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NMR evidence on the structure of the uranyl-malate complex
J. inorg, nucl. Chem., 1974, Vol. 36, pp. 1803-1807. Pergamon Press. Printed in Great Britain.
N M R EVIDENCE ON THE S T R U C T U R E OF THE U R A N Y L - M A L A T E COMPLEX JUL10 D. PEDROSA and VICTOR M. S. G1L The Chemical Laboratory, University of Coimbra, Portugal (Received 18 May 1973)
Abstract--Comparison of the proton coupling constants and chemical shifts for malic acid and its 1: 1 dimeric complex with UO22÷at the same pH (around pH = 3) led to conclusions about the conformation of the ligand and the structure of the dimer. These results corroborate one[6] of the various hypotheses previously put forward for such a structure, the remaining ones being unambiguously ruled out. The existence of geometric isomers is also indicated.
INTRODUCTION THE URAr~I. ion is known to form polynuclear complexes with malic acid, the nature of which depends on the pH of the system. In the region of pH = 2-4 the dominating species is a 1:1 binuclear complex which is highly stable. These conclusions are based on spectrophotometric[1-3] polarographicE41 and potentiometric[3, 5, 6] studies. Several plausible structures have been proposed for this dimer[3, 5, 6], all of them assuming tridentate chelation involving the ionized carboxylic groups and the hydroxyl group of the malic acid. This is confirmed by i.r. spectroscopy[7]. However, different views have been held regarding the bridges between the uranium atoms. Thus, Feldman et al. E3,5, 8] favour the existence of two olation bridges as in II, whereas Rajan and Martell[6] suggest a structure I where the OH groups of the ligands act as bridges between the U atoms. In the first case, the carboxylate groups of each ligand molecule would both be bonded to the same uranyl ion; in the latter, one is bonded to one uranyl and the other to the second UO22+. The conformation of the ligand differs according to the hypothesis adopted. NMR spectroscopy has proved particularly suitable for the study of the conformation of malic acid both free[9-11] and as a ligand[ll], particularly in view of the dependence of the vicinal H-H coupling constants upon dihedral angles. In the literature there is only a brief reference to NMR spectra of the uranyl-malate system, reporting an enhanced broadening and highfrequency shift of the malate proton signals as the concentration of UO22+ is increased[8]. In this paper, we give the proton coupling constants and chemical shifts for malic acid and its 1 : 1 complex with UO22+ at the same pH (around pH = 3). A discussion of these gives indications of the conformation of the ligand in the complex and of the type of dimer present. These NMR results corroborate the second hypothesis, I,
mentioned above and clearly rule out the other. Additionally, the NMR spectra reveal the existence of geometric isomers of the dimer.
EXPERIMENTAL Commercially available pure uranyl nitrate hexahydrate and dl-malic acid were used without further purification. Aqueous 0.2 M solutions of malic acid and solutions 0-2 M in malic acid and 0.2 M in UO2÷ were adjusted to the same pH in the region 2--4by addition of NaOH. They were subsequently evaporated and the solids dissolved in D20 keeping the concentration at 0-2 M. The proton NMR spectra were run at room temperature on a Varian HA-100spectrometer; tert.-butanol was used as internal reference.
RESULTS Only spectral data corresponding to pH = 3 will be discussed; the conclusions are the same for other values in the region (pH = 2-4) investigated. The spectra are compared in Fig. 1. This clearly shows the remarkable effect of complexation with UO 2+ on the proton chemical shifts of malic acid. Figure 2 shows the expanded high-frequency signals. The two close quartets for the uranyl-malate solution reveal the presence of ligand molecules in slightly different conditions; the corresponding two low-frequency complex signals are not resolved. The proton coupling constants and the chemical shifts were obtained on the basis of an A B X analysis and are given in Table 1. Signal broadening limited the accuracy of the measurements. The spectral parameters for malic acid agree well with previous results [9-12].
1803
1804
JI~ILIO D. PEDROSAand VICTOR M. S. GIL
©
B,A
©
6 I
5 I
4 I
3 I
2 I
1 I
t-Bu [
Fig. I. 100 MHz proton NMR spectra of D20 solutions of malic acid(L) and malic acid + uranyl nitrate (ratio 1 : 1)(C) corresponding to pH = 3.3. Table 1. Proton coupling constants (Hz) and chemical shifts (in ppm) referred to t-butanol Malic acid 1:1 UO~+-malate
JAB JAx JBx 6A 6n 6x
(-)16.7 7.4 4.2 1-56 1-65 3-29
A detailed analysis of JAx and JBx in terms of dihedral angles and substituent effects has shown that forms (a) and (c) are the most important contributing ones [10, 11], the respective weights being about (a), 40 per
(-117-7 11.4 1.5 + 0.2 2.52 2.62 5.91 : 5.93*
to H z
* Values for the two X quartets (Fig. 2). DISCUSSION The observed vicinal H - H coupling constants for malic acid have been regarded as weighted averages of the corresponding values in the three staggered rotational isomers [9-11 ] :
CO2H
CO2H
COzH
J
J X(L)
CO2H (a)
OH
H (x)
( ~)
(c )
x(c)
Fig. 2. Expanded high-frequency signal (X part) of spectra (L) and (C) of Fig. 2.
1805
Structure of the uranyl-malate complex cent and (b), 50 per cent[ll]. Possibly an important factor is intramolecular hydrogen bonding involving OH and CO2H in a gauche situation. Complexation, particularly chelation, is expected to alter the relative weights of the three rotamers, hence JAx and JBx. Thus, the 1 : 1 complexes of malate with Zn(II)[1 1] have been found to have much closer values of Jax and JBX, suggesting that the preferred conformation in the presence of the metal ion becomes (c). A different trend is observed in the case of UO 2+ from that with Zn 2 +. The difference between Jax and Jnx becomes much more marked. This is a clear indication that (a) is the preferred form in the presence of UO 2+. Another difference with respect to the Zn complex is that a UO22+-malate complex is much more stable[6] ; in fact so stable that a slight excess of malic acid immediately gives rise to additional NMR signals corresponding to free malic acid molecules. This means that the observed spectral parameters for the l : l UO22+-malate system must be regarded as corresponding to a frozen conformation rather than taken as a weighted rotational average. We thus conclude that the conformation adopted by the ligand in the uranyl complex is identical or close to (a). This conclusion is only compatible with the dimer structure 1 postulated by Rajan and Martell[6], it being possible as far as the ligands are concerned for the uranyl ions to have their principal axes parallel to each other : 0
//
\ c j °..
/°Jc\ ,,U 02/ ..
/ CH2
".
/"
HC_____.__. O,"" H'-.
~x. H
/0" \
/
CH
,
c~O"
// 0
An approximate estimate of the vicinal coupling constants in form (a) gives Jax = 14.5 Hz and JBx = 1.8Hz[ll]. The values we observed are smaller, particularly Jax. This may be due in part to the bonding of OH to UO~ +, and the accompanying increase of the effective electronegativity of the oxygen atom of OH[13, 14]. However, this would not be expected to produce a change in Jax of the order of 3 Hz. Another contributing factor may be a twisting of structure (a) in the sense
CO2H H.. \ - ~OH IX) " ~ ~ H H/ I IA) (B) CO2H ~)
The HA-C-C-H x dihedral angle decreases and the HB~2-C-H x one increases which would then lead to a decrease both of Jax and Jsx[15]. The analysis of a molecular model indicates that such twisting is necessary so that the axes of the bonds between the ligands and the uranium atoms all become close to the equatorial plane of the uranyl ions, leading to a nearly octahedral arrangement around each U atom, without appreciable steric hindrance. Form (a) but not form (a') would imply a strong repulsion between the very close oxygen atoms of the hydroxyl and carboxylate groups gauche to each other. That arrangement leaves the two oxygen atoms (belonging to the carboxylate groups) not participating in the chelation, nearly in the equatorial plane of the ions UO~ + and pointing outwards, which obviously reduces repulsions (Fig. 3).
(I)
0
H(A)
The hypothesis II due to Feldman et al.[3, 5, 8] would require conformation (c) as in the case of the Zn complex : 0
H
_C~ O ~ I
H -'--"
H,; /
II
/O. /
",,
/C~cH2 ~\ / U02 - -
"-UO2
..0/-" ~c
..,uS. o
0
\
HE
0
"o'"
o
," " ' . . - ' - 0 "o
H .~-%CH
O~cxl
/ c
o (II)
0
Fig. 3. The most likely conformation of malic acid in the dimeric complex with UO22+.
JtJLIO D. PEDROSAand VICTORM. S. GIL
1806
The structure shown in Fig. 3 is also consistent with the proton chemical shifts. The shifts observed on comparing malic acid with the complex (Table 1), namely A6 a = 0-96, A6 B = 0.97, A6 x = 2.62, are too big to be explained by differences in the electron density of the H atoms resulting from replacement of the O - H bonds (in CO2H) by O - U bonds and from the new hydroxyl-uranium bond (note also that the complex has no net charge). A rough estimate of this contribution may be inferred from the corresponding A6 values observed on going from malic acid to the Zn complex, in aqueous solution (0.2 M, pH = 6), although the conformation of the ligand is different : these values are A 6 A = 0 . 2 2 , A6B = 0 - 2 0 and A6x = 0 . 0 5 . The major part of the A6 values for the uranyl case must then be ascribed to through-space electric field and magnetic anisotropy effects due to the UO2 groups. These effects have previously been invoked to explain chemical shifts for the uranyl-citrate systemI8]. A linear UO 2 group has no electric dipole moment but has an electric quadrupole moment. According to Fig. 3 the C H ~ bond lies almost in the equatorial plane of the UO2 groups and thus it does not experience an appreciable polarization. The same cannot be said of the CH~A~and CH~x~ bonds. These are nearly parallel to the UO 2 axis, in such a position that C - - H + polarization occurs, thus contributing to a highfrequency shift. The polarization is more pronounced for CH~x), because it is closer. The magnetic susceptibility tensor of a linear UO 2 group is markedly anisotropic. This, too, leads to a high-frequency shift of the various proton signals if, as Fig. 3 implies, the protons lie in the paramagnetic region of the field due to the electronic currents induced in UO 2 by the external magnetic field. Again, because of the smaller distance between H~xI and the U atoms, the effect is more pronounced for this proton. Protons A and B are expected to experience a similar effect, because although the distances H~A~-U are smaller, H~8~ lies closer to the plane of maximum paramagnetism, i.e. the equatorial plane of the UO2 groups. It thus becomes clear why A6x is much greater than A3A or A6B. On account of the difference between the electric field effects for protons A and B one would expect a positive internal chemical shift 6 A - 6B. The reason for the closeness of the 6 values observed (in fact 6 A - 6 B is negative) probably lies in the fact that, according to Fig. 3, the C-HCB) bond is polarized in the sense C - - H + by the CO groups near the equatorial plane and pointing outwards as C-H~nI. We now make an estimate of the order of magnitude of the electric field and magnetic anisotropy effects for H(A) and H~x). We assume for simplicity that the CH(A ) and CH~x) bonds are parallel to the axis O - U - O . The distances between the protons and the U nuclei, and the angles the H - U lines make with the O - U - O axes are roughly taken as follows : rA,u, = 3 A OA, 1 60 ° rA,v., = 3.5 A OA, 2 65 ° =
=
rx.u, = 2.5A rx,u~ = 3 A
Ox.l = 60 ° Ox.2 = 65 °.
For the electric field effect, we break down the quadru¢r pole moment of the U O / g r o u p s mto two equal dipole moments located midway between the U and O nuclei, calculate the field at the mid point in the C H bonds and use Buckingham's formula[16]. The results per Debye unit for such dipoles are : 6A ~ = 0"3 ppm per Debye unit 6~ = 0.6 ppm per Debye unit. The effect of the magnetic anisotropy of the UOz groups is calculated using McConnell's formula[l 7]. A minimum value for that anisotropy is - 80 × 10 -6 c.g.s. unit[8, 18]. The corresponding minimum shifts are then 6~"' = 0.9 ppm 6}' a = 1.5 ppm. The value 6~ "a' = 1.2 ppm helps to make 6B >/~A, in spite of 6~ ~ 0. These values then have the right order of magnitude to explain the observed A6 values accompanying complexation. The proton chemical shifts are thus in agreement with the structure presented for the dimeric complex. Finally, it is noted that geometric isomers of the complex are expected, all consistent with the geometry shown in Fig. 3. They are: the trans and cis d - m a l a t ~ - ( U O z h - d - m a l a t e complexes and the corresponding optical isomers, and the trans and cis d-malate-(UO/)z/-malate isomers. The coupling constants of the [our geometric isomers are not expected to differ; only the chemical shifts may vary slightly. An X proton, being closer to the other ligand molecule in distance and in the number of intervening bonds, is the most likely to show a different chemical shift. This is apparent in Fig. 2, which shows two X spectral patterns. Work with active malic acid is being carried out in order to decide which isomers give rise to which spectrum. A study similar to the present one is also being undertaken for other pH regions. Acknowledgements--This work is included in the Project of
Molecular Structure (CQ-2) of.the Instituto de Aha Cultura, Portugal. Thanks are due to Professor F. Pinto Coelho for his comments. REFERENCES
1. 1. Feldman and W. F. Neuman, J. Am. chem. Soc. 73, 2312 (1951). 2. I. Feldman and J. R. Havill, J. Am. chem. Soc. 76, 2114 (1954). 3. I. Feldman, J. R. Havill and W. F. Neuman, J. Am. chem. Soc. 76, 4726 (1954). 4. W. F. Neuman, J. R. Havill and I. Feldman, J. Am. chem. Soc. 73, 3593 (1951). 5. I. Feldman, C. A. North and H. B. Hunter, J. phys. Chem. 64, 1224 (1960).
Structure of the uranyl malate complex 6. K. S. Rajah and A. E. Mart.elL J. #7org. m~ct+ Chem. 26, 1927 (1964). 7. Y. Y, Kharitonov and Z. M. Alikhanova, Soriet Radioc'hem. 6, 680 (1964). 8. R. Bramley, W+ F. Reynolds and I. Feldman, J. Am. the,+. Sot'. 8"7, 3329 (1965). 9. L. E. Erickson. J. Am. chem. Soc. 87, 1867 I1965). 10. K. G. R. Pachler, Z. analvr. Chem. 224. 211 (1967). I I, J. S. Mariano and V M. S. Gil, MMec. Phrs. 1,7, 313 <1969).
1807
12. R. A. Alberty and P. Bender. J. Am. t'hem. Soc. 81. 542 (1959). 13. R J, Abraham and G, Gatti, J. chem. So~. (B) 961 (1969). 14+ K. G. R, Pachler, Tetrahedron 2'7, 187 I1971). 15. M. Karplus, J. chem. Ph.vs. 30, 11 (1959): J. Am. them Soc. 85. 2870:1963). 16. A. D. Buckingham, Can. J. Chem. 38, 300 (1960}. 17. H. M. McConnell, J. chem. Phys. 27. 226 (1957). 18. M. P. Sahakari and A. J. Mukhedkar. J. mo,.~. ,uc/. Chem. 33, 888 (19711.
N M R EVIDENCE ON THE S T R U C T U R E OF THE U R A N Y L - M A L A T E COMPLEX JUL10 D. PEDROSA and VICTOR M. S. G1L The Chemical Laboratory, University of Coimbra, Portugal (Received 18 May 1973)
Abstract--Comparison of the proton coupling constants and chemical shifts for malic acid and its 1: 1 dimeric complex with UO22÷at the same pH (around pH = 3) led to conclusions about the conformation of the ligand and the structure of the dimer. These results corroborate one[6] of the various hypotheses previously put forward for such a structure, the remaining ones being unambiguously ruled out. The existence of geometric isomers is also indicated.
INTRODUCTION THE URAr~I. ion is known to form polynuclear complexes with malic acid, the nature of which depends on the pH of the system. In the region of pH = 2-4 the dominating species is a 1:1 binuclear complex which is highly stable. These conclusions are based on spectrophotometric[1-3] polarographicE41 and potentiometric[3, 5, 6] studies. Several plausible structures have been proposed for this dimer[3, 5, 6], all of them assuming tridentate chelation involving the ionized carboxylic groups and the hydroxyl group of the malic acid. This is confirmed by i.r. spectroscopy[7]. However, different views have been held regarding the bridges between the uranium atoms. Thus, Feldman et al. E3,5, 8] favour the existence of two olation bridges as in II, whereas Rajan and Martell[6] suggest a structure I where the OH groups of the ligands act as bridges between the U atoms. In the first case, the carboxylate groups of each ligand molecule would both be bonded to the same uranyl ion; in the latter, one is bonded to one uranyl and the other to the second UO22+. The conformation of the ligand differs according to the hypothesis adopted. NMR spectroscopy has proved particularly suitable for the study of the conformation of malic acid both free[9-11] and as a ligand[ll], particularly in view of the dependence of the vicinal H-H coupling constants upon dihedral angles. In the literature there is only a brief reference to NMR spectra of the uranyl-malate system, reporting an enhanced broadening and highfrequency shift of the malate proton signals as the concentration of UO22+ is increased[8]. In this paper, we give the proton coupling constants and chemical shifts for malic acid and its 1 : 1 complex with UO22+ at the same pH (around pH = 3). A discussion of these gives indications of the conformation of the ligand in the complex and of the type of dimer present. These NMR results corroborate the second hypothesis, I,
mentioned above and clearly rule out the other. Additionally, the NMR spectra reveal the existence of geometric isomers of the dimer.
EXPERIMENTAL Commercially available pure uranyl nitrate hexahydrate and dl-malic acid were used without further purification. Aqueous 0.2 M solutions of malic acid and solutions 0-2 M in malic acid and 0.2 M in UO2÷ were adjusted to the same pH in the region 2--4by addition of NaOH. They were subsequently evaporated and the solids dissolved in D20 keeping the concentration at 0-2 M. The proton NMR spectra were run at room temperature on a Varian HA-100spectrometer; tert.-butanol was used as internal reference.
RESULTS Only spectral data corresponding to pH = 3 will be discussed; the conclusions are the same for other values in the region (pH = 2-4) investigated. The spectra are compared in Fig. 1. This clearly shows the remarkable effect of complexation with UO 2+ on the proton chemical shifts of malic acid. Figure 2 shows the expanded high-frequency signals. The two close quartets for the uranyl-malate solution reveal the presence of ligand molecules in slightly different conditions; the corresponding two low-frequency complex signals are not resolved. The proton coupling constants and the chemical shifts were obtained on the basis of an A B X analysis and are given in Table 1. Signal broadening limited the accuracy of the measurements. The spectral parameters for malic acid agree well with previous results [9-12].
1803
1804
JI~ILIO D. PEDROSAand VICTOR M. S. GIL
©
B,A
©
6 I
5 I
4 I
3 I
2 I
1 I
t-Bu [
Fig. I. 100 MHz proton NMR spectra of D20 solutions of malic acid(L) and malic acid + uranyl nitrate (ratio 1 : 1)(C) corresponding to pH = 3.3. Table 1. Proton coupling constants (Hz) and chemical shifts (in ppm) referred to t-butanol Malic acid 1:1 UO~+-malate
JAB JAx JBx 6A 6n 6x
(-)16.7 7.4 4.2 1-56 1-65 3-29
A detailed analysis of JAx and JBx in terms of dihedral angles and substituent effects has shown that forms (a) and (c) are the most important contributing ones [10, 11], the respective weights being about (a), 40 per
(-117-7 11.4 1.5 + 0.2 2.52 2.62 5.91 : 5.93*
to H z
* Values for the two X quartets (Fig. 2). DISCUSSION The observed vicinal H - H coupling constants for malic acid have been regarded as weighted averages of the corresponding values in the three staggered rotational isomers [9-11 ] :
CO2H
CO2H
COzH
J
J X(L)
CO2H (a)
OH
H (x)
( ~)
(c )
x(c)
Fig. 2. Expanded high-frequency signal (X part) of spectra (L) and (C) of Fig. 2.
1805
Structure of the uranyl-malate complex cent and (b), 50 per cent[ll]. Possibly an important factor is intramolecular hydrogen bonding involving OH and CO2H in a gauche situation. Complexation, particularly chelation, is expected to alter the relative weights of the three rotamers, hence JAx and JBx. Thus, the 1 : 1 complexes of malate with Zn(II)[1 1] have been found to have much closer values of Jax and JBX, suggesting that the preferred conformation in the presence of the metal ion becomes (c). A different trend is observed in the case of UO 2+ from that with Zn 2 +. The difference between Jax and Jnx becomes much more marked. This is a clear indication that (a) is the preferred form in the presence of UO 2+. Another difference with respect to the Zn complex is that a UO22+-malate complex is much more stable[6] ; in fact so stable that a slight excess of malic acid immediately gives rise to additional NMR signals corresponding to free malic acid molecules. This means that the observed spectral parameters for the l : l UO22+-malate system must be regarded as corresponding to a frozen conformation rather than taken as a weighted rotational average. We thus conclude that the conformation adopted by the ligand in the uranyl complex is identical or close to (a). This conclusion is only compatible with the dimer structure 1 postulated by Rajan and Martell[6], it being possible as far as the ligands are concerned for the uranyl ions to have their principal axes parallel to each other : 0
//
\ c j °..
/°Jc\ ,,U 02/ ..
/ CH2
".
/"
HC_____.__. O,"" H'-.
~x. H
/0" \
/
CH
,
c~O"
// 0
An approximate estimate of the vicinal coupling constants in form (a) gives Jax = 14.5 Hz and JBx = 1.8Hz[ll]. The values we observed are smaller, particularly Jax. This may be due in part to the bonding of OH to UO~ +, and the accompanying increase of the effective electronegativity of the oxygen atom of OH[13, 14]. However, this would not be expected to produce a change in Jax of the order of 3 Hz. Another contributing factor may be a twisting of structure (a) in the sense
CO2H H.. \ - ~OH IX) " ~ ~ H H/ I IA) (B) CO2H ~)
The HA-C-C-H x dihedral angle decreases and the HB~2-C-H x one increases which would then lead to a decrease both of Jax and Jsx[15]. The analysis of a molecular model indicates that such twisting is necessary so that the axes of the bonds between the ligands and the uranium atoms all become close to the equatorial plane of the uranyl ions, leading to a nearly octahedral arrangement around each U atom, without appreciable steric hindrance. Form (a) but not form (a') would imply a strong repulsion between the very close oxygen atoms of the hydroxyl and carboxylate groups gauche to each other. That arrangement leaves the two oxygen atoms (belonging to the carboxylate groups) not participating in the chelation, nearly in the equatorial plane of the ions UO~ + and pointing outwards, which obviously reduces repulsions (Fig. 3).
(I)
0
H(A)
The hypothesis II due to Feldman et al.[3, 5, 8] would require conformation (c) as in the case of the Zn complex : 0
H
_C~ O ~ I
H -'--"
H,; /
II
/O. /
",,
/C~cH2 ~\ / U02 - -
"-UO2
..0/-" ~c
..,uS. o
0
\
HE
0
"o'"
o
," " ' . . - ' - 0 "o
H .~-%CH
O~cxl
/ c
o (II)
0
Fig. 3. The most likely conformation of malic acid in the dimeric complex with UO22+.
JtJLIO D. PEDROSAand VICTORM. S. GIL
1806
The structure shown in Fig. 3 is also consistent with the proton chemical shifts. The shifts observed on comparing malic acid with the complex (Table 1), namely A6 a = 0-96, A6 B = 0.97, A6 x = 2.62, are too big to be explained by differences in the electron density of the H atoms resulting from replacement of the O - H bonds (in CO2H) by O - U bonds and from the new hydroxyl-uranium bond (note also that the complex has no net charge). A rough estimate of this contribution may be inferred from the corresponding A6 values observed on going from malic acid to the Zn complex, in aqueous solution (0.2 M, pH = 6), although the conformation of the ligand is different : these values are A 6 A = 0 . 2 2 , A6B = 0 - 2 0 and A6x = 0 . 0 5 . The major part of the A6 values for the uranyl case must then be ascribed to through-space electric field and magnetic anisotropy effects due to the UO2 groups. These effects have previously been invoked to explain chemical shifts for the uranyl-citrate systemI8]. A linear UO 2 group has no electric dipole moment but has an electric quadrupole moment. According to Fig. 3 the C H ~ bond lies almost in the equatorial plane of the UO2 groups and thus it does not experience an appreciable polarization. The same cannot be said of the CH~A~and CH~x~ bonds. These are nearly parallel to the UO 2 axis, in such a position that C - - H + polarization occurs, thus contributing to a highfrequency shift. The polarization is more pronounced for CH~x), because it is closer. The magnetic susceptibility tensor of a linear UO 2 group is markedly anisotropic. This, too, leads to a high-frequency shift of the various proton signals if, as Fig. 3 implies, the protons lie in the paramagnetic region of the field due to the electronic currents induced in UO 2 by the external magnetic field. Again, because of the smaller distance between H~xI and the U atoms, the effect is more pronounced for this proton. Protons A and B are expected to experience a similar effect, because although the distances H~A~-U are smaller, H~8~ lies closer to the plane of maximum paramagnetism, i.e. the equatorial plane of the UO2 groups. It thus becomes clear why A6x is much greater than A3A or A6B. On account of the difference between the electric field effects for protons A and B one would expect a positive internal chemical shift 6 A - 6B. The reason for the closeness of the 6 values observed (in fact 6 A - 6 B is negative) probably lies in the fact that, according to Fig. 3, the C-HCB) bond is polarized in the sense C - - H + by the CO groups near the equatorial plane and pointing outwards as C-H~nI. We now make an estimate of the order of magnitude of the electric field and magnetic anisotropy effects for H(A) and H~x). We assume for simplicity that the CH(A ) and CH~x) bonds are parallel to the axis O - U - O . The distances between the protons and the U nuclei, and the angles the H - U lines make with the O - U - O axes are roughly taken as follows : rA,u, = 3 A OA, 1 60 ° rA,v., = 3.5 A OA, 2 65 ° =
=
rx.u, = 2.5A rx,u~ = 3 A
Ox.l = 60 ° Ox.2 = 65 °.
For the electric field effect, we break down the quadru¢r pole moment of the U O / g r o u p s mto two equal dipole moments located midway between the U and O nuclei, calculate the field at the mid point in the C H bonds and use Buckingham's formula[16]. The results per Debye unit for such dipoles are : 6A ~ = 0"3 ppm per Debye unit 6~ = 0.6 ppm per Debye unit. The effect of the magnetic anisotropy of the UOz groups is calculated using McConnell's formula[l 7]. A minimum value for that anisotropy is - 80 × 10 -6 c.g.s. unit[8, 18]. The corresponding minimum shifts are then 6~"' = 0.9 ppm 6}' a = 1.5 ppm. The value 6~ "a' = 1.2 ppm helps to make 6B >/~A, in spite of 6~ ~ 0. These values then have the right order of magnitude to explain the observed A6 values accompanying complexation. The proton chemical shifts are thus in agreement with the structure presented for the dimeric complex. Finally, it is noted that geometric isomers of the complex are expected, all consistent with the geometry shown in Fig. 3. They are: the trans and cis d - m a l a t ~ - ( U O z h - d - m a l a t e complexes and the corresponding optical isomers, and the trans and cis d-malate-(UO/)z/-malate isomers. The coupling constants of the [our geometric isomers are not expected to differ; only the chemical shifts may vary slightly. An X proton, being closer to the other ligand molecule in distance and in the number of intervening bonds, is the most likely to show a different chemical shift. This is apparent in Fig. 2, which shows two X spectral patterns. Work with active malic acid is being carried out in order to decide which isomers give rise to which spectrum. A study similar to the present one is also being undertaken for other pH regions. Acknowledgements--This work is included in the Project of
Molecular Structure (CQ-2) of.the Instituto de Aha Cultura, Portugal. Thanks are due to Professor F. Pinto Coelho for his comments. REFERENCES
1. 1. Feldman and W. F. Neuman, J. Am. chem. Soc. 73, 2312 (1951). 2. I. Feldman and J. R. Havill, J. Am. chem. Soc. 76, 2114 (1954). 3. I. Feldman, J. R. Havill and W. F. Neuman, J. Am. chem. Soc. 76, 4726 (1954). 4. W. F. Neuman, J. R. Havill and I. Feldman, J. Am. chem. Soc. 73, 3593 (1951). 5. I. Feldman, C. A. North and H. B. Hunter, J. phys. Chem. 64, 1224 (1960).
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