Algorithm for Selecting Organic Compounds to Verify the Resolution of Electron Ionization Mass Spectrometers

Abstract

The ion coalescence phenomenon complicates the evaluation of the effective resolution of Fourier-transform mass spectrometers. We propose an approach for confirming the resolution of an electron ionization Fourier-transform mass spectrometer using pairs of organic substances identified by automatically generated formula differences. The proposed method is compared with the search for organic substances in the National Institute of Standards and Technology (NIST) database. Under the given conditions of the mass spectrometer resolution range up to 45000–50000 at 100 m/z, 166 pairs of suitable compounds were found using the proposed method, while a search in the NIST database yielded only 88 pairs of compounds. This enabled the selection of six pairs of organic compounds that were most suitable for confirming the resolution of the high-resolution mass spectrometer using molecular ion peaks, and four pairs of compounds that allowed the resolution to be confirmed using fragment ion peaks. The resolution of the Fourier-transform mass spectrometer designed for gas analysis was experimentally evaluated by analyzing the spectra of a mixture of organic compounds selected using the proposed method.

INTRODUCTION

The ion coalescence phenomenon observed in all types of Fourier-transform mass analyzers^1,2) is caused by Coulombic interactions between ion clouds. This interaction does not allow resolving peaks of compounds with close molecular masses in mass spectra, even if the formal resolution of the mass spectrum, determined through the peak width, is sufficient. In this regard, it is necessary to experimentally confirm the real resolution of Fourier-transform mass spectrometers to accurately determine their analytical abilities. This is of particular importance for mass spectrometers in which ionization occurs inside an electrostatic ion trap, which does not allow the ions to be normalized by energy and leads to broadening of the peaks in the mass spectra.

Modern organic chemistry is represented by compounds based on the hydrocarbon chain with almost all known chemical elements.^3,4) However, as a rule, low-molecular-mass organic substances contain only nonmetals from periods 2–4 of the Periodic Table of the Elements, forming various classes of organic compounds. The double bond equivalent⁵⁾ is a satisfactory tool to assess molecular formulas from the exact mass value for compounds with relatively simple elemental compositions that contain only a small variety of heteroatoms. The nitrogen rule helps to increase the elemental coverage for formula prediction. However, several limitations still persist. A heteroatom can exist in different valences, significantly expanding the variability of formulas. The number of functional groups in an organic compound can reach the number of hydrogen atoms in an aliphatic hydrocarbon chain, while the functional groups will be different in polyfunctional compounds. The generation of molecular formulas of compounds for given monoisotopic molecular masses with a certain accuracy makes it possible to determine substances with similar molecular masses without their preliminary separation using mass spectrometric data.^6,7) In addition, it is very useful for screening substances with similar monoisotopic molecular masses for their subsequent use in experimental confirmation of the resolution of mass spectrometers.

Currently, there are several algorithms for searching for the molecular formula of a substance based on its experimental mass: the brute-force enumeration algorithm,⁸⁾ the branch and bound method,⁹⁾ and direct selection from a database.¹⁰⁾

• The brute-force enumeration algorithm is based on listing all possible combinations of elements that form an organic compound, taking into account restrictions on the maximum permissible number of atoms. The theoretical monoisotopic molecular mass is calculated and compared with the experimental one for each combination. If the difference between these masses is less than a given threshold Δ, then such a combination of elements is considered a potentially possible molecular formula. It is necessary to note that not every possible arrangement of atoms in a chemical compound corresponds to a correct molecular formula. The rules given below are based on the fact that neutral chemical compounds correspond to molecular graphs.⁶⁾ It is necessary to satisfy the constraints determined by the valences of the atoms for the formula to be correct.⁷⁾ These restrictions were first formulated in reference 11, and their detailed derivation is presented in reference 12. The advantages of the brute-force enumeration algorithm include the ease of its implementation, full coverage of the space of molecular formulas, and ease of adaptation to any set of elements and mass range. The main drawback of the algorithm is its high computational complexity. With an increase in the number of elements and the permissible number of atoms, the set of combinations grows exponentially.

• The branch and bound method is a more efficient approach to finding the molecular formula of a substance based on its monoisotopic mass, which significantly reduces computational costs by eliminating obviously unsuitable combinations. The method is based on representing all possible combinations of atoms as a decision tree. At the first level of the decision tree, the number of atoms of the first element that compose the compound is determined. At the next level, the number of atoms of the second element is specified, and so on for subsequent elements. Each point in the decision tree corresponds to one unique combination of atoms. In this case, the conditions for cutting off branches are applied: a limit on the difference Δ between the theoretical and experimental masses, as well as restrictions on the valences of atoms presented in reference 7. If at least one of these conditions is not met, the branch is cut off, and further combinations from this point are not considered. The advantage of the branch and bound method is its higher performance compared to the brute-force algorithm, as the exclusion of inappropriate branches reduces the computational complexity of the algorithm. However, this method becomes ineffective when the molecular mass is large.⁹⁾

• In the method of direct selection from a database, the molecular formula is determined by comparing the known exact mass of the substance with molecular masses previously stored in a database of chemical compounds. The compound is considered a valid candidate if the difference between the masses is within the deviation. The advantages of this method include its simplicity of implementation and high speed of operation. The drawback is that the ability to identify a compound depends on the completeness and accuracy of the database, that is, if the substance is not in the database, it will not be found.

In this paper, we attempted to describe the composition of organic compounds with a single formula for further generation of molecular formulas of organic substances. The implemented code was used to search for pairs of organic compounds suitable for verifying the resolution of a high-resolution mass spectrometer. The pairs of organic compounds selected using this code were used to experimentally confirm the resolution of the lab-made mass spectrometer based on an ion trap with electron ionization.

THEORETICAL DETAILS

We proposed separating the saturated and unsaturated hydrocarbon fragments to describe the brutto composition of any organic compound. Then, we describe the heteroatoms of functional groups based on their valence, adding hydrogen atoms if necessary. Further, the molecular formula of the organic compound is formed due to contamination of the hydrocarbon chain and functional groups. We have replaced the traditional concept of valence with coordination for the correct generation of molecular formulas of organic compounds. In the context of solving this problem, coordination should be understood as the number of atoms surrounding the atom in question. Thus, the coordination of carbon atoms at a double bond >C=C< in alkenes equals 3, and at a triple bond in alkynes it equals 2. Similar reasoning was applied to heteroatoms.

The brutto composition of organic compounds can be described by the following formula:

$$\begin{array}{l}{C}_{n-f_1}{H}_{(v_{C_1}-2)\left(n-f_1\right)+a}{C}_{f_1}{H}_{(v_{C_2}-2)f_1}{E}_{1·f_2}{H}_{(v_{E_1}-2)f_2+1}\cdots \hfill \\ E_{n{f}_{n+1}}{H}_{(v_{E_n}-2)f_{n+1}+1}\hfill \end{array}$$ (1)

where

n is the number of carbon atoms in the hydrocarbon chain; f₁ is the number of multiple bonds in the hydrocarbon skeleton; ν_C1 is the coordination of a saturated carbon atom (equal to 4); ν_C2 is the coordination of an unsaturated carbon atom (equal to 3 or 2); a is the substitution parameter (a = 1 − for monosubstituted, a = 0 for disubstituted, a = −1 for trisubstituted compounds, etc.); E_n is the designation of a heteroatom of a given type; f_n is the number of functional groups of a given type.

The substitution parameter a adjusts the number of hydrogen atoms remaining in the hydrocarbon chain after adding substituents. It can take values from 1 for monosubstituted hydrocarbons to the value of (2 − m), where m is the number of substituents in the hydrocarbon chain. It is obvious that Formula (1) degenerates into a formula describing the brutto composition of saturated hydrocarbons C_nH_2n+2 in the absence of substituents and multiple bonds in the hydrocarbon chain.

Since we are talking only about the molecular formula of organic compounds, which do not describe specific isomers, for monosubstituted hydrocarbons, there will be only one variant of the composition C_xH_yE₁. For disubstituted hydrocarbons (a = 0), there are two possible molecular formulas, C_xH_yE′₂ and C_xH_yE′E′′, containing different heteroatoms. Trisubstituted hydrocarbons will already have four different molecular formulas, and tetrasubstituted hydrocarbons will have eight, that is, when adding another substituent, the number of molecular formulas grows exponentially with a denominator of two. By varying the variables in Formula (1) and substituting different heteroatoms, new molecular formulas of different classes of organic compounds will be generated, and by simultaneously replacing hydrogen atoms with several heteroatoms, formulas of heterofunctional organic compounds will be generated.

The number of carbon atoms in a hydrocarbon chain can be found by dividing the molecular mass of the substance by the atomic mass of carbon. This value must be reduced by one each time different functional groups are added. For example, suppose the nominal molecular mass of a substance is 79 g/mol. In that case, the maximum possible number of carbon atoms in the hydrocarbon chain equals the integer value (79 ÷ 12) = 6. When selecting the multiplicity of bonds in the hydrocarbon structure, it turns out that the minimum possible number of hydrogen atoms in a hydrocarbon skeleton unsubstituted by heteroatoms is 6, that is, the corresponding formula is C₆H₆. However, the nominal molecular mass of C₆H₆ is 78 g/mol, and any substitution of H by a heteroatom will result in a nominal mass greater than 79 g/mol. This means that to find a compound with a nominal mass of 79 g/mol, the number of carbon atoms must be reduced by one and one heteroatom must be introduced. By selecting a substituting heteroatom, we find the molecular formula C₅H₅N, corresponding to a nominal mass of 79 g/mol. It is obvious that the pyridine formula C₅H₅N is not the only formula corresponding to the nominal mass of 79 g/mol; further shortening of the hydrocarbon chain and substitution with various heteroatoms leads, for example, to the formula C₂H₆ClN.

The above-described process of generating formulas of organic compounds is implemented in Python code, which takes a nominal mass as input and outputs a list of molecular formulas of substances corresponding to the given nominal mass. Sorting the resulting list by specifying the exact molecular mass allows the selection of formulas of suitable compounds. This is useful for interpreting the results of high-resolution mass spectrometry if it is possible to obtain the mass number of the molecular ion. This code was written to search for pairs of organic substances with similar molecular mass values, which would confirm the resolution of the mass spectrometer.

It is known that, by definition, the resolution of a mass spectrometer is determined as¹³⁾

$$R=\frac{m/z}{\mathrm{\Delta }m/z^{\prime }}$$ (2)

Consequently, specifying the nominal molecular mass and searching for pairs of compounds with close values of exact monoisotopic molecular masses will allow the validation of the resolution of the mass spectrometer in various ranges. Suppose the required resolution of the mass spectrometer is specified. Then, the value of ∆m is calculated from (2), and only those pairs of substances whose difference in monoisotopic molecular masses is equal to the value of ∆m are filtered from the list of generated pairs of compounds. It is advisable to specify not a certain value of R but its range to find pairs of compounds capable of confirming the resolution of real mass spectrometers. Thus, the code requests the desired range of the mass spectrometer resolution and the nominal molecular mass as input and outputs a list of complementary pairs of compounds corresponding to the specified range of R.

This approach is suitable for searching for pairs of compounds capable of producing molecular ions. However, under conditions of electron ionization, for many organic compounds the intensity of the molecular ion peak is low, or the molecular ion may be absent altogether.¹⁴⁾ Given that the list of complementary pairs of organic compounds for a given range of resolution can reach hundreds of molecular formulas, and each molecular formula implies a number of isomeric compounds that require verification for the presence of a molecular ion, the task of searching for pairs of compounds seems to be of little use for real applications. We propose using formula differences of complementary pairs of compounds to solve this problem. The formula difference should be understood as a set of atoms that must compose the molecule of an organic compound or ion and provide a given value of ∆m. For example, the complementary pair of compounds C₅H₁₂O₄ and C₅H₁₃ClN₂ (corresponding monoisotopic masses 136.073559 and 136.076726 Da) corresponds to the formula difference O₄−HClN₂. To maintain the value of ∆m constant, the same number of carbon and hydrogen atoms, and if necessary, heteroatoms, is added to each of the complementary formula differences. Further search for the most suitable compounds to confirm the resolution of the mass spectrometer involves drawing the structures of molecules or ions in a chemical editor (e.g., ACD/ChemSketch) based on the composition of complementary formula differences and the desired molecular mass. To construct the most suitable pair of compounds, we suggest the following guidelines:

• 1.Calculate the nominal molecular mass of the organic compound M_N(Comp) by multiplying Δm by the desired resolution value.
• 2.Use the following formula to calculate the nominal molecular mass of the added fragments: M_N(af) = M_N(Comp) − M_N(fd), where M_N(af) is the nominal molecular mass of the added fragments, M_N(fd) is the nominal molecular mass of the formula difference, and M_N(Comp) is the nominal molecular mass of the organic compound.
• 3.
  Use a chemical editor to construct molecular structures of a pair of compounds, assuming that they will yield molecular ions upon electron ionization.

  • 3.1
    For each of the complementary formula differences, add an equal number of carbon and hydrogen atoms, and if necessary, heteroatoms, taking into account the value of M_N(af).
  • 3.2
    When constructing molecular structures, hydrophilic functional groups should be avoided and replaced with hydrophobic ones. For example, alcohol groups should be replaced with ether groups. Hydrophobic groups in the molecule facilitate the easier transfer of the substance into the gas phase.
  • 3.3
    Linear hydrocarbon chains of the reconstructed molecules should be avoided, as under electron ionization conditions such compounds will yield a large number of fragment ions. When verifying the resolution of the spectrometer for molecular ion peaks, preference should be given to aromatic structures, which are known to have an intense molecular ion peak and a small number of fragment ion peaks.
  • 3.4
    For designed molecules, it is necessary to check in the National Institute of Standards and Technology (NIST) database that the molecular ion peak intensity is not lower than 10. In cases where the molecular ion peak intensity according to the NIST database is low, compounds can be selected from which the desired ion can be efficiently obtained by fragmentation.
• 4.When reconstructing molecules, attention should be paid to their chemical activity. Compounds that are unstable, easily oxidized, or easily subject to electrophilic attack should be avoided. The substances of the selected pair should not react with each other.
• 5.Additionally, when selecting a compound for verifying the resolution of the spectrometer, attention should be paid to its toxicity and commercial or synthetic availability.

Since the basis of organic compounds is a hydrocarbon chain, the same set of formula differences may be suitable for confirming different ranges of mass spectrometer resolution. This approach is more advantageous than a simple generation of molecular formulas of organic compounds within a given ∆m interval. However, this approach requires some skill in reconstructing molecular structures or fragment ions from complementary formula differences.

We have implemented Python code to solve the above problem. This code takes as input complementary compounds for different nominal molecular masses obtained using a previously created code and outputs complementary formula differences with exact monoisotopic masses of the fragments. For any desired resolution, the recommended monoisotopic mass of the organic compound is determined. From these data, it is easy to manually set up structures of complementary organic compounds that allow the desired resolution of the mass spectrometer to be confirmed.

CALCULATIONS AND RESULTS

The resolution of mass spectrometers is not a constant value over the entire range of mass numbers.¹⁵⁾ Let us specify the resolution of the mass spectrometer in the range of 45000–50000 at m/z values in the region close to 100 Da. Then, ∆m will be within 0.002–0.003, and the corresponding ranges of molecular masses will be in the region of 90–100 and 135–150 Da. Herewith, we will assume that the substance produces a molecular ion during electron ionization.

The search for pairs of compounds satisfying the following criteria ∆m ∈ [0.001–0.005], m ∈ [70–150], was performed using the NIST electron ionization mass spectra database. The total number of pairs of compounds found that met these criteria was 54,883. After selection of possible organic compounds and removing isomers from the pairs found, the number of selected pairs of compounds was 1740. To remove possible organometallic compounds, some of which are toxic complexes with organic ligands, we introduced an additional selection condition so that the list would include only organic substances that may contain, in addition to the hydrocarbon chain, the following heteroatoms: B, N, O, F, Si, P, S, Cl, Br, and I. The introduction of such a condition made it possible to reduce the list of potential candidate substances to determine the instrument resolution to 1568.

A direct search for substances in the NIST database for a given resolution range is not provided, so we applied an additional filter to the found list of substance pairs with the condition R ∈ [45000–50000] in accordance with Eq. (2). This resulted in a list of 88 substance pairs. The diagram (Fig. 1) presents the results of such a filtration. Only 32 substance pairs out of these 88 have a molecular ion in the electron ionization mass spectrum with a peak intensity of at least 10%.

Fig. 1. Results of filtering the list of substance pairs with the criterion R ∈ [45000–50000].

The Python code we implemented allowed us to generate molecular formulas of organic compounds using the algorithm described in the “Theoretical Details” section. One hundred and sixty-six pairs of suitable compounds were found using the following boundary conditions: m ∈ [70–150], R ∈ [45000–50000], allowing for possible heteroatoms of B, N, O, F, Si, P, S, Cl, Br, and I. The results of generating molecular formulas to verify the resolution in the given range are presented in the diagram (Fig. 2).

Fig. 2. Results of generating molecular formulas of organic substances using the code (boundary conditions: m ∈ [70–150], R ∈ [45000–50000], possible heteroatoms of B, N, O, F, Si, P, S, Cl, Br, and I).

On the one hand, the molecular formulas generated by the script required verification and drawing of the proposed structural formula; on the other hand, in such an implementation, we can only discuss the resolution verification of molecular ions. We used formula differences for each pair of found substances to overcome this limitation. Complementary formula differences were obtained using a Python code we wrote that took a list of pairs of substances as input and output pairs of formula differences with an indication of the ∆m value. Applying this code to a list of previously found 1568 pairs of compounds resulted in 279 different formula differences, and to a list corresponding to the specified range of mass spectrometer resolution of 45000–50000 (88 pairs of substances) resulted in 22 formula differences. Application of this code to the list of compound pairs obtained by generating molecular formulas (166 compound pairs) allowed us to obtain 15 analogous formula differences (see Fig. 3). Pairs of formula differences of organic compounds are presented in Table 1.

Fig. 3. Block diagram of procedures for screening organic compounds suitable for verifying the resolution of a mass spectrometer: (A) from the NIST database and (B) by generating molecular formulas. NIST, National Institute of Standards and Technology.

Table 1. Formula differences of pairs of organic compounds to verify the resolution of the mass spectrometer in the range of 45000–50000, with possible heteroatoms of B, N, O, F, Si, P, S, Cl, Br, and I.

Formula difference 1	Mass of the formula difference 1 (Da)	Formula difference 2	Mass of the formula difference 2 (Da)	Δm (Da)
Obtained by searching the NIST database
B1F2O2	80.9959	C1H6Cl1Si1	80.9925	0.0034
C1F1	30.9984	H3Si1	31.0003	0.0019
C1F3Si1	96.9721	H2O4P1	96.96896	0.00314
C1H1N2S2	104.9582	Cl1F2O2	104.9554	0.0028
C1H2O1	30.0105	B1F1	30.0077	0.0028
C1H3S2	78.9676	Cl1N2O1	78.9699	0.0023
C1H4Br1	94.9495	Cl1N2S1	94.9471	0.0024
C1O3	59.9847	H1N2P1	59.98776	0.00306
C2F2	61.9968	H2N2S1	61.9939	0.0029
C2H1Cl1	59.9766	N2S1	59.9783	0.0017
C2H1O2	56.9976	F3	56.9952	0.0024
C2O2S1	87.9619	H3Cl1F1P1	87.96436	0.00246
C3H1Cl1O1	87.9715	F3P1	87.96896	0.00254
C4	48.0000	H4O1Si1	48.003	0.003
C4H2Cl2	119.9532	N4S2	119.9566	0.0034
C4H4O2	84.021	N6	84.0186	0.0024
C4O3	95.9847	H4N2S2	95.9816	0.0031
C5H4O1S1	111.9982	N6Si1	111.9955	0.0027
F4	75.9936	O3N2	75.9909	0.0027
H1Cl1N2	63.9828	O4	63.9796	0.0032
H1F4P1	107.9752	C4N2S1	107.9783	0.00314
H1N6S1	116.9985	C5F3	116.9952	0.0033
Obtained using the algorithmic methods
H1F1Si1	47.9831	O3	47.9847	0.0016
C1F1	30.9984	H3Si1	31.0003	0.0019
H5F1Si1	52.0143	B2N1O1	52.0166	0.0023
H2N2F1	49.0202	O1B3	49.0228	0.0026
B3F1O2	84.0161	N6	84.0186	0.0025
F4	75.9936	N2O3	75.9909	0.0027
H4P1Si1	63.0019	F1O1N2	62.9995	0.0024
H6F1P1Si1	84.0159	N6	84.0186	0.0027
H6Si2	62.0006	F1O2B1	61.9975	0.0031
H3F1	22.0218	B2	22.0186	0.0032
H4B1F1O4	98.0185	N7	98.0217	0.0032
F1N3	61.0077	B3Si1	61.0048	0.0029
O2B2F1	73.0068	H3N3Si1	73.0096	0.0028
F4	75.9936	H1O4B1	75.9967	0.0031
C2H1O2	56.9976	F3	56.9952	0.0024

NIST, National Institute of Standards and Technology.

The sequence of procedures for selecting organic compounds from the NIST database suitable for verifying the resolution of the mass spectrometer is presented in the block diagram (Fig. 3A). A direct search for organic compounds for the same purposes using the generation of molecular formulas is presented in the block diagram (Fig. 3B).

Experimental detail

To verify the resolution of the experimental lab-made mass spectrometer based on a harmonized Kingdon trap with two merged internal electrodes¹⁴⁾ with electron ionization for gas analysis,^16,17) the following pairs of substances were selected: pyridine–p-cresol, dimethylformamide (DMF)‒isopropyl ether of trimethylsilane, 1-(2-furyl)-1-butanone‒trimethylchlorosilane, and styrene‒trimethyl ether of boric acid. To obtain the required compounds and prepare the necessary mixtures, reagents suitable for high-performance liquid chromatography (Sigma-Aldrich, Merck KGaA, Darmstadt, Germany) were used, and auxiliary substances necessary for the synthesis were of analytical grade.

Isopropyl ether of trimethylsilane and trimethyl ether of boric acid were synthesized by esterification of trimethylchlorosilane (TMCS) with isopropanol, and boric acid with methanol, respectively, followed by fractional distillation. Synthesis of 1-(2-furyl)-1-butanone was carried out by the Grignard reaction from furfural and magnesium propyl bromide obtained from 1-propanol and potassium bromide using concentrated acid. The oxidation of the Grignard reaction product was carried out using sodium dichromate in an acidic medium.

The studied mixtures were prepared by mixing two components in molar ratios proportional to the peak intensities of the target ions and recalculated to the corresponding volume ratios (3). The target peak intensities for each mixture component were found in the NIST database.

$$\frac{I_1}{I_2}\sim \frac{n_1}{n_2}\to \frac{V_1}{V_2}=\frac{I_2{M}_1{\rho }_2}{I_1{M}_2{\rho }_1}$$ (3)

where I₁ and I₂ are the intensities of the target ions; n₁ and n₂ are the amounts of substances; V₁ and V₂ are the volumes; M₁ and M₂ are the molecular masses; ρ₁ and ρ₂ are the densities of component 1 and component 2, respectively.

Thus, test mixtures for verifying the resolution of the experimental mass spectrometer were prepared in accordance with the calculated volume ratios (Table 2).

Table 2. Volume ratios of test mixtures for verifying the resolving power of the mass spectrometer.

No.	Components	m/z target ion	Ratio of peak intensities of target ions	Volume ratios of components
1	Pyridine‒p-cresol	79	999:207	1:6
2	DMF‒isopropyl ether of trimethylsilane	73	999:677	1:3
3	1-(2-Furyl)-1-butanone‒trimethylchlorosilane	95	999:388	1:2.5
4	Styrene‒trimethyl ether of boric acid	104	999:360	1:3

DMF, dimethylformamide.

Each mixture (10 μL) was placed in a microvial and injected into the liquid sample port of the experimental mass spectrometer. The working pressure in the vacuum chamber was (1–3) ×10⁻⁸ mbar, and the partial pressure of the investigated sample was 2 ×10⁻⁸ mbar.

Mass spectra of the investigated samples were recorded by varying key parameters (excitation amplitude, signal processing modes, and mass range of excited ions) to optimize the resolution of target ion peaks. The signal detection time was set to the maximum value, namely, 1 s, to achieve the best resolution. The mass range of the excited ions was selected according to the mass of the target ion with a deviation of ±5 m/z. The excitation amplitude of the ion packet was optimized to obtain high signal intensity and maximum resolution of the target ions. Excitation time of ions was usually about 0.65 ms.

DISCUSSION

To find organic compounds suitable for confirming the resolving power of a high-resolution mass spectrometer, it is preferable to use a proposed script that generates molecular formulas according to the flowchart of their selection procedures (Fig. 3) rather than searching via the NIST database. This approach is simpler and faster than the latter.

The number of pairs of formula differences found in the NIST database using the criteria m ∈ [70–150], R ∈ [45000–50000], with heteroatoms of B, N, O, F, Si, P, S, Cl, Br, and I, was 22, and using the molecular formula generation code, it was 15 pairs. Both approaches showed that heterofunctional compounds are required to verify the resolving power of a high-resolution mass spectrometer. It should be assumed that with an increase in the resolution of the mass spectrometer, the number and diversity of heterofunctional groups in the selected molecules increases.

From the list of pairs of formula differences of organic compounds presented in Table 1, six pairs were selected based on the least diversity of heterofunctional groups: CF–H₃Si; C₂HO₂–F₃; C₄–H₄OSi; C₄H₄O₂–N₆; F₄–O₃N₂; HClN₂–O₄. The results of reconstructing suitable structures, taking into account the guidelines described above in the “Theoretical Details” section are presented in Table 3. All compounds presented in Table 3 are liquid or solid substances that have a corresponding molecular ion peak with an intensity higher than 10%. When selecting a pair of compounds, attention was also paid to the absence of chemical interaction between them. We assume that binary mixtures obtained by mixing the presented pairs of compounds in proportions equal to the ratio of the intensities of their molecular ion peaks will be suitable for practical verification of the resolving power of high-resolution mass spectrometers.

Table 3. Organic compounds, potential candidates for verifying the resolving power of a high-resolution mass spectrometer.

Formula difference 1	Formula difference 2	Molecular formula 1	Molecular formula 2	Structure 1/cas#	Structure 2/cas#	m/z 1	m/z 2	Required resolution
CF	H3Si	C6H5F	C5H8Si			96.037528	96.039526	48100
C2HO2	F3	C6H6O3	C4H5F3O			126.031694	126.029249	52000
C4	H4OSi	C13H10	C9H14OSi			166.0783	166.0814	53000
C4H4O2	N6	C7H10O2	C3H6N6			126.0681	126.0654	47000
O3N2	F4	C5H8N2O3	C5H8F4			144.053492	144.056213	53000
HClN2	O4	C6H7ClN2	C6H6O4			142.029776	142.026609	45000

Formula differences are also suitable for reconstructing fragment ions of molecules that are relevant to the desired resolution range of the mass spectrometer as mentioned above. In cases where the peak intensity of a molecular ion is low according to the NIST database, compounds can be selected from which the desired ion will be obtained efficiently by fragmentation.

For example, the structure of the fragment ion C₄H₅O⁺ of 2-butenoic acid (C₄H₆O₂) and the corresponding molecular ion of 1,2,4-triazole C₂H₃N^+•₃ were reconstructed from complementary formula differences C₂H₂O−N₃ with ∆m = 0.0012. These substances enable the verification of the resolution of the mass spectrometer at 51,500 for the peak with m/z 69. From the same pair of formula differences, the structures of fragment ions C₄H₄O^+• of 2-methylenebutanedioic acid and C₂H₂N⁺₃ of 1,2,4-triazole were reconstructed, which makes it possible to verify the resolution of the mass spectrometer at 50,500 for the peak with m/z 68. Under electron ionization conditions, the same fragment ions can be obtained from different compounds, which can be used to verify the resolution of the mass spectrometer. This allows us to select the most suitable substances. Thus, substances containing a labile hydrogen atom can be derivatized to enhance vaporization, while the target fragment ions, for which resolution is verified, remain unchanged (Table 4).

Table 4. Fragment ions from various substances for verifying the resolution of the electron ionization mass spectrometer.

Substance 1	Substance 2	Ion 1	Ion 2	R (m/z)
2-Butenoic acid or tert-butyl-dimethylsilyl ester of 2-butenoic acid or trimethylsilyl crotonate	1,2,4-Triazole	C4H5O+	C2H3N+•3	51500 (69)
2-Methylenebutanedioic acid	1,2,4-Triazole	C4H4O+•	C2⁢H2⁢N+3	50500 (68)
7-Azoindole or 4-aminobenzonitrile, or 3-pyridylacetonitrile	1-Chloro-2,2-dimethylpropane	C6H5N+	C4H8Cl+	8500 (91)
Trimethylchlorosilane	3-Chloro-1-fluoro-2-methylprop-1-ene or 1-chloro-3-fluorobut-2-ene	C3H9Si+•	C4H6F+	37000 (73)

To confirm the resolution of the experimental mass spectrometer, the following resolving power ranges were proposed: up to 5000, 5000–10000, 10000–15000, 15000–20000, 20000–30000, and 50000–55000. The screening of substances for the preparation of test mixtures was carried out according to the procedure specified in the “Calculations and Results” section, taking into account the availability of reagents. In the resolution range up to 4000, the formula difference C₃O₂−H³⁷₃ClSi in the mass range of 62–125 Da was selected. Based on the guidelines for the reconstruction of structure molecules given in the “Theoretical Details” section, a furfural-TMCS pair is proposed from available substances in the lab, but they interact with each other. Substitution of a hydrocarbon substituent for the carbonyl hydrogen in the furfural molecule significantly reduces its reactivity without losing the target ion. Thus, 1-(2-furyl)-1-butanone was chosen instead of furfural.

The formula difference N−CH₂ in the resolution range of 5000–10000 resulted in a pyridine‒p-cresol pair, in which the target ion for pyridine is molecular, and for p-cresol it is fragmentary.¹⁵⁾

In the resolution range of 10000–15000, the formula difference NO−H₂Si in the mass range of 70–83 Da was selected. Based on the formula difference, the pair DMF–TMCS was proposed. However, these substances react with each other at the carbonyl group of DMF, necessitating the replacement of the nucleophilic center of TMCS with a less reactive substituent, which would produce a fragment ion C₃H₉Si⁺ upon ionization. Thus, isopropyl ether of trimethylsilane was proposed instead of TMCS. The search for substances for verifying the resolution in the region of 50000–55000 led to a pair of formula differences HBO₃−C₅. From this pair, taking into account the availability of reagents, the pair of compounds styrene‒trimethyl ester of boric acid was proposed. These compounds yield molecular ions in the 104 m/z region with peak intensities sufficient for their use in a mixture, allowing for verification of the resolution in the specified range. The organic compounds selected for the preparation of test mixtures to verify the theoretical resolution (R_t) of the experimental electron ionization mass spectrometer are presented in Table 5.

Table 5. Organic compounds for verifying the resolution power of the experimental electron ionization mass spectrometer.

Formula difference	Molecular formula, cas# of component 1	Molecular formula, cas# of component 2	m/z target ion of component 1	m/z target ion of component 2	Rt
C3O2−H337ClSi	C8H10O2 (4208-57-5), 1-(2-furyl)-1-butanone	C3H9ClSi (75-77-4), trimethylchlorosilane	C5H3O2+ 95.01276	C2H376 ClSi+ 94.9892	4000
N−CH2	C5H5N (110-86-1), pyridine	C7H8O (106-44-5), p-cresol	C5H5N+ 79.04165	C6H7+15) 79.05423	6300
NO−H2Si	C3H7NO (68-12-2), dimethylformamide	C6H16OSi (1825-64-5), isopropyl ether of trimethylsilane	C3H7NO+ 73.05221	C3H9Si+ 73.0468	13500
HBO3−C5	C3H9BO3 (121-43-7), trimethyl ester of boric acid	C8H8 (100-42-5), styrene	C3H9BO3+ 104.06392	C8H8+ 104.062052	55500

The resolution was determined from the recorded mass spectra as the value of (m/z)/(Δm/z), where Δm was determined as full width at half maximum (FWHM).¹³⁾ The mass spectrum of the mixture of pyridine and p-cresol shows good separation of the target ion peaks, which indicates their resolution (Fig. 4B). The mass spectra of mixtures of TMCS‒1-(2-furyl)-1-butanone and DMF‒isopropyl ether of trimethylsilane also demonstrate separation of the target ion peaks of these substances (Figs. 4A and 4C). The mass spectrum of the mixture of styrene‒trimethyl ether of boric acid in the region of their molecular ions is represented by only one peak, and, therefore, they are not resolved on this mass spectrometer (Fig. 4D).

Fig. 4. Fragment of the mass spectrum of the mixture of (A) TMCS-1-(2-furyl)-1-butanone (3:1 v/v), R_t = 4000; (B) pyridine and p-cresol (1:6 v/v), R_t = 6300; (C) DMF and isopropyl ether of trimethylsilane (1:3 v/v), R_t = 13500; and (D) styrene‒trimethyl ester of boric acid (1:3 v/v), R_t = 55500. DMF, dimethylformamide; TMCS, trimethylchlorosilane.

Indeed, the value of R, found based on the FWHM for each of the peaks in the first three pairs of compounds, is higher than the theoretically calculated value (see Table 5) from the values of the monoisotopic masses of the corresponding ions (Figs. 4A–4C). For the ions from the fourth pair of compounds, on the contrary, this value is lower than the theoretically calculated resolution; however, the peak width in the mass spectrum (2.06 mDa) is significantly narrower than could be expected for two unresolved peaks in the absence of ion coalescence (3.75 mDa). This indicates the compression of ion clouds during their coalescence due to the increase in the number of ions in the cloud.¹⁾ On the other hand, the deviation of the detected mass difference in the case of the DMF–isopropyl ether of trimethylsilane pair, which is more than double from the theoretical value (12.16 mDa instead of 5.4 mDa), shows the presence of space–charge effects that repel ion clouds from each other.^18,19) This can yield a reduced capability of multielectrode Kingdon ion traps in the accurate mass measurement of multiply charged ions.

Thus, the proposed procedure for selecting pairs of substances made it possible to verify the resolution of the lab-made mass spectrometer based on a harmonized Kingdon trap with two merged internal electrodes in the ranges up to 5000, 5000–10000, and 10000–15000 using the following pairs of compounds: TMCS and 1-(2-furyl)-1-butanone, pyridine and p-cresol, DMF, and isopropyl ether of trimethylsilane, respectively.

CONCLUSIONS

The proposed description of the brutto composition of organic compounds using a single formula, and the implementation of the procedure for generating molecular formulas of organic substances using Python code based on this formula, made it possible to quickly search for substances with a given difference in molecular masses. The procedure was applied to screening for pairs of organic compounds suitable for verifying the resolving power of a high-resolution mass spectrometer in the 100 Da region. The results of the screening using the program code led to 166 pairs of organic compounds satisfying the criteria, m ∈ [70–150], R ∈ [45000–50000] with possible heteroatoms of B, N, O, F, Si, P, S, Cl, Br, and I, and using the NIST database to find 88 pairs. However, some of the generated formulas of compounds are not described in known databases and cannot be recommended as substances suitable for verifying the resolution of the mass spectrometer. From the list of complementary pairs of organic compounds obtained by generating molecular formulas using the code, 15 pairs of formula differences were selected, and 22 formula differences were obtained from the pairs found using a search in the NIST database. Although the molecular formula generation code resulted in fewer pairs of formula differences than the NIST database search, it is significantly faster because it directly yields pairs of compounds that are potentially suitable for verifying the resolution of mass spectrometers in the desired range of mass numbers and resolutions. Thus, the screening for pairs of compounds is carried out in three stages: generating a list of pairs of compounds corresponding to the desired range of molecular mass and resolution, obtaining complementary pairs of formula differences, reconstructing compound structures from these differences, and verifying these compounds in the database. The first two steps are implemented using Python code, while the last step is done manually using chemical editors.

From the pairs of formula differences found, those with the smallest number of heteroatoms were selected, and structures of real organic compounds, potentially suitable for verifying the resolving power of a high-resolution mass spectrometer in a given range, were drawn. When drawing the structures, attention was paid to the volatility of the compounds, giving preference, if possible, to ether groups or compounds with labile hydrogen atoms for the possibility of their derivatization. When finally selecting a pair of compounds for preparing a mixture, the absence of chemical interaction between them was taken into account. Thus, six pairs of organic compounds were proposed that were most suitable for verifying the resolution of a mass spectrometer in the range of 45000–53000, with a maximum resolution in the region of 100 Da. Additionally, the possibility of verifying the resolution of mass spectrometers by reconstructing fragment ions from pairs of formula differences was demonstrated.

The proposed procedure for screening pairs of substances was experimentally tested to verify the resolution of a lab-made mass spectrometer based on a harmonized Kingdon trap with two merged internal electrodes in the ranges up to 5000, 5000–10000, 10000–15000, and 50000–55000.

Mass Spectrom (Tokyo) 2025; 14(1): A0176

Funding Statement

The authors gratefully acknowledge the financial support from the Ministry of Science and Higher Education of the Russian Federation within the framework of Agreement No. 075-03-2025-662/6.

AUTHOR CONTRIBUTIONS

Conceptualization: S.V.S. Methodology: S.V.S., A.V.S., and S.I.P. Software: S.V.S. and A.V.S. Validation: V.G.T., A.S.K., and S.I.P. Investigation: V.G.T, S.S.V., V.A.E., and E.A.F. Resources: D.V.K., E.A.F., and I.A.P. Data curation: V.G.T., S.V.S., and A.S.K. Writing—original draft preparation: S.V.S. Writing—review and editing: E.S.S. and S.I.P. Visualization: S.V.S. Supervision: D.V.K. and I.A.P. Funding acquisition: I.A.P. All authors have read and agreed to the published version of the manuscript.

CODE AVAILABILITY STATEMENT

The code related to this study is available at https://github.com/Silkin-sv/MS-resolution-search (accessed on July 2, 2025).

DATA AVAILABILITY STATEMENT

The datasets presented in this article are not readily available due to the funder’s restrictions. Requests to access the datasets should be directed to the corresponding author.

CONFLICTS OF INTEREST

The authors declare no competing interests.