The Kendrick mass defect
Before we can create Kendrick plots we need to understand exactly how to calculate Kendrick mass and Kendrick mass defects for a given molecule. Let’s start with the Wikipedia pages on mass spectrometry and monoisotopic mass. Being a physicist I must confess I wasn’t aware of the multitude of mass definitions that need to be carefully distinguished. Also, I wasn’t aware that different definitions of mass defect are being used in physics and chemistry.
Reason for this difference between physics and chemistry seems to be that within nuclear physics it is necessary to distinguish between the mass of proton versus neutrons. Within chemistry this distinction would unnecessarily complicate the analysis. Instead, a premise of chemical mass spectrometry is that both protons and neutrons carry a similar mass of 1/12th of the weight of a carbon atom.
The nominal mass for an element is the mass number [the number of protons plus neutrons] of its most abundant naturally occurring stable isotope, and for an ion or molecule, the nominal mass is the sum of the nominal masses of the constituent atoms.[4][5] Isotope abundances are tabulated by IUPAC:[6] for example carbon has two stable isotopes 12C at 98.9% natural abundance and 13C at 1.1% natural abundance, thus the nominal mass of carbon is 12. The nominal mass is not always the lowest mass number, for example iron has isotopes \(^{54}\)Fe, \(^{56}\)Fe, \(^{57}\)Fe, and \(^{58}\)Fe with abundances 6%, 92%, 2%, and 0.3%, respectively, and a nominal mass of 56 Da. For a molecule, the nominal mass is obtained by summing the nominal masses of the constituent elements, for example water has two hydrogen atoms with nominal mass 1 Da and one oxygen atom with nominal mass 16 Da, therefore the nominal mass of H2O is 18 Da.
In mass spectrometry, the difference between the nominal mass and the monoisotopic mass is the mass defect.[7] This differs from the definition of mass defect used in physics which is the difference between the mass of a composite particle and the sum of the masses of its constituent parts.[8]
The exact mass of an isotopic species (more appropriately, the calculated exact mass[9]) is obtained by summing the masses of the individual isotopes of the molecule. For example, the exact mass of water containing two hydrogen-1 (1H) and one oxygen-16 (16O) is 1.0078 + 1.0078 + 15.9949 = 18.0105 Da. The exact mass of heavy water, containing two hydrogen-2 (deuterium or 2H) and one oxygen-16 (16O) is 2.0141 + 2.0141 + 15.9949 = 20.0229 Da.
When an exact mass value is given without specifying an isotopic species, it normally refers to the most abundant isotopic species.
To my understanding the terms exact mass and monoisotopic mass are equivalent.
Let’s check how we can calculate the expected up the nominal mass and the exact mass for given monomer with the mendeleev python package.
Kendrick mass and Kendrick mass defect
According to wikipedia the Kendrick mass for a family of compounds \(F\) is given by
\[ \mathrm{Kendrick~mass}~(F) = (\mathrm{observed~mass}) \times \frac{\mathrm{nominal~mass~(F)}}{\mathrm{exact~mass~(F)}}.\]
For hydrocarbon analysis, \(F = \mathrm{CH_2}\).
This is not very clear.
As a numerical example, suppose we measure the hypothetical molecule \(\mathrm{C_2H_4}\). The exact (or mono-isotopic) mass would be 28.03130012892 u.
The exact mass for the Kendrick monomer unit \(\mathrm{CH_2}\) is 14.01565006446 u. This means the the exact Kendrick mass is
\[ (28.03130012892) \times \frac{14}{14.01565006446 } = 28~ \mathrm{Kendrick~mass~units} \].
The Kendrick mass defect of a specific measured molecular mass is the fractional part of the Kendrick Mass. Alternatively, it is the difference between the precise Kendrick mass and the nominal Kendrick mass.
The exact (or monoisotopic) mass of each chemical element deviates from the nominal mass that one would expect based on the number of nucleons (protons plus neutrons) present in the nucleus. This deviation is unique for each type of atom or molecule and is called the mass defect…
Further introduction is given by (Fouquet 2019).