[Big-Daddy]

The Larmor frequency for a certain isotopic type of NMR (e.g. ¹³C-NMR or ¹⁹F-NMR) refers to the frequency at which nuclei of that isotope which experience no shielding effect will resonate (as I understand it?). This therefore provides a reasonable order-of-magnitude estimate for the chemical shifts (in δ ppm) undergone by nuclei of a certain isotope.

How is this Larmor frequency calculated for a certain isotope, given the magnitude of the magnetic field B which acts on it?

[Corribus]

I'm not sure what you want beyond what's offered at the Wikipedia page.

http://en.wikipedia.org/wiki/Larmor_frequency

Just as a little bit of useless information, NMR spectroscopy is fairly unique because unlike most spectroscopic methods, in which static energy level gaps are probed by varying the light frequency, in NMR spectroscopy the light frequency is held constant and the energy level gaps are varied by changing the external magnetic field strength.  The changing field strength causes the energy gaps to modulate, giving rise to a peak when there is a resonance condition with the (constant) light source. 

As a result, the spectroscopic information you get from NMR is all relative to some arbitrary value.  There are no nuclear spin transitions in the absence of a magnetic field. 

People often refer to NMR instruments by a MHZ value.  The MHZ value refers to the frequency at which a proton comes into resonance at the magnetic field strength of the instrument, which is usually measured in Tesla.  Since different NMR instruments have different strength magnets, the proton nuclear energy level splitting is different on different instruments.  This would make comparing spectral data from instrument to instrument impossible, which is why that crazy ppm scale is used - to effectively normalize for the field strength.  Higher field strength instruments give better resolution, though, because there is more "spectral room" between the resonance conditions of the various protons in a molecule when the energy level splittings are larger.

(It's actually a bit more complicated than what I've described here, because unlike a UV-Vis or FTIR, we're not measuring absorption of the light here.  The radio frequency is actually pulsed and what we measure is the relaxation of the excited, polarized nuclei back to thermal equilibrium.  When the nuclear spins are excited, they generate a small voltage, and this drop off in the voltage as the nuclei relax is what is sensed by the instrument in what is called free induction decay.  I actually find it a bit of a shame that NMR has been relegated to something of a one trick pony in chemistry, being almost exclusively used for chemical identification of organic molecules.  It's actually a very powerful tool that has many more potential uses, but such advanced applications of the technique has become a lost art in many ways.)

[Big-Daddy]

OK, thanks.

How can I make an order-of-magnitude estimate of what chemical shifts each nucleus will show for the type of spectrum? e.g. for ¹H spectra the chemical shifts are usually between 0 and 11 or so, whereas for ¹³C spectra they are usually between 10 and 220 or so. Why is this, and how could I estimate this for the spectra of other isotopes?

[Corribus]

I believe it is due to the fact that the gyromagnetic ratio (and magnetic moment) of ¹³C is quite a bit lower than that of ¹H.  Since the ppm scale is a relative scale based on a "proportion of change" between the real nuclear spin energy gap and a reference value, for an identical degree of shielding, the proportion will be larger for ¹³C than for ¹H, which has a much larger energy gap reference value (because of it's large magnetic moment). 

I'm not sure if that makes sense or not.  I'm finding it difficult to describe what I mean.

[Big-Daddy]

I believe it is due to the fact that the gyromagnetic ratio (and magnetic moment) of ¹³C is quite a bit lower than that of ¹H.  Since the ppm scale is a relative scale based on a "proportion of change" between the real nuclear spin energy gap and a reference value, for an identical degree of shielding, the proportion will be larger for ¹³C than for ¹H, which has a much larger energy gap reference value (because of it's large magnetic moment). 

I'm not sure if that makes sense or not.  I'm finding it difficult to describe what I mean.

[tex]δ = \frac{f_{sample}-f_{reference}}{f_{reference}}[/tex]

I believe this is the chemical shift equation. I've understood that ¹H nuclei has a larger magnetic moment and thus a larger energy difference between its two excited spin-states, than ¹³C nuclei. But why is f_sample-f_reference bigger for ¹³C than ¹H, given the same relative degree of shielding?

[Wastrel]

How much charge you can push around before a molecule becomes energetically unhappy may be part of it.  Hydrogen has 1 electron, a bare proton has a chemical shift of 31, difficult to get more deshielded than that.  Carbon has 6 so a bigger d+ or d- is achievable.  Silicon has 14 and known chemical shifts for Si-29 in organic compounds range from around -400 to around +600 relative to TMS.