Quantum chemical analysis of the orientational lone-pair effect on spin-spin coupling constants

Journal of Molecular Structure (Theochem), 210 (1990) 175-186 Elsevier Science Publishers B.V., Amsterdam

175

QUANTUM CHEMICAL ANALYSIS OF THE ORIENTATIONAL LONE-PAIR EFFECT ON SPIN-SPIN COUPLING CONSTANTS* R.H. CONTRERAS, C.G. GIRIBET, M.C. RUIZ DE AZUA and C.N. CAVASOTTO Departamento de Fisica, Facultad de Ciencias Exactas y Natwales, UBA, Ciudad Universitaria, Pab.1, (1428), Buenos Aires (Argentina) G.A. AUCAR Departamento de Fisica, Facultad de Ciencias Exactas y Agrimensura, UNNE, (3600) Corrientes (Argentina) L.B. KRIVDIN Department of Chemistry, University of Irkutsk 664003 (U.S.S.R.)

ABSTRACT The quantum-chemical analysis of factors defining the stereospecific behaviour of nuclear spinspin coupling constants is shown to be an important aid in obtaining experimental information on molecular structures from high-resolution NMR spectroscopy. The analyses presented in this paper are based on the contributions from localized molecular orbitals within the polarization propagator approach (CLOPPA) method and examples are given where factors defining heteroatom lone-pair orientational effects on spin-spin coupling constants are discussed.

INTRODUCTION

The usefulness of high-resolution NMR spectral parameters in determining configurations and conformations is increasing rapidly. In general, two different approaches are used. The first involves empirical correlations based on an ever increasing number of experimental measurements which are now better known. It is important to point out that improvements in experimental techniques allow, at present, information on magnetic isotopes of very low natural abundance to be obtained, thereby notably broadening the scope of NMR spectroscopy for different types of compounds. The other approach to studying the different relationships between molecular structural problems and NMR parameters is to analyse theoretically the electronic origin of these parameters. This theoretical analysis has followed two different pathways. In one of them, ab initio calculations, where spin-spin *Presented at the 18th International Congress of Theoretical Chemists of Latin Expression, held at La Plata, Argentina, 23-28 September, 1989.

0166-1280/90/$03.50

0 1990 -

Elsevier Science Publishers B.V.

176

coupling constants are mainly based on the pol~ization propagator approach using different degrees of approximation, are used to reproduce the measured values, taking into account the following interactions: the Fermi contact, the paramagnetic spin-orbital and the spin-dipolar couplings. To these three contributions the first-order contribution known as the diama~etic spin-orbit interaction is frequently added. The most recent results of such an approach are summarized briefly in Ref. 1.For larger molecules it is still not possible to use ab initio wave~ctions and in such cases se~empirical methods are employed. The alternative approach to analysing the electronic origin of spin-spin coupling constants is to use methods which allow one to discriminate between different transmission mech~isms. These methods were reviewed a few years ago [ 21. Although a few results obtained with one of those methods using ab initio wavefunctions have been reported [ 31, in general the calculations were implemented within semiempirical approaches. It is worth noting that these results were intended to be used to obtain an insight into factors that define the stereospecific behaviour of coupling constants in larger molecules. The most recent of these methods is the contributions from localized orbitals within the pol~i~tion propagator approach (CLOPPA) [4 3. In this paper a brief account of the main features of this method are described and several examples of practical applications are given. A BRIEF OUTLINE OF THE CLOPPA METHOD

The CLOPPA scheme is intended for analysing coupling constants starting from a unideterminantal ground-state wavefunction. Within this approach, the indirect spin-spin coupling constant between nuclei N and N',J(NN'), can be written as a sum of terms J(NN’) = C Jiajb(NN ) where i and j are occupied localized molecular orbitals (LMOs ) representing either bonds or lone pairs; a and b are vacant LMOs representing antibonding orbitals; and i,a and j,b together can be interpreted as excitations from occupied fi andj) to vacant (a and b) LMOs. The sum in eqn. (1) is carried over all LMOs belonging to the compound, the J( NN’ ) coupling of which is being studied. There are three second-order contributions to J(NN’ ): ~~NN’)=~c(NN’)+~ps*~NN’)+~~(NN’~

(2)

which correspond, respectively, to the Fermi contact (FC), the parama~etic spin-orbital (PSO) and the spin-dipolar (SD) interactions (51. The PSO and

SD contributions are anisotropic. Their isotropic contributions are given by eqns. (3) and (4), respectively. JPSo(NN’)=f[J$?;o(NN’)+fl;o(NN’)+Jf),SO(NN’)]

(3)

JsD(NN’)=$(JS,D(NN’)+JS,D(NN’)+JS,,D(NN’) +2[~~(NN’)+~~(NN’)+~~(NN’)]~

(4)

The three contributions in eqn. (2) can be written as sums like that in eqn. (l), i.e. Jio,jb(NN’)=J~~~(NN’)+J~~~(NN’)+~~6(NN’)

(5)

Each term in eqn. (5), taking into account eqns. (3) and (4), can be written as ~~*(NN’)

=~FcU~~~3~i~~U~~~‘

J$;2DIcy(NN’ ) = k psou;~$”

(6)

lPi,,jb u;s$”

(7)

Jsaffl( NN’ ) = kSDU~~~~’3Pi,,jbU~f@fl

(8)

where3P and ‘P are the triplet and singlet polarization propagators respectively, which were here evaluated at the random phase approximation (RPA) level [6,7]; a and p are Cartesian components. The k factors are constants which involve, among other things, the rna~e~~i~ ratios of nuclei N and N’ . Hereafter, the Uia,Nterms are known as the perturbators. Their form for each of the three interactions are: u&=

(iI&)

]a)

u;s$,a = (i]L%/ifir& ]a>

(3) (16)

(11) where EN is the angular momentum operator defined with respect to nucleus N, and nN,= r&t.,,+ The examples presented in this work were evaluated using INDO groundstate wavefunctions [ 81 and perturbators were calculated using the monocentric approximation [91. In addition, the factors s& (0) and ( rg3 > were taken as semiempirical parameters for a given atom [lo]. For studying certain s~reos~ci~~ aspects of spin-spin couplings the CLOPPA method is adequately complemented by the IPPP scheme [ 111. This approach is particularly useful for studying the following three problems: (i) the through-space transmission of spin-spin couplings; (ii) the transmission through a K electronic system of the spin information associated with the Fermi contact interaction; and (iii) the multipath transmission of couplings in polycyclic compounds. The first problem corresponds to the well-known phe-

178

nomenon of very large couplings between two nuclei several bonds apart but otherwise proximate in space [ 2,121. The second problem is a mechanism which is responsible for many long-range couplings [ 131. Good examples of the third problem are given in Ref. 14. Recently [ 151, the IPPP approach [ 111 has been modified using ideas similar to those of the CLOPPA method, in such a way that the IPPP results can also be analysed in terms of contributions from LMOs corresponding to bonds, lone pairs and antibonds. Expressions for this modified IPPP method are quite similar to those of eqns. (1) and (6)- (8). The differences are as follows. The sum in eqn. (1) is truncated in such a way that it runs only on LMOs belonging to the molecular fragment whose contribution is sought. In eqns. (6)- (8) the polarization propagators 3Piajband ‘Piajb must be replaced by their expression inner-projected onto the subspace spanned by all LMOs belonging to the chosen molecular fragment [ 151. The Liiwdin technique [ 161 is employed to realize these inner projections. APPLICATIONS OF THE IPPP-CLOPPA

METHOD TO STUDY THE LONE-PAIR

EFFECT ON COUPLING CONSTANTS

The importance of the lone-pair effect on coupling constants and its relationship to molecular structures was recently reviewed by Gil and von Philipsborn [17]. The first part of this section is devoted to a brief review of the results of the IPPP and CLOPPA analyses already published in which important lone-pair effects are described. They refer mainly to the through-space transmission of coupling constants. In the second part, a few results of unpublished applications of the CLOPPA method are presented. These mainly correspond to the analysis of stereospecific aspects of one- and two-bond couplings. The lone-pair effect on three-bond and longer range coupling constants For coupled nuclei placed several bonds apart a few studies have been made in which the IPPP method [ 111 was applied to determine the role played by lone pairs belonging to at least one of the nuclei involved in the coupling analysed. In these cases such couplings can be described as being transmitted mainly through space, since substantial values were obtained when the polarization propagator was inner-projected onto a local subspace defined by bonds, lone pairs and antibonds surrounding both coupled nuclei. The IPPP analysis of 3J(F,CH3_,F, ) (n= 1 to 3) in ck-fluoropropenes [ 181 allowed the following interesting features for its through-space component to be determined: (i) this component is heavily dominated by the Fermi contact interaction; (ii) it strongly depends on the C-H orientation; and (iii) for n= 3

179

the proximity of lone pairs belonging to different fluorine atoms inhibits the through-spacetransmission. Couplingsoriginatingin the areabetweenC and F atoms were also discussed for o-~uoroace~phenone and relatedcompounds 1193and for 8-~,l-naphthaldehyde and relatedcorners [ZO3. In the last case, eqn. (6) with the innerprojected polarization propagator (PP) was applied to assess the role played by each of the F lone pairs, the C-F and C-H bonds, and their corresponding antibonds. The importance of the C-H bonding and antibondingorbitals was thus determined,giving support to the expression “through-space transmission of J( CF) couplings via an intermediateC-H bond”. Another interestingcase in which eqn. (6) with the inner-projectedPP was applied [ 211 is the though-space tr~smission of J( FF) couplings in compound I. Such a compound was studied in order to mimic the peculiar behavH H&IF

F I

CF3. ,F CF3&$

_

m 6 iour of 5$(FF) coupling in II wherethe experimentalvalue (196.4 Hz) [ 221 is the largest known for a coupling of this type. One of the main featuresfound with the IPPP method is the exponentialdecaywiththe F-F distance,in agreement with empiricalcorrelationsalreadyknown [ 231. The orientationallone-paireffect in vicinalcouplingsis nicely illustratedby compounds III-VI. In III [24], not only the through-space component of eont~bution depend on the P lone pair 3J( PP), but also the “trough-and” orientation.The conformation depicted for compound IV is also very efficient l!u

180

for through-space transmission of the Fermi contact interaction of its 3J( SeSe) coupling [ 251. This component strongly depends on the SeCC angle, and takes account of the experimental difference [26] between the cis and truns couplings in the cis and tram isomers of compound IV, although it should be recalled that the cis-truns difference is also strongly influenced by the throughbond orbital interaction [ 241. For the IPPP analysis of compounds IV and V [ 24,271 it is required to include the 77Separameterization in both the CNINDO 3.3.3 program [8] and in the IPPP segment. To this end, Galasso’s parameterization was used [ 281. In compound V also, the through-space transmission of the Fermi contact interaction takes account of the cis-truns difference of the 3J( Se-C) coupling observed in both isomers [ 271. In this case it is interesting to observe that the orientation of a methyl C-H bond with respect to the in-plane Se lone pair is also very important [ 261, showing a behaviour quite similar to that found for the 3J( PC) coupling in VI [ 281. It is worthy of note that higher efficiency of the through-space transmission in V than in VI cannot be taken into account by considering only the different magnetogyric ratios of YSe and 31Pnuclei The difference of the 2,3J(PC) coupling in the syn (VII) and anti (VIII) conformations of 7- (phosphamethyl)norbornenes was analysed [ 291 with the IPPP-CLOPPA method in order to assess what orientational effect the P lone pair has on that coupling. The role played by the proximate antibonding orbitals was also discussed in detail. It was found [ 291 that the marked difference of that coupling between both conformers originates from the Fermi contact interaction which is the only important one in this case. The lone-pair effect on one- and two-bond couplings In this section the CLOPPA approach is applied to the analysis of the role played by an N or P lone pair in selected types of one- and two-bond couplings. The examples were chosen to show both the versatility of the CLOPPA method and the origin of the lone-pair effect. Y / CH3

C=N m

0 \

cH3\=N0 OH

CH3CH2\_N0 CH3’

x

‘OH

H’

x’

XII

\

Fb

OH

CH3\=N0 CH3CH2’ CH3

P=C

IX’

=

\

CH3 ’

C=N m

‘OH

0 ‘OH

181

One of the options of the CLOPPA method allows the summation of all Jiajb terms that involve a given localized molecular orbital, whether it is an occupied or a vacant one. In this way the influence of a lone pair on a given coupling constant can be obtained merely by summing all JMjb terms where i and/or j correspond to that lone pair. Hereafter, such a sum will be shown as CLp. ‘J(15N-X) couplings in VIII to XI (X= ‘H or 13C) In Table 1 the total 2J( 15N-H) couplings and CLp are shown for compounds VIII and IX. It is important to recall that, within the monocentric approximation, the non-contact terms of couplings involving a proton are identically zero. Experimental values, taken from the literature, are also shown in the table. A fair agreement is observed between calculated and experimental couplings. This agreement strongly supports the use of the CLOPPA method with all the approximations described above to obtain an insight into the electronic factors defining the lone-pair effect. It is important to recall that the 15Nmagnetogyric ratio is negative and, therefore, when comparing couplings involving different types of nuclei, care should be taken with the sign. The results shown in Table 1 indicate that the sum of Jiajb terms involving the N lone pair takes account of the truns-cis difference. The lone-pair orientation could affect several factors. For instance: (i) the lone pair orientation could affect the electronic distribution of a nearby bond - this could be referred to as a ground state wavefunction effect; and (ii) terms of type Jiajb imply excitations from occupied i andj orbital&o vacant a and b ones - some of these excitations could involve the lone pair, and the respective Jiajb values could strongly depend on the lone-pair orientation. According to results displayed in Table 1, in compounds VIII and IX the trum-cis difference of two-bond J( NH) couplings can be taken into account via type (ii) effects [ 311. It is interesting to point out that an effect of type (i) was found in ‘J( CH) couplings for the proton ortho to a methoxy group in veratrole, methylenedioxybenzene and related compounds [ 321. Also of interest are the values of CLp for VIII (given in Table 1) and 2J(15N-H) in pyridine. While in VIII c LP= - 28.99 Hz, in pyridine CLp = - 23.42 Hz. The smaller absolute value in TABLE 1 *J( 15N-lH) couplings (in Hz) in compounds VIII (cis) and IX (truns) Compound

Ex~.~

Calc.

,YLpb

VIII (cis) IX (trans) A( trans-ck)

- 15.50 3.00 18.50

- 16.51 0.95 17.46

- 28.99’ - 11.54= 17.45

“Taken from Ref. 30. bathe sum of all Jbjb contributions where either i or j corresponds to the N lone pair (see text). “Taken from Ref. 3.

182

the latter is thought to originate from the longer N-C bond distance in pyridine as compared with the N-C bond length in VIII. This indicates that contributions from excitations involving the N lone pair increase with decreasing distance to the coupled proton. In Fig. 1 (a) excitations yielding the largest contribution to the truns-cis difference in VIII and IX are shown. The LMOs, in addition to the N lonepair, involved in those excitations are shown by broad lines for bonds and by dashed lines for antibonding orbitals. In Fig. l(b) the analogous contributions to the ci.s and trms 2J( 15N,CH2) couplings in compounds X and XI are shown, while in Fig. 1 (c) the corresponding values for 25( 15N,CH3) in the same compounds are displayed. It is interesting to observe the similarity between these terms for different types of coupling. 2J(31P- “F) couplings in XII Although the truns-cis differences in N-C couplings in X and XI are mainly determined by the Fermi contact term, for other types of nuclei non-contact terms may define the orientational lone-pair effect. An example in which the truns-cis difference in 2JpF couplings is mainly defined by the PSO interaction is that of compound XII. In Table 2 the total FC, PSO and SD terms calculated at the RPA-INDO level are shown for compound XII (X = F). Total couplings

/ CH3 -8.07

\

OH

CH3CH2\GN0

(b)

CH3

/

-3.29’0H

CH3\ 0 C-_N CH3CHf

6.63’OH

CH3CH2\_&_No

(cl CH3CH2/-3.55’0H

CH&97

‘OH

Fig. 1. Main excitations defining the Fermi contact trans-cis difference in two-bond couplings in oximes. The following notation is used to show which other LMOs are involved in addition to the N lone pair: bonds are shown by broad lines while antibonding orbitals are represented by dashed lines. The corresponding Jiojb contributions are given in Hz. In all cases the antibonding C-N orbital is the done. (a) ‘J( 15N-lH) couplings in compounds VIII and IX. These excitations yield a contribution to d( truns-cis) of + 17.17 Hz. (b) *J( 15N-CH2) couplings in compounds X and XI. These excitations yield a contribution to A(trans-cis) of +9.92 Hz. (c) *J( “N-CH3) couplings in XI and X. These excitations yield a contribution to A(truns-4~) of + 10.52 Hz.

183 TABLE 2 The P lone-pair orientational effect on ‘Jrr couplings (in Hz) in XII” 2&r(&) FC PSO SD Total Exp.b(X=CFs)

157.02 -30.14 68.60 195.48 191

2JpF( truns ) 145.02 -99.20 62.26 108.06 104

A( trans-cis) - 12.00 - 69.06 - 6.36 - 87.42 -87

“Calculations were carried out for X=F with an MNDO optimized geometry. bTaken from Ref. 34. TABLE 3 Sums of contributions (in Hz) to cis and trans 2J( 31P-1gF) in XII, ~~~~ ’

2JPF cis +0.99

CZ%F,

A (tFUnS-CiS) trans - 29.25

- 30.24

+ 16.30

+ 3.84

- 12.46

-3.08

- 48.56

- 45.48

a (1) indicates the LMO involved in all Jinjb summed over: LP (P ), the P lone pair; B (P-X), P-X bonding orbital; LP (x-F), n-type lone pair of the coupled fluorine atom.

are compared with the experimental values for XII (X = CF, ) . It is observed that the largest contribution to the trans-cis difference is made up by the PSO contribution. However, all three terms contribute in the same sense to the truns4.s difference. Calculations were performed for XII (X=F) since for X = CF, the ground-state wavefunction is close to a Hartree-Fock instability of the non-singlet type. Such “quasi-instability” manifests itself as an eigenvalue of the triplet polarization propagator, close to zero [33]. In such a condition the RPA scheme fails to describe properly either the FC or the SD terms (eqns. (6) and (8)). H owever, this is not the case for the PSO term which can be properly taken into account within the RPA scheme. In compound XII (X=F) such a quasi-instability is not present and it was therefore chosen to perform a CLOPPA analysis. It is worthy of mention that the RPA PSO term is practically the same in XII (X = CF3) and in XII (X = F ) . In Table 3 different sums of contributions to the PSO term of cis and trms 2J( 31P-1gF) couplings in XII are shown. The sums of contributions to the PSO term involving the P lone pair, CzEyr,, take into account part of the truns-cis difference of the total orbital interaction (see Table 2). The difference (tram) - I:& (ck) is made up of several Jzs$ contributions, none c &, of which are dominant.

184

As the P-X bond could play a role similar to that of the P lone pair, the sum of contributions involving that bond, Cg’$&), are also shown in Table 3. It is interesting to observe the different behaviour between both occupied LMOs: for the coupling involving the F nucleus placed cis to the P lone pair, Cg+&) is positive, while Cz&, is negative for the coupling involving the F nucleus placed tram to the P lone pair. The sums of contributions involving the F x-type lone pair of the coupled fluorine nucleus, C~~~~_r), are shown. The difference between the two is surprising and constitutes an important contribution to the tram+cis difference of the total PSO terms. Such terms are also made up from many terms showing the same trend, but none of them are dominant. It is important to point out that most of these JE:T terms do not involve the P lone pair. ‘Jf’5Ar,X) collies in VIII, IX, XIII and Z-F-pyridinefX= ‘H, 13Cor “‘F) The N lone-pair contributions to the Fermi contact term, CEg, of one-bond couplings are also of opposite sign for cis and trans orientations. A few examples are shown in Table 4. The comparison of analogous C-C and C-H couplings in VIII, IX and XIII shows a similar influence of the orien~tion~ N lone-pair effect on the FC term of both types of couplings. However, the sum of contributions involving the LP are not exactly proportional to total couplings. The comparison of C:g in VIII with that in pyridine indicates that for ‘JCH couplings the longer C-N distance in the latter as compared with the former yields a reduction of contributions originating in excitations involving the N lone pair. The C”L”pfor lJFc in 2-F-pyridine is also positive, in spite of the total Fermi contact term of that coupling being negative. This indicates that the cis lonepair effect for the Fermi contact term in one- and two-bond couplings is positive when the magnetogyric ratio of both coupled nuclei are of the same sign, TABLE 4 N lone-pair orientational effect on the Fermi contact contribution in some one-bond couplings” (in Hz) Compound

Coupling

VIII IX XIfI XIII Pyridine P-F-Pyridine

‘Jcn ‘JCH

Exp.

‘Jcc(cis) *Jcc ( tmz.s)

lJW-HW ‘JCF

-

177s 163b 49.3’ 41.9” 177.63d 236.3’

3.72 -6.56 2.48’ - 2.14’ 2.95 14.42

*As in Table 1, 12 is the sum of all JFG,, contributions where either i or j correspond to the N lone-pair. bTaken from Ref. 35. eTaken from Ref. 36. dTaken from Ref. 37. Taken from Ref. 38.

185

and negative when they are of opposite sign. The situation is reversed for the tram effect. It is interesting to observe that in XIII the PSO and SD terms are noticeably insensitive to the N lone-pair orientation [ 361. CONCLUDING REMARKS

The examples discussed in this paper show the flexibility of the CLOPPA method to analyse different aspects of the electronic origin of spin-spin coupling constants. When it is used in connection with the IPPP approach [ 111 its capabilities are noticeably broadened. Among the problems in which the use of both methods yields an intuitive insight, although with a theoretically sound background, are the following: the study of multipath transmission in multicyclic compounds [ 141, the analysis of the transmission of the Fermi contact interaction through an electronic R system [ 111, the through-space transmission by spatial proximity [ 151, and the role played by lone pairs in defining the stereospecific behaviour of some couplings [36]. This last problem is illustrated in the present paper with a few examples. The results of the CLOPPA-IPPP method reported in this paper were obtained using an INDO ground-state wavefunction and the polarization propagators were evaluated within the random-phase approximation. However, the CLOPPA-IPPP methods are designed in such a way that both approximations can be improved. For instance, the ground-state wavefunction can be evaluated at an ab initio level [ 31, and a better approximation can be used when calculating the polarization propagator. This last point is particularly important when the ground-state wavefunction is near an unrestricted Hartree-Fock instability [ 391. ACKNOWLEDGEMENTS

Grants from the Argentine National Research Council (CONICET) from the University of Buenos Aires are gratefully acknowledged.

and

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