# Chemical shift value and proton NMR spectroscopy

I am a bit confused about what chemical shift value signifies in proton NMR spectroscopy. If the proton of the standard substance TMS absorbs X Joules of energy to go into resonance, than a substance with a chemical shift value of 2.5ppm means it absorbs:

energy absorbed= X- (2.5X/10^6)?

Could someone please tell me if this is what chemical shift value is mathematically. In my book, it says the substance absorbs "2.5 millionth less amount of energy than TMS to go into resonance"... but I don't really understand this.

• en.wikipedia.org/wiki/Chemical_shift has a pretty good explanation (see the Chemical Shift Referencing section). Dec 4 '13 at 7:27
• The chemical shift is a measure of how much energy it takes to flip a nuclear spin relative to a standard. For 13C and 1H that standard is tetramethylsilane(TMS). long's answer below talks about Hz, and you can calculate the energy differences using Planck's constant. That being said, this topic is almost never used chemically beyond a basic level understanding. All that matters is that different chemical shifts correlate to different types of chemical environments. Unless you are really grooving on the physics don't dwell on it. Mar 10 '14 at 19:58

Firstly, the ppm scale is a dimensionless scale that describes the energy level of a signal relative to a reference (usually TMS). Significantly, it is magnetic field independent, and so allows comparison of signals recorded on different systems (not just a 300MHz vs a 600MHz spectrometer, but between all different 600MHz spectrometers, because no two will have been set up at identical Bo fields).

The chemical shift scale is defined as:

$$\delta =(v-v_r )*10^6/v_r$$ , where $v_r$ is the spectrometer reference frequency (of TMS, say)

Now, for a 600MHz NMR spectrum, each ppm represents 600Hz. So, if the resonance frequency of a signal at 0ppm is 600,000,000Hz, the signal at 1ppm represents an energy of 600,000,600Hz. At 2.5ppm, the frequency is 600,001,500Hz.

The chemical shift scale is often confusing in its labelling, but the thing to remember is that as you go to higher chemical shift values, you go to higher frequencies.

Higher ppm == downfield == Deshielded == higher frequency

Lower ppm == upfield == Shielded == lower frequency

• downfield and upfield are outdated and should no longer be used, since NMR no longer scan the spectrum. Other then that, excellent answer. Dec 18 '13 at 2:30
• Upfield and downfield are fine, NMR always scans the spectrum, it just does so by Fourier transform these days. Mar 10 '14 at 20:00
• Yes, upfield and downfield are accepted terminology, and this is unlikely to ever change. A metal hydride at -20ppm is upfield of an aromatic proton at 8.3ppm. A methyl amine at 3.5ppm resonates downfield from the TMS signal at 0ppm
– long
Mar 10 '14 at 22:14