-type orbitals. P,, are elements 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 calculation 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 these EFG components the traceless tensor

+

V is diagonalized to obtain its principal components chosen according to the convention of equation (2). The eigenvalues of the EFG tensor, V x x ,V y yand V,,, and the calibrated I4N quadrupole moment Q have been used to calculate NQCCs and 77 through equation (1) and

(4) 3. Calculation of I4N nuclear quadrupole moments In order to calibrate the 14N nuclear quadrupole moment, the molecular structures of the target molecules were optimized by using local and gradient corrected functionals and different extended basis sets. A comparison between optimized molecular structures and available experimental ones [31-37], from table I , shows that better general agreement is obtained by using the VWN functional. To derive the calibrated DFT I4N nuclear quadrupole moment a least-squares linear regression analysis of the calculated V,, (table 2) versus the corresponding experimental NQCCs [3849], was employed. In table 3 the calibrated DFT 14Nnuclear quadrupole moments Q and the corresponding correlation coefficients, for different functionals and basis sets, are listed. The best correlation coefficient is obtained by using the local VWN functional, as expected due to the agreement between theoretical and experimental geometries, and the EPRIII/A2 basis set. It is worth noting that the correlation coefficient obtained at the same level of theory with the relatively small TZVP/A2 basis and auxillary function sets is almost identical. This result indicates that the relatively small and computationally less expensive TZVP/A2 basis is appropriate for highly accurate NQCC calculations. In this last case the good agreement can be ascribed to the fact the basis set is optimized for local DFT calculations, and we may conclude that DFT optimized basis set may be used to compensate for some failures in the functionals. A graphical display of the derived calibrated quadrupole moments against the different 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 the functional. The calibrated values of Q for the VWN functional are, generally, larger than the GGA values. Although it is not the goal of this work to obtain an accurate Q value for I4N, the values obtained are all close to the recommended experimental value of 2.044 fm2 reported in [15]. This value corresponds to a scale factor of 0.975. It is noteworthy that our best calibrated value (1.9922 fm2) agrees with that (1.941(2) fm2) obtained by Bailey [8] at B3PW91/6-311+ G(df,pd) level using for the calibration 39 molecules at experi-

1041

14N nuclear quadrupole moments by DFT Table 1. Bond lengths (in Molecule

Basis

Structure

VWN

NF3

TZVP/A2

NF FNF

1.383 102.5 1.376 102.5 1.375 101.7 1.104 1.095 1.099 1.156 1.082 1.153 1.082 1.156 1.080 1.158 1.470 1.334 109.8 1.153 1.474 1.329 109.8 1.157 1.415 1.330 110.0 1.168 1.357 1.212 1.077 1.162 1.358 1.208 1.077 1.166 1.357 1.212 1.076 1.168 1.355 1.209 1.262 1.162 1.355 1.205 1.258 1.166 1.355 1.209 1.258 1.161 1.436 1.104 110.6

EPR-III/A2 ANO/A2 N2

HCN

TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2

NN

CN HC

EPR-III/AZ ANO/A2


A) and angles (in deg) for optimized molecular structures.

CF3CN

TZVP/A2

CN

cc

FC FCC EPR-III/A2

ANOIA2

HCCCN

TZVP/A2

CN

cc cc

HC EPR-III/A2

ANO/A2

FCCCN

TZVP/A2

CN

cc cc FC

EPR-III/A2

ANO/A2

CH3CN

TZVPlA2

CN

cc

HC HCC

PW86-PS6

B88-P86

B88-LYP

Exp.

1.426 102.5 1.419 102.5 1.420 101.6 1.113 1.104 1.106 1.164 1.078 1.158 1.076 1.163 1.075 1.165 1.483 1.362 109.9 1.159 1.486 1.356 109.8 1.163 1.484 1.337 109.8 1.175 1.368 1.216 1.072 1.169 1.368 1.213 1.071 1.173 1.368 1.217 1.072 1.175 1.367 1.212 1.285 1.169 1.368 1.209 1.282 1.173 1.366 1.212 1.282 1.167 1.459 1.101 110.4

1.414 102.6 1.407 102.6 1.407 101.7 1.112 1.103 1.105 1.163 1.078 1.158 1.076 1.162 1.075 1.165 1.485 1.353 109.9 1.159 1.488 1.348 109.8 1.163 1.486 1.349 109.8 1.175 1.366 1.217 1.072 1.169 1.368 1.213 1.072 1.173 1.376 1.217 1.072 1.175 1.365 1.213 1.278 1.169 1.366 1.210 1.275 1.173 1.365 1.313 1.276 1.167 1.456 1.102 110.3

1.429 102.5 1.423 102.6 1.423 101.7 1.112 1.103 1.105 1.163 1.076 1.157 1.074 1.162 1.07 1.165 1.487 1.362 109.9 1.159 1.490 1.367 109.9 1.163 1.488 1.358 109.9 1.174 1.368 1.216 1.070 1.169 1.370 1.212 1.069 1.173 1.369 1.216 1.069 1.174 1.367 1.212 1.286 1.168 1.369 1.209 1.283 1.173 1.367 1.212 1.283 1.167 1.463 1.100 110.2

1.365" 102.4"

1.098"

1.153" 1.065"

1.154" 1.492" 1.328" 110.0"

1.161b 1 ,376' 1,206' 1.062'

1.159' 1.369' 1.201' 1.270'

1.159" 1.468" 1.107" 109.7" continued

1042

E. Sicilia et al. Table 1. Continued.

Molecule

Basis

Structure

EPR-III/A2

ANO/A2

NH3

TZVP/A2

NH HNH

EPR-III/A2


ANO/A2 CNCN

T ZVP/A2

CN NC CN

EPR-III/A2

ANO/A2

BFZNH,

TZVP/A2

BF BN NH FBF HNB

EPR-III/A2

ANO/A2

FCN

TZVP/A2

CN FC

EPR-III/A2 ANO/A2 HCCNC

TZVP/A2

NC CN

cc

HC EPR-III/A2

ANO/A2

VWN

PW86-P86

B88-P86

B88-LYP

1.155 1.436 1.102 110.4 1.159 1.437 1.102 110.4

1.162 1.460 1.099 110.2 1.165 1.457 1.100 110.2 1.032 105.8 1.023 107.3 I .023 106.5 1.197 1.311 1.173 1.191 1.311 1.168 1.194 1.309 1.172 1.354 1.406 1.022 117.7 122.6 I .350 1.402 1.013 117.6 122.4 1.355 1.402 1.012 117.6 122.4 1.170 1.288 1.164 1.284 1.169 1.286 1.196 1.310 1.21 1 1.073 1.190 1.310 1.214 1.068 1.194 1.308 1.215

1.162 1.457 1.100 110.2 1.165 1.457 1.100 110.2 1.031 105.9 1.023 107.3 1.023 106.3 1.198 1.308 1.173 1.921 1.308 1.168 1.195 1.307 1.172 1.349 1.405 1.020 17.7 22.6 1.346 1.402 1.013 17.7 22.4 1.350 1.403 1.012 117.7 122.4

1.161 1.464 1.098 110.4 1.165 1.464 1.099 110.2 1.032 105.9 1.022 106.7 1.023 106.7 1.197 1.312 1.173 1.191 1.312 1.168 1.194 1.310 1.171 1.353 1.407 1.021 117.6 122.6 1.350 1.403 1.013 117.6 122.5 1.355 1.405 1.012 117.6 122.5 1.169 1.288 1.164 1.284 1.169 1.286 1.196 1.312 1.210 1.072 1.190 1.311 1.214 1.067 1.194 1.309 1.215

1.030

106.9 1.029 105.5 1.023 107.2 1.189 1.296 1.166 1.184 1.296 1.161 1.187 1.294 1.165 1.333 1.392 1.022 117.7 122.0 1.333 1.391 1.020 117.6 122.5 1.335 1.390 1.015 117.7 122.2 1.163 1.263 1.157 1.260 1.163 1.261 1.188

1.296 1.207 1.077 1.183 1.295 1.210 1.014 1.186 1.293 1.211

1.170

1.281 1.164 1.278 1.170 1.281 1.197 1.308 1.211 1.074 1.191 1.308 1.215 1.069 1.194 1.306 1.215

Exp.

1.012" 106.7"

1.181' 1.312d 1.158'

1.325' 1.402' 1.003' 117.9' 121.5'

1.159" 1.262"

1.175/ 1.317f 1.203/ 1.055f

continued

I4N nuclear quadrupole moments by DFT Table 1. Molecule

Basis

Structure

CCF3NC

TZVP/A2

CN NC FC FCN

EPR-III/A2


ANO/A2

1043

Continued.

VWN

PW86-P86

B88-P86

B88-LYP

1.075 1.395 1.181 1.332 109.2 1.398 1.174 1.326 109.3 1.393 1.178 1.328 109.3

1.068 1.410 1.189 1.359 109.1 1.413 1.182 1.353 109.2 1.393 1.178 1.328 109.3

1.071 1.409 1.185 1.347 109.3 1.413 1.182 1.345 109.1 1.409 1.186 1.348 109.1

1.068 1.412 1.188 1.359 109.2 1.416 1.182 1.354 109.1 1.416 1.182 1.354 109.3

Exp. 1.407q 1.171q 1.324y 108.8q

‘Reference [31]. ’Reference [32]. ‘Reference [33]. dReference [34]. eReference [35]. /Reference [36]. gReference [37].

mental geometries. By using the calibrated DFT I4N quadrupole moment, NQCCs for the target molecules have been calculated with the aid of equation (1). They are listed in table 4 together with the experimental values. The correlation between calculated and experiment NQCCs is plotted in figure 2. Both table 4 and figure 2 reveal that the local VWN values are closer to the experiment, the maximum error being 0.43, 0.43 and 0.65 MHz for the TZVP, EPRIII and A N 0 basis sets, respectively. The corresponding average errors are 0.13 MHz for TZVP/A2, 0.12 MHz for EPRIII/A2 and 0.23 MHz for ANO/A2. We underline again that the calibrated 14N VWN/TZVP value of quadrupole moment is accurate enough for reliable predictions of 14N NQCCs. Figure 3 presents the calculated NQCCs (U) using experimental structure parameters at VWN/EPR-111 level of theory in conjunction to the I4N recommended value [15] of Q = 2.044 fm2. The deviations in these calculated NQCCs with respect to the experimental ones is reduced by using both experimental structure (0) and optimized parameters (0) coupled with the calibrated I4N nuclear quadrupole moment at the same level of theory.

4. Application to aromatic and other ring systems In order to prove the usefulness of the present approach, we have carried out the computation of the EFG tensor components, from which the NQCC and the asymmetry parameter 71 can be obtained, for some aromatic and non-aromatic compounds. On the basis of the results of the calibration of the I4N quadrupole moment, the EPRIII/A2 basis in conjunction with the VWN functional were used for these computations. The molecular structures of all the selected compounds were fully optimized at this level of theory.

4.1. Aromatic systems Nuclear quadrupole constants and anisotropy parameters, calculated using the procedure just discussed, of the selected aromatic systems are listed in table 5 along with experimental values. Coupling constants have derived from microwave spectra for pyridine [50, 511, pyrrole [52], imidazole [53], and pyrazole [53]. The agreement between experimental and theoretical values for these four heterocyclic compounds is good, with a larger deviation being found in the case of imidazole. The differences with respect to a recent theoretical evaluation [16] of NQCCs for the same molecules reflect the differences in the approach used in the calibration procedure. The aromatic diamine 1,8-bis(dimethylamino)naphthalene (DMAN) has already attracted considerable attention for its structure and properties. The crystal and molecular structure of DMAN have been determined by X-ray diffraction [54]. It has been shown that the molecule is strained, with a large deviation of the naphthalene skeleton from planarity. The central CC bond is twisted so that the N(CH3)2 groups are on different sides of the naphthalene plane. On the basis of a previous ab inito and fluorescence study [55] the optimization of the geometry for two different conformations of the molecule has been performed. The structure of the most stable conformer is depicted in figure 4 and the corresponding most relevant geometrical parameters are reported in table 6 and compared with those obtained in the crystallographic studies. Results of calculations confirm that the molecule is markedly non-planar and h g C2 symmetry in the absence of any crystal packing forces. The values of the largest components of the EFGs for the nitrogen atoms in DMAN have been determined by Wozniak et al. with I4N NQR spectroscopy at room temperature

E. Sicilia et al.

1044

Table 2. Calculated principal components V,, (in au) of the electric field gradient tensor for different exchange-correlation functionals and basis sets using optimized molecular structures. Molecule NF3

N2 HCN

CF3CN


HCCCN

FCCCN

CH3CN

NH3 CNCN#

BF2NH2

FCN

HCCNC

CF3NC

CN#CN

Basis

VWN

PWP86-P86

TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2

- 1407 - 1.423

- 1.273

-

1.285 - 1.222 -1.113 - 1.132 - 1.051 -0.956 -0.987 -0.913 -0.937 -0.979 -0.931 -0.863 -0.903 -0.858 -0.841 -0.879 -0.834 -0.827 -0.873 -0.830 -0.849 -0.869 -0.859 -0.751 -0.786 -0.738 -0.828 -0.774 -0.770 -0.476 -0.513 - 0.445 0.281 0.271 0.295 0.344 0.323 0.359 0.357 0.340 0.364

- 1.316 - 1.259

-

1.363

- 1.133

-1.159 - 1.053 - 1.002 - 1.037 -0.943 -0.986 - 1.034 -0.968 -0.912 -0.956 -0.897 -0.888 -0.931 -0.872 -0.865 -0.914 -0.855 -0.819 -0.843 -0.838 -0.810 -0.848 - 0.786 -0.759 -0.712 -0.715 - 0.532 -0.570 -0.495 0.215 0.204 0.255 0.268 0.247 0.31 1 0.291 0.283 0.325

[56] and at 77 K [57]. The authors, assuming a value of 2.02 fm2 for I4N nuclear quadrupole constant [58] and measuring the components of the EFG tensor, have obtained the corresponding nuclear quadrupole coupling constants for the two non-equivalent nitrogens reported in table 5. It is evident that the good agreement of the calculated values with the experimental ones obtained at 77K is due to the increase of symmetry of

-

B88-P86

B88-LYP

1.303

- 1.288 - 1.301 - 1.237

-1.120 -1.144 - 1.059 -0.966 -0.999 -0.921 -0.945 -0.988 -0.933 -0.872 -0.914 -0.863 -0.848 -0.888 -0.839 -0.837 -0.885 -0.835 -0.841 -0.850 -0.852 -0.758 -0.795 -0.741 -0.815 -0.765 -0.763 - 0.482 -0.518 -0.480 0.256 0.245 0.279 0.315 0.293 0.337 0.332 0.312 0.348

1.140 -1.162 - 1.072 -0.993 - 1.029 -0.947 -0.973 - 1.019 -0.967 -0.896 -0.889 -0.873 -0.873 -0.917 -0.867 -0.864 -0.915 -0.865 -0.867 -0.890 -0.877 -0.782 -0.822 -0.768 -0.835 -0.782 -0.775 -0.508 -0.550 - 0.486 0.251 0.243 0.271 0.320 0.303 0.344 0.330 0.314 0.342 -

the molecule at low temperatures, while the discrepancy in the anisotropy parameter reflects the crystallographic environment.

4.2. Other ring systems The calculated coupling constants and asymmetry paramenters for the selected other ring compounds are collected in table 7 together with the experimental

I4N nuclear quadrupole moments by DFT

1045

Table 3. Calibrated nuclear quadrupole moments Q (in fm2), for the density functional methods considered, obtained by using the correlation between the calculated V Z Z (table 2) and the experimental nuclear quadrupole coupling constants x.The corresponding correlation coefficients are reported in parentheses. Basis TZVP/A2 EPRIIIIA2


ANO/A2

I

VWN

PW86-P86

B88-P86

B88-LYP

2.0162 (0.9974) 1.9922 (0.9979) 2.01 11 (0.9969)

1.9750 (0.9893) 1.9711 (0.9921) 2.001 1 (0.989 1)

2.0027 (0.99 18) 1.9976 (0.9941) 2.0201 (0.9920)

1.9773 (0.9898) 1.9623 (0.9917) 1.9871 (0.9893)

I

I

I

PW86-P86 B88-P86 B88-LYP Figure 1. Dependence of the calibrated I4Nnuclear quadrupole moment (in fm’) on the exchange-correlation functional and basis set. VWN

6

results. The choice of these molecules is due to considerable effort made in recent years to use I4N, through NQR spectroscopy, as a sensor for the detection of compounds with physiological or energetic interest. The optimized structure of the cyclotetramethylenetetranitramine (p-HMX) is reported in figure 5. In this molecule there are four peripheral and four 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 the ring and two in the peripheral NOz groups, each pair containing two equivalent I4N nuclei. Experi-

mentally nuclear quadrupole interaction parameters (x and 71) have been measured for ring nitrogens by the conventional NQR technique [59] and through the use of special double-resonance techniques [60] for the two pairs of equivalent nuclei in the NO2 groups. For the two sets of ring nuclei, termed equatorial and axial, the measured constants and anisotropy parameters have been assigned on the basis of the temperature dependance of the NQR frequencies. On the other hand, no assignments of the nuclear quadrupole interaction parameters has been made experimentally for the peripheral nitrogen nuclei. We have calculated the coupling

1046

E. Sicilia et al.

VWN

PW86-P86 2 -

NF3 1 -

N2

3 HCN 4 CF3CN

0h

8

-3-

CY

-9z

NH3

0

9 CNCN# 10 BF2NH2 11 FCN 12 HCCNC 13 CF3NC

-4-

-6 -7 -5

-81 -8

14 C N K N


-

-I

9 -2 -

5 HCCCN 6 FCCCN I CH3CN

-7

-6

-5

-4

-3

-2

0

-1

I

-8

2

"

-7

-6

'

-5

'

-3

'

-2

'

-1

TLVPIAZ

0

EPR-IIVM

A

ANOIAZ

'

0

'

I

2

Exp. NQCC (MHz)

E ~ PNQCC . (MHz)

B88-P86

r""'

B88-LYP 2 -

2 -

I -

I -

0-

0-

-1

'

4

0

-

E -3 U h

g

-2

8-4z

-d a -6-5

-7

-

-81 -8

'IZVPIAZ EPR-WAZ ANOIAZ

TZVPIAZ EPR-IWAZ ANOlA2

0 0

A

'

'

'

'

'

'

'

'

'

I

-7

-6

-5

4

-3

-2

-1

0

I

2

ExP. NQCC (MHZ)

-8

-8

-7

-6

-5

-4

-3

-2

-I

0

I

2

Exp. NQCC (MHZ)

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

constants and the asymmetry parameter for I4N nuclei both in the ring and in peripheral NO2 groups, attempting in the latter case an assignment of the observed values. Analysing the results reported in table 7, it appears that there is excellent agreement between theory and experiment, the largest deviation being found in the values of the asymmetry parameter for the ring nitrogen atoms. Experimental information on the I4Nnuclear quadrupole interaction of cocaine and heroin molecules is available [6 1,621. In both molecules, see figures 6 and 7, there is one I4N nucleus, and then only one set of nuclear quadrupole interaction parameters, x and r], has been observed experimentally by NQR spectroscopy in polycrystalline samples. The agreement between theoretical

and experiment NQCC values is satisfactory (see table 7), but poorer than for the previously considered compounds not included in the calibration. The source of the existing discrepancies can be the use of the optimized geometrical structures in conjunction with the calibrated Q values. Indeed, this coupling, as shown in figure 3 for the NF3 molecule, could be a rough choice for the computation of NQCCs. Moreover, the influence of the environment would also not be neglected. 5. Conclusion We have reported the values of the nuclear quadrupole moments of I4N obtained through a calibration procedure in the framework of density functional theory. The calibration involved the optimization of

1047


Table 4. Calculated nuclear quadrupole coupling constants x (in MHz) using optimized molecular structures and calibrated nuclear quadrupole moments. Molecule NF3

N2 HCN

CF3CN


HCCCN

FCCCN

CH3CN

NH3 CNCN#

BF2NH2

FCN

HCCNC

CFiNC

CN#CN

Basis TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-IIIIA2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-IIIIA2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2 TZVP/A2 EPR-III/A2 ANO/A2

VWN 6.665 -6.661 - 6.440 -5.367 - 5.425 -4.975 -4.746 -4.854 -4.456 -4.671 -4.840 -4.574 -4.320 -4.475 -4.239 -4.208 -4.358 -4.120 -4.098 - 4.278 -4.040 -3.880 -3.946 -3.960 -3.837 - 3.968 -3.714 -3.596 -3.333 -3.379 - 2.520 - 2.668 - 2.339 1.019 0.955 1.205 1.269 1.156 1.469 1.378 1.325 1.375 -

PWP86-P86

B88-P86

B88-LYP

- 5.907 -5.951 - 5.745 -5.165 - 5.243 -4.942 -4.436 -4.571 -4.293 -4.348 -4.534 -4.377 - 4.005 -4.182 -4.034 - 3.902 -4.071 -3.921 - 3.838 -4.043 -3.902 - 3.939 - 3.932 -4.038 - 3.485 - 3.640 - 3.469 -3.842 -3.585 -3.620 -2.209 -2.376 -2.092 1.304 1.255 1.387 1.596 1.496 1.688 1.656 1.575 1.711

-6.131 -6.177 - 5.976 - 5.270 - 5.369 - 5.026 -4.545 -4.689 -4.371 - 4.446 -4.637 -4.428 -4.103 -4.289 -4.096 - 3.990 -4.168 - 3.982 - 3.938 -4.154 -3.963 - 3.590 -3.947 -4.044 -3.567 -3.731 -3.517 -3.835 -3.591 -3.621 -2.268 -2.43 1 -2.278 1.204 1.149 1.324 1.482 1.375 1.599 1.562 1.464 1.652

5.998 -5.775 - 5.296 -5.357 - 5.005 -4.613 -4.744 -4.421 -4.520 -4.698 -4.515 -4.163 -4.099 -4.076 -4.056 -4.228 -4.048 -4.014 -4.219 -4.039 -4.027 - 3.997 -4.095 - 3.633 - 3.790 -3.586 -3.879 -3.605 -3.618 -2.360 -2.536 -2.269 1.166 1.120 1.265 1.487 1.397 1.606 1.533 1.448 1.597

- 5.984

Exp. -7.093a

-

-5.39h

-4.70783‘

-4.666d

- 4.3 1924‘

-4.239 1 3

-4.2292d

-4.08965”

-

3.781 13h

-3.193‘

-2.671

0.9454k

1.06’

1.32152h

‘Reference [38]. hReference [39]. ‘Reference [40]. dReference [41]. eReference [42]:IReference [43]. YReference[44].hReference [45]. ‘Reference [46]. ’Reference [47]. kReference [48]. ‘Reference [49].

geometrical parameters and the calculation of the EFG tensors at several levels of theory for a chosen set of molecules. Since experimental structural data are not employed, the technique used can greatly expand the range of the theoretical description of NQR spectro-

scopy. This might help in obtaining more reliable knowledge of many important classes of compound for which experimental information is not available or has to be interpreted. By using the nuclear quadrupole moments obtained, highly accurate NQCCs were calculated for


I048

E. Sicilia et al.

-4

-6

-2

2

0

Exp. NQCC (MHz) Figure 3. Comparison between measured and VWN/EPR-I11 calculated, by using different approaches, nuclear quadrupole coupling constants (in MHz).

Table 5.

I4N nuclear quadrupole coupling constants x (in MHz) and a symmetry parameter 77 for aromatic systems. X

Molecule Pyridine

Nucleus

77

Theory

Exp.

Theory

Exp.

-5.071

-4.87 & 0.04' -4.908' - 2.704' -2.537' -4.032d -3.02d -4.4gd 5.5541'; 5.6345/ 5.6033'; 5.6975/

0.394

0.43"

0.104 0.149 0.083 0.503 0.673 0.018 0.014

0.04'

-2.691 -2.501 -4.204 - 3.053 -4.531 5.544 5.562

0.18' 0.12d 0.523' 0.647' 0.0419'; 0.0399 0.0439'; 0.0388

'Reference [SO]. 'Reference [51]. 'Reference [52]. dReference [53]. eReference [57]. /Reference [56].

medium and large size systems. The best correlated value of the nuclear quadrupole moment was obtained by using the VWN functional in conjunction with the extended EPRIII/A2 basis and auxiliary sets. Finally, the value of the correlation coefficient for Q calibration, obtained using the same functional and the less computational expensive TZVP basis set, is almost identical to

the VWN/EPR-111. Then, the corresponding value of Q is highly recommended for studying medium and large size systems to obtain reliable results. Work is in progress in our laboratories to extend the same calibration method to the density functional evaluation of nuclear quadrupole moments for other nuclei of chemical interest.


14N nuclear quadrupole moments by DFT

Figure 4. Numbering scheme and atomic arrangement of DMAN molecule.

Table 6. Selected geometrical parameters (in DMAN. Parameter

VWN/EPRIII

C( 1)-C(6) C(5)-C(6) C(4)-C(5) C(3)-C(4) C(5)-N( 11) N( 1I)-C( 12) C(4)-C(5)-C(6) C(3)-C(4)-C(5) C(6)-C(5)-N( 1 1) C(5)-N(ll)-C(l2) C(5)-N( 1l)-C(15) C(2)-C(3)-C(4)-C(5) C(l)-C(6)-C(5)-N(ll) C(6)-C(5)-N(I 1)-C(12) C(6)-C(5)-N( 11)-C(15)

1.429 1.434, 1.435 1.383, 1.385 1.392, 1.395 1.389, 1.391 1.441, 1.440 119.1, 119.0 122.1, 121.8 120.9, 120.7 117.5, 117.4 116.0, 116.3 3.3, 3.2 166.4, 166.0 -56.1, -56.6 167.8, 167.5

1049

Figure 5. Numbering scheme and atomic arrangement of pHMX molecule.

A,deg) of Exp."

1.425 1.429, 1.408 1.383, 1.373 1.387, 1.410 1.395, 1.399 1.467, 1.465 119.4 118.6 121.4, 121.4 120.8, 120.1 118.5 118.0 117.1, 117.2 3.0, 3.0 168.5, 167.9 -59.4, -60.6 162.7, 160.9

Figure 6. Atomic arrangement of cocaine molecule.

'Reference [54]. For double entries the first refers to the parameter denoted in the first column, while the second entry refers to the other half of the naphthalene system.

This work was partially supported by the VIGONI exchange program. Financial support from the Universita degli Studi Calacria and MURST is gratefully acknowledged. References [l] DUFFY,P., CHONG,D. P., and DUPUIS,M., 1995, J. chem.. Phys., 102, 3312. M., and SALAHUB, D. R., 1996, [2] KOSTER,A. M., LEBOUF, Theoretical and Computational Chemistry, Vol. 3, edited by J.S. Murray and K. Sen (Amsterdam: Elsevier).

Figure 7. Atomic arrangement of heroin molecule.

E. Sicilia et al.

1050 Table 7.

I4N nuclear quadrupole coupling constants x (in MHz) and asymmetry parameter 77 for other ring systems. X

77

Molecule

Nucleus

Theor

Exp.

Theory

Exp.

P-HMX

N(10), N(12) N(9h N(11) N(2), "6) N(4), N(8)

0.840 0.703 6.098 6.175 5.753 5.955

0.840" 0.806" 5.791' 6.025' 5.0229' 5.3136d

0.905 0.922 0.445 0.378 0.074 0.0 17

0.42" 0.48" 0.4977b 0.5180' 0.39Sd 0.028d

Cocaine Heroin


"Reference [60]. bReference [59]. 'Reference [61]. dReference [62].

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