# What factors are important for quantitative analysis of a proton 1D-NMR spectrum?

Besides elucidating or verifying a chemical structure, NMR can also be used e.g. for quantifying a mixture of different chemicals.

Depending on the quality of the spectrum and the specific substance, integrating the NMR signals for the same molecule can result in significant variations from the actual ratio of nuclei, which is known from the chemical structure.

What factors do affect the quantification of NMR signals in a proton 1D spectrum? What precautions should one take during acquisition and processing of NMR spectra to make sure that the spectra can be analyzed quantitatively?

The signals you get in a simple 1D proton spectrum are in most cases roughly quantitative, though there are some exceptions and some aspects you need to consider if you need high accuracy.

### Acquisition

There are several things you need to keep in mind while setting up the experiment to ensure that the resulting NMR spectrum will be quantitative.

The spectrum should be of high quality, any artifacts and noise will affect the quantification.

Relaxation delay

The relaxation delay is the time between experiments, if it is too short some protons won't relax completely back to the equilibrium state. This affects the intensity of the NMR signal and will cause the integrals of those signals to be off.

The relaxation delay (including the acquisition time) should be around $$5 \cdot \mathrm{T_1}$$. You can either estimate the $$\mathrm{T_1}$$ or measure it.

13C satellites

The 13C satellites are around 1% of the total signal, if you need high accuracy you should use decoupling to get rid of those.

Other aspects

You also need to ensure that the pulses used in the experiment have a reasonably flat excitation profile for the area you're looking at. This is usually no problem for standard 1D proton experiments, but might be a problem for other kinds of experiments or if you have an unusually long pulse and/or and unusually wide distribution of your chemical shifts.

### Processing

Baseline

The baseline should be absolutely flat and at exactly zero, any error there will lead to large errors in the quantification. Using a digital filter during acquisition is a good idea for that (baseopt option for Bruker spectrometers), this will ensure a very flat baseline at zero, as long as no other problems distort the baseline.

Phasing

The phase-correction should be exact, it might be necessary to perform a manual phase-correction.

• <sup>13</sup>C satellites are not a problem, as they are in almost all cases of a know integral (0.55% of the center line). Also the integral regions have to be optimized. Typically one chooses to take a width which is a fixed multiple of the line width of the corresponding line. By doing that one can get very accurate results. – GorillaPatch May 21 '12 at 20:51
• Yeah, I wouldn't count them as a major problem, but you'd have to be consitant about them; You can't have one peak with both included, another with neither and a third with only one. – Canageek May 25 '12 at 21:56

Mad Scientist provides some good advice. I have a different approach that either renders some of those actions unnecessary or cancels them out through signal averaging.

One big issue for quantification is the signal to noise ratio. Doing many of the things in Mad Scientist's answer will increase the signal to noise ratio, but the easiest two changes are increasing the concentration and taking more scans. If you can increase the concentration in your sample, do it. I often would increase the concentration to the point where I would be able to collect publication quality 1D 1H NMR spectra in a single scan. If you collect just one scan, then the problems resulting from poor phase averaging and from delay times that are shorter than the relaxation time.

If you are unable to change the concentration, then increasing the number of scans increases the signal to noise by the square root of the number of scans. 4 scans provides twice the singal to noise as 1 scan. 16 scans provides twice the signal to noise as 4 scans, and so on. When you opt to take multiple scans, then you must be worried about the things that Mad Scientist mentions. A phasing problem that aggregates over 100+ scans will not help you. Having too short a delay time such that all of your spins are not relaxed only gets worse over a large number of scans. In a recent project, I had to quantitatively integrate the 1D 1H NMR spectrum of a reaction mixture, looking for minor products and unreacted species (less than 5% of the total sample). I ended up taking a 3200 scan proton spectrum with long delay times. I was not popular with my fellow grad students, but I did get the data I needed.

• I know someone who burned 2 weekends of 600 MHz NMR time trying to quantify natural abundance deuterium. Didn't work, but hey, what your prof says 'Do X'.... – Canageek May 25 '12 at 21:57