**1. Introduction**

220 Atmospheric Model Applications

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The most relevant chemical reactions that take place in the atmosphere involve free radicals and volatile organic compounds (usually termed VOC). In the troposphere, the main sink of volatile organic compounds (VOC) is oxidation, initiated typically by reaction with hydroxyl (OH) free radicals. Many of these processes give rise to the formation of new radicals, which ultimately cause higher OH radical levels and thus higher rates of reactions of the other VOC present.

Kinetic investigations of the OH radical reaction with VOC's are essential for the evaluation of their significance in air pollution. Reaction rate coefficients are used, for example, in estimating their tropospheric lifetimes, or in atmospheric chemical model calculations which are used to generate distribution maps of air pollutants under given meteorological and topographical conditions. Furthermore, the use of temperature dependent reaction rate coefficients in model calculations increases their accuracy, since the temperature gradient of the troposphere and the seasonal temperature variations can be taken into consideration.

As a result of almost three decades of research, the rate constants and mechanisms of the initial reactions of OH and NO3 radicals with VOCs are now reliably known or can be estimated. Significant advances have been made in our understanding of the mechanisms of the reactions subsequent to the initial OH and NO3 radical attack on selected VOCs and of first-generation products formed from these reactions. Extensive and comprehensive reviews on the current state of knowledge of atmospheric reactions of VOCs have been written periodically over the years. Modern rate constant measurements are often precise, and individual values are known fairly well. In addition, methods exist for estimating rate

Reactivity Trends in Radical-Molecule

need to be taken into account.

**2. Theoretical methodology** 

can be effectively computed.

Idaboy (2009).

**2.1 B//A approach** 

tropospheric reactions, is presented.

Tropospheric Reactions – A Quantum Chemistry and Computational Kinetics Approach 223

well as multiphase reactions in liquid droplets contribute to the atmospheric chemistry. For example, the potentially reactive surface of mineral aerosols may be a significant sink for many volatile organic compounds in the atmosphere, and consequently it could influence the global photooxidant budget. In addition, the special nature of H2O as a third body may

In this work, we summarize the theoretical methodology employed in our work to study the mechanisms and kinetics of the reaction of a variety of COV with OH radicals, in the gas phase and in the presence of mineral aerosols. Also, the possibility of single-water molecule

*Ab initio* quantum chemical calculations can provide results approaching benchmark accuracy for small molecules in the gas phase (Martin & de Oliveira, 1999) and they have proven to be very useful to complement experimental studies. Small molecules in the gas phase are typically addressed by high-level methods such as CCSD(T), QCISD(T) and MRCI, which in many cases are as accurate as experiments (Friesner, 2005). A wide variety of properties such as: structures (Thomas, 1993); thermochemistry (Guner, 2003); spectroscopic quantities (Stanton & Bartlett (1993); and kinetics (Fernandez-Ramos, 2006)

In this section, a summary of the theoretical methodology employed in our work since 1994, and a discussion of the various methods in connection with the kinetics calculations of

Electronic structure calculations have been performed using MP2 and DFT methods. The reliability of DFT methods to properly describe chemical reactions has been discussed

Although the calculations performed in the atmospheric chemistry related to the VOC oxidation cover a list of different quantum chemistry methods that have been used over the years, our latest work has been performed using the M052X density functional method (Zhao, 2006) developed specifically for kinetic calculations by Professor Truhlar and his group. The M05-2X functional has been parametrized to take into account dispersion forces. This functional has previously been tested to model complex reactions, and it has been shown that it provides excellent structures, energies and kinetics results at a reasonable computational cost, thus allowing treatment of large systems (Vega-Rodriguez & Alvarez-

We have used a procedure that has become common in the study of the stationary points of chemical reactions of polyatomic systems because it is relatively inexpensive from a computational point of view and it usually reproduces correctly the main features of the reaction path. It is known as B//A approach, and it consists of geometry optimizations at a given level (A) followed by single point calculations, without optimization, at a higher level (B). Based on our previous experience, the use of B//A approach at CCSD(T)//BHandHLYP level of theory properly describes the energetic and kinetics

catalysis of OH reactions with volatile organic compounds is discussed.

elsewhere (Siegbahn & Blomberg, 1991; Fernandez-Ramos, 2006).

constants for the reactions of VOCs with OH and NO3 radicals which can be used when data are not available. A realistic uncertainty estimate for most VOCs is a factor of 2. Data concerning rate constants for the reactions of the radical intermediates are much more limited and are usually restricted to the simplest cases. It has been assumed that the higher molecular weight radicals react with the same rate constant as their low molecular weight counterparts.

Theoretical calculations provide the data needed to support application of thermochemically-based estimation methods and to evaluate proposed reaction sequences. Estimates of reaction heats and free energies are also used to rule out chemically unreasonable reaction schemes. In recent years the development of theoretical methods for the calculation of potential energy surfaces has led to the direct computation of rate constants. These computational techniques have been tested by comparison with available data for known reactions, and then applied to understand and predict mechanisms and reaction rates. In addition, computational methods provide a useful tool for reducing the time required in the laboratory by suggesting specific product compounds for analysis in chamber experiments. For example, for many combustion systems, detailed kinetic models often consist of up to several thousands of elementary reactions whose kinetic parameters are mainly estimated from those available for similar reactions. Computational kinetics affords one of the simplest and most cost-effective methods for calculating thermal rate constants, by applying the conventional transition state theory (TST), which requires only structural, energetic, and vibrational frequency information for reactants and transition states. On the basis of the TST framework, much progress has been made in developing direct ab-initio methods for calculating rate constants from first principles.

For the last decade the main emphasis of our research in atmospheric chemistry has been to investigate mechanisms and kinetics of many different atmospherically important reactions of selected VOCs and of their reaction products. In particular, we have studied the OH and NO3 initiated oxidation of several groups of organic compounds (alkanes, alkenes, dienes, aromatics, aldehydes, carboxylic acids, alcohols, ethers, etc.) under tropospheric conditions, as well as water-assisted reactions and heterogeneous processes in the presence of mineral aerosol surfaces.

One of our major findings has been the correct explanation of the anti-Arrhenius behavior that is common to many radical-molecule reactions. Indeed, many of these reactions present negative activation energies, i. e. their rate constant decreases with increasing temperature. Following the suggestion of Singleton and Cvetanovic proposed in 1976 (Singleton & Cvetanovic, 1976) and using quantum chemistry methods, we showed that the existence of a stable Van der Waals pre-reactive complex in the entrance of the reaction channel explains satisfactorily the observed kinetic data. Thus, radical-molecule reactions must be seen as complex reactions consisting of more than one elementary step. This mechanism and the resulting rate constant expression are derived in the next Section.

Heterogeneous processes that involve the impact of aerosols and trace vapors on the VOC atmospheric chemistry is a fairly new field of research, and its importance has steadily grown due to its environmental importance. Laboratory studies, together with field observations and modeling calculations, have clearly demonstrated the importance of heterogeneous processes in the atmosphere. In this sense, it is very important to understand the role of particulate matter and the extent to which heterogeneous reactions on solids as well as multiphase reactions in liquid droplets contribute to the atmospheric chemistry. For example, the potentially reactive surface of mineral aerosols may be a significant sink for many volatile organic compounds in the atmosphere, and consequently it could influence the global photooxidant budget. In addition, the special nature of H2O as a third body may need to be taken into account.

In this work, we summarize the theoretical methodology employed in our work to study the mechanisms and kinetics of the reaction of a variety of COV with OH radicals, in the gas phase and in the presence of mineral aerosols. Also, the possibility of single-water molecule catalysis of OH reactions with volatile organic compounds is discussed.
