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Keywords:

  • Atmospheric oxidation;
  • Hydroxyl radicals;
  • Nitrate radicals;
  • Ozone;
  • Quantitative structure-activity relationships

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CONCLUSION
  5. REFERENCES

Organic compounds are chemically transformed in the troposphere by reaction with photochemically generated oxidants that include hydroxyl radicals, nitrate radicals, and ozone. The reaction rates are a measure of atmospheric persistence and are necessary for developing environmental exposure assessments. Since relatively few experimentally measured rate constants are available, environmental risk/exposure assessors must estimate degradation rates. Rates can be predicted through use of quantitative structure-activity relationships (QSARs). QSAR methods are described for estimating reaction rates with hydroxyl radicals, nitrate radicals, and ozone. QSAR accuracy and limitations are also discussed.


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CONCLUSION
  5. REFERENCES

Organic compounds emitted or formed in the troposphere are removed by physical processes such as wet and dry deposition and by chemical transformation processes that include reaction with photochemically generated oxidants such as hydroxyl (OH) radicals, nitrate (NO) radicals, and ozone [1–4]. In the troposphere, compounds with liquid-phase vapor pressures as low as 0.00133 mPa (10−8 torr) at ambient temperatures can exist, at least partially, in the vapor-phase [4]. The primary transformation processes in the troposphere are reaction with hydroxyl radicals, nitrate radicals, and ozone [3,5]. Unfortunately, little is known about the rate of reaction of chemicals adsorbed onto particulate matter [6]. The rates at which vapor-phase organic compounds react are a direct measure of their atmospheric persistence, and, hence, reaction rates are a necessary parameter in developing environmental exposure assessments [7].

Atmospheric rate constants have been measured experimentally for only a small fraction of the chemicals of environmental concern. For example, rate constants for the gas-phase reaction with OH radicals have been measured for approximately 750 organic compounds [8]. Therefore, the number of compounds released to the atmosphere from anthropogenic and biogenic sources and formed in the atmosphere via photo-oxidative or other reactive mechanisms greatly exceeds the number of compounds with experimentally determined rate constants. Since experimental measurement can be difficult, time-consuming, and expensive, methods of estimating rate constants have become increasingly important to chemical producers and regulatory agencies for the preparation of environmental risk/exposure assessments [7] and for screening for chemicals of concern due to persistence [6].

This work reviews various quantitative structure-activity relationship (QSAR) estimation methodologies with respect to hydroxyl radicals, ozone, and nitrate radicals reaction rate constants that are readily available for evaluating environmental risk and exposure.

Hydroxyl radical QSARs

All gas-phase organic compounds react with OH radicals with the exception of saturated compounds containing only carbon and halogens (such as chlorofluorocarbons) [1]. In the troposphere, reaction with OH radical is the primary removal process for most gas-phase organic compounds [1]. Therefore, a need exists for reliable estimation of OH radical reaction rate constants for chemicals lacking experimental measurement.

An extensive list of literature sources presenting estimation methods is available [1]. Methods vary from single classes of chemicals to comprehensive estimation methods. This article describes several comprehensive methods that can be readily applied by risk/exposure assessors. Complete detailed descriptions of the methods are not presented here but are available from the original sources.

Atkinson method

Currently, the Atkinson method is the most widely applied OH radical rate-estimation methodology. It is formulated and described by Roger Atkinson and coworkers [1,2,5,9–11]. The Atkinson method is a group/fragment methodology based on observations that gas-phase OH radical reactions with organic compounds proceed by the following four pathways: H-atom abstraction from aliphatic C-H and O-H bonds, OH radical addition to olefinic (>C=C<) and acetylenic (-C≡C-)bonds, OH radical addition to aromatic rings, and OH radical reaction with selected nitrogen, sulfur, and phosphorus atom units. The total estimated rate constant is the summation of the four reaction pathways. A brief description of each pathway is given below. Example calculations are available from the Atkinson references above.

H-atom abstraction from aliphatic C-H bonds. The rate constants for H-atom abstraction from -CH3, -CH2-, and >CH- depends upon the identity of the substituents attached; the following three equations are applied.

  • equation image(1)
  • equation image(2)
  • equation image(3)

where kprim, ksec, and ktert are the group rate factors (coefficients) for H-atom abstraction from CH3, -CH2-, and >CH-, respectively, and where F(X), F(Y), and F(Z) are the substituent factors (coefficients) for the substituent groups X, Y, and Z, respectively. At 25°C, equations become

  • equation image(4)
  • equation image(5)
  • equation image(6)

Rate constants are in units of 10−12 cm3/molecule-sec. Table 1 lists some example F(X) substituent factors.

OH addition to olefinic/acetylenic bonds. The calculation of rate constants for addition to >C=C< or -C≡C- bonds depends upon the number and identity of substituent groups around the bond. Conjugated double bond systems are evaluated by considering the entire conjugated >C=C-C=C< system as a single unit. The generic equation for calculating olefinic/acetylenic addition rate constant at 25° is

  • equation image(7)

where k(olefinic/acetylenic unit) is the group rate constant for the single unit (see Table 2) and C(X)n represents the substitute factors (coefficients) for the nonhydrogen attachments to the olefinic/acetylenic unit (also listed in Table 2); n is the number of substituent factors that can be 1 or more. The single units shown in Table 2 have from one to four possible nonhydrogen attachments. For units having multiple nonhydrogen attachments, the C(X) factors are multiplied in a similar manner to the F(X), F(Y), and F(Z) factors for H-atom abstraction.

OH addition to aromatic rings. The equation for estimating OH addition to phenyl rings is [1]

  • equation image(8)

where Σσ+ is the summation of the electrophilic substituent constants of the substituents on the ring. The value of Σσ+ depends on the position of OH radical addition to the ring; the position having the most negative value of Σσ+ is applied. A compilation of common electrophilic substituent constants (σ+) is available from Brown and Okamoto [12].

For estimating OH addition to aromatic rings other than the phenyl ring, the above equation can be modified using the parent value of the aromatic ring unit instead of the −11.71 equation constant. For example, naphthalene has a measured OH radical rate constant of 21.6 × 10−12 cm3/molecule-sec at 25°C [13]. The log of 21.6 × 10−12 is −10.6655; therefore, the equation for a naphthalene ring unit would be: Log10kadd (cm3/molecule-sec) = −10.6655 − 1.34Σσ+.

OH radical interaction with nitrogen, phosphorus, and sulfur groups. OH radicals can interact with specific nitrogen, phosphorus, and sulfur groups through an initial OH addition or H-atom abstraction [1]. Table 3 lists group rate constants for these interactions with N-, S-, and P-containing organics.

Accuracy. Figure 1 illustrates the correlation between Atkinson method estimates and experimental values [8] for 720 compounds. Approximately 30 compounds with experimental values were excluded from the correlation because values are reported as less than a specific value. For example, the experimental OH rate constant for the chlorofluorocarbon fluorotrichloromethane is reported as <5 × 10−16 cm3/moleculesec; for these types of chlorofluorocarbons, the Atkinson method estimates a rate constant of 0.00. The statistical estimation accuracy (logarithmic basis) for the 720 compound data set is: Correlation coefficient (r) = 0.977 (r2 = 0.955), standard deviation (SD) = 0.246, and absolute mean error = 0.138. On a nonlogarithmic basis, approximately 90% of Atkinson method estimates are within a factor of two of experimental values, and 95% are within a factor of three.

Table Table 1.. Common Atkinson hydroxyl radical substituent factors F(X) at 25°Ca
SubstituentFactor F(X)
  1. a See Atkinson [1], Kwok and Atkinson [5], and Atkinson [10] for a more complete listing.

−CH31.00
−CH2-1.23
−CH2Cl0.36
−CH2Br0.46
−CH2F0.61
−CH2C(=O)-3.9
−CH2ONO20.20
−CH2CN0.12
>CH-1.23
−CHCl20.36
−CHF20.13
−CHBr20.46
>CHC(=O)-3.9
>CHONO20.20
>C<1.23
−CCl30.069
−CF30.071
>CC(=O)-3.9
>CONO20.20
−CF2Cl0.031
−F0.094
−Cl0.38
−Br0.28
I0.53
=O8.7
−Aromatic1.0
−OH3.5
−O-8.4
−ONO20.04
−CN0.19
−OC(=O)R1.6
−C(=O)Cl0.067
−C(=O)-0.75
−CHO0.75
−C(=O)OR0.31
>C=C<1.0
−SH7.8
−S-7.8
−SS-7.8
−NH29.3
−NH-9.3
−N<9.3
−NO20.0
−OP-20.5
−SP-20.5

Limitations. The Atkinson method is reasonably reliable when applied to compounds similar to those used in its derivation. However, extrapolation to chemical structures significantly different from those in the experimental database may result in significant estimation error [1,5].

Table Table 2.. Atkinson group rate constants and substituent factors for hydroxyl radical addition to olefins and acetylenes at 25°Ca
StructureGroup rate constants k × 1012 cm3/molecule-sec
CH2=CH-26.3
CH2=CH<51.4
−CH=CH- (cis-)56.4
−CH=CH- (trans-)64.0
−CH=C<86.9
>C=C<110.0
CH=C-7.0
−C=C-27.0
CH2=CH-CH=CH-105
CH2=CH-C=CH2105
CH2=CH-CH=C<142
CH2=CH-C=CH-142
CH2=C-CH=CH-142
−CH=CH-CH=CH-142
CH2=C-C=CH2142
CH2=CH-C=C<190
CH2=C-CH=C<190
−CH=CH-CH=C<190
CH2=C-C=CH-190
−CH=CH-C=CH-190
>C=CH-CH=C<260
−CH=C-CH=C<260
−CH=CH-C=C<260
CH2=C-C=C<260
−CH=C-C-CH-260
Example substitute factors C(X)
SubstituentFactor C(X)
  1. a See Atkinson [1], Kwok and Atkinson [5], and Atkinson [10] for a more complete listing.

−Alkyl1.0
−F0.21
−Cl0.21
−Br0.26
−CH2-Cl0.76
−CN0.16
−CHO0.34
−C(=O)CH30.90
−O-alkyl1.3
−Phenyl1.0
Table Table 3.. Atkinson group rate constants for the reactions of hydroxyl radicals with N-, S-, and P-containing organic compounds at 25°Ca
Group (R = alkyl)1012 × k (cm3/molecule-sec)
  1. a Atkinson [1].

R-NH221
R-NH-R63
R-N(-R)-R66
R-SH32.5
R-S-R1.7
R-S-S-R225
R-N-NO0
R-N-NO21.3
P(=O)0
P(=S)53
N-C(=O)-S11.9
S-C(=O)-N11.9
thumbnail image

Figure Fig. 1.. Correlation of Atkinson hydroxyl (OH) radical rate estimations versus experimental data for 720 compounds (rate constant units in cm3/molecule-sec).

Download figure to PowerPoint

Availability. An adaptation of the Atkinson method has been computerized in a program called the Atmospheric Oxidation Program that is capable of predicting OH rate constants for any organic structure [7,14] (http://www.epa.gov/oppt/exposure/docs/episuitedl.htm). This program can also estimate rate constants for ozone reaction with olefins and acetylenes.

Klamt molecular orbital method

The Klamt Molecular Orbital Method (MOOH) is described in two journal articles [15,16]. The method is based on the electronic properties of the OH radical reaction sites, which are derived from a semiempirical molecular orbital (MO) calculation for the molecule. Various MO-charges, frontal orbital energies for the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital, and other MO-descriptors are considered. MOOH calculates separate OH radical reaction rate constants for hydrogen abstraction from aliphatic carbon atoms (kabs), OH addition to C=C bonds (kadd), and OH addition to aromatic rings (karom). The corresponding estimation equations are [16]:

  • equation image(9)

where kmath image is the rate constant for the direct abstraction of a hydrogen atom bonded to a sp3-carbon atom and ECHH is the charge-limited effective HOMO energy of the H-atom. For oxygenated molecules, the kmath image rate constant is modified to consider various steric factors [15].

  • equation image(10)

where kmath image is the rate constant for OH addition of an individual sp2-carbon atom, ECHC is the effective HOMO-energy of the C-atom, and QLC is the effective lowest-unoccupied molecular orbital charge of the C-atom.

  • equation image(11)

where kmath image is the rate constant for OH addition to an aromatic carbon atom, EEHC is the energy-weighted effective HOMO-energy, and Emath image is the energy required to deform the molecule in a way to enable OH addition.

Table Table 4.. Hydroxyl radical reaction rate estimations from ionization energies; polycyclic aromatic hydrocarbon (PAH). All rates in units of 10−12 cm3/molecule-sec
CompoundIEaMeasured OH ratebEstimated OH ratecEstimated OH rated
  1. a Ionization energy data from the National Institute for Standards and Technology [20].

  2. b Atkinson [3,13], Kwok and Atkinson [25], Brubaker and Hites [26], and Bunce et al. [27].

  3. c Using aromatic and aliphatic equations from Gusten et al. [18].

  4. d Using heterocyclic and naphthalene equations from text.

Heterocyclics
  Pyrrole8.211103.81114.0
  Imidazole8.8135.90.4736.2
  Oxazole9.909.10.014.5
  Thiazole9.501.410.049.6
  Furan8.8840.50.3731.6
  2-Methylfuran8.3861.92.1082.5
  3-Methylfuran8.7093.50.6944.7
  2,5-Dimethylfuran8.03132.17.15161.5
  Furan-2-aldehyde9.2235.10.1116.5
  Pyridine9.250.370.10
  2-Vinylpyridine8.9256.70.32
  2,3-Benzofuran8.3637.32.25
  Dibenzofuran8.093.95.80
  Quinoline8.6314.40.88
Naphthalenes
  Naphthalene8.1421.64.8735.8
  1-Methylnaphthalene7.9653.09.1478.8
  2-Methylnaphthalene7.9152.310.998.2
  2,3-Dimenthylnaphthalene7.8976.311.7107.2
  1-Nitronaphthalene8.605.40.974.8
  2-Nitronaphthalene8.635.60.884.2
  1-Naphthol7.7655018.4190.0
  2-Naphthol7.8717012.5117.0
Other PAHs
  Acenaphthene7.755819.1
  Acenaphthylene8.121105.22
  Phenanthrene7.891311.7
  Anthracene7.444056.4
  Fluorene7.911210.9
  Fluoranthene7.905011.3
  Pyrene7.425060.5
Aliphatic acids
  Formic Acid11.330.450.98
  Acetic Acid10.560.83.36
  Propionic Acid10.441.164.92
  Butyric Acid10.172.48.05
  Isobutyric Acid10.242.07.09

Table 4 lists the statistical estimation accuracy of the MOOH method and the other OH radical rate methods described here.

Accuracy. The initial MOOH method [16] used a training set of 159 compounds and achieved (logarithmic basis) a correlation coefficient (r) = 0.99 (r2 = 0.985) and a standard deviation = 0.15. A separate 38-compound validation set had a standard deviation of 0.20. When the model was extended to oxygenated compounds [15], a 93-compound training set achieved a standard deviation of 0.20.

Limitations. As a result of limited experimental data, the MOOH method cannot adequately evaluate nitrogen, sulfur, or phosphorus reactions with OH radicals. However, when sufficient data become available, the method should be extendable to calculate these reaction rates [15]. The MOOH method has promise as a more scientific approach (as compared to the empirical group-fragment approaches) when based on sound chemical principles [1]; however, an expanded experimental database is presently required.

Availability. A computerized version of the MOOH method is available [17] (http://www.cosmologic.de/); however, a basic experience with semiempirical MO-calculations is beneficial for obtaining reliable results [16].

Ionization energies

The ionization energy (IE), sometimes called the ionization potential (IP) (usually designated by IE, IP, or, Ei), is the energy required to remove an electron from a molecule or atom. Ionization energy is typically reported in units of electron volts (eV). Gusten et al. [18] correlated measured ionization energies and OH radical rate constants for 161 organic compounds (32 aromatic and 129 aliphatic). Statistical evaluation yielded the following two linear equations.

  • equation image(12)
  • equation image(13)

where kOH is the OH radical rate constant at 27°C (cm3/molecule-sec) and Ei,v is the vertical ionization energy (eV). The correlation coefficient (r) for both equations is 0.95. Because of divergent values, the aromatic and aliphatic data cannot be satisfactorily combined into a single linear equation. In addition, carboxylic acids, polycyclic aromatics, and heterocyclic aromatic compounds were not included in the regression because of a lack of experimental data.

Table Table 5.. Adapted Atkinson and Carter group rate constants (Kozone) for ozone reaction with olefins and acetylenes at 25°C. The C(X) factors from Table 7 are not applied to the rate constants in the first column (for alkyl R). All rates in units of Kozone × 1017 cm3/molecule-sec
 For alkyl RFor any nonalkyl R
  1. a Used even when all R attachments are alkyls.

CH2=CH-R1.20.175
R-CH=CH-R (cis-)13.00.175
R-CH=CH-R (trans-)20.00.175
CH2=C(R)-R1.20.175
R-CH=C(R)-R43.00.175
R-C(-R)=C(R)-R120.00.175
CH2=C(R)-CH=CH21.40.81
CH2=CH-CH=CH-R5.260.81
CH2=C(R)-C(R)=CH218.00.81
CH2=C(R)-CH=CH-R18.00.81
R-CH=CH-CH=CH-R32.00.81
[C=CC=C]-R3100.00.81
[C=CC=C]-R4 (or more)1,000.00.81
CH2=C=CH-R0.015a
R-CH=C=CH-R0.015a
[C=C=C]-R30.015a
[C=C=C]-R40.015a
CH=C-R0.003a
R-C=C-R0.003a

Experimental data are now available for aliphatic acids, polycyclic aromatic hydrocarbons, and heterocyclic aromatics. Table 4 lists measured OH rate constants for these types of compounds with corresponding ionization energies and estimated OH rate constants using the two ionization energy equations. Aliphatic acids are overestimated by a factor of two to four, naphthalenes are underestimated by a factor of roughly five to six, and heterocyclic aromatics are generally underestimated by one to two orders of magnitude. Simple linear correlation of the IE and measured rate data from Table 5 yields the following two class-specific equations.

  • equation image(14)
  • equation image(15)

where kOH is the OH radical rate constant (cm3/molecule-sec) and IE is the ionization energy (potential) in eV.

The following equations were derived for plain unsaturated aliphatics (alkenes, cycloalkenes, dienes, cyclodienes, and terpenes having only alkyl substituents) and for chlorinated olefins [19]:

  • equation image(16)
  • equation image(17)

where kOH is the OH radical rate constant (cm3/molecule-sec) and IP is the ionization potential in eV.

Limitations. One major limitation of these methods is finding experimental ionization energies. The National Institute of Standards and Technology has an available database of ionization energies for several thousand compounds [20] (http://webbook.nist.gov/), but this represents only a fraction of the commercially available organic compounds. Estimating OH rates from estimated ionization energies will introduce additional error into final calculations. In addition, class-specific equations are only applicable to a narrow range of compound structures.

Ozone rate constant QSARs

Tropospheric ozone has been identified as a key product of photochemical air pollution [21]. In addition, ozone reacts with certain classes of organic compounds, especially the alkenes, and contributes to their atmospheric degradation. Significant tropospheric degradation rates between ozone and organic compounds are generally limited to organics containing unsaturated carbon-carbon bonds (such as alkenes, haloalkenes, alkynes, and oxygen-containing compounds with >C=C< bonds) and a very few nitrogen-containing compounds [1]. Ozone reaction with unsaturated compounds proceeds by an initial addition to the unsaturated carbon-carbon bond.

Current QSARs for estimating ozone reaction rate constants are generally limited to structures containing unsaturated carbon-carbon bonds. This limitation is not serious, since this is the only major class of compounds requiring estimation for risk-exposure assessment.

Adapted Atkinson and Carter ozone method

The basic methodology of the Atkinson and Carter ozone method is described in a journal article [21]. The methodology has been adapted and updated somewhat [14] since additional experimental ozone rate constant data have become available since the original publication date in 1984. It is limited to predicting ozone reaction rate constants for olefinic and acetylenic compounds.

The method is similar to the Atkinson OH radical method for estimating OH addition to olefinic/acetylenic bonds. The calculation of rate constants for reaction with >C=C< or -C≡C- bonds depends upon the number and identity of substituent groups around the bond. Conjugated double-bond systems are evaluated by considering the entire conjugated <C=C-C=C< system as a single unit. The generic equation for calculating olefinic/acetylenic addition rate constant at 25°C is

  • equation image(18)

where k(olefinic/acetylenic unit) is the rate constant for the single unit (Table 5) and C(X)n are the substitute factors (coefficients) for the nonhydrogen attachments to the olefinic/acetylenic unit (Table 6); n is the number of substituent factors that can be 1 or more. For units having multiple nonhydrogen, the C(X) factors are multiplied together. When the rate constant units from Table 5 have only alkyl attachments, the C(X) factors are excluded from the above equation. Therefore, the estimated ozone rate constants for an analogous series of plain alkenes such as propene, 1-butene, 1-pentene, 1-hexene, 1-heptene, 1-octene, and 1-decene are exactly the same (1.2 × 10−17 cm3/molecule-sec); observed rate constants for all these compounds are very close to the estimated rate [21].

Table Table 6.. Adapted Atkinson and Carter C(X) substituent factors for ozone reaction with olefins and acetylenes. If the exact substituent is not listed, use the closest analog when possible. If the substituent is substantially different, use a C(X) factor of 1.0
SubstituentC(X) factor
−CH36.5
−Alkyl6.5
−Aromatic12.0
−C(=O)-CH32.7
−CHO0.16
−2nd-CHO3.0
−C=N0.05
−F0.40
−Cl0.143
−Br0.14
−CH2-Cl0.90
−O-C5.0

Accuracy. Using an experimental ozone rate constant database of 112 alkenes and alkynes that spans five orders of magnitude, the Adapted Atkinson and Carter method has the following statistical accuracy (logarithmic basis) [22] (http://www.epa.gov/oppt/exposure/docs/episuitedl.htm): Correlation coefficient (r) = 0.94, SD = 0.52, and absolute mean error = 0.35.

Example calculation

1,1-Difluoroethene [CH2=C(F)F]: from Table 5, the base unit is CH2=C(R)-R, which has a value of 0.175 × 10−17; from Table 6, the C(X) value for C(-F) is 0.40; therefore:

  • equation image

The observed rate constant for 1,1-difluoroethene is 0.019 × 10−17 [21].

Ionization potentials

Ionization potentials can be used for predicting ozone rate constants. The following equations were derived for plain unsaturated aliphatics (alkenes, cycloalkenes, dienes, cyclodienes, and terpenes having only alkyl substituents) and for chlorinated olefins [19].

  • equation image(19)
  • equation image(20)

where kOzone is the ozone reaction rate constant (cm3/molecule-sec) and IE is the ionization potential in eV.

Nitrate radical QSARs

Nitrate radical reactions are potentially important tropospheric loss processes for alkenes, other compounds containing unsaturated >C=C< or -C≡C- bonds, organosulfur compounds, phenolic compounds, and certain nitrogen-containing compounds [1,3,23]. Nitrate radicals are formed in the atmosphere by the following reaction sequence [23].

  • equation image

Nitrate radical concentrations in ambient air are very low during daylight hours, because the nitrate radical photolyzes rapidly in sunlight and reacts rapidly with NO and O3 [23]. Concentrations begin to increase during the early evening and nighttime hours because of the absence of photolysis and low nighttime NO concentrations. Therefore, the gas-phase reaction between nitrate radicals and organic compounds in air is an important removal process only at nighttime.

Correlation to OH radicals rates

Initial nitrate radical reaction mechanisms generally parallel the corresponding OH radical reaction mechanisms [1], suggesting a possible correlation between NO3 and OH radical reaction rates. Atkinson [23] found an approximate linear relationship between NO3 and OH rates for 28 alkenes. Sabljic and Gusten [24] examined the correlation of a more diverse set of compounds (various aliphatic classes) and derived the following equation.

  • equation image(21)

where kNO3 is the NO3 radical rate constant, kOH is OH radical rate constant, and the rate constant units are cm3/molecule-sec. This equation is appropriate only for aliphatic compounds. Sabljic and Gusten [24] found that aromatic benzene classes (such as phenols, cresols, and trimethylbenzenes) deviated systematically from the correlation (and were removed from the correlation), but they did not report corresponding correlations. In addition, aliphatic classes (such as sulfides and disulfides) deviate greatly from the correlation.

Grosjean and Williams [19] derived the following equation for unsaturated aliphatics.

  • equation image(22)

where the rate constant units are in cm3/molecule-sec.

Limitations. Estimating NO3 radical rates from OH radical rates is currently limited to aliphatic classes that include alkenes, alkanes, aldehydes, and ethers. The above equations are useful because reaction with alkenes is important environmentally. One possible limitation is availability of measured OH radical rate data. However, in the absence of measured rate data, estimated OH radical rate data can probably be used, because current OH estimation methods are relatively accurate. For example, when OH estimations [14] are used in place of measured OH data for the Sabljic and Gusten [24] correlation set, NO3 rate estimations are nearly identical statistically.

From the currently available data set [3,14,23,25], approximately 165 organic compounds have both measured OH and NO3 radical rate constants. Sufficient data are available to extend this methodology to aromatic compounds of importance (i.e., phenols) and other chemical classes. But for now, the methodology is only applicable to various aliphatic classes.

Ionization energies

Sabljic and Gusten [24] correlated measured ionization energies and NO3 radical rate constants for 69 organic compounds. Statistical evaluation yielded the following two linear equations.

  • equation image(23)
  • equation image(24)

where kNO3 is the NO3 radical rate constant (cm3/molecule-sec) and Ei,v is the vertical ionization energy (eV). The first equation applies to aliphatic alkenes, alkanes, aldehydes, and ethers and to the phenols. The benzene derivatives for the second equation include alkyl benzenes, tetralin, and methoxybenzene.

Grosjean and Williams [19] derived the following equation for plain unsaturated aliphatics (alkenes, cycloalkenes, dienes, cyclodienes, and terpenes having only alkyl substituents).

  • equation image(25)

where kNO3 is the ozone reaction rate constant (cm3/molecule-sec) and IE is the ionization potential in eV.

Limitations. As noted above for other ionization energy methodologies, acquisition of experimental ionization energy data is a major limitation. In addition, equations are only applicable to the specific classes of compounds from which they were derived.

Atkinson nitrate radical method for olefins

The Atkinson method for estimating NO3 radical rate constants for olefins is analogous to the Atkinson methodology for estimating ozone or OH radical addition to olefins [1]. Calculation for addition to >C=C< bonds depends upon the number and identity of substituent groups around the bond. The generic equation for calculating the olefinic rate constant at 25°C is:

  • equation image(26)

where k(olefinic unit) is the rate constant for the single unit (see Table 7) and C(X)n are the substitute factors (coefficients) for the nonhydrogen attachments to the olefinic unit. By definition, the C(X) factor for C(-alkyl) = 1.0. Currently, other C(X) factors are not available from the literature.

Accuracy and limitations. Table 8 lists experimental and Atkinson method-estimated NO3 radical rate constants for 67 olefinic compounds. For the initial 53 olefins (which excludes the aldehydes and haloalkenes), the Atkinson method has the following statistical accuracy (logarithmic basis): Correlation coefficient between calculated and observed values (r) = 0.915, SD = 0.456, and absolute mean error = 0.354. The C(X) factors for all 53 compounds are assessed as C(-alkyl); C(-olefin) appears in various compounds, but C(-olefin) can be assessed in the same manner as C(-alkyl) with good accuracy. However, as shown in Table 8 for aldehydes and haloalkenes, very poor estimates result when C(X) factors of C(-Cl) or C(-CHO) are assumed to have the same value as (C-alkyl). Simple approximation from the experimental data indicates C(-Cl) has a value of about 0.03 and C(-CHO) of roughly 0.09.

Table Table 7.. Atkinson group rate constants for nitrate (NO)3 radical addition to olefins at 25°Ca
 k (cm3/molecule-sec)
Structural unitNO3 reaction
  1. a Atkinson [1].

CH2=CH-1.0 × 10−14
CH2=C<3.3 × 10−13
−CH=CH- (cis)3.5 × 10−13
−CH=CH- (trans)3.9 × 10−13
−CH=C<9.4 × 10−12
>C=C<5.7 × 10−11

In contrast to the ozone and OH radical methodology, the current NO3 methodology does not consider conjugated olefinic units as a single unit for estimation. For example, the ozone method considers 1,3-cyclohexadiene as R-CH=CH-CH=CH-R, whereas the NO3 method considers it R-CH=CH-R + R-CH=CH-R. By analogy to the ozone and OH methods, increased accuracy occurs when larger conjugated units are applied; but more importantly, much better accuracy results when conjugated units are applied to multiple C(X) factors that are not equal to 1.0.

The Atkinson NO3 method is presently limited to olefins with a very limited number of C(X) factors. The current experimental NO3 radical database exceeds 170 compounds [3,14,23], indicating that the method is expandable to other chemical classes with significant NO3 reaction rates (e.g., phenols) and that it carries increased application within the olefin class. Expansion to all chemical classes is not really necessary because the predominant atmospheric removal mechanism for most chemical classes is reaction with OH radicals.

CONCLUSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CONCLUSION
  5. REFERENCES

QSARs are available to predict atmospheric oxidation rate constants for reactions with tropospheric hydroxy radicals, nitrate radicals, and ozone. For the majority of organic compounds, gas-phase reaction with hydroxyl radicals is the dominant atmospheric degradation process. Two comprehensive OH radical QSAR methodologies (the Atkinson OH method and the MOOH molecular orbital method) are capable of estimating OH radical rate constants for diverse organic structures. In addition, ionization energy QSARs can predict OH rate constants for various chemical classes. With regard to ozone and nitrate radicals, current QSARs are basically limited to olefinic compounds. However, olefins are one of the few chemical classes to have significant environmental degradation rates via atmospheric reaction with ozone or nitrate radicals. Sufficient experimental data are now available to extend nitrate radical QSARs to other chemical classes (e.g., phenols, sulfides) with significant degradation rates and to extend the olefinic QSARs to cover more diverse types of olefins.

Table Table 8.. Experimental and Atkinson method estimated nitrate radical rate constants for olefins. Source of measured data: Atkinson [3,26], U.S. Environmental Protection Agency [14]
 k (cm3/molecule-sec) 
OlefinMeasuredEstimated 
  1. a Assuming C(X) = C(-CHO) = 0.09.

  2. b Assuming C(X) = C(-Cl) = 0.03.

  3. c Assuming C(X) = C(-CH2-{Cl,Br}) = 0.43.

Propylene9.40E-151.00E-14 
1-Butene1.20E-141.00E-14 
Cyclopentene4.60E-133.90E-13 
Cyclohexene5.26E-133.90E-13 
Cycloheptene4.80E-133.90E-13 
trans-2-Butene3.90E-133.90E-13 
1,3,5-Cycloheptatriene1.18E-121.17E-12 
1,3-Butadiene1.00E-132.00E-14 
1,3-Cycloheptadiene6.46E-127.80E-13 
1,3-Cyclohexadiene1.20E-117.80E-13 
1,4-Cyclohexadiene6.60E-137.80E-13 
2,3-Dimethyl-1,3-butadiene2.10E-126.60E-13 
2,3-Dimethyl-2-butene5.70E-115.70E-11 
2-Carene1.94E-113.90E-13 
2-Methyl-1,3-butadiene6.78E-137.20E-13 
2-Methyl-2-butene9.33E-129.40E-12 
2-Methyl-3-butene-2-ol2.10E-141.00E-14 
3,7-Dimethyl-1,3,6-octatriene2.23E-111.88E-11 
3-Isopropenyl-6-oxo-heptanal2.60E-133.30E-13 
3-Methylene-7-methyl-1,6-octadiene1.05E-119.73E-12 
4-Acetyl-1-methylcyclohexene1.05E-119.40E-12 
5-Methyl-5-vinyltetrahydrofuran-2-ol2.00E-141.00E-14 
6-Methyl-5-haptene-2-one7.50E-129.40E-12 
Allyl alcohol1.30E-141.00E-14 
α-Cedrene8.20E-129.40E-12 
α-Copaene1.60E-119.40E-12 
α-Humulene3.50E-111.92E-11 
α-Phellandrene8.52E-119.79E-11 
α-Pinene6.16E-129.40E-12 
α-Terpinene1.80E-101.88E-11 
β-Pinene2.51E-123.30E-13 
Bicyclo[2.2.1]-2,5-heptadiene1.00E-127.80E-13 
Bicyclo[2.2.1]-2-heptene2.45E-133.90E-13 
Bicyclo[2.2.2]-2-octene1.44E-133.90E-13 
But-1-en-3-ol1.20E-141.00E-14 
Camphene6.54E-133.30E-13 
Caryophyllene2.05E-119.73E-13 
cis-1,3-Pentadiene1.40E-123.60E-13 
cis-2-Butene3.50E-133.50E-13 
cis-3-Hexen-1-ol2.70E-133.50E-13 
cis-3-Hexenylacetate2.50E-133.50E-13 
cis-Ocimene2.20E-111.84E-11 
D-Limonene1.22E-119.73E-12 
δ-Carene9.10E-129.40E-12 
γ-Terpinene2.93E-111.88E-11 
Linalool1.10E-119.40E-12 
Longifolene6.80E-133.30E-13 
Sabinene1.01E-113.30E-13 
Styrene1.51E-131.00E-14 
Terpinolene9.26E-116.64E-11 
trans-1,3-Pentadiene1.60E-124.00E-13 
trans-2,4-Hexadiene1.60E-117.80E-13 
trans-Ocimene2.20E-119.73E-12 
Aldehydes
Acrolein1.11E-151.00E-14 
trans-2-Hexenal1.20E-143.90E-13 
trans-Cinnamaldehyde1.90E-143.90E-13 
trans-Crotonaldehyde5.10E-153.90E-13(9.00E-16)a
E,E-2,4-Hexadienedial5.34E-157.00E-13(3.51E-14)a
E,E-2-Methyl-2,4-hexadienedial1.02E-149.73E-12(3.15E-14)b
E,Z-2,4-Hexadienedial5.26E-157.00E-13(3.51E-14)a
Haloalkenes
1,1-Dichloroethene1.23E-153.30E-13(2.97E-16)b
trans-1,2-Dichloroethene1.07E-163.90E-13(3.51E-16)b
Trichloroethylene2.18E-169.40E-12(2.54E-16)b
Vinyl chloride4.30E-161.00E-14(3.00E-16)b
cis-1,2-Dichloroethene1.39E-163.30E-13(2.97E-16)b
3-Bromopropene3.80E-151.00E-14(4.30E-15)c
3-Chloropropylene4.90E-151.00E-14(4.50E-15)c

The primary limitation of QSAR prediction methodologies is the experimental data set upon which the method is trained. This includes accuracy of the experimental measurements and types of structures included in the data set. For best reliability, an estimation method should be applied only to classes of compounds used to develop that particular method [1]. Extrapolation to other chemical classes may result in questionable predictions.

REFERENCES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CONCLUSION
  5. REFERENCES
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