Research: Science and Education
Understanding Chemical Shifts in Systems: 13C, 15N, 17O NMR H. Dahn Institut de Chimie Organique, University of Lausanne, BCH, CH-1015 Lausanne, Switzerland;
[email protected] Because NMR chemical shifts depend upon the structure of the compound investigated, chemists currently use shift values δ as the starting point to discuss their NMR spectra. In most cases, however, these data are not physically interpreted; or, if they are, it is just by trying to apply the rule “the higher the electron density around an atom, the more it is shielded” (the lower is its shift value). This rule has been particularly valuable in 1H NMR and for restricted classes of compounds, and it is founded on a theoretical basis. But quite often it turns out to be entirely inadequate, for example, for nuclei other than 1H, and particularly with π systems. To start with an example: one might expect that the ipso carbon of phenyllithium (PhLi), which is richer in electrons than an ordinary aromatic H-bearing carbon in PhH, should resonate at higher field, that is, be more shielded. However, the contrary is true: the shift value δ(13Carom–Li) = 185.7 ppm (1) shows 56 ppm weaker shielding than δ(13Carom–H) = 129.7 ppm (2). One is tempted to attribute this to the presence of the electric charge; but this cannot be correct, for in saturated alkyllithium compounds RLi the deshielding effect is absent. In n-butyllithium one finds δ(13CH2–Li) = 11.8 ppm, similar to the RH value in the same compound (and even slightly more shielded): δ(13CH2–H) = 13.9 ppm (3). So the deshielding in PhLi must be due to the presence of π electrons. Another example is the observation that the shift value of carbon, which increases in going from ethane CH3–CH3 (δ(13C) = 6.5 ppm) to ethene CH2=CH2 (δ(13C) = 123.5 ppm), decreases from the latter to ethyne CH≡CH (δ(13C) = 71.9 ppm) (3). The explanation of these and many analogous observations has long since been elaborated by theoreticians (3, 4 ), but is often ignored by organic chemists; it is the purpose of this article to present it, however, without entering into the fine points of the theory. Chemical Shift and Shielding If one brings a naked atomic nucleus, say 13C6+, into a magnetic field of given strength, it will show resonance at a specific electromagnetic frequency—the NMR phenomenon. If one repeats the (virtual) experiment with an isolated 13C atom in its electron envelope (not taking into account that some of the electrons are unpaired), the electrons will cause “diamagnetic” shielding σ d and resonance will occur at lower frequency (higher field). If, in a third experiment, the 13C atom is bound in a molecule, the neighboring atoms and their electrons will, in general, diminish the shielding; this is expressed as σ p, normally a deshielding term (i.e., having a negative value; σ p is called “paramagnetic”, although the term has nothing to do with the paramagnetism of molecules with unpaired electrons): σ total = σ d + σ p
For carbon the resonance of the naked nucleus 13C6+ is evaluated at δ(13C) = 185.4 ppm on the conventional TMS shift
scale (4 ); it is thus in the region of the carbonyl carbon. The isolated 13C atom with its 6 electrons (ignoring unpairing) would yield δ(13C) = ᎑76 ppm. The 6 electrons thus would cause a shielding of 261 ppm. Finally, in methane, the isotropic resonance is found at δ (13 C) = ᎑2.3 ppm (3), strongly deshielded compared with the isolated C atom. For oxygen the corresponding figures are δ (17O)(O8+) = 307.9 ppm for the naked nucleus, δ (17O)(Oatom) = ᎑87 ppm for the isolated atom, and δ (17O)(H2O) = 0.0 for water; the last is the standard of the conventional 17O shift scale (4 ). The shielding σ (X) is measured on absolute scales, the resonance of the naked nucleus being equal to zero and higher shielding being positive. These are the scales used in theoretical treatments and in calculations. Chemists are more familiar with the conventional shift scales δ (X). The conversion of the two scale types, for the examples treated here, uses the equations (4) δ (13C) = 185.4 – σ (13C)
(TMS scale)
δ ( N) = ᎑135.8 – σ ( N)
(MeNO2 scale)
δ ( O) = 307.9 – σ ( O)
(H2O scale)
15 17
15
17
Anisotropy To discuss the relationship between chemical bonds and NMR shift values, one has first to remember that neither is an isotropic property. Because the shielding of an atom is due to the electrons, and the distribution of electrons is not spherical around an atom bound in a molecule, it is clear that the shielding (σ) and the chemical shift (δ) measured must depend upon the orientation of the molecule in the magnetic field: they must be anisotropic. The spatial distribution of the shift values in the Cartesian axis directions x, y, z is (approximately) represented by the tensor components δ xx, δ yy , and δ zz (the customary xx-symbolism stems from the matrix treatment). The usual isotropic shift value, as measured in solution or in the gas phase, is the average of these 3 tensor components: δ isotr = (δ xx + δ yy + δ zz)/3. The spatial distribution of the shift values can be determined experimentally (3, 4), for instance by NMR measurements of solids or of solutions in liquid crystal phases. Calculations ab initio (e.g., using the IGLO, LORG or GIAO program) directly furnish the tensor components in a chosen molecular axis system. In general one finds good agreement between calculation and experiment (5), depending of course on the quality of the basis set used. It turns out that shielding and shift can present very important anisotropy. For instance, in the 13C spectrum of ethene, the shift value measured perpendicular to the molecular plane (direction x, parallel to the π orbitals, Fig. 1), shows the shift tensor component δ xx(13C) = 24 ppm, a value that is not far from the value of an alkane carbon. In contrast, the direction y in the molecular plane and perpendicular to the axis is more than 200 ppm deshielded: δyy(13C) = 234 ppm (2). In π systems in general the anisotropy is particularly
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Research: Science and Education
13C
x H C
y H
24 ppm
z
x
H C H
z y
120 ppm
234 ppm
Figure 1. Molecular axis system x,y,z and 13C shift tensor components δ xx , δ yy, δ zz of ethene (δ(TMS) = 0; deshielding positive).
strong. Thus one loses valuable information when using the customary shift value of a compound measured in solution, δisotr , instead of its 3 tensor components. The explanation of the spatial distribution of the shielding values is the central part of the quantum chemical treatment of shielding and chemical shifts. The Theory of Shielding The division of the total shielding of an atom into a diamagnetic (shielding) part and a paramagnetic (in general, deshielding) part applies to atoms in a molecule, too, including their tensor components. Here, the diamagnetic part σ d of the shielding in general depends only slightly upon the molecular structure. The characteristic shift differences for an atom in different environments are caused primarily by differences in the paramagnetic part σ p (4). This deshielding part σ p is described by a quantum mechanical equation given by Ramsey in 1950 (4). Because an exact solution is not accessible, one has to use approximations; this can be accomplished by the ab initio calculations mentioned above. An older simplification proposed by Karplus and Pople in 1963 (eq 1) is still useful for the qualitative discussion of NMR shift data, including the interpretation of the results of ab initio calculations (3, 4): σ p(X) = ᎑K × ∆E ᎑1 × r ᎑3 × ΣQ
(1)
Here K is a constant; ∆E is the energy difference between two molecular orbitals (originally it had the meaning of an average excitation energy of the molecule, see below); r measures the orbital radius of the 2p electrons of the atom (it varies from one atomic species to another, but is only slightly sensitive to differences in the molecular structure [3, 4 ]); ΣQ contains, among other things, the bond order and electron density familiar to the chemist. We will discuss primarily the influence of ∆E ᎑1, the energy difference between any occupied and any unoccupied orbital. This term is often ignored, although it plays a decisive role in deshielding in particular in π systems; we will neglect the r ᎑3 and ΣQ factors. When a molecule is brought into a magnetic field, its molecular orbitals are modified owing to the field-induced circulation of the electrons. The perturbation is expressed by mixing unoccupied orbitals into each occupied molecular orbital. As in other cases of mixing of orbitals (e.g., hybridization), the degree of mixing, and thus its effect, increases with decreasing energy difference between the orbitals. So does the deshielding, hence ᎑ σ p ∼ ∆E ᎑1. In principle each mixing-in to each orbital has to be taken into account, but frequently the HOMO–LUMO combination is the most effective one. However, combinations involving more stable occupied or more energy-rich unoccupied orbitals can play a significant 906
role, too. All deshielding effects in the same spatial direction are then added up. When considering the orbital-mixing operations for chemical shifts, one has to respect a selection rule: A combination of an occupied and an unoccupied orbital is magnetically active only when the corresponding (hypothetical) electron transfer comprises an angular momentum. This condition of “charge circulation” has to do with the well-known fundamental principle of electromagnetism, that a circulating electric charge creates a magnetic moment. The latter is directed perpendicular to the plane of charge circulation. Thus a spherical orbital, like 1s or 2s, cannot yield magnetically active orbital mixing. For the same reason a π–π* orbital combination, which corresponds to the HOMO–LUMO transition for alkenes, is magnetically inactive because both orbitals point in the same direction. However the σCH–π* and the π–σCH* combinations of alkenes are active in the NMR, yielding deshielding contributions perpendicular to the σ–π plane of charge circulation. The term ᎑ σ p ∼ ∆E ᎑1 provides the theoretical basis of the empirically well-known correlation of chemical shift values with UV–vis absorption wavelengths, for instance in carbonyl compounds. It concerns the long-wave, UV-“forbidden” transitions; because they are magnetically active, the corresponding peaks in the circular dichroism (CD) spectra would be even more appropriate for the correlation than the (often not well defined) “forbidden” UV maxima (6 ). The transitions corresponding to the σCH–π* and the π–σCH* combinations in alkenes mentioned above have been identified in the UV and CD spectra (7). The π systems possess low-lying unoccupied π* orbitals that allow efficient combinations with appropriate energy-rich occupied orbitals. These usually offer the most important deshielding contributions, although occasionally combinations of the occupied π orbital with an unoccupied orbital (other than π*) also contribute. On the other hand, when both π and
Table 1. Experimental Tensor Component Values of the 13 C Chemical Shifts of Benzene and the ipso-C of Phenyllithium Tensor Component δy y δz z
δi s o t r
Molecule
δx x
Ph–H (2)
9
146
234
130
᎑18 (᎑25)
327 (330)
248 (252)
186 (186)
᎑
Ph –Li
+
NOTE: All values are given in ppm. IGLO-calculated values are in parentheses; δ(TMS) = 0; deshielding positive.
13
13
CH
9 ppm
x
x z y
π*
y
x
+
z
Li
234 ppm H C
C
146 ppm
+
C Li
-18 ppm
z
n
y
248 ppm
327 ppm
Figure 2. Molecular axis systems and 13C shift tensor components δxx, δyy, δzz of Carom–H (as in benzene) and of the ipso C-atom of phenyllithium (δ(TMS) = 0; deshielding positive). In PhLi the combination of the occupied n orbital (HOMO) with the unoccupied π* orbital (LUMO) implies a “charge circulation” in the z,x plane, creating a magnetic vector in the y direction.
Journal of Chemical Education • Vol. 77 No. 7 July 2000 • JChemEd.chem.wisc.edu
Research: Science and Education π* are absent, as for instance in alkanes, the ∆E
᎑1
term loses importance and therefore the deshielding part σ p and the δ(13C) values are particularly small. The same is true for all 1 H shift values, when compared with the shift values of higher elements; this is the reason why here, discussions of electron densities alone are applicable.
Phenyllithium The anisotropy of the deshielding of the ipso carbon of PhLi compared with PhH is very characteristic. It was found (1) that the difference ∆ in the isotropic shift values (∆δisotr = +56 ppm) is due almost exclusively to the difference in δyy, the shift component in the molecular plane perpendicular to the C–Li direction (∆δyy = +181 ppm; Fig. 2). It is surprising to see that the component in the C–Li direction contributes only very slightly (∆δzz = +14 ppm), and that in the direction of the π-orbitals acts even in the opposite sense (∆δxx = ᎑27 ppm) (Table 1). To explain in quantum chemical terms that the σyy component of the deshielding of the ipso carbon of phenyllithium is prevalent, the high-lying n orbital of C ᎑Li+ (or Cδ ᎑ Liδ+) is essential. It has to be compared with the much more stable σCH orbital of PhH (1); both are oriented in the z direction (Fig. 2). Each combines with the lowest unoccupied orbital, π*, in the x direction, to give the combinations nCLi –π* and σCH–π*, respectively. Both combinations yield magnetic moments in the direction perpendicular to the z,x plane, that is, the deshielding paramagnetic tensor component σ pyy . Because of the great energy difference between the orbitals nCLi and σCH the two combinations are expected to contribute to a very different extent to the shift. They act strongly deshielding in the case of the high-lying n orbital of PhLi, but only very slightly deshielding in the case of the more distant σCH orbital of PhH, both of course in the y direction. This agrees with the experimental δ(13C) values cited above (1). Carbenes The carbene carbon in (angular) singlet carbenes is strongly deshielded compared with the sp3 carbon of methane (8). The explanation is the same as that for phenyllithium: the deshielding action of the n–π* orbital mixing. This is a case of strong deshielding where electrical charge is absent. Conclusion In a general way one can say that the ab initio calculations furnish the (deshielding) NMR effects ᎑ σpii in the direction i of the chosen Cartesian coordinates, separately for each (nonspherical) occupied orbital. The individual contributions then have to be summed. If the calculating program does not indicate directly the unoccupied orbitals that are mixed in (as for instance in IGLO), they are not difficult to find. Since the directions of the occupied orbital and of the resulting magnetic moment are known, the third direction is automatically given. All one has to do is to select its identity among the lowest-lying unoccupied orbitals of that direction, which in most cases is easy to guess: very often it is π*. In π systems, orbital combinations that use either the π or the π* orbital will be among the most deshielding, as both are close to the HOMO–LUMO border (or part of it). Combinations in which neither π nor π* is present will be less effective, as ∆E is larger; by necessity the small deshielding magnetic
moments that result will lie in the direction of the π orbital (direction x in Figs. 1, 2). It is significant that in all planar π systems (alkenes, carbonyl, aromatic and heteroaromatic compounds, with the main exception of linear systems, for which see below) this direction perpendicular to the molecular plane is the one that is the least deshielded (highest shielded). Carbonyl Groups The same principles as used above can yield the shift characteristics of carbonyl groups, particularly of the oxygen atom, including its difference from carbonyl carbon. The influence of donor and acceptor groups X in carbonyl derivatives –CO–X (9) is equally explained. Table 2 gives the 3 calculated shift tensor components on the oxygen atom of formaldehyde. The component δzz(17O), oriented in the direction of the C–O bond (Fig. 3), is the most deshielded, whereas δxx(17O), in the direction of the π orbital, contributes least to the total deshielding. One would expect that the HOMO–LUMO combination n–π* furnishes the largest deshielding contribution to σ and is thus the most important for the shift value δ. How is it localized? The two n orbitals of the carbonyl O lie in the molecular plane; they are frequently presented symmetrically in directions oblique to the C–O axis. An alternative description, often used by quantum chemists (10), differentiates them into two orbitals in the y and z directions (ny, nz). The nz orbital is stabilized by hybridization with the σcc orbital lying in the same direction; thus ny is the higher in energy, HOMO (10). As a consequence, the orbital combination ny– π *, involving LUMO, is the magnetically strongest one. It lies in the y,x plane and creates a deshielding paramagnetic component σ pzz in the z direction (and thus increases the shift value δzz). Experimental measurements with benzophenone have confirmed that z is the most deshielded direction at the carbonyl O atom (11). Calculations show that other orbital combinations contribute less than 10% of the total paramagnetic deshielding
Table 2. IGLO-Calculated 17O Shift Tensor Components for CH2O and HCONH2 Molecule
Tensor Component δxx δyy δzz
δisotr
δexptl
CH2O
᎑102
840
1475
737
648
HCONH2
᎑ 44
551
620
376
310
NOTE: Values in ppm, from ref 9 using δ = 308 – σ; δ(H2O) = 0; deshielding positive.
13C
x
62 ppm x z y
H C
y 184 ppm
17O
-102 ppm
z
x z
O
H
y
282 ppm
1475 ppm
840 ppm 13
Figure 3. Molecular axis systems and C and 17O shift tensor components δxx, δyy, δzz of formaldehyde (δ(TMS) resp. δ(H2O) = 0; deshielding positive). On oxygen, the y-directed component of the n orbitals is the HOMO (see text), the x-directed π* is the LUMO. The “charge circulation” in the y,x plane creates a magnetic vector in the z-direction. On carbon, the n orbitals, and hence this important deshielding effect, are absent.
JChemEd.chem.wisc.edu • Vol. 77 No. 7 July 2000 • Journal of Chemical Education
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Research: Science and Education
Molecule
Tensor Component
Orbital Mixing
σ p ii(1 7 O)
CH2O
62
282
184
176
197
σ pxx total σ p x x
divers — σC O –π* π–σC O * nz –π* —
0 to +16 +31 ᎑515 ᎑170 ᎑208 ᎑924.a
HCONH2
66
254
129
149
168
ny –π* σC H –π* —
᎑1379 ᎑107 ᎑1568.a
σ pyy total σ p y y σ
p zz
total σ p z z σ p is o tr
—
᎑820.b
N OTE : Values in ppm; absolute scale, σ (O8+) = 0; deshielding negative (9 ). aIncluding minor contributions. bσ p p p p isotr = (σ xx + σ yy + σ zz)/3.
in the z direction of formaldehyde-17O (Table 3). The equally deshielding tensor component σ pyy of the formaldehyde oxygen is contributed essentially by the σ CO–π * and nz–π * combinations, both lying in the z,x plane and acting magnetically in the y direction. Because they do not include the HOMO orbital, they are magnetically less effective than n–π*. In Table 3 the most important deshielding contributions for 17O are listed (indicated not as shift values δ but, for reasons of additivity, as shielding values σ on the absolute scale) (9). In carbonyl compounds R–CO–X the group X, an electron donor or acceptor, influences the reactivity of the carbonyl carbon in nucleophilic additions and also, by the chemical resonance –C(=O)X ↔ –C(–O᎑)=X+, the polarity of the CO group and the charge density on oxygen. X also determines the energy levels of the n and π* orbitals and thus the HOMO–LUMO energy difference. This is demonstrated by the fact that with increasing donor power of X the n–π* absorption in the UV is shifted toward shorter wave lengths (12). Therefore the deshielding component on oxygen formed by ny–π* mixing, that is, σ pzz pointing in the z direction of oxygen (and consequently δzz), is the one most strongly touched by changes of X. This is illustrated by a comparison of 17O shift data of formamide with formaldehyde in Table 2 (9). As σ pzz, the most important deshielding tensor component, decreases with increasing electron donation by X and with increasing polarity of the carbonyl group, the total isotropic shift δisotr(17O) of the carbonyl oxygen of R–CO–X decreases in the series X = H ≈ R > Cl > F ≈ OR ≈ NR2 > O, from δisotr(17O) ca. 550 ppm for –CHO and –COMe to ca. 220 ppm for –COO᎑. The shift value δisotr(17O) can be used as a measure of the polarity of the carbonyl group, in the absence of other scales for this important variable (13). The shift value of the carbonyl carbon atom δ(13C) contrasts with that of oxygen in that it does not reflect the degree of polarization of the CO group and its electrophilicity as a function of the substituent X. The reason is that the most important ny–π* combination is absent for δ(13C), simply because the n orbitals are localized on O and not on C. It has been demonstrated (Table 4) that the most deshielded shift tensor component for δ(13C) is no longer δzz but δyy, for form908
Table 4. IGLO-Calculated 13C Shift Tensor Components for CH2O and HCONH2
Table 3. Most Significant IGLOCalculated Orbital Contributions p ii (1 7 O) to the Paramagnetic Part of the Shielding of the O Atom in CH2 O
δxx
Tensor Component δyy δzz
δisotr
δexptl
NOTE: Values in ppm, from ref 9 using δ = 185 – σ ; δ (TMS) = 0; deshielding positive.
aldehyde as for formamide. As calculations have shown (9), this deshielding is determined essentially by the σCO–π* combination acting in the y direction. For the z direction of δ(13C), only the less effective σCH–π* and σCX–π* combinations are available. The same considerations can be applied to explain why in benzoyl compounds YC6H4–COX the effect of substituents Y on 17O is normal—that is, corresponds to the substituents’ donor–acceptor properties—whereas that on the carbonyl 13C is different (“reverse”) (9). Linear Systems: Alkynes As mentioned above, ethyne HC≡CH (δ(13C) = 72 ppm) is more shielded than ethene (δ(13C) = 123 ppm). This is found despite the abundance of π electrons, which in the case of ethene are responsible for its deshielding relative to ethane (δ(13C) = 6 ppm). Increase of shielding has been found for other linear π systems too, for δ(13C) (14) as for δ(15N) (15) as for δ(17O) (16 ). For instance dinitrogen (N2, δ(15N) = ᎑75 ppm) is more shielded than the diimine PhN=NPh (δ(15N) = 125 ppm). A particularly striking example is the increase of shielding of O as well as of N when comparing the linear cation NO2+ (δ(15N) = ᎑128 ppm; δ(17O) = 205 ppm) with the angular anion NO2᎑ (δ(15N) = 232 ppm; δ(17O) = 650 ppm) (15). In Table 5 the shift differences ∆δ(X) = δ(Xlin) – δ(Xnonlin) are given as further examples. It is evident that the phenomenon of increase of shielding in linear molecules is not restricted to diatomic compounds or to sp hybridization, nor does it depend upon the state of charge. It is valid simultaneously for all atoms of a linear system, with the exception of pseudo linear systems like ketene or allene. Occasionally chemists have tried to explain the higher shielding of one atom of a linear system with increased electron density by attributing a preferential weight to one of the resonance formulas, for example in ᎑N=C=O ↔ N≡C–O᎑. This argument, however, ignores the observation that all atoms of the NCO ion are found shielded with respect to a nonlinear comparison (16 ). As Table 5 shows, the average shielding effect of linearity, ∆δ(X), increases in the series 13C < 15N < 17O, although with greater variability of ∆δ(15N). This order repeats that of the shift effects in general, which in turn are influenced by the r ᎑3 factor of eq 1. The individual value of ∆δ(X) depends, of course, upon the nonlinear comparison chosen, which to a certain degree is arbitrary; those of Table 5 were selected so that the number of electronegative ligands did not change, (i.e., by using only H or Me or Ph). Already in 1957, Pople had given the theoretical explanation for the apparently anomalous increase of shielding of ethyne (17 ). In rod-shaped molecules the deshielding part in the direction of the molecular axis, σ p||, is zero, leaving in
Journal of Chemical Education • Vol. 77 No. 7 July 2000 • JChemEd.chem.wisc.edu
Research: Science and Education Table 5. 1 3 C, 1 5 N, and 1 7 O Shift Differences between Some Linear Molecules and Nonlinear Analogues ∆δ(1 3 C) ∆δ(1 5 N) ∆δ(1 7 O) Linear Nonlinear HC⬅CH
CH2 =CH2
᎑51
—
— —
N⬅N
PhN=NPh
—
᎑204
MeC⬅N
Me2 C=NMe
᎑50
᎑63
—
C=O ↔ ᎑ C⬅O + Me2 C=O
᎑22
—
᎑218
MeC⬅O]+
Me2 C=O
᎑57
—
᎑272
O=C=O
MeC(=O)OMe
᎑47
—
᎑297
NO2 ] MeNO2
— —
᎑360 ᎑131
᎑445 ᎑385
Me2 N–C(=O)Me
᎑30
᎑22
᎑306
O=N=O]
+
N=C=O] ᎑
᎑
NOTE: Shift difference: ∆δ(X) = δ(Xlin) – δ(X nonlin); experimental values, in ppm; δ(TMS) resp. δ(MeNO2) resp. δ(H2 O) = 0; deshielding positive.
this direction only the diamagnetic shielding σ d||. This yields a diminished shift value δ||. On the other hand the deshielding in the directions perpendicular to the axis, and consequently δ⊥, stay valid. Measurements of the shift values have confirmed that for ethyne δ|| is strongly shielded (δ|| = ᎑90 ppm), whereas δ⊥ is about normal (δ⊥ = +150 ppm) (2, 11). As one of the deshielding components disappears, the isotropic (average) shielding of the molecule increases. The reason why σ p|| becomes zero lies in the orbital symmetry of rod-shaped molecules (symmetry C∞v): A magnetic vector in the direction of the molecular axis would have to originate from an orbital mixing in the plane perpendicular to it; this is the plane of the π and π* orbitals. Because the two π orbitals (and the two π*) are degenerate, a transition is not accompanied by charge circulation and a π–π* mixing cannot generate a deshielding magnetic moment in the direction of the axis. On the other hand, orbital mixings that generate deshielding tensor components perpendicular to the axis, for instance σCC–π* and σCH–π*, remain magnetically active. Since in linear π systems the shielding in the direction of the axis is determined essentially by the remaining diamagnetic part σ d|| and the diamagnetic shielding term in general shows little sensitivity to variations of structure (in contrast to the paramagnetic term), the σ ||(X) values of linear molecules approach the theoretical σ value of the (purely diamagnetic) shielding of the isolated atom: σ ||(X) ≈ σ (atom). This has in fact been found—for instance (expressed in shift values) for ethyne: δ || = ᎑90 ppm (14 ), compared with δ (Catom) = ᎑76 ppm (4). Conclusion The NMR spectra of π systems show strong (de)shielding effects, particularly with atoms other than 1H. This is mainly
because, in the presence of a magnetic field, the low-lying unoccupied π* orbital allows combinations with energy-rich occupied orbitals of appropriate spatial orientation. The underlying principles can be understood using simple qualitative MO discussions; these follow, in a general way, the same reasoning as the very successful ab initio calculations. Literature Cited 1. Berger, S.; Fleischer, U.; Geletneky, C.; Lohrenz, J. Chem. Ber. 1995, 128, 1183. 2. Duncan, T. M. A Compilation of Chemical Shift Anisotropies; Farragut Press: Chicago, 1990. Zilm, K. W.; Coulin, R. T.; Grant, T. M.; Michl, J. J. Am. Chem. Soc. 1980, 102, 6672. 3. Kalinowski, H. O.; Berger, S.; Braun, S. Carbon-13 NMR Spectroscopy; Wiley: Chichester, 1988. 4. Jameson, C. J.; Mason, J. In Multinuclear NMR; Mason, J., Ed; Plenum: New York, 1987; p 51. Grüttner, J. B. In Recent Advances in Organic NMR Spectroscopy; Lambert, J. B.; Rittner, R., Eds.; Norell: Landisville NJ, 1987. Harris, R. K. Nuclear Magnetic Resonance Spectroscopy; Pitman: London, 1983. Gerothanassis, I. P.; Kalodimos, C. G. J. Chem. Educ. 1996, 73, 801. 5. Kutzelnigg, W.; Fleischer, U.; Schindler, M. In NMR Basic Principles and Progress; Diehl, P.; Fluck, E.; Günther, H.; Kosfeld, R., Eds.; Springer: Berlin, 1990; Vol. 23, p 165. 6. Dahn, H.; Péchy, P.; Flögel, R. Helv. Chim. Acta. 1994, 77, 306. 7. Merer, A. J.; Mulliken, R. S. Chem. Rev. 1969, 69, 639. Gross, K. P.; Schnepp, O. Chem. Phys. Lett. 1975, 36, 531. 8. Arduengo, H. J.; Dixon, D. A.; Kumashiro, K. K.; Lee, C.; Power, W. P.; Zilm, K. W. J. Am. Chem. Soc. 1994, 116, 6361. Herrmann, W. A.; Köcher, C. Angew. Chem., Int. Ed. Engl. 1997, 35, 577. 9. Dahn, H.; Carrupt, P.-A. Magn. Reson. Chem. 1997, 35, 577. 10. Jorgensen, W. L.; Salem, L. The Organic Chemist’s Book of Orbitals; Academic: New York, 1973. 11. Scheubel, W.; Zimmermann, H.; Haeberlen, U. J. Magn. Reson. 1985, 63, 544. 12. Yates, K.; Klemenko, S. L.; Csizmadia, I. G. Spectrochim. Acta, Part A 1969, 25, 765. 13. Dahn, H.; Péchy, P.; Toan, V. V. Angew. Chem., Int. Ed. Engl. 1990, 29, 647; Magn. Reson. Chem. 1997, 35, 589. 14. Beeler, A.; Orendt, A.; Grant, D.; Cutts, P.; Michl, J.; Zilm, K.; Downing, J.; Facelli, J.; Schindler, M.; Kutzelnigg, W. J. Am. Chem. Soc. 1984, 106, 7672. 15. Mason, J. In Nuclear Magnetic Shielding and Molecular Structure; Tossell, J. A., Ed.; Kluwer: Dordrecht, 1993; p 449. 16. Dahn, H.; Péchy, P.; Carrupt, P.-A. Magn. Reson. Chem. 1996, 34, 283. 17. Pople, A. J. Proc. R. Soc. London, Ser. A 1957, 239, 541, 550.
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