Calculations of hydrogen—fluorine and fluorine—fluorine nuclear magnetic spinspin coupling anisotropies for fluorinated ethenes and benzenes oriented in liqiud crystal solvents

Volume 19, number 4

CHEMICAL PHYSICS LETTERS

1.5 April 1973

CALCULATIONS OF HYDROGEN-FLUORINE AND FLUORINE-FLUOKINE NUCLEAR MAGNETIC SPIN-SPIN COUPLING ANISOTROPEES FOR FLUORINATED ETHENES AND BENZENES ORIENTED IN LIQUID CRYSTAL SOLVENTS C.W. HAIGH and S. SYKES DeFGirtmenr of Chenzistp, University College. Swanse4, Received 22 December

SA 2 8PP. UK

1972

Spin-spin couphng tensors are calculated using self-consistent perturbation theory and INDO wavefunctions, in order to estimate whether neglect of their anisotropy influences molecular dimensions deduced from the NMR spectra of partially oriented solutes. It is found that anisotropy of cis and r~arrs and many aromatic HF couplinps can be neglected but that frans FF couplings arc markedly anisotropic. Comparisons arc made R’ith the limited experimental results.

NMR spectra ic or lyotropic

of solutes liquid

partially

crystals

oriented

in nernat-

are of considerable

cur-

rent interest [I]. The usual spin hxniltonian contains a Zeeman term, an isotropic coupling term, and also a term involving anisotropic couplings Dkl between pairs of nuclei (k, f): this last term depends mainly on the direct dipole-dipole interaction, but also on the indirect interaction involving the electronic wavefunction. It may be written D,, = D; f’ f Dzd

(1)

171 =

gl ‘4 idkbq+jkl,q I .

0)

The several dkiq are simply related to the components of the internuclear vector; the jk!,q are measures of the anisotropy of the indirect coupling tensor Jkl. The C4 are molecu’ar quantities specifying the statistics of solute orientation; and the summation is over real second-order spherical harmonics, so that in general m = 5. For molecules of C, or C2h symmetry, with the use of piincipal axes, m is reduced to 3, the terms being, in order, (3z2- r*), (x2-u2) and (.x>~); and we have

i,,

1 =

( lj3\/Jj (2/k[zz-Jk,,, - Jk[,,,,>;

i,,,

2 =

( 1/d-i%(Jklxx -

;

JklJ

(3) For molecules of C2, or D2t, symmetry! m = 3, and only the first two equations in (3) are needed. For molecules with a three-faid or higher axis, m = 1, and only jk[, r arises. If the second term in (1) or (2) is negIected, as his Often been the practice, the Dkl (= Dj$: through the dkLq

allow the geometry of the solute molecule to be determined (to within an overall multiplicative factor) In view of the importance of this method of structure determination, and in the light of recent work [I-6]

suggesting

some L3rfd temx

were not negii@ble,

it

seemed of interest to calculate the Jk[ tensors and hence the okd terms theoreticahy. very few o’ther calculations have been reported [7-I 11. [n this work, then, we seek to estimate the magnitude of the lDEd/D$I ratios. As a step in relating Jkl’tensors to the experimental data, we find it convenient

to define

plrljljdll;

I

&=l&/d2;

F71

pp

15 April 1973

CHEMICAL PHYSICS LETTERS

Volume 19, number 4

{~;+j;]/[d;+d:]}“*.

FFgcm-

(4

FFCiS FFtrans*

(To simplify

the notation, we have suppressed the suffices k, 1.) For molecules with a three-fold or higher rotation axis [8,9,! I] only p1 arises, and, of Cl. For from (1) and (2), Dsd/D $1’ is independent molecules of C2, 0.1D,, symmetry, p1 and p2 are depends on (C,&), a quantity used; and Dfid/D$ which varies with solvent, concentration and temperature. But if Cldkl,l and C2dkl,2 have the same sign, the larger of p1 and p2 provides an upper bound to ~~“/D~fri. For molecules of C, or Clh symmetry,pi is chosen as being independent of the arbitrary choice of x and y axes: it can be shown that if C4, dkr4, q = 1,2,3, all have the same sign, then the larger of p1 and pi provides an upper bound to lDEd/DifrI. We have adapted the seif-consistent perturbation theory of Blizzard and Santry [ 12]‘? (see also ref. [ 1I]) to calculate the contact, orbital and dipoiar

tern))) and the contact-dipolar cross term, at the INDO level of approximation. Atomic values were used for the one-centre integrals S*(O) and W3> [ 171, and, in general, standard geometries were adopted [!8]. We have first examined all the fluorinated ethenes C~HJ_,,F,, and most of the fluorinated benzenes CgEIg_,,F,,, in view of the careful experimental studies recently reported [2-41. We have calculated aU the JH, and JFF tensors; and a pictorial summary of our results is presented in fig. 1. It is immediately clear that in general HF couplings have much lower

7 Unfortunately, cqs. (64) and (73) of ref. [ 121are incorrect; rhcy should be of the urne form as (22). They were not however used in the ac:ual ralcuiations of ref. [ 121. Owing to a progrummitig error. all the dipolx terms cited in ref. [ 121 should be multiplied by a factor of 2. These corrections are now xccpted by the original authors [ 131. Re-calc&lion of the correlations in their tab!e II does not result in major changes. ‘The rcccnt calcuhtions of Brown and Davies (14,151 on isotropic couplings did USCthe incorrect cqs. (64) and (73) of rel: [ 121 to calculate the ap contribution to the dipolar lrrm. Whcrc these ivorkcrs have x-calculated their dipolar results, it appears that the published values should be multip!icd by a factor of about 13. (This would bc equivalent to using an (sm3) value

for the dipolar

term

larger

than

for the

orbi:al term [ 161.) The Gpolar terms reported in ref. [4] are so smafl that the main conclusions of that paper are unaffected.

FFortho-FFmela

I

I I

IFFF.Y~

I

HF$tm

I

HFZ

HFlrans-

HFo& HFnck HFpem-

0

8

0.5

\

I

10

I.5

20

2.5

I

30

e max x 100

vaIues for spin-spin couFig. 1. Range of Pmay anisotropy in fluorinated kthenes and benzenes. For molecules of

plings

DBh symmetry, prnax = pl. For t?dCCUkS of Czv, D,h symmetry, prnaX is the greater of p 1, p2. For mOkCUkS of C,h, C, SymmeW, pmax is tile greater of p,, pi. *The FF WU?JZ values range from 2.4 to 6.9%.

anisotropies than FF couplings, as measured by pm= vaIues. We consider first the results for the fluorirzated efhenes. As explained above, prnxx is an estimated upper bound to D&“/Dgi’l only if there is no cancellation between the terms making up D$‘. From a consideration of the signs of the experimental Cl and C, values for several ethenes of C2, or DZh symmetry, and by tenirtive extrapolation from the C,, C2, C, values of monoluoroethene (of C, symmetry) [S], we deduce that this condition is likely to be fulfilled for all cz3 and trans couplings investigated (except perhaps JpFrs in trifluoroethene), but not for the genz couplmgs. Now dk,,4 values vary as the inverse cube

of the internuclear distance; thus the error in dimen. sions arising from the neglect ofDzd is (under these conditions) less than one-tltird of pmrrK. Our calculations thus indicate that this neglect is permissible for HF cis and tru~zsand for FF cis couplings; but that iargcr errors (up to 2%) could arise from the neglect of the anisotropy of J!$T. Apart from the question of cancellation, we place !ittlu reliance on our Jgenzresults for reasons to be discussed more fully elsewhere; iiter alia these couplinzs are exceptionally sensitive to small changes in assumed geometry [ 191. This is a pity, for by far the most detailed study in this field iS of JFF in 1, I-difluoroethene [2,3]; we find poor agreement ltith these results. The isotropic J$ are poorly predicted [ 121, though the trends on increased fluorination are satisftictorily reproduced. Accordingly some caution

Volume 19, number 4

CHEXlICAL PHYSICS LETTERS

should be exercised in accepting predictions conceming the anisotropy of this type of coupling. On the other hand, in the case of tram FF couplings, our calculations well reproduce the negative sign, the magnitude and the small (algebraic) increase on fluorination found for the isotropic part [ 121; this strongly reinforces our prediction of major anisotropy. No simple direct comparison with experimental data is yet possible, for in attempting a confrontation with Spiesecke and Saupe’s interesting results on tetrafluoroethene [6] we find the desired term is entangled with our unreliable estimates of the anisotropy of the other two couplings. As to the anisotropy of JH, tensors, our calculated values for cis-difluoroethene are too small to assist in resolving the difficulties experienced by Buckingham and Dunn [5] in interpreting their spectrum of this compound. Turning to the j7zigl;orinated benzenes, we find that the signs of the available C4 values do not allow us to conclude in this series that prna values are necessarily estimated upper bounds to Dyl,s /Dzfi; but we can of course compare with experimental results when the Cq are known. Table 1 shows this comparison for one molecule; the agreement in sign and magnitude for Dg seems encouraging. However our calculations ind , which Gerritsen had to neglect, also suggest that Dz3 might also be significant. For the four other compounds studied by Gerritsen [2] our catoulations are in fair overall agreement with the (not quite so precisely delineated) experimental Dkd values. But we do ag.lin find that certain DKd values which he had Table

1

Indirect coupling anisotropies from experimentala) work)

in 1,3-difluorobenzcnc, &rived C4 values [2] and calculated Jk/ (this

Coupling type

Nudlci

:

HF orrho

3 3 1

5 6 3

HF HF HF FF

1

3

FF meta

2

3

ortho meta para meta

Dzd(Hz) -. 1.3

(Dkd/D;;)x 100 calculated -0.1

1.7

1.6 0.i -0.3 -1.0 experimental -1.4 + 0.25 2.9 f 0.5

-0.1 0.4 2.1

a) Solvent system 3 of ref. [2]. Closely similar results for D$ were obtained for the two other solvent systems studied.

I5 April 1973

to neglect may be appreciable, particul=ly for certain HF ortho and FF ortho couplings; and this clearly affects the comparison. Thus our calcuIations suggest ortho, meta and para FF couplings can,all, in appropriate cases, have comparatively high Did/o$‘I values; but no simple general prescription can be given. Most, but definitely not a& HF couplings are predicted to have small /DEd/D$I ratios. These preliminary results seem to indicate that one may use calculations at this level to determine which f)kd values for a particular molecule may reasonably be neglected in order to simplify the interpretation of the spectra.

References [ 11 P. Diehl and P.hf. Hsnrichs in: Chem. Sac. Spccfilist Report on NhlR, Vol. 1, ed. R.K. Harris (1972) p. 321, and references therein. [ 21 J. Gcrritsen, Thesis, Free University. Amsterdam (197 I), and references therein. [ 31 J. Gcrritsen and C. MacLean, J. Msg. Resnnancc 5 (1971) 44, and references therein. [4] J. Gcrritsen, G. Koopmans, H.S. Rollcma and C. \lacLean, J. Msg. Resonance 8 (1972) 20. and references therein. [S] A.D. Buckingham and M.B. Dunn, Mol. Phys. 19 (1970) 721. [6] H. Spiesecke and A. Saupe, Mol. Cryst. Liquid Cryst. 6 (1970) 287. [7] A.D. Buckingham and I. Love, I. &fag. Resonance 2 (1970) 338. I81 H. Nakatsuji, H. &to, 1. Xlcrishima and T. Yonezawa, Chem. Phys. Letters 4 (1970) 607. I91 H. Nakatsuji, K. Hirao. H. Kato and T. Yonczawa, Chem. Phys. Letters 6 (1970) 541. 1101Sl. Bnrfield, Chem. Thys. Letters 4 (1970) 518; Erratum 5 (1970) 316. 1111 R. Ditchfield and L.C. Snyder, I. Chem. Phys. 56 (1972) 5823. 1121 A.C. Blizzard and D.P. Santry, J. Chem. Phys. 5.5 (197 1) 950. [13] D.P. Santry, private communication; Erratum, I. Chcm. phys., to be pub!ished. 1141 I. Brown and D.W. Davies, Chem. Commun. (1972) 939. 1151 I. Brown and D.W. Davies, Chem. Phys. Letters L5 (1972) 455. [I61 D.W. Davies, private communication. D.H. K’hiffen, X.P.L. 1171 J.R. Morton, J.R. Rowhndsand Report BPR 13 (1962). _ 1181 J.A. Pople and M. Gordon, J. Am. Chem. Sot. 89 (1967) 4253. [ 191 A. Tow1 and K. Schaumburg, Mol. Phys 22 (197I)49.