Proton-transfer rate constants for the determination of organic indoor air pollutants by online mass spectrometry

Proton transfer reaction mass spectrometry (PTR-MS) has become an indispensable analytical tool for indoor related sciences. With high-resolution techniques not only is the online monitoring of the selected ions in the gas phase possible, but also, with some limitations, the identification of substance mixtures without chromatographic separation. The quantification is carried out with the help of kinetic laws, which require knowledge of the conditions in the reaction chamber, the reduced ion moblilities and the reaction rate constant kPT under these conditions. Ion–dipole collision theory can be used to calculate kPT. One approach is an extension of Langevin's equation and is known as average dipole orientation (ADO). In a further development, the analytical solution of ADO was replaced by trajectory analysis, which resulted in capture theory. The calculations according to ADO and capture theory require precise knowledge of the dipole moment and the polarizability of the respective target molecule. However, for many relevant indoor related substances, these data are insufficiently known or not known at all. Consequently, the dipole moment μD and polarizability α of 114 organic compounds that are frequently found in indoor air had to be determined using advanced quantum mechanical methods. This required the development of an automated workflow that performs conformer analysis before computing μD and α using density functional theory (DFT). Then the reaction rate constants with the H3O+ ion are calculated according to the ADO theory (kADO), capture theory (kcap) and advanced capture theory for different conditions in the reaction chamber. The kinetic parameters are evaluated with regard to their plausibility and critically discussed for their applicability in PTR-MS measurements.


Introduction
A milestone in the analytical chemistry of the gas phase was the development of online mass spectrometry, which is, inter alia, suitable for numerous applications in food control, medicine and environmental research. 1,2 The method was developed for very volatile and volatile organic compounds (VVOCs and VOCs) and is preferably used when their concentration has to be determined down to the ppt range and with high time resolution. The rst applications in atmospheric chemistry aimed to examine ambient air. [3][4][5] However, the suitability of online mass spectrometry for indoor applications was quickly recognized. 6,7 A basic distinction is made between selected ion ow tube mass spectrometry (SIFT-MS) 8 and proton-transfer-reaction mass spectrometry (PTR-MS), 9,10 with the latter being mainly established in indoor air sciences. 7 The use of PTR-MS to analyze human respiratory gas has been known for many years. [11][12][13] Other successful areas of PTR-MS application and other mass spectrometry techniques with indoor-related questions involve ozone-initiated chemistry, 6,14-16 photocatalytic reactions, 17,18 measurements in museums, 19,20 exposure under living conditions 21-23 and gas phase/particle partitioning. 24 However, online mass spectrometry has pros and cons. The coverage of a wide mass range and the high time resolution are oen offset by calibration problems. In addition, only molecules whose proton affinity is greater than that of water can be studied, since H 3 O + is the preferred reagent for proton transfer. Ions of the same nominal mass cannot be distinguished with a low-resolution quadrupole mass lter without disproportionate effort, their selective analysis requires a time-of-ight (ToF) detector. Not all molecules can be detected via the [M + 1] + ion but rather fragment in the reaction tube, which makes both qualication and quantication more difficult. 25,26 In a PTR-MS system quantication takes place from the signals of the ions involved, the device settings and the reaction constant of the proton transfer k PT . However, it is a fundamental problem of the PTR-MS method that reliable k PT values are only available for a comparatively small number of molecules. On the other hand, k PT can theoretically be calculated. The theory of ion-polar molecule collisions developed by Su and Bowers,27,28 also called average orientation dipole -ADO theory, is well suited for a reasonable estimation of reaction constants. In later works, Su and Chesnavich 29 have taken an alternative route. The results of trajectory calculations were parameterized to give expressions which allow the calculation of k PT . This approach is known as capture theory. Finally, Su 30 parameterized the trajectory calculations for the relative kinetic energy dependence of the rate constant at various temperatures. The ADO and the capture theory were discussed and compared by Ellis and Mayhew. 31 Whichever theory is used, precise data on the dipole moment and polarizability of the target compound under the current reaction conditions are always required. The most critical quantity is the dipole moment. Even for a small and rigid molecule like acetaldehyde, the results of quantum mechanical calculations are between 2.65 D, 32 2.88 D 33 and 2.94 D (this work), depending on the level of theory. Generally, the span between these quantum chemically calculated dipole moments increases with molecular size and exibility, which can be attributed to routinely considering only a single molecular geometry. This ignores conformational exibility and thermal effects, which is far from reality. These effects can signicantly impact geometries and geometry-dependent properties like dipole moments (see below). For many molecules that play a role in the indoor environment, no reliable gas phase dipole moments are known at all.
In this work, we provide quantum chemically calculated, thermally averaged ensemble dipole moments and polarizabilities for 114 organic molecules. On that basis, we calculate and discuss rate constants for proton transfer reactions of organic compounds with H 3 O + ions according to ADO theory and capture theory. Particular attention is paid to Su's 30 advanced capture theory, because this allows the calculation of k PT as a function of the electric eld strength in the PTR-MS reaction chamber. We believe that these data are of particular value for the reliable determination of organic indoor air pollutants.

Soware
The program OriginPro 2021b (64-bit) (OriginLab, Northampton, MA) was used for all non-quantum mechanical calculations, non-linear regression analyses, statistical evaluations and the drawing of some images. ChemDraw 16.0.1.4 (Perki-nElmer Informatics Inc.) was used for drawing chemical structures. DFT calculations were performed using the program package TURBOMOLE 7.5.1. 34

Quantum chemical calculations
Density functional theory (DFT) is routinely used to calculate dipole moments and polarizabilities for organic molecules. However, these calculations need reasonable starting geometries for all investigated compounds as input. Getting these geometries by hand for 114 organic compounds is tedious work and would limit further up-scaling of the developed workow for an even larger number of compounds. Therefore, a workow had to be developed as a rst step that allows the automatic calculation of the relevant properties from more readily available inputs, such as CAS numbers.
The PubChem 35 database provides with its Power User Gateway (PUG) an URL-based API (application programming interface) for programmatic access to its contents. Using a simple command-line program dubbed PubGrep, we were able to get reasonable starting structures for all molecules by translating the given input to a PubChem Compound Identication (CID) rst and aerward getting the corresponding 3D structure information from the database. If no 3D structure information was available, the 2D structure information was taken instead and converted into a 3D structure using the 2D to 3D structure converter included in our xTB program suite. Because dipole moments are highly dependent on the geometric structure of the molecule, a conformational sampling was performed using the program CREST 36 with the GFN2-xTB 37 semiempirical method. The resulting conformer ensemble was re-ranked with the program CENSO 38 and the r 2 SCAN-3c 39 composite DFT method with an energy threshold of 2.0 kcal mol −1 (8.4 kJ mol −1 ). These conformer ensembles were nally used to calculate the dipole moments and polarizabilities with the uB97X-V 40 DFT method. This functional is reported to perform very well for dipole moments with an RMS regularized error (RMSE) of just over 5% for small organic or inorganic molecules. 41 A simplied schematic of this workow is visualized in Fig. 1. Due to the rapid convergence of the computed dipole moment with the size of the applied AO basis (remaining completeness effects of about 0.1%), the def2-TZVPP basis set was chosen for computational efficiency. Instead of just using the lowest lying conformer for these calculations, the properties were calculated as a Boltzmann-weighted average over all conformers in the DFT rened ensemble at 298.15 K up to a Boltzmann threshold of 99% as with the Boltzmann-weighting factor p i as G i is the DFT computed free energy of conformer i, T is the absolute temperature and k B is the Boltzmann constant.

Fundamentals of PTR-MS
The principle of PTR-MS is based on chemical ionization of organic molecules. H 3 O + ions are generated as primary reagents in an ion source. These enter the dri reaction chamber, where they collide with the sample gas molecules. In this process, a proton is transferred, resulting in the formation of ionized organic molecules and water as shown in eqn (4). Organic compounds, whose proton affinity is higher than the proton affinity of water (691 kJ mol −1 ) 42 can be measured according to this principle.
[RH + ] and [H 3 O + ] are the concentrations of the product and the primary ion, respectively. The dri time t r and dri velocity v d are related to the instrumental settings according to eqn (6). 33 L d is the length of the dri tube, U d the applied dri voltage, and u 0 is the reduced ion mobility, 5 which itself depends on the actual instrument settings.  (6) is given by eqn (7).
Usually, the ratio E/N is expressed in Townsend (Td) where 1 Td = 10 −21 V m 2 . The values of u 0 for H 3 O + ions and the H 3 O + $(H 2 O) cluster were experimentally determined by Dotan et al. 43 as a function of E/N. Note that these data can also be found as a graph in Warneke et al. 3 and in the book of Ellis and Mayhew. 31 In both publications, the data from Dotan et al. 43 Table 1 shows values for u 0 , v d and t r at different E/N with a dri tube length L d = 9.6 cm. Clusters are not discussed further, the data  44 The E/N value not only affects the energy of the ions in the dri chamber, but also the fragmentation behavior of the molecules. In chemical ionization, the [M + 1] + ions are oen formed preferentially, but many molecules tend to fragment, a well-studied example being terpenoids. 25,45 Normally, molecules fragment more with higher E/N. A comprehensive fragment ion database is provided by Pagonis et al. 46 4 Determination of k PT values 4.1 Calculation of the reaction rate constant k ADO from dipole orientation theory A widely used approach to calculate k PT follows the ion-dipole collision theory developed by Su and Bowers. 27 Eqn (8) is an extension of Langevin's approach. The term k L describes the classical Langevin rate coefficient for the interaction of an ion with a non-polar molecule. The contribution of the interaction between ion and dipole is given by k m D .
In eqn (8), q is the charge of the ion, a the polarizability of the neutral reactant with dipole moment m D , m m the reduced mass of the reactants and 3 0 the vacuum electric permittivity. C is a temperature dependent dimensionless "locking" parameter (0 # C # 1) that accounts for the permanent dipole moment of the molecule. All quantities are given in SI units. Conversion factors to other units as well as values of the fundamental constants are given in the ESI. †

The locking parameter C
C is a function of the dipole moment m D and the square root of the polarizability a of the neutral molecule. For an entirely nonpolar molecule, C = 0 and then eqn (8) corresponds to the classical Langevin approach. Temperature-dependent values for C as a function of m D /a 1/2 were published by Su and Bowers 47 and Su et al. 48 The data sets for 300 K and 350 K were tted with the empirical eqn (9) in order to be able to calculate k ADO for the respective target molecules. The t parameters are presented in Table 2, the t curves are shown in Fig. 2 and the data are provided in the ESI (Appendix A). † Extending their ADO theory, Su et al. 48 developed an approach that takes into account the moment of inertia of a molecule. The authors explain that, strictly speaking, their extended theory only provides exact values for small linear molecules with a moment of inertia I # 10 −39 g cm 2 . Moreover, Su et al. 48 mention that the temperature dependent C values from Su and Bowers 47 contain a "minor error". Unfortunately, corrected data for 350 K were not presented, only for 300 K (see Fig. 2B). We therefore used the data from Su and Bowers 47 in our work in order to be able to make comparisons with other k PT values.

Calculation of the collision rate constant k cap by trajectory analysis
An alternative to analytical expressions for calculating rate coefficients for ion-molecule interactions is to model reaction processes by trajectory calculations. Su and Chesnavich 29 have published corresponding parameterizations of this method, Table 2 Fit parameters according to eqn (9) for the data sets C = f(m D , a) (see ESI) at 300 K and 350 K. Here m D is given in Debye and a in 10 −24 cm 3  known as capture theory, with which temperature-dependent rate constants can be determined. First, the reaction rate k L according to Langevin (see eqn (8) with C = 0) is determined. In order to obtain the capture rate coefficient k cap , k L is multiplied by the parameterized quantity K cap according to eqn (10) and (11).
All quantities are given in SI units. The full trajectory analysis method for K cap is provided with the respective units in the ESI (Appendix B). † It is a disadvantage of Su and Chesnavich's 29 capture theory that only for small molecules K cap is a function of T R and independent of the moment of inertia I. Ellis and Mayhew 31 state that for the reactions taking place in the PTR-MS, K cap is insensitive to the moment of inertia. In principle, however, this must be checked individually for each molecule. The question whether the conditions of the capture theory are fullled depends not only on I but also on m D and a. We have not performed a rigorous analysis of all the compounds being relevant here, as k cap is presented and calculated for comparison purposes only.

Calculation of the collision rate constant k * cap by advanced trajectory analysis
In a later work, Su 30 presented improved parameterizations that cover a wider temperature range. This takes into account the effect that the temperature of the ions traveling along a dri tube is higher than the dri tube temperature T d because they experience additional energy from the electric eld. Eqn (12) for the total mean ion kinetic energy KE ion was originally developed by Wannier 49 and later discussed by de Gouw et al. 5 in relation to PTR-MS applications.  Table 1. The collision energy of an ion-molecule reaction is then obtained from eqn (13). This is the kinetic energy KE CM relative to the center of mass of the colliding system that is available for the reaction process. 31 In eqn (12) and (13) m ion is the mass of the respective ion H 3 O + or H 3 O + $H 2 O, m air is the average mass of dry air and m m is the mass of the target molecule. The reaction constant k * cap is then obtained according to eqn (14) from the Langevin constant k L and the factor K C , which according to Su 30 depends on the parameters s and 3 to be calculated from the dipole moment m D , polarizability a and KE CM .
The full trajectory analysis method is provided in the ESI (Appendix C). † The inuence of the kinetic energy on the reaction constant is discussed by Ellis and Mayhew 31 using acetone at 300 K as an example. The difference to thermal energy is also signicant for the increased temperature in a PTR-MS dri tube (353 K was assumed here). A value of KE CM = 0.20 eV then results for acetone at E/N = 120 Td, the thermal energy from 3/2$k B $T accounts to 0.05 eV. As already pointed out in detail by Cappellin et al., 50 the particular advantage of k * cap is that it can be used over a wide temperature range. Moreover, there is a direct connection with the electric eld in the dri tube via the dri velocity v d , see eqn (7). This allows the rate constants to be calculated as a function of the E/N value for the respective dri tube temperature.

Dipole moments
The essential parameters for calculating k ADO , k cap and k * cap are the dipole moment m D and the polarizability a. Both quantities are linked to the molar polarization via the Debye equation. 51 For PTR-MS measurements, values are required for the complete, thermally averaged conformer ensemble in the gas phase, because changes in the molecular geometry affect the dipole moment in particular. This effect has not been considered so far in our context. It has already been mentioned that published values can vary considerably. For gas phase 2butoxyethanol, we calculate a dipole moment of 2.42 D aer conformer analysis, while Iglesias et al. 52 4 D). The maximum Dm D value is as high as 2.62 D for dimethyl phthalate. Moreover, tabulated data oen has the disadvantage that the experimental conditions are unknown. Reliable data are only tabulated for a limited number of molecules, 54,55 but quantum chemical tools for their calculation are nowadays routinely available. 50 In this respect, quantum mechanical calculations computed for conformer ensembles appear as the only reasonable alternative, especially in the case of large and non-rigid molecules. The polarizabilities are much less susceptible to conformer changes than the dipole moments. Since the quality of many of the  dipole moments available in the literature could not be evaluated and in order to avoid inconsistencies, only dipole moments and polarizabilities that were determined quantum mechanically according to the method described in Section 2 were used to calculate k ADO , k cap and k * cap . All dipole moments, polarizabilities and calculated k * cap values are listed in Table 3. The k ADO and k cap values are listed in the ESI † (Appendix D).
However, if one refers to the literature, the question now arises as to how precisely the dipole moment of a molecule is available for the conditions prevailing here and what range has to be expected when calculating the reaction constants. For example, experimental values of 1.84 D 55 and 1.87 D 56 in the liquid state have been published for n-butyl acetate. Our calculations resulted in a value of m D = 2.06 D. The difference between experiment (liquid phase) and theory (gas phase) is striking but not surprising. Dipole moments in gas phase and liquid phase are hardly comparable. Molecular geometries are impacted by dispersion and solvent interactions and will therefore oen look very different in these phases, changing the resulting dipole moments.
Attig et al. 57 calculated dipole moments of n-butyl acetate using quantum mechanical methods with 18 different levels of theory. The minima and maxima were 1.97 D and 2.35 D, respectively. However, these values are obtained only for the lowest-lying conformer and are not directly comparable to our thermally averaged results over a conformer ensemble. The computed dipole moment for the lowest-lying conformer in our ensemble is 2.15 D, i.e., very close to the calculated value of Attig et al. 57 (2.18 D) using the B3LYP/6-311++G(d,p) level of theory, which is arguably the best of their methods. A more recent benchmark study on the accuracy of dipole moments for DFT calculations 41 suggests a root mean square error (RMSE) of about 5% for the here employed method (see Section 2.1) which is quite close to the assumption by Cappellin et al. 50 regarding the uncertainty in the quantum chemical calculation for the dipole moment. Fig. 3 shows the dependence of the k PT values, which were calculated with the three methods presented, on the dipole moment using the example of n-butyl acetate. For comparison with our value of 2.06 D, the experimentally determined dipole moments in cyclohexane 55,56 and calculated dipole moments by Attig et al. 57 for three assigned conformers were taken. Regardless of the calculation method, the rate constants for this  molecule vary by 5-10% when the dipole moments differ by about 10%. However, it should be noted that uncertainties in the polarizability were not considered. For n-butyl acetate, Fig. 3 shows reasonable values for the dependence of k PT on the dipole moment. However, the results must not be generalized, since higher dipole moments have a greater inuence on k PT . The differences between the calculation methods are discussed in Section 5.2.
The reliability of theoretical k PT calculations stands and falls not only with the precision of the dipole moment and the polarizability, but it is also important to get the "right" molecule. The question may therefore arise as to which isomer a dipole moment is to be calculated for. A good example is furfural shown in Fig. 4, whose dominant trans isomer at 298.15 K has a calculated dipole moment of 3.60 D, while 4.31 D is given for the cis isomer. 58 Moreover, the energy of the trans isomer is 3.1 kJ mol −1 lower than that of the cis isomer. 59 A similar case concerns acrolein with the more abundant cis isomer 60 (m D (cis) = 2.81 D). The dipole moment of the trans isomer is m D (trans) = 3.43 D. Acrolein was already discussed in a previous publication. 61

Reaction rate constants
Application of the ion-dipole collision theory is the most common method for determining k PT in PTR-MS and SIFT measurements. It should only be mentioned at this point that other formulas can be used to calculate reaction constants in related techniques such as multiple-ion laminar ow tube spectrometry (MIFT). 62, 63 Zhao and Zhang 32 provide k ADO values at 300 K for a total of 136 substances. However, Cappellin et al. 33 doubt that these data can be used for PTR-MS applications and argue with the electric eld strength, which induces far more energetic collisions than those at room temperature. Blake et al. 10 point out that the ADO theory tends to result in lower rate constants than experimentally determined k PT values. With reference to Wannier 49 it is assumed that the effective temperature for ionmolecule collisions is higher than the temperature in the dri tube. For an ion with a dri velocity in the range of 900 m s −1 , the thermal energy accounts for only a small part of the total kinetic energy. The calculation of the k ADO data listed in the ESI † was carried out according to Su and Bowers 27,28 using their data for the locking parameter C at 350 K, 47 a common temperature for PTR-MS measurements. It was already mentioned that Su et al. critically discussed these data in a later publication. 48 Ellis and Mayhew 31 also state that the ADO theory underestimates experimental k PT values at 300 K, but found good agreement with k cap values calculated according to Su and Chesnavich. 29 This is not surprising, because only molecules with small moments of inertia I were included in the comparisons. The molecule with the highest molecular weight was toluene. Nevertheless, Ellis and Mayhew 31 come to the reasonable conclusion that the theoretical values are just as reliable as the experimental values and that uncertainties of 20-30% must generally be expected. The k cap values for the 114 target compounds of this work are listed in the ESI † (Appendix D) and were calculated for 353 K according to Su and Chesnavich. 29 The parameterizations for determining K cap (T R ) are also listed in the ESI. † The ion-dipole collision theories used here have already been discussed by several authors, 9,10,31,50 but essentially for small molecules. Tsikritea et al. 64 state that the ADO theory and the capture theory according to Su and Chesnavich 29 are appropriate when the rotational constants of the molecules are high. Calculated k PT of larger molecules relevant for the indoor environment has only rarely been compared with experimental data, but the available results are satisfactory. Strictly speaking, on account of their symmetry, none of the molecules relevant to indoor analysis as well as those listed in Table 3 meet the preconditions of Su and Chesnavich. 29 However, assuming the molecules to be linear rotors, the parameterization provided by Su 30 is reasonable and the calculation of k * cap should yield reliable results. The calculated values show the expected E/N dependent deviation from k cap (see Fig. 5).
In general, one must be very careful and critical when comparing calculated and experimentally determined k PT values. The rate constants depend not only on the temperature T d in the reaction chamber, but also on the pressure p d and in particular on the electric eld in the dri tube, because these Fig. 4 Dipole moments of the cis and trans isomers of furfural in the gas phase, 58 percent of each isomer, and the energy difference between the two conformers. 59 variables have a direct inuence on the ion mobility. The advanced capture theory takes these aspects into account. The ion energies KE ion required to calculate the k * cap values listed in Table 3 are based on the ion mobilities measured by Dotan et al. 43 (see Table 1). The details of the parameterization for calculating k * cap from K C (s, 3) can be found in the ESI. † In total, k * cap was calculated for seven different E/N values between 80 Td and 140 Td at a temperature of 353 K. The advantages of Su's 30 advanced capture theory over ADO theory and the original capture theory were discussed in detail by Cappellin et al. 50 Using the example of seven sulfur compounds, it was also shown that the k * cap values are larger than the k ADO values. In a later work, Cappellin et al. 33 measured k PT values at E/N = 120 Td and T d = 363 K for 11 substances that also play a role indoors. Excellent agreement with the calculated k * cap values for these conditions was found. In all cases, the deviations between theory and experiment were less than 10%. Cappellin et al. 33 also provide an extensive table of calculated k * cap values of organic compounds at 363 K as a function of E/N. Table 3 in this work essentially extends the list of Cappellin et al. 33 with a large number of indoor-related compounds. In addition, as already mentioned, the applied quantum mechanical method for calculating dipole moments and polarizabilities is superior to previous approaches.
As far as our results are concerned, there is the expected good agreement with the data of Cappellin et al. 33 The small deviations (#5%) are due to the different data for dipole moment and polarizability as well as the different temperature (353 K vs. 363 K). The deviations in furfural are due to the fact that Cappellin et al. 33 confused the dipole moments for the cis and trans isomer. The rate constants for glyoxal in Cappellin et al. 33 are for the trans isomer and in our work for the cis isomer.
Of particular interest is the comparison of the different theories. For this purpose, k ADO and k cap are plotted versus k * cap in Fig. 5, for 100 Td, 120 Td and 140 Td, respectively. The blue line represents the 1 : 1 ratio. It can be seen that at 100 Td the k ADO values are slightly below the k * cap values from about 3.0 × 10 −9 cm 3 s −1 . At 120 Td the agreement between k * cap and k ADO is excellent, at 140 Td the k ADO values deviate slightly upwards. Referring to the values shown in Fig. 5, the highest differences between k * cap and k ADO for 100 Td and 140 Td are in the range of 10%, for 120 Td they are #5%. In this respect, for our assumed conditions and substances, we cannot conrm the statement by Ellis and Mayhew 31 that ADO theory generally tends to underestimate the rate coefficients.
A different picture emerges for k cap . In the three cases displayed, the calculated k cap values are well above the 1 : 1 line and show the expected systematic deviations from k * cap . However, in  Table 3 and from the ESI. † the case of u 0 = constant, both k cap and k * cap do well agree within z±10% in the limit E/N / 0. Hence, the advanced trajectory analysis and its parametrization with a eld dependent kinetic energy term has proven to be a sound and reasonable extension of the capture theory. In contrast to k ADO , the deviations of k cap to k * cap increase with increasing rate constant and E/N. The highest deviations of about 30% occur at 140 Td with strongly polar substances such as acetonitrile, N-methyl-2-pyrrolidone and cis-furfural. In general, it is clear that deviations become more likely with increasing polarity and moment of inertia of the substance. For m D / 0 all theories merge into the Langevin equation. In addition, the capture theory according to Su and Chesnavich 29 has methodological weaknesses when applied to larger molecules. In the calculation of the trajectories Chesnavich et al. 65 have approximated all molecules as linear rotors irrespective of their effective symmetry. This means at least that the individual moments of inertia of the three mutually perpendicular axes of the molecule are averaged, which is a rough approximation for large molecules.

Conclusion
Proton transfer rate constants, which are necessary for the quantitative determination of airborne organic compounds in PTR-MS measurements, were calculated for 114 indoor air pollutants using ion-dipole collision theory at different levels. It was shown that this requires reliable dipole moments and polarizabilities, which are accessible for the respective ensemble containing the energetically lowest conformers in the gas phase via quantum mechanical calculations. The automation of these methods is necessary in order to be able to process a large number of molecules in a reasonable amount of time. In agreement with earlier work we conclude that the advanced capture theory according to Su 30 provides the most reliable rate constants k * cap , since the conditions in the PTR-MS reaction chamber are taken into account with the energy of the ions KE ion , as is the E/N ratio. However, the ion mobilities in the reaction chamber as a function of E/N are required for the calculation. 3,43 For T d = 353 K and E/N = 120 Td, the ADO theory also provides reasonable values.
Aer analyzing the available experimental and theoretical data, we also agree with previous estimates that the rate constants can be determined with an accuracy of 10-25%. The uncertainties increase with the size of the molecule and increasing dipole moment. For more precise assessments, round-robin tests with certied gas standards are also required, which are not yet available for PTR-MS measurements.