# Does diamagnetic anisotropy only apply to a proton bonded to triple bonded carbon?

Lecture tells me that double bond, with the sp^2 bonding will have more s-character, which will hold the electons closer to nucleus, which means a more deshielded proton which means downfield chem shift. But it doesnt follow the same idea with triple bond, with sp bonded carbon, and this is where diamagnetic anisotropy becomes a factor.... But is D.A. a factor with double bond also and why? Thats what I dont understand, because both double and triple will have pi bonds.. thanks for any help

• Diamagnetic anisotropy depends on having some sort of ring of double or triple bonds which can setup a current moving through the molecule. The moving charges generate an additional magnetic field. – MaxW Mar 20 '16 at 0:36
• thanks for answer maxW. I understand that the moving charges generates additional field, but why do we assume the additional field will add to external field? If we change the orientation of the ring then wouldnt it oppose the external field? Or if the direction that the pi electrons circulate is reversed, would that also change the additional field? – trav95 Mar 20 '16 at 1:00
• sigma value (ppm) for triple bonded acetelyne is about 2 - 2.5ppm, yet sigma for double bond is about 4.5-6.5 .. yet dont both double bonded and triple bonded molecules have circulating pi electrons? if so, then why would H attached to sp Carbon be more shielded than an H attached to a sp2 carbon? thanks for any more help – trav95 Mar 20 '16 at 1:08
• I understand now that its the external field that causes the pi electrns to circulate, so this is just right hand rule if it opposes the field. But I still dont understand why H attached to sp triple bonded carbon will have a lower sigma value than H attached to sp2 double bonded carbon? – trav95 Mar 20 '16 at 1:32
• You're going to want to make different questions or include those questions in your original post somehow. – SendersReagent Mar 20 '16 at 1:49

In principle, diamagnetic anisotropy can be invoked for any bond or any functional group; however, there's only a few situations where it's commonly used to understand patterns of shielding/deshielding. A decent discussion of this can be found in Silverstein's textbook (Spectrometric Identification of Organic Compounds), but I seem to recall that a couple of his figures are drawn in a confusing manner...

In short, this picture relies on the fact that pairs of electrons are diamagnetic, i.e., when immersed in a magnetic field, they get magnetized against the direction of the magnetic field:

$M=\chi B_0$

(M is the induced magnetization, B0 is the applied magnetic field, and $\chi$ is the magnetic susc., which is negative for diamagnetic objects). Thus, any electron density in a stable molecule (ignoring radicals) will become magnetized against the magnetic field (this is why we speak in terms of shielding).

We can picture molecular orbitals or valence bond orbitals of interest to us simply as a cloud of electron density that becomes magnetized in a magnetic field. Anisotropy means that effect depends on an angle: we're familiar with the picture of a magnetic dipole having magnetic field lines that curve around from the N end back to the S end – so something below or above the electron cloud will be in the (so called) shielding cone whereas things off to the side will be in the deshielding plane. Note, this is true for anything that is diamagnetic - there's no need for mystical ring currents or anything like that; any electron cloud placed in a magnetic field will be magnetized and, because it's diamagnetic, will reduce the local magnetic field above and below the electron cloud, but increase it off to the sides.

However, the molecules are tumbling rapidly in solution, so most of this effect simply averages away to zero... We need special situations where a proton of interest is held in a fixed position relative to the electron cloud of interest to get an noticable effect. Common example:

1. Flat conjugated systems like benzene, but also larger annulenes and related molecules. Most chemists are familiar with the argument that hydrogens outside the ring are deshielded by the "ring current" – while some may debate the existence of the ring current, the pi system is, by its nature, diamagnetic, so it's not surprising that any protons held in the outer edge are deshielded while methylenes held in a position above or below the ring are significantly shielded. There are beautiful examples of annulenes with protons inside the large aromatic ring that have negative chemical shifts due to the large shielding anisotropy of the pi system.
2. Triple bonds have two pi bonds that are 90º to each other. It's a little harder to "see", but you can look at various possible orientations in a magnetic field and see that you can rationalize some shielding of the carbons in the triple bond.
3. Cyclohexane derivatives. While not as dramatic as the benzene example (and confusingly illustrated in the Silverstein book), you can picture the sigma skeleton of the cyclohexane as a large cloud of electron density, so it should have a shielding cone above/below the ring and a deshielding plane off to the sides of the ring. This turns out to be true! For a system that has a relatively fixed chair conformation and a diastereotopic methylene, you'll always find the equatorial hydrogen deshielded relative to the axial hydrogen.

I'm sure there are more examples, but those are the only examples that I have seen work consistently enough to be useful.

In short, any bond arrangement that is non-spherical will have an element of anistropy associcated with it. The key, as S.Burt quite rightly points out above, is that in solution state NMR, this anisotropy usually averages out to zero through rapid tumbling. However, when the orientation of the nucleus of interest with respect to the electron cloud of the bond orbitals is fixed, this anisotropy will prevail, and generate an influence on chemical shift.

Many common functional groups have proposed anisotropy cones; especially aromatic systems, alkenes and alkynes. Even C-C single bonds have an element of anisotropy. As usual, I would refer you to the excellent online resource of Hans Reich for more detailed examples. (https://www.chem.wisc.edu/areas/reich/nmr/05-hmr-02-delta.htm#05-hmr-02-delta-anisotropy)

However, this provides nothing new to the answer above. What is an interesting addition comes from the 2104 review article by Marija Baranac-Stojanovic (RSC Adv., 2014,4, 308-321. DOI: 10.1039/C3RA45512B) 'New Insight into the anisotropic effects in solution-state NMR spectroscopy'.

This review examines a number of computational methods which brings into question a number of traditional models of anisotropy. Specifically, it suggests, for example, that the ring current of benzene is substantially overstated, with the influence of the σ electrons making the dominant contribution to the local shielding. Also, it is suggested that the overall anistropy cone for the single C-C bond should be reversed, which, by traditional models, would result in Hax being deshielded relative to Heq. However, when total contributions of all local bonds are considered, and not just the C-C bonds, experimental and theoretical chemical shift values align. There are a number of good examples also of the role of sterics in influencing chemical shift over the customary justification of anisotropy. This review makes for a good read which may cause some of us to reconsider the strength with which we promote anisotropy as a factor in chemical shift at the undergraduate level.