Chen The electron capture detector

its use, but the actual uncertainty, that is, its deviation from the truth, is unknowable. However, the reported value of a measurand cannot be used effectively without some estimate of this uncertainty. Thus, limits to the error must be inferred from the repeatability or precision of the method of measurement and from reasonable estimates of the bias or systematic error of the measurement process, their accuracy. Both precision and accuracy are characteristics of the measurement procedure, not the value. The random errors can be established by multiple determinations if we assume there are no systematic errors. Then if a more precise procedure is developed, the differences in the values can be used as a measure of the systematic error. If these two procedures are used to measure other quantities of the same type and the differences persist, then a systematic error between the two methods of measurement can be inferred. Ideally, the two procedures give the same value within the mutual uncertainties, which would imply that there are no systematic uncertainties and the ‘‘best’’ value according to the least-squares principle is the weighted average.

There are four possible scenarios given the uncertainty required for a specific application of the measurand. In the worst case the random and systematic errors are larger than the required error and both the systematic and random errors must be reported. In the best case the random and systematic errors are smaller than the required error, in which case the number can be specified with the proper number of significant figures based on the combined errors. One method of specifying this quantity is to indicate the uncertainty in the final quoted figure in parentheses after the value. Another technique is to subscript the first insignificant figure. In the second best case the systematic errors are negligible and the standard deviations can be given with the explanation that these are random uncertainties. If the random errors are negligible and the systematic errors are not, then the systematic uncertainties must be estimated and given along with the random errors. In general, uncertainties should not be ascribed to more than two figures.

5.6EVALUATION OF EXPERIMENTAL RESULTS

The objective of any review of experimental values is to evaluate the accuracy and precision of the results. The description of a procedure for the selection of the evaluated values (EvV) of electron affinities is one of the objectives of this book. The most recent precise values are taken as the EvV. However, this is not always valid. It is better to obtain estimates of the bias and random errors in the values and to compare their accuracy and precision. The reported values of a property are collected and examined in terms of the random errors. If the values agree within the error, the weighted average value is the ‘‘most appropriate value.’’ If the values do not agree within the random errors, then systematic errors must be investigated. In order to evaluate bias errors, at least two different procedures for measuring the same quantity must be available.

A very useful tool in establishing the accuracy and precision of a measurement is a timeline of all the measurements. Very often, a technique will improve over time

98 EXPERIMENTAL PROCEDURES AND DATA REDUCTION

Figure 5.13 A precision and accuracy plot of the atomic electron affinities determined before 1967 versus the current ‘‘best’’ values. The deviations from the unit slope and zero intercept line result from random and systematic errors.

so that its precision improves as a result. At some point this will not be true, and an estimate of the ultimate accuracy and precision of the value can then be established. The clustering of the values about a mean with a random distribution of the errors will signal this. Such is the current situation with the electron affinities of the main group atoms. The atomic electron affinities have been reported in numerous handbooks, the widely used NIST tables, and historical reviews.

In a 1953 review of electron affinities the values for hydrogen, the halogens, carbon, and oxygen using flame, surface ionization, magnetron equilibrium techniques, lattice energy calculations, and electron impact determinations were evaluated. By 1960 the first accurate and precise electron affinity of S, C, and O were reported using photodetachment studies [23]. Before 1970 other photon methods were applied to the halogens and other main groups of elements.

The values of the atomic electron affinities determined before 1967 are plotted against the current EvV in Figure 5.13. This is a precision and accuracy (or P and A) plot. The plot of the electron affinities of the charge transfer acceptors (Figure 4.15) was also a P and A plot. It is used to concisely illustrate the quality of the experimental data. By comparing the data to a line with unit slope and zero intercept, an immediate picture of the precision (random) errors and accuracy (bias) errors can be visualized and outliers identified. By inspection the electron affinities of O (2 eV), Cl (4 eV), and F (4 eV) are suspected outliers. The higher values deviate

from the most precise confirmed values by more than twice the standard deviation of the averages. They are outliers and not included in the averages. If we use the ‘‘best’’ values of the Ea at the time, the slope of the linear regression line is 1:03 0:05, while the intercept is 0:08 0:10 eV, which includes the unit slope and zero intercept.

In the past decade many of the atomic Ea have been determined by photodetachment threshold techniques with a precision of parts per million. The earlier values are used to verify the magnitude of these values since they overlap the more precise values within the uncertainty. The electron affinities of Br are as follows 3.76(50) eV, 1927, flame method; 3.49(2), 1944, magnetron; 3.45(20), 1960, lattice energy; 3.53(12), 1960, photoionization; 3.363(3), 1963, photodetachment; 3.363588(2), 1989, photodetachment. The simple average is A ¼ ð3:76 þ 3:49 þ 3:45 þ 3:53 þ 3:363 þ 3:363588Þ=6 ¼ 3:49ð15Þ. This is less accurate and less precise than the 1989 photodetachment value. However, if the weighted average is taken using equations 5.2, this is no longer true:

XhX i

0:0000002 or 3.363588(2), the same as the last value. Before the photon values the weighted average was 3:49 0:02 eV. With the 1963 photoionization value it became 3:366 0:003 eV, which is equal to the current EvV. The P and A plot in Figure 5.13 shows the systematic uncertainties of 0.15 eV in the earlier values for all the halogens.

The precision of the experimental methods can be examined for different species by using a timeline. Plots of the value reported versus the date of the determination for nitrobenzene and SF6 are shown in Figures 5.14 and 5.15. In the NIST compilation six electron affinities for SF6 cluster around 1.07 eV: 1.07(7) (NIMS, 1994); 1.05(10) (TCT, 1985); 1.0(5) (TCT, 1971); 0.9(2) (collisional ionization, 1978), 1.1(2) (electron swarm, 1966), and 1.49(22) (magnetron, 1964). The simple average is 1.11(17) eV, while 1:08 0:05 eV is the weighted average of these values. In the determination of the magnetron values one low value was discarded. If it is included in the average, the magnetron value is 1.4(4) eV and the weighted average is 1.07(5). This is the ‘‘best’’ value and its random uncertainty. Other NIST values range from 0.3 to 0.8 eV up to 3.16 eV. The lower values are different from the largest value by more than the uncertainty and can be assigned to excited states, whereas the photodetachment value is a different quantity, the vertical detachment energy.

REFERENCES 101

5.7SUMMARY

The experimental procedures for obtaining ECD and NIMS data have been described. Examples of the calculations are given for the various classes of molecules. For each group specific test molecules are provided. The aromatic hydrocarbons and aldehydes are Eql(1/1or 1/2) molecules, CS2 is a Eql(2/2) molecule, haloalkanes are DEC(1) molecules, and the halobenzenes and nitromethane are DEC(2) molecules that dissociate via a molecular ion. A graphical procedure for obtaining parameters from ECD data and the calibration of NIMS data using SF6 and nitrobenzene is presented. The use of multiple electron affinities of O2 to define negative-ion states from ECD data is illustrated. A method for the analysis of published NIMS spectra measured at two temperatures reveals the electron affinities of molecules when combined with substitution effects. We then explored the use of precision and accuracy plots and timelines for the evaluation of electron affinities.

REFERENCES

1.Wiley, J. R.; Robinson, J. M.; Ehdaie, S.; Chen, E. S. D.; Chen, E. C. M.; and Wentworth,

W.E. Biochem. Biophys. Res. Comm. 1991, 180, 841.

2.Laramee, J. A.; Mazurkiewicz, P.; Berkout, V., and Deinzer, M. L. ‘‘Discrete Electron Capture Negative Ion Mass Spectrometry,’’ in Encyclopedia of Analytical Chemistry, New York: Wiley, 2000.

3.Wentworth, W. E.; Chen, E. C. M; and Lovelock, J. E.; J. Phys. Chem. 1967, 70, 445.

4.Huang, J.; Sun, K.; Zhang, Y.; Rao, H.; Cai, H.; and Stearns, S. D. J. Chromatogr. A 1999, 842, 229.

5.Lin S. N. Ph.D. dissertation, University of Houston, 1969.

6.D’sa, E. D. Ph.D. dissertation, University of Houston, 1978.

7.Shuie, L. R. Ph.D. dissertation, University of Houston, 1984.

8.Chen, E. C. M.; Shuie, L. R.; D’Sa, E. D.; Batten, C. F.; and Wentworth, W. E. J. Chem. Phys. 1988, 88, 4711.

9.Chen, E. C. M.; Wiley, J. R.; Batten, C. F.; and Wentworth, W. E. J. Phys. Chem. 1994, 98, 88.

10.Stemmler, E. A. and Hites, R. A. Electron Capture Negative Ion Mass Spectra. New York: New York, VCH, 1988.

11.Chen, E. C. M.; Carr, S. D.; Wentworth, W. E., and Chen, E. S. D. J. Chromatogr. A 1998, 827, 91.

12.Wentworth, W. E.; Becker, R. S.; and Tung, R. J. Phys. Chem. 1967, 71, 1652.

13.Wentworth, W. E. and Chen, E. C. M. J. Gas Chromatogr. 1967, 5, 170.

14.Wentworth, W. E; George, R.; and Keith, H. J. Chem. Phys. 1969, 51, 1791.

15.Chen, E. C. M.; George, R.; Carr, S. D.; Wentworth, W. E.; and Chen, E. S. D. J. Chromatogr.

A1998, 811, 250.

16.Chen, E. C. M. and Chen, E. S. D. J. Chromatogr. A 2002, 952, 173.

17.Wentworth, W. E. Mol. Cryst. Liq. Cryst. 1989, 171, 271.

102 EXPERIMENTAL PROCEDURES AND DATA REDUCTION

18.Chen, E. C. M. Ph.D. dissertation, University of Houston, 1966.

19.Chen, E. C. M.; Welk, N.; Chen, E. S.; and Wentworth, W. E. J. Phys. Chem. A 1999, 103, 9072.

20.Massey, H. S. W. Negative Ions. New York: Cambridge University Press, 1976.

21.Pritchard, H. O. Chem. Rev. 1953, 52, 529.

22.Chen, E. S.; Wentworth, W. E.; and Chen, E. C. M. J. Mol. Struc. 2002, 606, 1.

23.Burch, D. S.; Smith, S. J.; and Branscomb L. M. Phys. Rev. 1958, 112, 171.

24.Pack J. L. and Phelps, V. Phys. Rev. Lett. 1961, 6, 111.

25.Vogt, D.; Hauffe, B.; and Neuert, H. Z. Physica. 1970, 232, 439.

26.Bailey, T. L. and Mahadevan, P. J. Chem. Phys. 1970, 52, 179.

27.Stockdale, J. A. D.; Compton, R. N.; Hurst, G. S.; and Reinhardt, P. W. J. Chem. Phys. 1969, 50, 2176.

28.Celotta, R. J.; Bennett, R. A.; Hall, J. L.; Siegel, M. W.; and Levine, J. Phys. Rev. At. Mol. Opt. Phys. 1972, 6, 631.

29.Schiedt, J. and Weinkauf, R. Z. Natforsch. 1995, 50a, 1041.

30.Baeda, A. P. M. Physica 1972, 59, 541.

31.Nalley, S. J. and Compton, R. N. Chem. Phys. Lett. 1971, 9, 529.

32.Tiernan, T. O.; Hughes, B. M.; and Lifschitz, C. J. Chem. Phys. 1971, 55, 5692.

33.Lacmann, K. and Herschbach, D. R. Chem. Phys. Lett. 1970, 6, 106.

34.Wentworth, W. E. J. Chem. Ed. 1965, 42, 96.

35.Wentworth, W. E. J. Chem. Ed. 1965, 42, 162.

36.Deming, W. E. The Statistical Adjustment of Experimental Data. New York: Dover, 1964.

37.Wentworth, W. E.; Hirsch, W.; and Chen E. C. M. J. Phys Chem. 1967, 71, 218.

104 COMPLEMENTARY EXPERIMENTAL AND THEORETICAL PROCEDURES

methods provide Ea from measurements of the equilibrium constant for thermal electron reactions at different temperatures. The molecular electron affinities obtained from the ECD and NIMS and the ‘‘direct capture’’ procedures with an MGN mechanism are absolute values. The term ‘‘absolute’’ means that the value is obtained directly from experimental data and fundamental constants. The equilibrium thermal charge transfer (TCT) method gives relative Ea based on the kinetics and/or thermodynamics of electron transfer reactions between molecules and anions. The thresholds for reactions with electron beam (EB) or alkali metal beams (AMB) are combined with bond dissociation energies or ionization potentials to obtain Ea. Photodetachment (PD), photoelectron spectroscopy (PES), and photoabsorption (PA) methods give Ea from measurements and the photon energy. The reduction potential and solution charge transfer methods cover the Ea range from 0.1 eV to 3.5 eV and confirm many of the values obtained in the gas phase. These are especially important when it is suspected that excited states are involved in gas phase measurements.

The ECD and NIMS procedures, last reviewed in 1989, were updated in Chapter 5 [1]. Reviews covering the MGN[2], TCT[3], AMB[4], EB[5], and ET[6] studies have been published. The PD and PES Ea for approximately 1,000 species have been summarized and compared with theoretical calculations. Few of these are large organic molecules [7]. The accuracy and precision of the methods are determined using precision and accuracy (P and A) plots. The sources of the uncertainties are identified. The EB and electron transmission (ET) techniques yield the vertical electron affinities and cross-sections for ion formation.

Only 10 to 15 molecular Ea have been measured by more than two techniques. The electron affinities of the diatomic halogens, oxygen, and nitrobenzene have been measured by four or more methods. The experimental values that are significantly lower than the evaluated value (EvV) are assigned to excited states based on precision and accuracy plots. The MGN values for SF6 and C6F6 are higher than the EvV but within two standard deviations. The EnCT values for the diatomic halogens are equal to the EvV. However, the values for some fluorocarbons are unexplainably higher than the EvV. With these stipulations the molecular electron affinities reported in the literature agree within twice the nominal uncertainties described in this chapter.

The electron affinities of the aromatic hydrocarbons have been calculated using Huckel theory and MINDO/3 procedures. The electron affinities of benzene, naphthalene, anthracene, and tetracene have been calculated by density functional and ab initio procedures [8]. The relationship between the experimental and calculated values is examined. The electron affinities of other organic compounds have been calculated using MNDO, density functional, and ab initio procedures [9]. A more thorough discussion of these experimental and theoretical methods can be found in Electron and Molecule Interactions and Their Applications, Volume 2, Chapter 6. The experimental and theoretical electron affinities of atoms, molecules, and radicals up to 1984 are listed but not evaluated [10]. The NIST site briefly discusses the various methods for determining electron affinities and gives an

unevaluated list of electron affinities that can be searched by combinations of elements [11].

The complementary techniques for determining rate constants for thermal electron attachment, detachment, and dissociation are the flowing afterglow, the microwave technique, the ion cyclotron resonance procedures, the swarm and beam procedures, the shock tube techniques, the detailed balancing procedures, the measurement of ion formation and decay, and the high-pressure mass spectrometer procedures. In all cases the measurement of an ion or electron concentration is made as a function of time so that kinetic information is obtained. In the determination of lifetimes for ions, a limiting value of the ion decay rate or k 1 is obtained.

The electron attachment reactions for inorganic molecules were reviewed in 1974. Those for organic molecules were summarized in 1984 [12, 13]. In many cases activation energies were not measured. If a nominal value for A1 and A 1 is assumed, the activation energies can be estimated. Recently, the flowing afterglow procedure has been extended to include electron and gas heating so that the dependence of the rate constants on thermal electron attachment can be examined for bulk temperature and electron temperature [14].

6.2 EQUILIBRIUM METHODS FOR DETERMINING ELECTRON AFFINITIES

In the equilibrium methods the electron is treated the same as any other chemical reactant. The measurement of the electron affinity of a molecule involves the measurement of the equilibrium constant for the reaction of thermal electrons with a molecule ðAB þ eð Þ ¼ ABð ÞÞ at some specific temperature or series of temperatures. The equilibrium technique requires (1) a source of thermal electrons, (2) a source of the test species, (3) a method of measuring the equilibrium concentrations of the neutral species, negative ions, and free thermal electrons, and (4) a temperature measurement. The equilibrium constant is directly related to the Ea by this equation:

ln KeqT3=2 ¼ ln A þ ln ðQanÞ þ Ea=RT ð6:1Þ

where ln A is 12.43 when evaluated from fundamental constants. If the partition function ratio Qan is independent of temperature, then the slope of a plot of ln KT3=2 versus 1,000/T will give the electron affinity when multiplied by R, the gas constant. If the measurement is made at a single temperature, heat capacity and entropy data must be available for the reactants and products, or assumptions must be made concerning Qan to determine the energy at absolute zero.

The three general equilibrium methods are ECD/NIMS, surface ionization, including the magnetron direct capture techniques, and the kinetic or detailed balancing measurement of the rate constants. The ECD method has been applied to about 150 molecules. The NIMS method involves the application of the ECD

106 COMPLEMENTARY EXPERIMENTAL AND THEORETICAL PROCEDURES

Figure 6.1 Plots of ECD and electron swarm data as ln KT3/2 versus 1,000/T for molecular oxygen. The ECD data with the higher b region were published in [18], while the other data appeared in [17]. The electron swarm data derive from [16]. This shows the equivalence of the ECD and electron swarm data. The calculated curve through the ECD data gives an AEa of 1.07 eV as determined by three techniques [111–113].

model to atmospheric pressure ionization and chemical ionization mass spectrometry. It has only been applied to a few molecules, but can be extended using additional published data [15]. The magnetron direct capture technique has been applied to approximately 20 molecules. The kinetic detailed balancing techniques have only been applied to a few molecules.

The first accurate excited-state electron affinity of molecular oxygen was determined using the equilibrium swarm method [16]. Figure 6.1 is a global plot of the swarm data for oxygen as ln KT3=2 versus 1,000/T. This is compared to two sets of ECD data used to determine the excited-state electron affinity of oxygen. One set has a larger a region and a higher value of K in the b region. Independent investigators used a highly purified carrier gas to reduce the recombination rate constant to obtain these data [17, 18]. Lines drawn through the two regions illustrate how first approximations to the parameters can be obtained for least-squares analysis. Also shown in Figure 6.1 are the calculated curves and high-temperature ECD data obtained in this laboratory and used to support the higher AEa for O2 [10, 11]. The ECD results were supported by atmospheric pressure ionization experiments in which the molecular negative ion was observed at 550 K where the change in slope is observed. The low response in the b region in the ECD data results from the low k1 value that was also measured in the swarm data. The swarm data gives a