Mass spectrometry, ionisation and fragmentation

The detector observes an ion produced by a defined process

Mass spectrometry produces and observes ions. Electron ionization, electrospray and other ionization processes have different mechanisms and can give different charge states, adducts or fragments. The neutral material originally present and the detected ion need not have the same formula, charge or mass.

For the spectral-axis convention used here, define ξ=(m_ion/u)/|z|, where m_ion is ion mass, u the unified atomic mass unit and z the signed charge number. The axis value is dimensionless after normalizing mass by u and dividing by the magnitude of charge number. Familiar “m/z” notation requires this convention to be understood; dividing by signed z would place a negative ion incorrectly on a negative mass axis.

Historical terminology can differ. An older Gold Book entry used mass-number wording, while the 2013 IUPAC recommendation defines its axis through ion mass/u and absolute charge number. Mass number is an integer nucleon count; it should not replace a specified isotope-dependent ion mass in the present calculations. Exact mass is calculated for specified isotopes, while accurate mass refers to a measurement.

Adduct and charge assignments determine the neutral-mass inference

An invented neutral entity M has assigned mass 1000.00000 u. Use rounded proton mass 1.00728 u in an explicitly additive mass model. Assigned [M+H]⁺ has ion mass 1001.00728 u and ξ=1001.00728. Assigned [M+2H]²⁺ has ion mass 1002.01456 u and ξ=501.00728.

The second ion is heavier than the first even though its axis value is about half as large. Reverse calculation for the doubly charged assignment gives neutral mass |z|ξ u−2m_proton=1000.00000 u. It relies on the stated adduct and charge, not axis position alone. Proton addition is different from adding a neutral hydrogen atom; the latter includes an electron.

Assign a synthetic isotope mass increment 1.0034 u. Its corresponding axis spacing is 1.0034 for a singly charged ion and 0.5017 for a doubly charged ion. The inputs are hypothetical and rounded, with binding-energy mass corrections omitted from the additive model. Charge/adduct assignments and any real isotope interpretation need their own evidence.

A narrower peak does not remove a centroid error

State the width criterion when reporting a resolving-power value. Here define FWHM resolving power R_FWHM=ξ/Δξ_FWHM, with full width at half maximum at the specified axis position. A different peak-width or valley criterion is a different convention and cannot be converted universally without a suitable peak model.

Give hypothetical ξ=500 and FWHM 0.0250. Then R_FWHM=20000. Separately, let a measured teaching input centroid be 500.005 while the known reference value is 500.000. Signed relative centroid error is 10⁶(500.005−500.000)/500.000=+10.0 ppm. These are invented inputs, not an instrument performance test.

Halving FWHM to 0.0125 doubles R_FWHM to 40000, but leaving that same centroid leaves the +10.0 ppm error unchanged. Precision, calibration, error, peak width and separation of two different ions are related practical concerns with different definitions. A width number alone does not guarantee a unique formula or two-peak separability.

An isotope envelope needs probability and response assumptions

Use fictional site label X, which does not denote an actual chemical element. Stipulate two independent X sites, each having light-state probability 0.750 and heavy-state probability 0.250, with assigned heavy mass increment 2.00 u. Suppose all resulting forms have equal detector response per entity and charge magnitude one.

The grouped probabilities for zero, one and two heavy sites are (0.75)²=0.5625, 2×0.75×0.25=0.3750 and (0.25)²=0.0625. They sum to one and give relative ratio 9:6:1 at assigned mass offsets 0, 2 and 4 u. The middle group contains two distinct site assignments, light–heavy and heavy–light.

Expected heavy-site count is 2×0.25=0.500. The plot shows this synthetic probability distribution against heavy-site count, not an actual mass spectrum or measured isotope intensities. It makes no chlorine, bromine or other natural-abundance assignment and cannot uniquely identify a real molecule.

Conservation is necessary but does not establish a fragment pathway

A formal net can be tested without claiming that it is observed. Choose precursor radical cation C₃H₆O⁺• and products C₂H₃O⁺ plus neutral methyl radical CH₃•. The selected net conserves C, H and O atoms and total charge +1.

Using assigned nominal atom masses C=12, H=1 and O=16, the nominal masses are 58, 43 and 15, and 58=43+15. Electron counts from atomic numbers and charge are 31 for the precursor, 22 for the charged product and 9 for the neutral radical, again closing the ledger. An odd-electron precursor is consistent with these chosen even-electron and radical products.

These are formal entity and nominal-mass inventories. They do not demonstrate a measured peak, actual fragmentation mechanism, preferred channel, complete reaction or an accurate/average mass result. Alternative balanced nets can exist. Chemical context and observed complementary evidence are required to identify a real pathway.

A plausible assignment still needs discrimination from alternatives

An axis value, isotope pattern or fragment can constrain an assignment, but isomers and alternative ion forms can share some observations. Sample preparation, separation, ionization and response should be traced to the chemical entity and quantity being reported.

Combine appropriate calibrated measurements and references, retaining uncertainty and unresolved candidates. This lesson uses hypothetical masses and probabilities and selected formal formula ledgers; it imports no reference spectra, operating settings or measured structural identification.

Worked examples

Try it yourself

1. Assign [M+3H]³⁺ using the same neutral and proton masses and isotope increment. Find axis value and isotope axis spacing.

   Show the answer and reasoning

   334.340613 and 0.334466667.

   Ion mass is 1003.02184 u; divide its mass/u and the 1.0034 increment by charge magnitude three.

2. Keep the hypothetical centroid 500.005 and reference 500.000 but halve FWHM to 0.0125. What changes and what stays fixed?

   Show the answer and reasoning

   R_FWHM becomes 40000; signed centroid error stays +10.0 ppm.

   The narrower width changes the width-based quotient, while the fixed reference difference leaves the relative error unchanged.

3. Use one fictional X site with the same heavy probability 0.250. Give the two grouped probabilities and assigned mass offsets.

   Show the answer and reasoning

   0.750 and 0.250, ratio 3:1, at offsets 0 and 2 u.

   The one-site possibilities are exhaustive; the two-site binomial multiplicity no longer applies.

4. Can formal H₂O loss from C₃H₆O⁺• conserve atoms, charge and electrons? Name the remaining ion and nominal mass, then state the inference limit.

   Show the answer and reasoning

   C₃H₄⁺• at nominal mass 40, plus H₂O at 18; the ledger balances but occurrence is unproven.

   Atoms and +1 charge are retained; electron counts 31=21+10 also close. A balanced alternative is not an observed pathway.

What to carry forward

• Specify the detected ion, adduct and charge.
• Normalize ion mass by u and divide by absolute charge number in the declared axis convention.
• Accompany resolving power with its width criterion and position.
• An isotope model requires stated probabilities and response assumptions.
• Formal atom and electron conservation does not establish observed fragmentation.