204
J. Phys. Chem. 1982, 86, 204-216
Application of Lanthanlde Nuclear Magnetic Resonance Shift Reagents in Conformatlonal Analysis of Flexible Chain Molecules. A Pseudocontact-Shift and RelaxatIon I nvestlgatIon Jean-Plerre Ouaegebeur LXpartement de Physico-Chimie, C.E.N. de Sacley 91 191, Gif sur Yvette Gedex, France
and Tamlo Yasukawa Chemical Institute of Nonsqueous Solutions, Tohoku University, Sendai, Japan (Received:June 10, 1981; In Flnal Form: September 9, 198 1)
The geometric factors involved in the 13C pseudocontact shifts in alkyl chain ligands coordinated to Ln(DPM), have been computed by taking the statistical averaged values over all confiations of these molecules in solution. The conformational energies about the C-C bonds in those flexible substrates are determined by considering a threefold torsional potential with a barrier height of 2.8 kcal mol-', and the attractive and repulsive energies between nonbonded pairs of atoms are described by a Lennard-Jones 6-12 potential function. The different energy minima are incorporated into a five-rotational-statemodel, and they reproduce quite well the experimental values of 13Cpseudocontact shifts in aliphatic amines (or alcohols) coordinated to lanthanide chelates, with Eg = 0.5 and Eghgi.= 3.0 kcal mol-'. Comparison is made with the traditional three-state scheme for rotation about C-C bonds. Making use of this computational model, we show that the simultaneousapplication of both dipolar-shift and relaxation data in 4-butylaniline and methyl hexanoate complexes with LII(DPM)~leads to compatible dynamical and conformational results and removes some likely ambiguities. In the case of 4-butylaniline, details are given first of the applications of 13C contact shifts to conformational analysis and, on the other hand, of the separation of scalar and dipolar shifts in the cobalt acetylacetonate (Co(acac)2)complex. The dipolar shifts in the tri-n-butyl phosphate ligand are likewise interpreted by this model by considering the steric repulsions occurring when P-0 and 0-C bonds are rotated simultaneously and taking account of steric requirements in the vicinity of the paramagnetic center for this bulky ligand. Finally, it is shown to what extent the kinetic parameters of the ligand exchange between the solution and complexes can be correlated to the stability of complexes with phosphorus ligands.
Introduction Since the introduction by Hinckley' of lanthanide shift reagents (LSRs) in nuclear magnetic resonance studies, their potential efficiency and applications have been the subject of several reviews.2 The formation of complexes between rare-earth chelates and organic molecules bearing a lone pair of electrons is generally rationalized in terms of Lewis acid-base interactions, and their action as shift reagents depends merely on their ability to form labile adducts in solution. In such paramagnetic systems, the electron nuclear interactions are revealed in two changes in the NMR spectra of nuclei in the substrate molecules: isotropic chemical shifts and nuclear relaxation enhancements. Besides the nature of the induced shifts and the possible contact contributions, a lot of questions have still been raised, and they concern, for instance, the presence of axial symmetry and the effects of conformational equilibria. Much energy was devoted to the development of computational models relating the paramagnetic shifts to some structural properties of LSR-ligand complexes, and numerous studies also emerged in combining shift and relaxation information for the elucidation of molecular str~cture.~ (1) Hinckley, C. C. J. Am. Chem. SOC.1969, 91, 5160. (2) (a) Mayo, B. C. Chem. SOC.Rev. 1973,2, 49. (b) Ammon, R. V.; Fischer, R. D. Angew. Chem., Znt. Ed. Engl. 1972,11,675. (c) Sievers, R. E.,Ed. "Nuclear Magnetic Resonance Shift Reagents"; Academic Press: New York, 1973. (d) Dobson, C. M.; Levine, B. A. 'New Techniques in Biophysics and Cell Biology"; Wiley: New York, 1976; Vol. 3, Chapter 2. (3) (a) Welti, D. H.; Linder, M.; Emst, R. R. J. Am. Chem. SOC. 1978, 100, 403. (b) Lenkinski, R. E.;Reuben, J. Zbid. 1976, 98, 4065. (c) Reuben, J.; Leigh, J. S. Ibid. 1972, 94, 2789. 0022-3654/82/2086-0204$01.25/0
Our interest in NMR of paramagnetic complexes was focused on the determination of conformations of flexible chain ligands coordinated to divalent or trivalent metal chelates. The dynamical behavior of such molecules undergoing multiple internal rotations was discussed previously either by considering the enhanced 13Cnuclear spin relaxation4-' or from the pseudocontact shifts experienced by these nuclei in lanthanide complexes.8 It was moreover shown in ref 9 to what extent simultaneous studies of 13C paramagnetic relaxation induced by Gd3+and of dipolar shifts arising from interactions with the whole isomorphous rare-earth series could lead to similar conclusions and thus to a better understanding of conformational dynamics in those nonrigid systems. We wish to report, in this paper, a more detailed examination of calculation of the geometrical factor involved in the pseudocontact-shift formulas. In flexible ligands coordinated to LSRs, this factor is calculated by taking the statistical average over all possible conformations of chains, and the energy of each conformation may be determined by including the interactions between nonbonded atoms, described by Lennard-Jones potential functions. (4) Tsutsumi, A.; Quaegebeur, J. P.; Chachaty, C. Mol. Phys. 1979,38,
1717.
(5) Quaegebeur,J. P.; Chachaty, C.; Yasukawa, T. Mol. Phys. 1979,37, 409. (6) Yasukawa, T.; Chachaty, C. Chem. Phys. Lett. 1976,43, 565. (7) Yasukawa, T.; Chachaty, C. Chem. Phys. Lett. 1977,51, 311. (8)Chachaty, C.; Quaegebeur, J. P.; Yasukawa, T.Chem. Phys. Lett. 1978, 59, 293. (9) Quaegebeur, J. P.; Belaid, S.; Chachaty, C.; Le Bail, H. J.Phys. Chem. 1981,85, 417.
0 1982 American Chemical Society
The Journal of Physical Chemistry. Vol. 86, No. 2, 1982 205
LanthanMe Shift Reagents
In LSR experiments sufficient sets of conformational parameters are generally measured and are governed by different equations so that it is possible to calculate from the averaged values of these parameters the molecular configurations as well as their populations. Both dipolar-shift and relaxation measurements, which are independent sets of parameters and have different geometrical dependences, are often necessary. In our approach to conformational analysis in solution, we attempted, on the examples of methyl hexanoate and 4-butylaniline coor= dipivaloylmethane), to dinated to L I ~ D P M (DPM )~ interpret the 13Cparamagnetic shifts and relaxation data in terms of a weighted average over a number of configurations. Our method of computation was further extended to the specific case of more bulky phosphorus ligands coordinated to these chelates where some other problems arising in connection with these systems were also considered.
Experimental Section Most of the substrates investigated were used without further purification. The tri-n-octylphosphine oxide (TOPO) was purchased from IRCHA (France) whereas tri-n-butyl phosphate (TBP)was supplied by Merck. The lanthanide 8-diketonates Ln(DPMI3 (DPM = dipivaloylmethane) were synthesized and purified by the method of Eisenstraut and Sievers.Io Methyl hexanoate was prepared by a stoichiometric reaction of hexanoyl chloride with anhydrous CH30H in dry ether. After being washed with a saturated NaHC03 aqueous solution and being dried on N G O r , the ester was distillated and kept on 13X molecular sieves. The 13Cparamagnetic shift measurements were carried out at 20 and 25.2 MHz on Varian CFT2O and Varian XLlOO spectrometers. Some subsidiary experiments on complexes of TOPO with LII(DPM)~were performed on a Cameca TSN 250 apparatus operating a t VI% = 62.86 MHz. The paramagnetic shifts being equal in ppm at different frequencies with respect to an internal reference of Me4Si,the conditions of fast exchange between the free ligand and the complexes were verified. The 13C and 31P TIrelaxation times were measured by inversion recovery (180°,T,WO sequences) or by progressive saturation (goo, T, 9 0' sequences) in the Fourier mode. The 31Ptransverse relaxation times were obtained from line-width measurementa after corrections for magnetic-field inhomogeneities. Our experiments were performed at 300 K and at constant ligand concentrations (30% v/v or in weight) in CDC13, the ratios p = [paramagnetic chelate]/[ligand] varying to 10" in order to keep a linear dependence of from these observed parameters upon p . The outer sphere relaxation which may not be ruled out for nuclei far from the paramagnetic center was estimated from the 13C relaxation enhancement of CDC1, or Me4Si. The fast exchange conditions T h 3 kcal mol-'). For the second bond in the molecule, i.e., in our case, the N-C (or 0-C) bond, the statistical-weight matrix will take the diagonal form 1
0
0
0
0
0 u'0 0 0
1
d and d* having the same meanings as u and u*, respectively. Combining (7-13) with eq 6, we may calculate the geometrical factor in eq 3 for each carbon in a ligand coordinated to a lanthanide ion. The five rotational isomeric state scheme is illustrated on the example of calculation of 13Cpseudocontact shifts in (n-he~ylamine)~ (or (n-hexyl al~ohol)~)-Ln(DPM)~ complexes. Examination of the spatial distribution of atoms in these systems reveals that some conformations of the chain may bring some of the nuclei in the near vicinity of the metallic ion. These conformations have been removed by assigning a steric hindrance, i.e., a minimum distance of approach for the carbons and protons from the paramagnetic center. This distance was taken approximately equal to the first coordination sphere radius (about 2.9 A for Ln3+and 2.1 A for Co2+). The main parameters used in these calculations were C-C = 1.533 A, N-C = 1.47 A, 0-C = 1.43 A, LN-C-C =
200
Quaegebeur and Yasukawa
The Journal of Physical Chemlstry, Vol. 86, No. 2, 1982 U
1
w
1 0-
10-I-
1 0-
I
d
10-
IO-?
10-
to-!
I
i
6
i
ti
s
6
coordinated to Ln(DPM),: (a)calculated by assuming a fivefold scheme with E , - E, and C,-C,+l bonds, respecthrety; (b) calculated on accountingfor nonbonded interactkns described by LennardJones potential functions. In a and b the statistical weights Uare calculated by taking account of the steric effect in the vicinity of the metaillc Ion. Flgurs 3. Spatial distribution of carbon C5 in hexylamine = 0.8 kcal nW1and 0.5 kcal mot' for rotations about N-Cl
TABLE 11: Relative Pseudocontact Shifts in Ln(DPM),-(n-Hexyl Alcohol), Complexes
TABLE I: &lative "C Pseudocontact Shifts in Ln( DPM),-(Hexylamine), Complexes ref C1 (Av/vo),xptP (AU/Uo)c&d
U
b
c d e
1 1 1 1 1 1
C2
C3
C4
C5
C6
0.466 0.461 0.463 0.462 0.462 0.462
0.237 0.236 0.237 0.266 0.250 0.248
0.128 0.130 0.136 0.138 0.139 0.137
0.0780 0.0781 0.0808 0.0853 0.0830 0.0819
0.0506 0.0514 0.0511 0.0508 0.0524 0.0523
See Table I in ref 8. Calculated with the fiverotational-state model ( E t = 0 kcal mol-' and E, = 0.5 kcal mol" for rotation about all C-C bonds) and assuming a minimum distance approach from metal equal to 2.9 A . Calculated with the Lennard-Jones potential function. Values obtained with the assumption of a three-state model. e Values calculated with the assumption that g'g' forms are entirely forbidden (EgtgT> 7.0 kcal mol ).
L0-C-C = LC-C-C = 112O, LLn-N-C = 125O, LLn-0-C = 122O, and Ln-N = Ln-O = 2.9 A. The rotational states about N-Cl and 0-Cl bonds were specified by -RT In d = 0.8 and 1.0 kcal mol-', respectively, and -RT In u'* = 2.0 kcal mol-l. In the calculations performed with Lennard-Jones functions, we have moreover taken N-H = 0-H = 1.01 A, LH-N-H = 108O, LH-N-C = 114O, and LH-QC = 120O. The results achieved with the 6-12 potential functions are very similar to those obtained by using identical energies for rotation about all C-C bonds, i.e., Et = 0, Egt = 0.5 kcal mol-1, and Egfgr.= 3.0 kcal mol-' (Tables I and 11). We may then conclude that conformational energies calculated for n-pentane can be extrapolated to n-alkyl chain moleculea of any length, in spite of slight differences encountered with Lennard-Jones po-
ref C1 (A~/~,),,ptl (AU/Vo)c&d
(I
0
b c a-c
1 1 1 1
C2
C3
C4
C5
C6
0.457 0.447 0.450 0.458
0.245 0.224 0.236 0.270
0.127 0.122 0.127 0.137
0.0712 0.0716 0.0741 0.0833
0.0465 0.0465 0.0461 0.0490
As in Table I.
tential functions in the spatial distribution of atoms (see Figure 3b for carbon C5) and which are attributed to small displacements of some rotational states as the alkyl chain increases.25 The steric effect prescribed in the vicinity of the paramagnetic center does not influence drastically the calculated values of pseudocontact shifts in those ligands (Tables I and 11) but may not be ruled out, as will be seen in the last part of this work. It should also be pointed out that the energy Eegr. = 3.0 kcal mol-' reduces the populations of these states to a low level but not to the point where they may be disregarded, i.e., for Egkg7,> 7.0 kcal mol-'. A last feature arising from Table I is that the five-state model yields more compatible results than the traditional three-state (t, g+, g-) one. In spite of the greater number of conformations generated with the fivefold scheme than in the three-state model (379 and 243, respectively, for n-hexylamine), the pseudocontact shift results on the basis of the latter approximation still remain in good agreement with the experimental ones. We have nevertheless chosen throughout this work the five isomeric rotational state scheme in order to take into account the effects of perturbation of the location of those states by
Lanthanide Shift Reagents
The Journal of Physical Chemistry, Voi. 86, No. 2, 1982 209
neighboring interactions in alkyl chain ligands. Nuclear Spin Dipolar Relaxation in Gd(DPW3 Cornplexes. Association of organic molecules with Gd3+chelo4 s at 300 K) is lates (a ground state with T1, accompanied first by contact shifta solely in the 13C NMR spectra and on the other hand by an enhancement of 13C relaxation rates in these ligands. The longitudinal and transverse relaxation times in a rigid paramagnetic complex undergoind isotropic reorientation are given by modified forms of Bloembergen and Solomon equations for Tl, # T2,:30
-
(15) wk and ws being the nuclear and e- Larmor frequencies, respectively, and Ak the scalar hyperfine coupling constant of nucleus k. The correlation times are defined by (71,2)-'
=
7R-l
+ (7e1,2)-'
(16)
with (Te1,2)-'
= (T1,zel-l
+ 7h-l
FZ
(T1,2e)-l
rRbeing the reorientational correlation time of electron spin-nuclear spin vector rk. The exchange rate 7h-l of ligand molecules between the complex and the solution has to be taken into account in the determination of T1,ZM-l from the observed values (TIJ-l)obedof the relaxation rates (see eq 6 and 7 in ref 9). This exchange rate is found to be generally negligible with respect to T1M-l except for TBP ligand where 7h-l is of the order of magnitude of (TIM-l)Pas in the case of other phosphorus ligands coordinated to Gd(DPM)3.g The complexes under study can be schematically depicted by the fragment Gd-X-Ywhere X = N and Y = C , for 4-butylaniline ligand, X = 0 and Y = C1 for methyl hexanoate ligand, and X = 0 and Y = P for tri-n-butyl phosphate ligand. In the case of Gd3+complexes, the scalar contribution to the longitudinal relaxation time, i.e., the second term in eq 14, may be neglected in comparison with the first dipolar term, and rR-lis moreover found to be generally greater than 10Tl;' (ref 4 and 9), so that the enhanced relaxation time for nucleus Y will be given by the reduced expression
..
r
1-1
q is the number of ligand molecules coordinated to Gd3+
and Tlf the relaxation time corresponding to the free substrate, the other parameters keeping their usual meanings. (30) Reuben, J.; Reed, G. H.; Cohn,M. J. Chem. Phys. 1970,52,161.
The reorientational correlation time T R is estimated as previously reported4 from the longitudinal relaxation time of the methine carbon of the DPM groups in the diamagnetic analogue complexes with La(DPM),. The coordination number q can then be deduced from eq 17 and is found to be 2 as for other nitrogen and phosphorus ligand^,'^ except for methyl hexanoate where q = 1. These values are compatible with a geometry in the vicinity of the paramagnetic center defined by rGd-X 2.8-2.9 A, rC/(Gd-X-Y) 120-130°, and rCd-Y 3.8-4.0 A. Besides the determination of geometry about the donor atom in the ligands, another important application of nuclear relaxation enhanced by the Gd3+ paramagnetic probe is the dynamical and conformational study of the coordinated molecules undergoing a large number of internal rotations. Though the practical limit of these measurements seems to be about five bonds away from the paramagnetic center, the simultaneous application of relaxation and dipolar-shift data provides complementary information in these flexible systems and allows us to remove some ambiguities which would be present if only one sort of data were used. The dynamical behavior of nonrigid ligands has been outlined previ~usly?~ and more precisely the 13Crelaxation rate enhanced by Gd3+ion was interpreted by considering the dipolar interaction of the two spins separated by several bonds undergoing jumps among three sites. Let us define the equilibrium positions of each nucleus j by with the dihedral angles 4i (i = 1,2,3) = cj-3+&.1+ sites i = 2 and 3 equivalent and di = Oo for the trans position. The population of each site will be given by PI = W2/(2Wl + W,) (18) P, = P, = W,/(2W, + W,)
-
- -
where Wl and W, are the jump rates between sites 1and 2 (or 3) and W3 is the jump rate between orientations defined by 4, and 4% Together with the different kinetic parameters, the influence of which has been detailed in a previous work: the overall motion of the complex is supposed to be isotropic with a Brownian diffusion constant D = ( 6 ~while ~ )the~ other ~ geometric parameters involved were the same as in the pseudocontact-shift calculations. The probabilities of occurrence of trans and gauche forms about C-C bonds (sites 1and 2 (or 3), respectively) can be related to the energy difference between those configurations by P,/P, = W1/W2 = exp[-(E, - E,)/RTI (19) in the approximation of the three-state scheme, so that application of relaxation and shift data will lead to compatible information concerning the conformer populations. This is quite well verified for T O P 0 coordinated to Ln(DPM)t and to a less extent for alkylamine ligand, where slight discrepancies are in fact observed! The reasons for those differences may be that, in the course of T1 calculations, the g*g* are completely precluded and no steric effect due to the paramagnetic center is introduced. Illustrative Examples Paramagnetic Complexes of 4-Butylaniline. Aniline and its substituted compounds bound to di- or trivalent metal chelates have been the subject of several works in our lab0ratory,3l-~~ where was more particularly investi(31) Chachaty,C.;Forchioni, A.;Vilet, J.; Ronfard-Haret,J. C.Chem. Phys. Lett. 1974,29, 436. (32) Chachaty,C.;Forchioni, A.;Ronfard-Haret,3. C. Mol. Phys. 1976, 31, 325.
210
ne Journal of Physical Chemistry, Vol. 86, NO.2, 1982
Quaegebeurand Yasukawa
gated the electron spin distribution in these ligands coordinated to nickel acetylacetonate, N i ( a ~ a c )together ~, with the configuration of the amino group and the intramolecular motions. Our purpose in studying the complexation of 4-butylaniline by L ~ I ( D P Mwas ) ~ b improved some relaxation results and to make use of pseudocontact-shift calculations for correlating some dynamical information. Under the assumption of an isotropic Brownian motion about the metal-nitrogen bond, the relaxation time of C, carbon enhanced by Gd3+is described as for C, nucleus by eq 17, so that
rp2/r,2 =
5* A A
.c
(20)
(T1M,Cp/TlM,C,)1'3
rrrand rpdefining the distances of C, and C, b the Gd(1II) ion, respectively. The knowledge of the reorientational correlation time TR (TR = 8.3 X s at 300 K) allows the determination of the geometry about the donor atom, Le., d = 2.9 A and LGd-N-C, = 122'. In the hypothesis of a rigid ligand, the relaxation rates of C, and C, nuclei are found to be in rather poor agreement with experimental values (Table III). A better fitting is achieved by assuming a fast internal motion of the phenyl ring about the N-C, bond. This motion occurs by 180' jumps between positions defined by $J1 = 90' and $2 = 4s = 270' (W2 = 2WJ, the phenyl plane remaining normal b the Ln-N-C, plane. This internal motion was also observed in phenyl-substituted phosphine oxide^.^ After separation of the scalar and dipolar contributions to the '3c paramagnetic shifts in Cbutylaniline coordinated to LII(DPM)~,the coupling constants of C1 and C2 in the butyl chain thus obtained can be related to the 7~ spin density located on C, carbon by = (1/2S)Qcpc,"
dQ,
c-
hl @I
rl
3r-
Q,
oc-
w m
4
N
om N
m
(21)
uc2 = (1/2S)(B1C + B2C(cos2a))pc,"
(22)
where a is the angle between the axis of the ?r orbital perpendicular to the phenyl ring and the projection of Cl-C2 on a plane perpendicular to C,-C1. Qc = 16.5 G and BIC
