Search Results

Reactive (or “odd”) nitrogen is emitted into the atmosphere in a variety of forms, with the most important being NOx (NO and NO2), ammonia (NH3), and nitrous oxide (N2O). Emissions of these species into the atmosphere have been summarized, for example, by the IPCC Fourth Assessment Report (the AR4; IPCC, 2007). Some discussion of NOx emissions and trends has also been presented in Chapter I. Emissions of NOx are mainly the result of anthropogenic activity associated with fossil fuel combustion and industrial activity. For the 1990s, the AR4 estimates total anthropogenic NOx emissions of 33.4 TgN yr−1, with natural emissions (mostly from soil and lightning) accounting for an additional 8.4–13.7 TgN yr−1. Ammonia emissions are comparable in magnitude to those for NOx, with anthropogenic emissions (45.5 TgN yr−1) again exceeding natural emissions (10.6 TgN yr−1). Although the majority of the ammonia produces aerosols or is scavenged by aerosol and is subsequently lost from the atmosphere, some gas phase oxidation does occur, which can in part lead to NOx production. The N2O source strength is about 17.7 TgN yr−1, with natural sources outweighing anthropogenic ones (IPCC, 2007). However, N2O is essentially inert in the troposphere, and thus the vast majority of its photooxidation and concomitant NOx release occurs in the stratosphere. The major NOx − related reactions occurring in the Earth’s troposphere are summarized in Figure III-A-1. As just alluded to, the species NO and NO2 are jointly referred to as NOx and are often treated collectively. This is because, under daytime conditions, these two species are rapidly interconverted, with the interconversion occurring on a much shorter timescale than the loss of either species.

Protic solvents have hydrogen bound directly to electronegative atoms, such as oxygen or nitrogen. They are characterized by their ability to form strong hydrogen bonds with suitable acceptors, particularly simple anions. They include alcohols, formamide and other primary and secondary amides, and formic acid. In methanol, dissociation constants of carboxylic acids, phenols, and protonated nitrogen bases show excellent correlations with corresponding values in water. The largest differences occur for carboxylic acids, which are typically 5 pK-units weaker than in water. Acids become increasingly weak in the higher alcohols, especially t-butanol, because of poorer ion solvation. Homohydrogen-bond formation is generally weak, but ion-pair formation becomes progressively stronger as the solvent polarity decreases. Formamide contains a polar carbonyl group in addition to the ability to hydrogen-bond to anions, and displays pKa-values close to those in water. Formic acid hydrogen-bonds strongly with anions, but poor solvation of the proton, which inhibits the dissociation of acids, normally prevails.

The total energy of a quantum-mechanical system can be written as the sum of its kinetic energy T, Coulombic energy ECoui and exchange and electron correlation contributions Ex and Ecorr, respectively: . . . E=T+Ecoui+Ex+Ecorr (9.1) . . . The only term in this expression that can be derived directly from the charge distribution is the Coulombic energy. It consists of nucleus–nucleus repulsion, nucleus–electron attraction, and electron–electron repulsion terms.

In partitioning space in the analysis of a continuous charge distribution, the requirement of locality, formulated by Kurki-Suonio (Kurki-Suonio 1968, 1971; Kurki-Suonio and Salmo 1971), should be preserved. It states that density at a point should be assigned to a center in the proximity of that point. In discrete boundary partitioning schemes, the density at each point is assigned to a specific basin, while in fuzzy boundary partitioning, the density at the point may be assigned to overlapping functions centered at different locations. The least-squares formalisms described in chapter 3 implicitly define a space partitioning scheme, based on the density functions used in the refinement that are each centered on a specific nucleus. Since the density functions are continuous, they overlap, so the fragments interpenetrate rather than meet at a discrete boundary. Such fuzzy boundaries correspond to smoothly varying functions, both in real and reciprocal space, and therefore to well-behaved fragment scattering factors, and reasonable fragment electrostatic moments. The interpenetratingfragment partitioning schemes are related to the Mulliken and Løwdin population analyses of theoretical chemistry. The topological analysis of the total density, developed by Bader and coworkers, leads to a scheme of natural partitioning into atomic basins which each obey the virial theorem. The sum of the energies of the individual atoms defined in this way equals the total energy of the system. While the Bader partitioning was initially developed for the analysis of theoretical densities, it is equally applicable to model densities based on the experimental data. The density obtained from the Fourier transform of the structure factors is generally not suitable for this purpose, because of experimental noise, truncation effects, and thermal smearing. The topological analysis of the density leads to a powerful classification of bonding based on the electron density. It is discussed in the final sections of this chapter. The stockholder partitioning concept is one of the important contributions to charge density analysis made by Hirshfeld (1977b). It defines a continuous sampling function wi(r), which assigns the density among the constituent atoms. The sampling function is based on the spherical-atom promolecule density—the sum of the spherically averaged ground-state atom densities.

The moments of a charge distribution provide a concise summary of the nature of that distribution. They are suitable for quantitative comparison of experimental charge densities with theoretical results. As many of the moments can be obtained by spectroscopic and dielectric methods, the comparison between techniques can serve as a calibration of experimental and theoretical charge densities. Conversely, since the full charge density is not accessible by the other experimental methods, the comparison provides an interpretation of the results of the complementary physical techniques. The electrostatic moments are of practical importance, as they occur in the expressions for intermolecular interactions and the lattice energies of crystals. The first electrostatic moment from X-rays was obtained by Stewart (1970), who calculated the dipole moment of uracil from the least-squares valence-shell populations of each of the constituent atoms of the molecule. Stewart’s value of 4.0 ± 1.3 D had a large experimental uncertainty, but is nevertheless close to the later result of 4.16 ± 0.4 D (Kulakowska et al. 1974), obtained from capacitance measurements of a solution in dioxane. The diffraction method has the advantage that it gives not only the magnitude but also the direction of the dipole moment. Gas-phase microwave measurements are also capable of providing all three components of the dipole moment, but only the magnitude is obtained from dielectric solution measurements. We will use an example as illustration. The dipole moment vector for formamide has been determined both by diffraction and microwave spectroscopy. As the diffraction experiment measures a continuous charge distribution, the moments derived are defined in terms of the method used for space partitioning, and are not necessarily equal. Nevertheless, the results from different techniques agree quite well. A comprehensive review on molecular electric moments from X-ray diffraction data has been published by Spackman (1992). Spackman points out that despite a large number of determinations of molecular dipole moments and a few determinations of molecular quadrupole moments, it is not yet widely accepted that diffraction methods lead to valid experimental values of the electrostatic moments.