Molecular formula from exact mass: why 5 ppm is often not enough
Author: Dr. Oliver Kraft, Dr. rer. nat., Organische Chemie · Updated 2026-08-04
Short and direct
An exact mass alone rarely determines a molecular formula. At m/z 152.0706 as [M+H]+ with 5 ppm tolerance exactly one candidate remains, C8H9NO2 at 0.03 ppm deviation. At m/z 195.0877 under the same conditions two remain: C8H10N4O2 at 0.25 ppm and C8H18OS2 at 2.66 ppm. Both sit inside the window. Mass does not separate them.
They are separated by two further quantities. The ring and double bond equivalent, RDBE, is 6.0 for the first and 0.0 for the second formula. A molecule with RDBE 0 has neither ring nor double bond, which barely fits a signal in this mass range from a typical pharmaceutical sample. On top comes a Bayesian prior on the elemental composition that puts 0.119 against 0.003. The overall score ends at 0.951 against 0.468.
The computed result
| Measured m/z | Candidate | Exact mass | Error (ppm) | RDBE | Overall score |
|---|---|---|---|---|---|
| 152.0706 | C8H9NO2 | 151.06332927 | 0.0349 | 5 | 0.993 |
| 195.0877 | C8H10N4O2 | 194.0803763 | 0.2458 | 6 | 0.9508 |
| 195.0877 | C8H18OS2 | 194.07990754 | 2.6611 | 0 | 0.4678 |
Computed 2026-08-03 with covams_formula, adduct [M+H]+, tolerance 5 ppm. Verbatim tool output.
Why is the mass error not the most important criterion?
Because the number of possible formulas grows with mass faster than measurement accuracy does. At low masses and with good calibration, mass suffices: at m/z 152.0706 a single candidate remains. At m/z 301.1234 the same 5 ppm window returns seven molecular formulas, from C21H16O2 with 14 double bond equivalents to C11H27O3P3 with none. The smallest ppm error does not belong to the most plausible candidate here. Beyond this point the deciding factor is no longer which is closest but which makes chemical sense.
In the second example below the wrong candidate has a mass error ten times larger, yet still sits inside the window. Sorting the candidate list by ppm and taking the first entry happens to be right here. Doing the same on a sample with poorer calibration is not.
What does RDBE tell you, and when may you discard with it?
RDBE counts rings and double bonds together. A negative value is chemically impossible and may always be discarded. A value of 0 means a fully saturated, open-chain molecule. That is possible but rare in a drug substance or degradation product sample, and the combination of RDBE 0 with two sulfur atoms makes the second formula in the example implausible, not impossible. The distinction matters: if you discard on RDBE, document why.
The most robust additional information remains the isotope pattern. Two sulfur atoms produce a distinctly elevated M+2 signal that is either present in the spectrum or not. In the computed example the isotope criterion is null because no spectrum was supplied. That is exactly the next measurement that settles the question for good.
Frequent questions
- How do I calculate ppm?
- Mass error in ppm is the difference between measured and theoretical mass, divided by the theoretical mass, times one million. At 195 daltons, 1 ppm corresponds to roughly 0.0002 daltons.
- Which tolerance should I choose?
- The one your instrument actually holds in system suitability, not the one from the data sheet. Too narrow a window discards the right formula, too wide a one produces a candidate list nobody reviews. 5 ppm is a common starting point for a well-calibrated high-resolution instrument.
- What is the difference between exact mass and molecular weight?
- Exact mass uses the mass of the most abundant isotope of each element, molecular weight uses the natural isotopic average. For C8H10N4O2 that is 194.0804 versus roughly 194.19. In high-resolution mass spectrometry the exact mass is always what is meant.
- Does the tool account for other adducts?
- Yes, the adduct is a call parameter. The default is [M+H]+. A wrongly assumed adduct is the most common reason no plausible candidate is found at all, in particular confusing [M+H]+ with [M+Na]+ and their difference of roughly 21.98.
- Can I include the isotope pattern?
- Yes. There is a separate tool that computes the theoretical isotope pattern from a molecular formula, and the formula assignment can score a measured pattern. In the example above the isotope score is null because no spectrum was supplied.
- What does the Bayesian score mean?
- It weights how often an elemental composition occurs in real molecules at all. Two sulfur atoms with no ring or double bond are rare, which is why the value for the second candidate drops to 0.003. That is a plausibility statement, not a proof.
Sources
- Kind T, Fiehn O (2007): Seven golden rules for heuristic filtering of molecular formulas from mass spectrometry. Basis of the RDBE and element-ratio filters.
The same calculation on your structures
The results above come from the same tools your language model can call over the Model Context Protocol. Test them free of charge, at your own pace.