Chen The electron capture detector

MORSE POTENTIAL ENERGY CURVES

157

Figure 7.15 Current ‘‘best’’ Morse potential energy curves for I2 and its anions. The X axis is the reduced internuclear distance S ¼ 1 ½re=r&, where r is the internuclear distance and re is the equilibrium internuclear distance. The data are taken from [18]. The 12 curves were predicted in [23].

been measured. Figure 7.15 illustrates the Morse potential energy curves for I2 and its anions using the S dimensionless variable, where S ¼ 1 ðre=rÞ. This type of plot spreads out the curves in the region where the experimental data are available and makes it easier to see the HIMPEC classifications of the curves. The two ground-state curves are M(3) and Mc(3) curves since all the Herschbach metrics are positive. The next curve is D(3) because the vertical process leads to dissociation. It is Mc(3) because it crosses the polarization state on the ‘‘backside.’’ These three states could lead to the formation of the molecular anion on electron impact. The remaining curves are all D(1) and Dc(1) curves because the EDEA is positive, but the Ea and VEa are negative and dissociative electron attachment occurs in the Franck Condon region. The calculated and experimental electron impact data for I2 appear in Figure 7.16. The good fit and the need for multiple negative-ion states are clear. The Morse parameters and dimensionless constants used to calculate these curves are given in Table 7.4.

7.3.4The Negative-Ion States of Benzene and Naphthalene

The negative-ion curves for benzene are very similar to those for H2. Five negativeion states should exist. The X polarization ground-state curve is an M(2) curve. There should be two bonding and two antibonding curves corresponding to the two dissociation limits, Ph þ H( ) and Ph( ) þ H. The two bonding curves are M(0) curves. The aromatic C H bond dissociation energy and electron affinities of the H atom and the phenyl radical have been measured experimentally, giving

158 CONSOLIDATING EXPERIMENTAL, THEORETICAL, AND EMPIRICAL DATA

Figure 7.16 Electron impact spectrum calculated from the current ‘‘best’’ Morse potential energy curves for I2 and I2( ) shown in Figure 7.15. The data are taken from [19].

the EDEA. The vertical electron affinities are the same for the two bonding states, but the Ea are different, at 0.74 eV determined from reduction potential data and at 1.15 eV based on electron transmission spectra. The internuclear distances and frequencies for the anions are close to the values for the neutral. The Morse parameters are given in Table 7.5. Figure 7.17 illustrates the curves. The two antibonding D(0) and Dc(0) curves are not shown. They have larger frequencies and internuclear distances than the bonding curves.

TABLE 7.4 Morse Parameters, Dimensionless Constants, and Experimental Data for Neutral and Ionic I2

	kA	kB	kR	D0 (eV)	re (pm)	ne (cm 1)	VEa	E (abs)
Neutral	1.00	1.00	1.00	1.54	267	215	—	—
A1(1/2)	1.187	0.645	2.242	1.007	320.5	110	1.67	—
A1(1/2)	1.194	0.651	2.264	1.007	320.5	111	1.61	—
B1(3/2)	0.491	0.649	1.702	0.225	371	52.5	0.30	0.87
B1(3/2)	0.491	0.649	1.702	0.225	392	49.5	0.50	1.01
B1(1/2)	0.125	0.557	1.992	0.012	537	10.6	1.35	1.68
B1(1/2)	0.173	0.601	2.297	0.020	501	14.7	1.69	1.65
C1(3/2)	0.376	0.523	2.789	0.080	475	25.3	1.83	1.68
C1(3/2)	0.383	0.587	3.080	0.075	460	27.5	2.27	1.69
C2(1/2)	0.628	0.654	3.118	0.194	400	50	2.35	2.11
C2(1/2)	0.663	0.524	3.491	0.194	439	40	2.82	2.45
D2(1/2)	0.501	0.439	3.569	0.108	510	25	3.45	3.03
D2(1/2)	0.509	0.461	3.691	0.108	500	26.3	3.61	3.03

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159

TABLE 7.5 Morse Parameters, Dimensionless Constants, and Experimental Data for Neutral and Ionic Benzene and Naphthalene

	D0	re	n	kA	kB	kR	Ea (R)	Ea (RH)
Benzene	5.16	1.09	3350	1.000	1.000	1.000	0.000	—
Polariz( ) gs 5.20		1.09	3350	1.008	0.996	1.008	0.000	0þ
M(0)( ) B	3.20	1.11	3000	0.695	1.137	0.779	0.750	1.10
M(0)( ) A	3.20	1.14	3000	0.824	1.137	1.095	1.100	0.78
Naphthalene	5.06	1.09	3350	1.000	1.000	1.000	0.000	—
Polariz( ) B	5.10	1.09	3350	1.008	0.996	1.008	0.000	0þ
M(0)( ) C	4.10	1.12	3300	0.955	1.094	1.126	0.750	0.2
M(2)( ) gs	3.80	1.10	3300	0.795	1.136	0.842	1.390	0.16
M(2)( ) A	3.75	1.10	3310	0.805	1.147	0.874	1.370	0.13

For naphthalene there should be nine negative-ion states: the polarization state, four bonding states, and four antibonding states. The ground state has a positive electron affinity of 0.16 eV and dissociates via the 1 C-H bond. The polarization state and a state dissociating via the 2-C-H bond have positive electron affinities of 0þ and 0.13 eV respectively. The excited-valence-state curve dissociating to H( )

Figure 7.17 Current ‘‘best’’ Morse potential energy curves for benzene and its anions. There are two additional ‘‘antibonding’’ curves going to each dissociation limit that are not shown. The adiabatic electron affinity corresponds to the polarization curve.

160 CONSOLIDATING EXPERIMENTAL, THEORETICAL, AND EMPIRICAL DATA

Figure 7.18 Current ‘‘best’’ Morse potential energy curves for naphthalene and its anions. There are four additional ‘‘antibonding’’ curves that are not shown, giving a total of eight valence-state curves. The adiabatic electron affinity corresponds to the valence state with an Ea of 0.16 eV. The polarization curve has an Ea of about zero.

has a negative electron affinity, 0.2 eV. The electron affinity of the 2-naphthalenide radical is 1.34(2) eV, while that of 1-naphthalenide is 1.39(2) eV. The experimental gas phase acidities differ by 0.05 eV, making the two curves very close since the 2- C-H and 1-C-H bond dissociation energies are only slightly different. The internuclear distances and frequencies for the anion should be similar to those of the neutral. Three anion states have been observed experimentally. The two lower valence-state curves are M(2) curves with a negative EDEA and positive Ea and VEa. Two bonding curves leading to H( ) are M(0) since molecular ion formation takes place in the Franck Condon regions and all three Herschbach parameters are negative. All the bonding curves are Mc(2 or 0) curves. The four antibonding curves are D and Dc(0). Figure 7.18 shows four of these curves.

The dimensionless constants for the ground state for I2( ) correspond to an increase in the attractive term but a larger increase in the repulsive term to give a smaller bond dissociation energy. In the case of bonds for aromatic hydrocarbons the attractive terms are decreased and the repulsive terms increased, but by a smaller amount than for I2( ) or H2( ). Notice that the relative bond order is given by BO ¼ DeðX2ð ÞÞ=DeðX2Þ ¼ ½kA2 =kR&. Thus, the bond orders for the aromatic hydrocarbons are larger than for the diatomic molecules. If there are no experimental data for the construction of negative-ion states of aromatic hydrocarbons, then these values can be used as first approximations or the theoretical values could be used.

EMPIRICAL CORRELATIONS

161

7.4EMPIRICAL CORRELATIONS

The isoelectronic equivalence is the simplest procedure for estimating electron affinities. It was applied to H2 and I2 and to the atomic electron affinities. Species with the same outer electronic configuration should have similar electron affinities and bond dissociation energies. This results in the relative constancy of the electron affinities of a given family of atoms. The equivalence of the bond dissociation energies for the X2( ) and Rg2(þ) ions is also based on this principle. The systematic variation of the electron affinities of the homonuclear diatomic molecules is another example.

Related procedures for estimating electron affinities make use of the concept of electronegativity (EN). These use the Mulliken [33] definition of ‘‘absolute’’ electronegativity, the average of the first ionization potential and the first electron affinity, EN ¼ (IP þ EA)/2. With an estimate of the Mulliken electronegativity and the experimental value of the ionization potential, the electron affinities can be calculated. When both the electron affinity and ionization potential are measured, the relationship between the EN and experiment can be examined. This has been accomplished for aromatic hydrocarbons and will be discussed in Chapter 10.

In the case of atomic species Linus Pauling defined a thermochemical scale of electronegativities and reported the correlation between the absolute scale and thermochemical scales as follows: ‘‘It is seen that the values of x [x ¼ (IP þ EA)/125] are closely proportional to those of the sum of the EA and IP except for hydrogen, which, with its unique electronic structure, might be expected to misbehave’’ [34]. There are other definitions of electronegativity related to these two definitions. Other properties such as the work functions of metals are also related to electronegativity. With these estimates the Mulliken EN for all elements can be obtained. The electronegativities of the alkali metals decrease slightly going down the Periodic Table from 3 eV for Li to 2.2 eV for Cs. The ionization potentials decrease from 5.4 eV for Li to 3.9 eV for Cs. The electron affinities calculated from these data are 0.6 eV for Li and 0.5 eV for Cs. These are only 0.03 eV different from those obtained in experiment. In Chapter 8 we will correlate the electron affinities for all elements with different measures of electronegativity.

The substitution and replacement rules have their origin in correlations between the thermodynamic and kinetic properties of chemical reactions that form part of traditional physical organic chemistry. The Hammett relations consolidate much experimental information based on properties of substituents. These rules are empirical. However, the effects have been attributed to conjugation, mesomeric, or resonance effects; inductive effects; and geometric effects. The substitution of a halogen atom will increase the electron affinity by an inductive effect. The substitution of a vinyl group will increase the electron affinity by conjugation. The substitution of a methyl group will lower the electron affinity by an inductive effect, but with multiple substitutions can increase the electron affinity by geometric effects. The electron affinity of biacetyl is expected to be higher than that of butadiene because of the increased electronegativity of the oxygen atom. The electron affinity of pyridine should be larger than that of benzene, and that of pyrimidine should be

162 CONSOLIDATING EXPERIMENTAL, THEORETICAL, AND EMPIRICAL DATA

larger than that of pyridine because of the greater electronegativity of the nitrogen atom. Multiple substitutions will generally go in the same direction but will be attenuated. These rules have also been incorporated in the simple Huckel theory in the modification of parameters upon substitution on a parent molecule. The replacement rules also have their foundation in simple perturbation theory [4, 35–37].

The substitution rules were originally described in 1963 for the estimation of electron affinities of organic charge transfer complexes. The origin of the rules and their uncertainty are reflected in the following passage:

The relatively great inaccuracy in the electron affinity values precludes discussion of the more refined effects induced by the structure of the compounds involved. Alkyl substituents tend to reduce the electron affinity, the effect becoming more pronounced as the number increases. Electrophillic (halogen, CN, NO2) groups tend to augment the electron affinity of a compound, this effect increasing with the number of substitutions. The cyano and nitro groups tend to increase the electron affinity to a larger extent than do the halogens, which do not differ appreciably in this respect. Molecules with two adjacent electrophillic carbonyl groups are relatively good electron acceptors. The relatively high electron affinity of CCl4 is noteworthy. . .. Carbon tetrachloride and chloroform are s acceptors which, despite their high electron affinity, have an EDA (electron donor acceptor) interaction which is lower than that of p acceptors with comparable electron affinities. [38]

In 1969 the effect of substitutions on electron affinities determined using the magnetron method was thus described: ‘‘While it is tempting to produce a set of numbers for group contributions to p electron affinities which may be used to correlate all of the experimental data, and to predict unknown affinities, the data are far too scanty to do this or to do more than put forward some tentative values.’’ The contribution of an F atom to the electron affinity was assigned a value of 0.2 eV, whereas that for Cl was 0.15 eV. The effect of a single cyano group was 0.8 eV, whereas that for a nitro group was 1 eV. The addition of a second cyano group was only 0.05 lower than the addition of a single cyano group. The passage continues, ‘‘While this leads to a conflict between the magnetron values and those of Compton, it must be remembered that the latter are vertical values and that therefore, they are upper limits. Other work by Compton suggests that the adiabatic attachment energy for benzene may be 0.65 eV lower than the vertical energy, and this difference would account for the supposed ring affinity.’’ The value of 0.65 eV is thus the rearrangement energy. If the modern value for the vertical electron affinity of benzene, 1.15 eV, is used, this gives an Ea of 0.5 eV, as compared to the value of 0.74 eV obtained from reduction potentials. If we use the group contribution of 0.2 eV, the AEa of C6F6 is 0.5 þ 6 0.2 ¼ 0.7 eV. The value predicted by Compton was 0.9 eV. These compare favorably with 0.86(2), the ECD experimental value. The accuracy of the values for benzene and hexafluorobenzene is notable since they were reported in 1969 [39].

By 1988 sufficient gas phase data were available to define substitution effects for the NO2 group and multiple substitutions. The new data were obtained from alkali

EMPIRICAL CORRELATIONS

163

Figure 7.19 Precision and accuracy plot of the corrected values of the electron affinities of halogenated and methylated benzoquinones. These should be compared to the parallel lines in Figure 6.17. The compounds are listed in Table 6.3.

metal beam and thermal charge transfer experiments. The leveling effect of the number of substituents was noted. In addition, a brief look at the effect of substituents on electron affinities obtained from half-wave reduction potentials was considered. This procedure will be extended to additional molecules in Chapter 10.

The CURES-EC values have been calculated for the methyland chlorosubstituted benzoquinones discussed in Chapter 6. They agree with the experimental and density functional calculated Ea. Based on the charge distributions of the C O group, the solution energy differences for the halogenated compounds should be smaller by approximately 0.20 eV than for the parent compound, while the methyl substituted compounds should be about 0.05 eV larger. The charge transfer complex values are also systematically lower than the gas phase values for the chlorinated compounds. This implies that the constants used for those compounds should be larger by about 0.20 eV for the chlorocompounds and 0.10 eV smaller for the methyl compounds. By adding a constant amount to each Ea in the different categories, the deviations are significantly reduced. Since only two additional parameters are used, correlation is made with three intercepts and a unit slope instead of the typical slope and intercept. As shown in the modified precision and accuracy plot in Figure 7.19, the zero intercept slopes for the two sets of data are essentially unity. This procedure will be extended in Chapter 10, and the values from reduction potential and charge transfer complex data will be tabulated for compounds with Ea measured in the gas phase and predicted for other compounds.

164 CONSOLIDATING EXPERIMENTAL, THEORETICAL, AND EMPIRICAL DATA

TABLE 7.6 Theoretical Electron Affinities (in eV) for

Benzene, Naphthalene, Anthracene, Tetracene, and

Pentacene and the Fully Fluorinated Compounds

	F	non-F	Ea=F
Benzene	0.86	0.00	0.14
Naphthalene	1.69	0.16	0.19
Anthracene	2.30	0.68	0.16
Tetracene	2.70	1.10	0.13
Pentacene	3.08	1.39	0.12
Hexacene	3.26	1.60	0.10
Heptacene	3.40	1.80	0.09
Octacene	(3.50)	1.95	0.08
Novacene	(3.60)	2.10	0.07

The effect of multiple substitutions can be determined by examining the perfluorinated acenes. The electron affinity of hexafluorobenzene has been measured using the ECD, PES, and TCT. It is 0.86 0.02 eV. When a fluorine atom is added, the Ea is increased 0.16 eV. The AM1(0033) minimum values for the perfluorinated acenes are provided in Table 7.6 with the experimental value for the nonfluorinted acenes. Also shown are the increments in the electron affinity per fluorine atom. The largest is 0.19 eV/F for perfluoronaphthalene. The Ea of the linear acenes are compared to those of the fluorinated compounds in Figure 7.20. The change in the increment is also shown. The electron affinities of the perfluorinated benzenes are predicted to vary from about 0.1 eV to 0.86 eV. This agrees with experiment, as will be shown in Chapter 11. The increment can be applied to the value for perfluorobenzoquinone to predict an electron affinity of 1.85 þ 4(0.19) ¼ 2.61 eV, the same as the value obtained from reduction potential data.

The linear acenes illustrate the effect of extended conjugation. As the number of rings is extended in both the hydrocarbons and perfluorinated hycrocarbons, the Ea increases. However, for a nonlinear extension the Ea may or may not increase. For example, the Ea of phenanthrene is 0.30 0.02 eV, while that for anthracene is 0.68 0.02 eV. Likewise, the Ea of benzanthracene is less than that of tetracene. The curves for the linear acenes are an upper limit for the electron affinities of polycyclic aromatic hydrocarbons with the same number of six membered rings. The inclusion of five or seven membered rings will increase the electron affinity above those with solely six rings. The simplest example is the Ea of azulene, 0.8 eV, versus that of naphthalene, 0.16 eV. Interestingly, the calculated electron affinity of the perfluorinated azulene is 2.6 eV or about 0.2 eV per fluorine atom.

Another systematic variation of the Ea is observed for the replacement of a CH by a nitrogen atom. The electron affinity of pyridine is expected to be larger than that for benzene and that for quinoline should be greater than that for naphthalene.

SUMMARY 165

Figure 7.20 Plot of the experimental electron affinities of the linear acenes and the calculated electron affinities of the perfluorinated linear acenes versus number of rings. The values are calculated using AM1. The values are given in Table 7.6.

Reduction potential data support this prediction. Also, the inclusion of multiple substitutions of CH by N in benzene is expected to increase electron affinity. On the basis of reduction potentials the Ea of pyridine is about zero; and that for the diazines ranges from 0.2 to 0.36 eV. The triazines vary from 0.5 to 0.9 eV. The predicted value for hexazine is 2.8 eV. These substitution and replacement effects can be used to predict electron affinities. Indeed, the first attempt at estimating the electron affinities of AGCUT was made using such correlations. These will be discussed in more detail in Chapter 12.

7.5SUMMARY

Speedy and accurate desktop computers and modern programs such as HYPERCHEM place quantum mechanical calculations within the reach of any experimental chemist. The CURES-EC procedure simulates equilibrium methods of measuring electron affinities by calculating the difference between the optimized forms of the anion and neutral. The READS-TCT determination of charge densities in anion complexes simulates thermal charge transfer experiments. The effect of

166 CONSOLIDATING EXPERIMENTAL, THEORETICAL, AND EMPIRICAL DATA

geometry on energies can be observed by calculating vertical electron affinities or electron affinities for different forms, such as the linear and bent anions of CS2. The charge densities calculated using HYPERCHEM can be utilized to classify molecules so that different solution energy differences may be used to determine more accurate electron affinities from reduction potentials and/or charge transfer complex energies. Experimental values of electron affinities can be tested against periodic trends that are predicted by simple quantum mechanical concepts. The classification of ionic Morse potential energy curves and their construction from experimental and theoretical data have been described. These can be used to assign experimental electron affinities to excited electronic states.

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