ab initio Modeling of Hydroxyl Radical Reactions with Prevalent Hydrocarbons

Objectives

• Develop an understanding of how to apply ab initio computational methods to examine a set reactions of environmental importance.
• Better understand the geometry and energetics of free radical atmospheric reactions
• Use theoretical quantum concepts to successfully model variations in hydroxyl reactivity for hydrocarbons found in ambient summertime air.

Background

The hydroxyl radical is formed primarily via the reaction between atomic oxygen and water.  Atomic oxygen in an excited state  (¹D₂) is formed by the decomposition of ozone from UV-B radiation:

(1)   O₃ + photon ( l < 320 nm)  --> O₂^* (¹D_g)    +  O^.* (¹D₂)
(2)   O^.* (¹D₂)   +   H₂O   -->   2 OH^.

    (3)   OH^.  + R-H  -->  H₂O   +   R^.                           Hydrogen Abstraction
    (4)   OH^.  + C=C  -->  H₂O   +   ^.C-C-OH              Hydroxyl Addition to Multiple Bond

In general, the lower the energy of the newly formed radical (compared to its neutral counterpart), the faster the reaction that will occur.  This assumes thermodynamic control, a situation that is normally the case for atmospheric free radical reactions that involve tropospheric ozone formation.  One effective tool is to use computational methods to calculate the total energy difference between reactants and products for a given hydroxyl radical / neutral organic reaction.  Experimental data on this rates are limited, particularly at low concentrations due to inherent limitations of smog chambers.

Computational Aspects

The energetics of non-isodesmic reactions are not well modeled by semi-empirical computational methods, and ab initio algorithms, preferably with methods that account for correlation effects, are often used.   Hartree-Fock (HF) techniques treat electron-electron interactions as a single electron interacting with a smeared average of all other electrons.  Because of this, Hartree-Fock calculations do not take electron-electron correlation into account and HF energies tend to be high since they overestimate electron-electron repulsions.  Since these electron coupling effects do not tend to cancel for nonisodesmic reactions, methods (such as Moller-Plesset 2 (MP2) perturbation) which account for electron-electron correlation are necessary to determine reaction energetics.

A comparison of product and reactant energies can be made by searching for the specific geometry that is the lowest energy structure for each reactant and product species.  Geometry optimization requires varying bond angles and lengths for a number of trial geometries, calculating the energy for each, and then continuing the process with new geometries (that are in the direction of lower energy) until a global energy minimum has been found.  This geometry optimization process can require the energy calculation of 10-100 individual structures for each molecule.  Since these types of calculations have to be repeated time and again, efficient geometry optimization methods are necessary.. Unfortunately, MP2 energy calculations can quickly become computationally expensive.

This problem can be addressed by using an uncorrelated method (such as HF) to determine optimum geometries and then using a more time-consuming and reliable electron correlation method (such as MP2) to predict the energy of each optimized structure.  This two step process allows the efficient calculation of each energy in a manner that incorporates the advantages of correlated methods.  Previous work has shown that uncorrelated methods perform just as effectively as correlated techniques in determining optimum geometries.

Problem

Table 1.  Most prevalent ambient hydrocarbons found in Charlotte urban air during summer ozone season for the years 1995-1999.

Year	1995	1996	1997	1998	1999
Top Ten  Hydrocarbons Ranked by Concentrations	Toluene Isopentane 2,2,4-Tmp* m/p-Xylene Ethylene Ethane Propane Benzene n-Butane 2-Methylpentane	Toluene Isopentane m/p-Xylene Propane Ethane Ethylene n-Butane 2,2,4-Tmp* Benzene n-Pentane	Toluene Isopentane Acetylene Propane m/p-Xylene Isoprene Ethylene Ethane 2,2,4-Tmp* n-Pentane	Isopentane Toluene Propane Ethane Acetylene m/p-Xylene n-Butane Ethylene n-Pentane 1,2,4-Tmb*	Toluene Isopentane Propane Ethane m/p-Xylene Ethylene Acetylene n-Pentane n-Butane 2,2,4-Tmp*
Top Ten Hydrocarbons Ranked by  Reactivity-Weighted Concentrations	Ethylene m/p-Xylene Toluene Isoprene 1,2,4-Tmb* Propylene Isopentane o-Xylene 3-Methyl-1-Butene 2-Methyl-1-Pentene	m/p-Xylene Toluene Ethylene Isoprene 1,2,4-Tmb* Propylene o-Xylene Isopentane 1,3,5-Tmb* 3-Methyl-1-Butene	Isoprene m/p-Xylene Ethylene Toluene Propylene 1,2,4-Tmb* Isopentane o-Xylene 1,3,5-Tmb* trans-2-Pentene	Ethylene m/p-Xylene 1,2,4-Tmb* Isoprene Toluene Propylene o-Xylene Isopentane 1,3,5-Tmb* trans-2-Pentene	Ethylene m/p-Xylene Toluene Isoprene Propylene o-Xylene Isopentane trans-2-Pentene cis-2-Pentene Ethylbenzene

*2,2,4-Tmp is 2,2,4-Trimethyle Pentane; 1,2,4-Tmb is 1,2,4-Trimethylbenzene; 1,3,5-Tmb is 1,3,5-Trimethylbenzene
 

Requirements

• Develop a plan (specific objectives, methods, data to be obtained) to examine these type of reactions.  Organize the types of molecules and the types of reactions that you wish to examine.  Include simpler molecules (even if not listed above) as a way to gather additional information.  Divide the workload among groups in the class so that different teams are working an various aspects of the project.

 
• Determine the optimum geometries and the total energy of each optimized structure for each reactant and product in the reactions being examined.  Use this information to predict the change in enthalpy for each reaction. Tabulate the information, depict the optimum geometries found, and discuss what your predictions indicate about relative reaction rates of various hydrocarbons with the hydroxyl radical..

 
• Conduct literature searches to identify the relative reaction rates and most probable sources of the reactive organic substances in Table 1.  Propose field sampling studies and lab testing that you could carry out to verify what you have found in the literature concerning the hydrocarbon emissions of majors sources in urban regions.

 
• Write up your report in a formal lab report format; prepare and present a 10 minute presentation on your work.

Proposed Schedule

• Two weeks of lab work to plan and to carry out the project. One additional week to prepare the report and presentation.