The molecular properties of the halogen pseudohalides studied by both ab initio and DFT methods

Journal of Molecular Structure 825 (2006) 93–100 www.elsevier.com/locate/molstruc

The molecular properties of the halogen pseudohalides studied by both ab initio and DFT methods Michael H. Palmer *, Alistair D. Nelson School of Chemistry, University of Edinburgh, Edinburgh EH9 3JJ, Scotland, UK Received 9 February 2006; received in revised form 28 March 2006; accepted 31 March 2006 Available online 26 May 2006

Abstract The dipole, quadrupole, and other second moments have been determined at the equilibrium structures of the halogen azides, isocyanates, and isothiocyanates, for both principal axes and inertial axes. The theoretical procedures used are Mo¨ller–Plesset (MP2) and DFT (B3LYP) methodologies, with TZVP and cc-pVTZ basis sets. There is systematic variation in the calculated directions of the dipole moments in the present series, where B3LYP and MP2 methodologies show differences up to 20 for the directions. This discrepancy is largest in ClN3, but quite significant for several other compounds, such as XNCO (where X = Cl, Br and I). The dipole moments of the compounds rotate through a wide angle, as the halogen changes; in contrast, the axes of the second moments rotate to a much smaller degree. The properties are compared with the limited microwave spectral data so far available, in the hope that the present study will encourage further experimental study. There is an urgent need for new experimental data on the dipole moment a,b-components for these compounds.  2006 Elsevier B.V. All rights reserved. Keywords: Ab initio calculations; Density functional calculations; Molecular properties; Dipole moments; Quadrupole moments; Second moments

1. Introduction Recently we reported [1,2] theoretical studies of the molecular and electronic structures of the compounds with general formula RAN@X@Y (Figs. 1 and 2); the substituents (R) were alkyl, silyl, germyl, stannyl, and plumbyl, while the compound classes were azides (X@Y@N), isocyanates (X = C, Y = O), and isothiocyanates (X = C, Y = S). This was followed by a related study of the halogen pseudohalides [3]. The structures were compared with results from experiment, and in particular with those from microwave (MW) and infrared (IR) spectra, and electron diffraction (ED). The results were sufficiently close, for predictions of structures for related compounds to be made with confidence, and showed some cases where the experimental data appeared to be in need of refinement. The

*

Corresponding author. Tel.: +441316504765; fax: +441316504743. E-mail address: [email protected] (M.H. Palmer).

0022-2860/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2006.03.104

present paper is concerned with the molecular properties of the halogen azides, isocyanates, and isothiocyanates (Fig. 2, where R = F, Cl, Br, I); preliminary results of this study have been published [4]. All members of the series are planar (CS symmetry). The wave-functions from those studies [1–3] provide a wide range of theoretical data concerning the first and second moments, and charge distribution; whilst in principle these can all be measured by MW spectroscopy, the number of quadrupolar centres makes analysis of the MW spectra of the present molecules very demanding tasks, and hence little work has been done in this area. For several compounds, even the dipole moments are not known, yet these are classical cases where the interaction of ‘push and pull’ of electrons around the halogen makes such studies important. Indeed, the theoretical data provide a very clear indicator concerning any assumptions which may be necessary to deconvolute the experimental spectra. Although these are hazardous compounds, their chemistry is well known, and much of the early knowledge has been reviewed [5–8].

94

M.H. Palmer, A.D. Nelson / Journal of Molecular Structure 825 (2006) 93–100

Fig. 1. The general structures of the pseudohalide skeleton.

Initially [4] a triple zeta valence + polarisation (TZVP) basis set [3,4,27–29] was used for H, C, N, O, F, S; this was subsequently augmented by the correlation consistent cc-pVTZ type [30–34], where we used our recent cc-pVTZ quality basis set for iodine [3]. All calculations used harmonic functions for all d-, f-, g-type GTOs, and CS symmetry for the structures; in the results given here, the molecule lies in the inertial axis (IA) a-,b-system, with the c-axis always as the out-of-plane direction. 2.2. Molecular properties

Fig. 2. Canonical forms contributing to the variations in structure for azides.

In common with amines, these molecules have the characteristic behaviour of interconversion, such that the potential energy surface of these compounds is a double minimum; the linear arrangement of atoms is a maximum in energy, and transition state between Figs. 1a and b. This behaviour relates to the classical resonance hybrids shown in Fig. 2 for the azide case; the NNN angle is large (170) showing the importance of 2a, which would generate a linear NNN structure; the trans-orientation in the structures shows the influence of 2b; the quasilinear behaviour of many of these compounds can be exemplified by 2c, where the bicovalent structure leads to a very shallow energy surface with respect to bending; a further canonical form applicable to the halogen series allows electron donation to the adjacent N1, with transfer of charge to N3. Individual members of the three series, which have been investigated by MW spectroscopy, are: FN3 [9], ClN3 [10], IN3 [11], ClNCO [12–14], BrNCO [15–17], INCO [18]. ED has led to structures for BrN3 [19], IN3 [20], and ClNCO [21]. The infrared spectrum of FNCO has been reported [22,23], but no structure has been obtained for this substance, or any members of the NCS series; thus the present study is predictive for this latter group. A considerable amount of quadrupole coupling data has been obtained from the MW spectra, and this is considered in a following paper. 2. Theoretical methods 2.1. Methods and basis sets We utilise the previously determined equilibrium structures from both the MP2 and B3LYP calculations [3]. The molecular properties, evaluated from the wave-functions, include dipole and molecular quadrupole moments; these procedures have been described in detail in our preceding papers [24–26].

2.2.1. Dipole moments (DM) In most theoretical calculations the equilibrium structure is determined in the centre of charge coordinate system. The dipole moment is the sum of nuclear (N) and electronic (E) terms, where N is placed at the origin. If the electronic term is positive, the dipole moment is positive, as exemplified by HF with the charge distribution Hd+–Fd; this convention is used in the present study. The most obvious method for measuring the dipole moments here is MW spectroscopy, where the inertial axis (IA) a,b-components can be obtained, in favourable cases, by the Stark effect [9]. 2.2.2. Second moments (SM) and molecular quadrupole moments (QM) The SM second rank tensor elements of the electronic charge distribution, in atomic units, are: Æx2æ, Æy2æ, Æz2æ, and Æxyæ (units a20 , experimentally cm2); the QM terms (ea20 , experimentally esu cm2) are similar, but also include the ‘principal’ QM value Æ3z2  r2æ, etc. Again, each contains nuclear and electronic terms, where the former are based purely on the atomic coordinates of the atoms. In each of the DM, SM, and QM operators, the average is over the ground state wave-function, at the equilibrium structure. Both SM and QM electronic terms have been measured in the inertial axis (IA) system from some MW spectra using Zeeman splitting of the lines [35,36]. Other methods such as birefringence [37] and crystallography [38] also give the QM, but the uncertainty of the global origins and thermal factors (respectively) makes the results difficult to compare with MW studies. The sign conventions of the present study are consistent with the experimental results, where CO2 and CS2 have opposite values of the QM tensor. For example, using the cc-pVTZ basis set we obtain 3.80, and +2.08 a.u. (respectively) for the QM, to be compared with the experimental values 4.3 (3) and +1.8 esu cm2 [39], respectively. We note in passing that these correspond to charge distributions (q) where qO and qS are 0.21 and +0.02e, respectively, at the cc-pVTZ level. For the present compounds where CS symmetry pertains, the theoretical principal axis (PA) values for both SM and QM are converted to IA values via the (CS symmetry) rotation matrix (Eqs. (1)–(3)). Here hax2 is the angle between a- and x2-SM/QM axes. Since both SM and QM

M.H. Palmer, A.D. Nelson / Journal of Molecular Structure 825 (2006) 93–100

are second moments, the rotation matrices are identical in form ha2 i ¼ ½hy 2 i cos2 ðhax2 Þ þ ½hx2 i sin2 ðhax2 Þ 2

hb2 i ¼ ½hy 2 i sin ðhax2 Þ þ ½hx2 i cos2 ðhax2 Þ 2

2

hc i ¼ hz i

ð1Þ ð2Þ ð3Þ

Previous studies [40] showed that SM electronic terms are nearly invariant to both methodology and basis set, and this was also found here. In tabulated linear correlations between theory and experiment, or between variables, standard deviations in the experimental variables are shown in parentheses. 3. Molecular properties results 3.1. Dipole moments Calculated dipole moments which show the range of values for each of the 12 molecules, determined with two basis sets (TZVP and cc-pVTZ), and two methodologies (MP2 and B3LYP), are shown in Table 1. We give molecular total and inertial axis (IA) components. Statistical correlations between the various procedures are used to determine some relationships, which are tabulated to avoid repetitive text (Table 2), followed by comments in relation to individual molecules. If the intercept in these correlations is smaller than its standard deviation (SD), we consider the line to pass through the origin (Table 2). Scale diagrams (ccpVTZ + B3LYP, Fig. 4) have the a- and b-axes horizontal and vertical, respectively, and show both dipole and quadrupole tensor axes; the origins are at the centres of mass (CM). The SM and QM results are shown in Tables 3 and 4, respectively, with similar IA data shown. Some more important previous calculated data are also shown in the Tables. 3.1.1. Overall comparisons of calculated dipole moments for the series The present results suggest that only small values can be expected for la in ClN3, ClNCS, and BrNCS, and for lb in FN3, IN3, INCO, FNCS, and INCS. Although a number of MW studies have been reported for the present series of compounds [9–18], the a-,b-DM components [9] have been reported only for FN3, and we are not convinced of their accuracy; quadrupole effects from the 14N and Cl, Br or I nuclei may be a difficulty in such determinations. Indeed, we have recently been informed that the lb component in FN3 is incorrect, while the la component is correct [49], for the reasons described above; this fits well with the present results. 3.1.2. Electronegativity There is a nearly linear relationship between the electronegativity of the substituent (R = halogen and including H) for most of the present compounds, using either the B3LYP or MP2 methodologies. The closest correlations

95

are with the Pauling scale, which appears to have better internal ratios of the H and halogen electronegativities. The cc-pVTZ + B3LYP results (Fig. 3) show that the Clgroup does not fit as well as the other series, but there is no cross-over in the magnitudes of the DM, which for the three series of compounds are always CO > NN > CS. The MP2 versus electronegativity correlation is closer than the B3LYP one, but only for the Cl, Br, and I series. The results (Table 2) of linear correlations including all (B3LYP), and when the F-series are omitted (MP2) are shown. Replacement of NbNc by CO (both mass 28 amu) leads to negligible change in the inertial axes, and the charge distributions do not differ significantly, but the DM of each isocyanate is smaller than the corresponding azide by about 0.2–0.3 Debye. From the correlation, the DM for a substituted azide (RN3) would be zero for an electronegativity of 3.3 units (such examples would be when R is NH2 or OH). The electronegativities of Cl and Br are close to the value for N, but with XN differences of opposite sign; this has been used previously [12] to suggest that the ClAN bond in ClNCO is essentially covalent, and hence provides an explanation for the 35Cl quadrupole coupling (QC) in ClNCO being similar to that in the free Cl atom. Such an explanation could also apply to BrNCO [16] and INCO [22]; the differences in QC for BrNCO and INCO relative to the Br- and I-atoms indicate that Br/I are electron releasing (Fig. 2d) in BrNCO and INCO; this issue is discussed in more detail in our following paper. 3.1.3. Methodology Plots of B3LYP versus MP2 data vary slightly with basis set, the slope being larger (cc-pVTZ), or smaller (TZVP) than unity; however, the results from the 4 procedures (Table 2) are reasonably concordant in magnitudes. In most cases, the absolute values for the DM are smaller when cc-pVTZ is compared with TZVP, but there are no systematic conclusions over the relative magnitudes of MP2 versus B3LYP values. The directions of the dipole moments vary greatly over the F–I series (X), but are relatively similar between the azide and isothiocyanates series, showing the effect of the extra electronegativity of the CO unit; we show (Fig. 4) the set of dipole and quadrupole moment axes from the B3LYP wave-functions, but the MP2 data are similar, except where discussed below. Superposition of each set of 4 molecules on the same centre of mass framework shows that for the azides, the MP2 data exhibit a clockwise (+) rotation of the DM away from the XN direction by 24 (Cl), 6 (F), 4 (Br, I); the isothiocyanates are rather similar with 5 (F), 10 (Cl), 10 (Br), and 2 (I). For the isocyanates, the effects are in the reverse direction, where B3LYP gives larger DM rotation than MP2, in the sequence 12 (I), 9 (Br), 5 (Cl), and 3 (F). Such discrepancies should be resolvable by future experimental MW work.

96

M.H. Palmer, A.D. Nelson / Journal of Molecular Structure 825 (2006) 93–100

Table 1 Total and inertial axis components of the dipole moments, by various procedures Molecule

Basis set and method

ltotal

la

lb

hla

hlRN

FN3

MW spectrum [9,49] cc-pVTZ + MP2 cc-pVTZ + B3LYP TZVP + MP2 TZVP + B3LYP 6-31G* + MP2 [9]a 6-31G* + SCF [9] 6-311G(2df) + B3LYP [45] cc-pVTZ+MP2 cc-pVTZ + B3LYP TZVP + MP2 TZVP + B3LYP 6-31G* + MP2 [46] DZ + d(Cl) [47] cc-pVTZ + MP2 cc-pVTZ + B3LYP TZVP + MP2 TZVP + B3LYP cc-pVTZ + MP2 cc-pVTZ + B3LYP TZVP + MP2 TZVP + B3LYP cc-pVTZ + MP2 cc-pVTZ + B3LYP TZVP + MP2 TZVP + B3LYP cc-pVTZ + MP2 cc-pVTZ + B3LYP TZVP + MP2 TZVP + B3LYP DZ+d(Cl) [47] cc-pVTZ + MP2 cc-pVTZ + B3LYP TZVP + MP2 TZVP + B3LYP cc-pVTZ + MP2 cc-pVTZ + B3LYP TZVP + MP2 TZVP + B3LYP cc-pVTZ + MP2 cc-pVTZ + B3LYP TZVP + MP2 TZVP + B3LYP cc-pVTZ + MP2 cc-pVTZ + B3LYP TZVP + MP2 TZVP + B3LYP cc-pVTZ + MP2 cc-pVTZ + B3LYP TZVP + MP2 TZVP + B3LYP cc-pVTZ + MP2 cc-pVTZ + B3LYP TZVP + MP2 TZVP + B3LYP

1.3 0.922 0.989 1.147 1.170 0.873a 1.60 1.059 0.506 0.431 0.675 0.573 0.92 0.48 0.803 0.625 0.964 0.858 1.205 1.073 1.551 1.348 0.898 0.768 1.050 0.843 0.731 0.725 0.905 0.894 0.57 1.062 1.113 1.248 1.427 1.427 1.621 1.904 2.067 1.854 1.760 2.229 2.011 0.663 0.664 0.871 0.849 0.896 0.853 1.024 1.074 1.360 1.428 1.762 1.752

1.1 0.900 0.980 1.130 1.165 0.863a 1.49 (y) 1.029 (y) 0.128 0.129 0.142 0.078 0.91 (x)b

0.7 0.202 0.126 0.192 0.112 0.134a 0.57 (x) 0.250 (x) 0.490 0.412 0.660 0.568 0.07(y)b

12.67 7.33 9.62 5.51 – – – 104.59 83.521 102.13 82.22

60.99 54.45 57.94 52.53 – – – 39.10 61.41 41.03 62.91

0.626 0.421 0.692 0.580 1.142 0.999 1.455 1.218 0.777 0.672 0.952 0.754 0.445 0.507 0.525 0.607

0.502 0.463 0.672 0.633 0.382 0.391 0.539 0.577 0.449 0.372 0.443 0.376 0.580 0.518 0.737 0.657

38.75 47.73 44.17 47.48 18.51 21.40 20.34 25.33 30.02 28.97 24.94 26.52 48.64 45.61 54.52 47.24

7.08 17.67 12.91 17.25 9.60 5.34 7.40 1.30 72.42 70.98 67.74 68.26 21.85 15.28 23.60 16.94

0.878 0.969 1.005 1.256 1.343 1.566 1.765 1.965 1.787 1.710 2.172 1.657 0.011 0.110 0.126 0.050 0.508 0.407 0.309 0.532 1.200 1.283 1.535 1.529

0.596 0.547 0.740 0.678 0.481 0.420 0.714 0.644 0.493 0.418 0.501 1.141 0.663 0.655 0.862 0.847 0.738 0.749 0.976 0.933 0.641 0.627 0.866 0.856

34.17 29.44 36.36 39.78 19.71 15.01 22.02 18.14 15.42 13.74 13.00 34.56 81.02 80.48 81.71 86.62 55.46 64.26 72.45 60.34 28.10 26.03 29.44 29.25

6.30 1.99 8.17 1.36 5.58 8.32 2.37 4.86 60.41 58.44 59.07 57.37 57.15 66.97 65.75 53.79 26.28 31.91 41.59 30.52 2.29 6.29 4.80 5.07

ClN3

BrN3

IN3

FNCO

ClNCO

BrNCO

INCO

FNCS

ClNCS

BrNCS

INCS

a In our hands, the 6-31G* HF and MP2 calculations reproduce the structural results and energy in [9], but the corresponding Mulliken analyses [9] (for the HF case) and DM [9] (for the MP2 case) are quite different. The present data are given in Table 1. The erroneous DM [9,49] can be explained by (double) scaling from atomic units to Debye [9], which also explains the unusual finding that the MP2 dipole moment is larger than in the corresponding HF calculation (as is reported in [9]). We have also reproduced a number of larger basis set calculations [40–45], where structures are given, but no dipole moments; some of the latter are included here. b The x-axis lies along the NCO average axis.

M.H. Palmer, A.D. Nelson / Journal of Molecular Structure 825 (2006) 93–100

97

Table 2 Linear correlations (y = A + Bx) in the present study Correlation

Basis sets/methodology

Methodology B3LYP/MP2 B3LYP/MP2 B3LYP/MP2

cc-pVTZ/TZVP TZVP cc-pVTZ

Slope B (SD)

Intercept A (SD)

1.009 (58) 0.987 (89) 1.060 (88)

Dipole moment/electronegativity (a) Azides cc-pVTZ/B3LYP (b) Isocyanates cc-pVTZ/B3LYP (c) Isothiocyanates cc-pVTZ/B3LYP

Correlation coefficient (R)

Overall STD

0.042 (71) 0.022 (121) 0.086 (96)

0.966 0.962 0.965

0.122 0.141 0.113

5.383 (181) 5.904 (335) 7.300 (611)

0.998 0.994 0.992

0.079 0.145 0.264

1.568 (59) 1.678 (110) 2.266 (202)

Table 3 Molecular quadrupole momentsa (esu cm2) in their principal and inertial axis systems, using the cc-pVTZ + MP2 procedure Molecule

Æx2æ

Æy2æ

Æz2æ(Æp2æ)

Ha,xx

Æa2æ

Æb2æ

FN3 ClN3 BrN3 IN3 FNCO ClNCO BrNCO INCO FNCS ClNCS BrNCS INCS

1.587 1.940 2.068 1.975 1.430 2.012 2.030 1.890 0.945 3.833 4.254 3.338

3.129 2.438 2.508 2.659 3.071 2.834 2.863 3.119 0.531 1.952 2.120 1.684

1.542 0. 498 0.440 0.684 1.642 0.820 0.833 1.229 0.414 1.881 2.134 1.653

66.881 43.488 39.274 42.348 69.158 48.643 45.179 50.727 34.262 14.384 9.383 8.559

2.402 0.134 0.234 0.128 2.501 0.718 0.432 1.112 0.477 3.476 4.085 3.226

0.860 0.365 0.674 0.556 0.860 0.104 0.401 0.117 0.063 1.595 1.951 1.573

a

Quadrupole moment (atomic units ea20 ) conversion: 1 a.u. = 1.344911 buckingham = 1.344911 1026 esu cm2.

Table 4 Electronic terms (cm2)a for the second moments of the electronic charge distribution using the cc-pVTZ + MP2 methodologies Molecule

Principal axis 2

FN3 ClN3 BrN3 IN3 FNCO ClNCO BrNCO INCO FNCS ClNCS BrNCS INCS a

hax2 2

2

2

Æx æ

Æy æ

Æz æ

Ær æ

15.104 45.503 69.690 82.087 13.917 44.644 66.141 69.980 66.983 139.620 207.653 263.524

42.528 43.259 52.875 72.666 49.161 54.265 68.204 98.874 37.224 20.876 18.943 22.847

4.335 5.998 7.237 9.258 4.257 5.900 7.138 9.253 6.027 7.671 8.909 11.020

61.967 94.760 129.802 164.010 67.335 103.808 141.483 178.106 110.234 168.167 235.504 297.390

66.881 43.488 39.274 42.348 69.158 48.643 45.179 50.737 34.262 14.384 9.383 8.559

Inertial axis Æa2æ

Æb2æ

19.332 44.322 59.613 76.941 18.379 48.844 67.044 81.558 46.656 28.204 23.959 28.178

38.300 44.440 62.952 77.812 44.700 50.064 67.279 87.296 57.551 132.292 202.637 258.193

The theoretical values (a20 ) are compared with the conventional experimental units (cm2) through the conversion factor 1 a.u. = 0.28003 · 1016cm2.

3.1.4. Signs of DM The centres of nuclear charge lie in the XNN/XNC triangle in all cases, but the centres of electronic charge are on opposite sides of the dipole vector for F, relative to the other halogens. Thus the signs of the dipole moments for the fluoro-series FAN@X@Y are reversed (negative end towards F) to those of the other halogen series, in agreement with Laplacian plots and other methods [38,39]. There has been no previous theoretical or experimental investigation of the dipole moments of BrN3 or IN3, and no experimental values for ClN3 or the isocyanates.

3.1.5. Individual compounds (a) Azides. In FN3 the calculated DM direction lies from near the FANa(1) bond bisector, to the terminal N-atom (Nc). For IN3 it lies almost parallel to the IN bond, while for ClN3 and BrN3 the dipole moment lies to either side of Na(1). The present calculated la/lb ratios for FN3 cover a wide range: B3LYP (8–10), MP2 (4.6–6) (Table 1). The results are in reasonably close agreement with the experimental value for la, but the present study suggests that the MW value of lb [9] may be in error; enhancing the basis set to cc-pVQZ leads to no improvement in the

98

M.H. Palmer, A.D. Nelson / Journal of Molecular Structure 825 (2006) 93–100

Fig. 3. Variation in calculated dipole moments with the electronegativity of the halogen.

la/lb ratio. It was noted [9] that the Stark effect is complicated by the interaction of the atomic quadrupole moments with the static electric field; also, no error bars were given for the experiment [9]; this has now been resolved, with lb being in error [49]. Some previous calculations [40–45] also show high la/lb ratios, but only the B3LYP + 6-311G* result (1.170D) [42] was close to experiment; this basis set is similar to the present TZVP one. Previous studies [44,45] have also shown that the DM la/lb ratio for ClN3 is particularly susceptible to basis set and methodology. The most rigorous previous study (6-311G(d,p) + MP2) [44] gave a much larger dipole moment and la/lb  1; the present study suggests that the a-/b-ratio is 0.31. We have also repeated the calculations in [9], and find some of the values to be incorrect, although we were able to reproduce the structures and energies. This is discussed further in the footnote to Table 1. (b) Isocyanates. Relative to FN3, the calculated DM for FNCO is rotated (relative to FAN) towards NC by 20, while that for ClNCO is similarly rotated by 60 (using both MP2 and B3LYP methods in each case). The B3LYP results show the largest difference from the MP2 series for ClN3 (Fig. 4). An experimental study of these compounds is thus important, to determine which theoretical route is the more reliable. The dipole moment directions of the Br and I compounds are closer to each other than to the Cl compounds. The calculated DM of ClNCO is in poor agreement with that calculated by Kosmus et al. [48], who used a lower level of theory and smaller basis set than those used here; the value obtained in this study should be closer to the (unknown) experimental value. 3.2. Molecular quadrupole moments The molecular quadrupole moments show much less variation with halogen change, and much less variation with methodology than the dipole moments. The positive QM

vector (Hxx) lies close to Na in each molecule, while the large negative (principal) value cuts the XANa bond in each case. For FN3, both the MP2 and B3LYP calculations suggest that Hyy lies almost parallel to the NaNb bond. The molecular quadrupole moments of the azides and isocyanates show a number of common features. The principal quadrupole moment tensor element is negative, while with the exception of FN3 and FNCO, the out-of-plane value is the smallest, and positive. The angle between the largest elements (Hyy) and the a-axis also varies in a similar manner across the series. The largest element (Hyy) is relatively close to the N@C bond direction. The principal difference between the isothiocyanates and the azides or isocyanates is that Hzz (Hcc) changes sign to become negative; Hyy is largely unchanged, and the largest element now becomes Hxx. Thus the sign of the largest element is reversed in the isothiocyanates relative to the other compounds. However, the larger angles ha,yy in the S-compounds are such, that the maximum quadrupole moment still lies relatively close to the a-axis. 3.3. Second moments of the electronic charge distribution As expected with the trans-orientation of these molecules, Æa2æ values are markedly larger than either Æb2æ or Æc2æ values. Although the differences are sometimes small, there is a consistent set of small changes between different members of the series. Thus using FN3, FNCO, and FNCS as examples, the value for Æa2æ in the azide is smaller in magnitude than that for the isocyanate, while the reverse is true for the value of Æb2æ. In the azide and isocyanate series, the difference on progressive substitution of F by Cl, Br, and I leads to an increase in magnitude of Æa2æ by 30 cm2 for each change. In contrast, the isothiocyanates increase more sharply, probably as a result of the increasing size of the XANAC angle in the S-series. This effect is noticeable in the comparison of the azides and isocyanates, where the value of Æa2æ is always larger in the latter, whereas the values of Æb2æ are slightly reduced. 4. Conclusions The rotation of the dipole moment vectors with progressive changes of halogen, or pseudohalide unit is demonstrated. There is systematic variation in the calculated directions of the dipole moments in the present series, where B3LYP and MP2 methodologies show differences up to 20 for the directions. This discrepancy is largest in ClN3, but quite significant for several other compounds, such as XNCO (where X = Cl, Br and I). In FN3 where la and lb components have been investigated, the latter value has been withdrawn [49]. The failure to identify the halogen isothiocyanates from mixtures of the expected reactants is disappointing, and further work seems important. All of these differences in results, from methodology change, should be resolvable from MW spectroscopy. Hence there is an urgent need for new MW studies of the dipole and second moment components, in order to determine whether the

M.H. Palmer, A.D. Nelson / Journal of Molecular Structure 825 (2006) 93–100

99

Fig. 4. The calculated dipole and quadrupole moment directions of the halogen pseudohalides.

B3LYP or MP2 values are correct. There is an especially urgent need to reinvestigate FN3, possibly with 15N incorporation, to re-determine the dipole moment a-,b-components. The second moments of the charge distribution, and the molecular quadrupole moments, which have common principal axes, also show progressive variation with both methodology and structural moiety, but the variations are much smaller than in the dipole moments. In most of this work, the results from the TZVP basis set are relatively close to those of the cc-pVTZ one, making TZVP still acceptable for large molecular systems. Acknowledgements We thank Edinburgh Parallel Computing Centre (EPCC) for the generous provision of computing resources; to Dr. M. F. Guest (Daresbury Laboratory) for provision of the GAMESS-UK suite of programmes, and to EPSRC for a grant to ADN.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]

M.H. Palmer, A.D. Nelson, J. Mol. Struct. 689 (2004) 161. M.H. Palmer, J. Mol. Struct. 692 (2004) 43. M.H. Palmer, A.D. Nelson, J. Mol. Struct. 782 (2006) 94. A.D. Nelson, PhD Thesis, University of Edinburgh, 2002. K. Dehnicke, Adv. Inorg. Chem. and Radiochem. 26 (1983) 169. K. Gholivand, G. Schatte, H. Willner, Inorg. Chem. 26 (1987) 2137. W.J. Frierson, J. Kronrad, A.W. Browne, J. Am. Chem. Soc. 65 (1943) 1696. W. Gottardi, Angew. Chem. Int. Ed. 10 (1971) 416. D. Christen, H.G. Mack, G. Schatte, H. Willner, J. Am. Chem. Soc. 110 (1988) 707. R.L. Cook, M.C.L. Gerry, J. Chem. Phys. 53 (1970) 2525. H.-O. Munz, H.-K. Bodenseh, M. Ferner, J. Mol. Struct. 695–696 (2004) 189. W.H. Hocking, M.C.L. Gerry, Chem. Commun. (1970) 448. W.H. Hocking, M.C.L. Gerry, J. Mol. Spectrosc. 42 (1972) 547. W.H. Hocking, M.L. Williams, M.C.L. Gerry, J. Mol. Spectrosc. 58 (1975) 250. H.M. Jemson, W. Lewis-Bevan, N.P.C. Westwood, M.C.L. Gerry, Chem. Phys. Lett. 108 (1984) 496.

100

M.H. Palmer, A.D. Nelson / Journal of Molecular Structure 825 (2006) 93–100

[16] H.M. Jemson, W. Lewis-Bevan, N.P.C. Westwood, M.C.L. Gerry, J. Mol. Spectrosc. 118 (1986) 481. [17] K.D. Hensel, M.E. Lam, M.C.L. Gerry, H. Willner, J. Mol. Spectrosc. 151 (1992) 184. [18] H.M. Jemson, W. Lewis-Bevan, N.P.C. Westwood, M.C.L. Gerry, J. Mol. Spectrosc. 119 (1986) 22. [19] M. Hargittai, I.C. Tornieporth-Oetting, T.M. Klapoetke, M. Kolonits, I. Hargittai, Angew. Chem. Int. Ed. Engl. 32 (1993) 759. [20] M. Hargittai, J. Molna´r, T.M. Klapo¨tke, I.C. Tornieporth-Oetting, M. Kolonits, I. Hargittai, J. Phys. Chem. 98 (1994) 10095. [21] H. Oberhammer, Z. Naturforsch. 26A (1971) 280. [22] J. Jacobs, B. Juelicher, G. Schatte, H. Willner, H.G. Mack, Chem. Berichte 126 (1993) 2167. [23] K. Gholivand, H. Willner, D. Bielefeld, A. Haas, Z. Naturforsch. 39B (1984) 1211. [24] M.H. Palmer, Z. Naturforsch. 47A (1992) 203. [25] M.H. Palmer, Z. Naturforsch. 51A (1995) 442. [26] M.H. Palmer, J.A. Blair-Fish, Z. Naturforsch. 53A (1998) 370. [27] T.H. Dunning, J. Chem. Phys. 55 (1971) 716. [28] A.D. McLean, G.S. Chandler, J. Chem. Phys. 72 (1980) 5639. [29] R. Ahlrichs, P.R. Taylor, J. Chim. Phys. 78 (1981) 315. [30] D.E. Woon, T.H. Dunning, J. Chem. Phys. 98 (1993) 1358. [31] R.A. Kendall, T.H. Dunning, R.J. Harrison, J. Chem. Phys. 96 (1992) 6796. [32] T.H. Dunning, J. Chem. Phys. 90 (1989) 1007.

[33] K.A. Peterson, D.E. Woon, T.H. Dunning, J. Chem. Phys. 100 (1994) 7410. [34] A. Wilson, T. van Mourik, T.H. Dunning, J. Mol. Struct. (THEOCHEM) 388 (1997) 339. [35] W.H. Flygare, Chem. Rev. 74 (1974) 653. [36] D.E. Stogryn, A.P. Stogryn, Mol. Phys. 11 (1966) 37. [37] A.D. Buckingham, Q. Rev. Chem. Soc., Lond. 13 (1959) 183. [38] M.A. Spackman, Chem. Rev. 92 (1992) 1769. [39] D.E. Stogryn, A.P. Stogryn, Mol. Phys. 11 (1966) 371. [40] M.H. Palmer, J. Mol. Struct. 405 (1997) 179. [41] M. Otto, S.D. Lotz, G. Frenking, Inorg. Chem. 31 (1992) 3647. [42] N.J.S. Peters, L.C. Allen, R.A. Firestone, Inorg. Chem. 27 (1988) 755. [43] S. Shen, J.R. Durig, J. Mol. Struct. 661–662 (2003) 49. [44] G. Chaban, D.R. Yarkony, M.S. Gordon, J. Chem. Phys. 103 (1995) 7983. [45] A. Schulz, I.C. Tornieporth-Oetting, T.M. Klapoetke, Inorg. Chem. 34 (1995) 4343. [46] Y. Zeng, L. Meng, S. Zheng, D. Wang, Chem. Phys. Lett. 378 (2003) 128. [47] M.A. McAllister, T.T. Tidwell, J. Chem. Soc. Perkin Trans 2 (1994) 2239. [48] W. Kosmus, E. Nachbaur, K. Faegri, J. Chem. Soc. Faraday Trans II 72 (1976) 802. [49] D. Christen, personal communication, March 2006.