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The Molecular Structure of Allenes and Ketenes, XII [1] Four-Bond Proton-Proton Spin-Spin Couplings in Allenes Wolfgang Runge Organisch-Chemisches Institut der Technischen Universität München Z. Naturforsch. 33 b, 932-936 (1978); eingegangen am 18. Mai 1978 Allenes, Proton-Proton Coupling Constants, Substituent Effects

Four-bond proton-proton coupling constants in allenes are reported. The substituent effects on the coupling constants are discussed on the basis of the dual-substituent parameter approach. Furthermore, the coupling constants are related to quantum-chemical indices (electron densities, overlap populations) obtained from semiempirical CNDO/S and ab initio STO-3G calculations.

The magnitudes of the coupling constants depend upon the polar natures of the substituents as well as upon their charge-transfer abilities (resonance effects) to a com-parable amount. In general, the coupling constants in 1,3-disubstituted allenes are nonadditive in ligand -specific parameters.

1. Introduction Proton chemical shifts of allenes have been

discussed in part X I of this series [1]. The present contribution is concerned with four-bond proton-proton spin-spin coupling constants 4J(HH) in variously substituted allenes (Table I).

Ht\ R / X

The experimental coupling constants are partly from the literature [2-10] and partly from this series of contributions [1, 11].

The substituent effects on the four-bond proton-proton couplings in allenes are discussed on several levels. At first, using the material now being available, it is analyzed whether the coupling constants are additive in ligand-specific parameters as has been suggested in Ref. [5] on the basis of only two independent tests. For this purpose use is made of algebraic (geometrophysical) concepts which have been applied to the general treatments of various molecular properties of allenes [1, 12].

Then, the dual-substituent parameter (DSP) approach [13] serves purposes of semiquantitative insights into the nature of the substituent effect on the four-bond couplings. This treatment is especially concerned with the relative importance of a and n mechanisms for the transmissions of substituent effects in monosubstituted allenes and, for instance, focusses attention to the question [5] why substi-

Requests for reprints should be sent to Dr. habil. W. Runge, Studiengruppe für Systemforschung, Werder-straße 35, D-6900 Heidelberg.

Table I. Four-bond proton-proton coupling constants of allenes R2HC = C = CHR3 [in Hz].

Coin-pound R2 R3 4 J ( H H ) Ref.

1 H H — 7.0 [2] 2 C H 3 H — 6.67 [5] 3 C2H5 H — 6.77 [5] 4 C H a C l H — 6.59 [6] 5 C 6 H 5 H — 6.95 [a] [ l i b , l i e ] 6 h 2 c = c h H — 6.64 [10] 7 COOCH3 H — 6.65 [a] [11c] 8 COCH3 H — 6.50 [ 7 ] 9 C N H — 6.79 [3]

10 C 6 H 5 ( C H 3 ) N H — 6.1 [9] 11 c h 3 0 H — 5.90 [a] [11c, 12b] 12 c h 3 s H — 6.40 [a] [11c] 13 C l H — 6.04 [a]

— 6.1 [2] 14 Br H — 6.06 [a]

— 6.1 [2] 15 I H — 6.27 [a]

— 6.3 [2] 16 (CH3)3Si H — 7.02 W [He] 17 POCI2 H — 6.61 [8b] 18 P O ( C 6 H 5 ) 2 H — 6.80 [8a, 8b] 19 c h 3 C H 3 — 6.35 [ 5 ] 20 c h 3 C l — 5.80 [ 4 ] 21 c 6 h 5 c h 3 — 6.92 [a] [ l i b , 12b] 22 C 6 H 5 C O O H — 6.80 [a] [11a, 12b] 23 C 6 H 5 CH3O — 6.20 [a] [12b] 24 C 6 H 5 P O ( C 6 H 5 ) 2 — 6.50 [8 a]

fa] This work; references in parentheses give hints to other investigations within this series of contribu-tions where other properties of the corresponding compounds are discussed.

tuents like Cl and CH3, which are apparently different with respect to their polar natures and (group) electronegativities, both reduce the (abso-lute) magnitudes of the four-bond proton-proton couplings in allenes.

W. Runge • The Molecular Structure of Allenes and Ketenes 933

At last, the long-range couplings in allenes are related empirically to quantum-chemical indices, such as electron densities or Mulliken overlap populations, in order to corroborate interpretations given on the basis of the DSP approach.

2. Results and Discussions 2.1. Nonadditivity of substituent effects on the four-bond couplings

In Table I experimental four-bond proton-proton coupling constants of allenes are summarized. These values reveal that there is a small, but significant substituent effect on the four-bond couplings. The overall variation of the couplings amounts to 1.10 Hz. It may be assumed that the experimental errors of the individual values do not exceed ± 0.07 Hz. Considering all the couplings in Table I the suggestion that the four-bond proton-proton couplings in allenes are additive in ligand-specific parameters [5] cannot be supported. Though the coupling constants of 19 and 20 are correctly predicted using eq. (1) («(H) = 0; r = —7.00 Hz from 1; x(CH3) = +0 .33 Hz from 2; «(Cl) = + 0.96 Hz from 13)

4J(HH) « r + X(R2) + X(R8) (1)

the couplings of the phenylallenes 21-24 cannot be reproduced with such a simple procedure to within ± 0 . 1 6 Hz. 0.16 Hz represent about 15% of the overall observable variation of the couplings and may be assumed to be a limit for an acceptable deviation between calculated and observed coup-lings.

Therefore, one may conclude that, in general, four-bond proton-proton coupling constants of allenes are nonadditive in one-particle functions (ligand-specific parameters).

For scalar molecular properties of allenes, such as carbon electron densities [12 c], 13C chemical shifts [12a, 12b], and XH chemical shifts [1], interactions between substituents attached to the same carbon atom (geminal substituents) have proven essential for an understanding of the observable phenomena. The results for the four-bond coupling constants, i.e. the nonadditivity in substituent effects, suggest that there may exist distinct interactions between the two substituents R 2 and R3 attached to different carbon atoms of the allenic skeleton. Such types of interactions may be immediately deduced if one

refers to the geometric models for the treatments of point-properties of allenic systems [1, 12].

The four-bond coupling may be viewed as a molecular property which depends simultaneously upon point-properties p of the two protons Hi and H4. Therefore, the coupling 4J(HiHi) is factored into functions depending only upon one argument, i.e. AJ(H1H4) is separated into a product of equiva-lent functions p(Hi) • p(Hi).

V ( H ! H 4 | R 2 , R 3 ) = p(HI|R2, R3 , H4) • p(H4|R3, R2 , HI). (2)

In its simplest form p is additive in ligand-specific parameters (p corresponds to P, a point-property of an allenic proton in a three-site pyramidal Cs

situation discussed in Ref. [1]; cf. eq. (1) in Ref. [1]). Then, from eq. (3) (y '(H) = 0) it is easily seen that the simplest ansatz for the description of the four-bond proton-proton couplings in allenes must con-tain an interaction term 7i(R2,R3) = 7r(R3,R2).

p(Hi|R2 ,R3 ,H4) = £' + a ' ( R 2 ) + / ( R 3 ) + y ' ( H 4 ) (3)

V(HiH4|R2 ,R3 ) = r + *(R2) + *(R3) + n( R2 , R3) (4)

Therefore, in general, an addition of substituent effects (eq. (1)) can only give rough numerical estimates of the observable four-bond couplings in 1.3-disubstituted allenes. Within the above approach additivity in substituent effects, as is observed in case of 19 and 20, must be viewed as accidental. It cannot be predicted on the basis of any group theoretical or quantum theoretical arguments.

As a concluding remark it should be noted that, on the basis of any purely algebraic model, there is no a priori justification for an ansatz like eq. (2). The most general form of a two-variable function f (xi ,x 2 ) should involve a correlated pair-function [14] j (xix2 ) (f(xi,x2) = g(xi) • h(x2) + j(xix2)). The roots for eq. (2), however, may be found in physics, as the energy of interaction of two nuclei A and B (in the spin Hamiltonian), is directly proportional to the dot product of the corresponding nuclear spin

operators, namely E A B ~ « / A B I A • IB , where I A and

IB do not depend upon the electronic wavefunctions [15, 16].

Using the factorization J ( X H ) = p(H) • q(X) one may immediately conclude that, for instance, one-bond couplings iJ (XH) in tetrahedral systems

934 W. Runge • The Molecular Structure of Allenes and Ketenes 934

H X R 1 R 2 R 3 (X = C, Si) are nonadditive in substi-tuent effects and that in treating one-bond couplings 1J( 1 3CH) in allenes one must take geminal inter-actions and interactions across the allenic system into consideration. Both these deductions are established by experiments [17, 18].

2.2. Discussions of substituent effects

From monosubstituted allenes, i.e. from the ligand-specific parameters « (R) , some insights into the physical effects underlying the mechanisms for the transmissions of the substituent effects on the four-bond proton-proton couplings may be obtained.

Usually, for spatially fixed orientations of the relevant protons substituent effects on long-range proton-proton couplings are discussed in terms of factors which influence primarily the a electronic structures of the molecules under consideration, i.e. they are related to (group) electronegativities or polarity effects [2, 5, 19]. In LCAO expansions for the descriptions of the electronic structures of planar unsaturated systems (ethylenes, benzenes, etc.) the hydrogen Is atomic orbitals (AOs) can only be part of the o electronic structures. In mono-substituted allenes, however, the hydrogen I s A O s of the methylene group protons may be involved in the allenic 71 system ("hyperconjugation") [11a, 11c, 12 c] and thus may undergo direct 71 resonance interactions with the substituents.

Therefore, one may expect that the variations of the couplings do not only originate from the substituent (or substituent-carbon bond) polarity, but also from its charge-transfer ability. Adopting the DSP approach [13] for a semiquantitative discussion of the substituent effects x (R) it has turned out that ^(R) correlates with the polar substituent constant oi [13, 20] and the resonance substituent constant <TR° [13] (linear correlation coefficient r = 0.967 omitting the groups C6H5 and CN) (Fig. 1).

x(R) = 1.10 <7i — 1.38 (Tr° + 0.11 (in Hz) (5)

The A-value (X = QRIQI = —1.25) of correlation (5) clearly demonstrates that polar and resonance factors are of comparable importance for an under-standing of the substituent effects on the four-bond couplings in allenes. Furthermore, eq. (5) reveals that for mesomeric acceptors, such as COOCH3, COCH3, CN, the resonance contribution counteracts

the polarity and resonance substituent constant within a DSP approach.

the polarity influence, which explains the relatively small substituent effects of these strongly polar groups. For the nonpolar groups (e.g. CH3 and H 2 C = C H ) the effect on 4 J(HH) results almost entirely from resonance contributions.

This interpretation of the substituent effects is corroborated qualitatively by the correlation (6) (r = 0.912) of x(R) with the difference in the CNDO/S electron densities [11c, 12c] (Phh(1) -Phh(4) ) (in IO - 3 e) of the hydrogen atoms involved in the coupling (Fig. 2).

* (R) = 0.0431 (Phh(1)-PHH(4)) + O.l l (6) (in Hz)

1.2- *(R) (HU)

/ CH3O

CL / 0B-

/(:H3S C H 3 C 0 X

OA-COO

H2C=CiycH2Cl C H V / C H 3

/ C 2 H ; -CN C6H5

PHHU>-PHH<1> (10"3E)

- 5 / (CH3)3S

H 5 15 25

Fig. 2. Correlation of the substituent effect on the four-bond proton-proton coupling and the difference in electron densities of the corresponding hydrogen atoms.

The cyano and the chloro groups show larger deviations from the correlation. The group POCl2

exhibits a serious discrepancy. All these three groups have been omitted in the regression analysis.

W. Runge • The Molecular Structure of Allenes and Ketenes 935

Correlation (6) has the same structure as eq. (5). Though of inferior quality than eq. (5) correlation (6) is conceptionally illustrative as it relates the cou-plings AJ(H1H4) directly to point-properties of the corresponding hydrogen atoms Hi and H4, respec-tively. On the other hand, it contains a correspond-ing information like eq. (5), as the electron density variations at H4 are essentially determined by n resonance (hyperconjugative) effects [12 c], whereas the electron densities at Hi are determined by a-type mechanisms.

Direct quantum-chemical calculations of long-range coupling constants are complicated owing to the question of whether only the Fermi contact term [15] or also the orbital [15] and spin dipolar term [15] contribute to the overall spin-spin cou-pling mechanism. Furthermore, the results of such quantum-chemical calculations depend sensitively upon the basis set. These difficulties manifest in the numerical results for four-bond couplings (including results for allene (1)) obtained with different quantum-chemical procedures [22].

Therefore, empirical or semiempirical correlations of long-range couplings with quantum-chemical indices continue to be of practical and theoretical value for discussions of substituent effects.

MO treatments of Ramsey's perturbation formula [15] for the Fermi contact term invoking an "average energy approximation" relate the coupling constant of the nuclei A and B to the square of the atom A s- atom B s element of the first-order density matrix, i.e. the bond order PsAsB [23]. Neglecting problems associated with the signs of the coupling constants variations in P2sAsB often reflect substituent effects on long-range couplings [24]. Using CNDO/S wavefunctions for the allenes [11c, 12 c] no correlation of 4J(HIH4) and P2sHsH f ° r the differently substituted molecules is found. On the

other hand, it has been suggested [25] recently that coupling constants may be related to Mulliken overlap populations QsAsB obtained from ab initio procedures. In Fig. 3 the four-bond coupling con-stants of monosubstituted allenes are plotted versus the hydrogen ls-hydrogen Is overlap populations resulting from ab initio STO-3G MO calculations [12 c].

If one neglects the points for the cyano and the chloro groups, these groups showing also deviations

Fig. 3. Correlation of the allenic four-bond proton-proton coupling constants and the Mulliken overlap populations of the protons involved in the coupling.

from the correlation with the CNDO/S qualities in Fig. 2, there is indeed a correlation (7) (r = —0.932) between 4J(HH) and QsHsH (in units of IO -3)

4J(HH) = — 1.035 QsHsH —13.258 (in Hz) (7)

3. Experimental and Quantum-Chemical The proton NMR spectra of the allenes have been

measured with a Varian A 60 spectrometer in CC14 and analyzed as outlined in Ref. [1]. The Mulliken overlap populations Q S H S H related to the protons Hi and H 4 obtained from STO-3G calculations in Ref. [12 c] are given below.

R H C2H5 H2C=CHCOOCH3 CN CH30 CH3S (CH3)3Si Cl

— Q S H S H X I O " 3 6 . 0 4 6 . 4 7 6 . 2 0 6 . 4 1 5 . 6 5 7 . 0 7 6 . 5 1 6 . 1 4 6 . 3 6

The CNDO/S electron densities for the monosubstituted allenes with the groups CH2C1 and POCI2 are as follows:

R Pcc(l') Pcc(2') Pcc(3') PHH(2) PHH(3) Pcc(l') Pcc(2') Pcc(3')

CHaCl 4.038 3.955 4.100 0.959 0.965 1.127 0.931 0.973 POCl2 4.075 3.856 4.046 0.950 0.943 1.202 0.728 0.988

936 W. Runge • The Molecular Structure of Allenes and Ketenes 936

The enumerations of the atoms correspond to those used in Refs. [11c, 12 c]. The calculations have been performed including d atomic orbitals for the chloro and phosphorus atoms.

This work was supported by the "Deutche For-schungsgemeinschaft' '.

Note added in prove

Only after submission of the manuscript the author became aware of the fact that in a paper on carbon-proton coupling constants of allenes (N. J.

Koo le and M. J. A. de Bie, J. Magn. Reson. 23, 9 (1976)) 4 J ( H H ) values for 1, 9 ,11 -14 , 16 are given. With the exception of 9 [3] these values agree with those in Table I to ± 0.10 Hz.

[1] Part X I : W. Runge, Z. Naturforsch. 32b, 1296 (1977).

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[3] D. Wendisch, Z. Naturforsch. 22b, 353 (1967). [4] E. I. Snyder and J. D. Roberts, J. Am. Chem.

Soc. 84, 1582 (1962). [5] D. F. Köster and A. Danti, J. Phys. Chem. 69, 486

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[11] a) W. Runge, G. Kresze, and E. Ruch, Liebigs Ann. Chem. 1975, 1361; b) W. Runge, W. Kosbahn, and J. Kroner, Ber. Bunsenges. Phys. Chem. 79, 371 (1975); c) W. Runge and W. Kosbahn, Ber. Bunsenges. Phys. Chem. 80, 1330 (1976).

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[20] Owing to the particular rotamer populations in allenes o\ constants of 0.52 for COCH3 and 0.25 for CH2CI must be used [18], different from the conventional values [13, 21]; for POCI2 tri = 0.52 and CTr° = 0.10 [18].

[21] N. B. Chapman and J. S. Shorter (eds), Advances in Linear Free Energy Relationships, Plenum Press, London 1972.

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[25] J. M. Andre, J. B. Nagy, E. G. Derouane, J. G. Fripiat, and D. P. Vercauteren, J. Magn. Reson. 26, 317 (1977).