Rule-based flagging

Equation (2.2) is sometimes referred to as the ideal gas law. However, for our present purposes, we must recognize that this law [like those summarized in (2.3a-d)] is merely a crude approximation that never describes any real gas exactly, except in the idealized limit of zero pressure (to be discussed in Section 2.3). Hence, we must sharply distinguish between crude empirical laws (which are at most approximate rules of thumb) and true thermodynamic laws as summarized in Table 2.1. A difficulty for the beginning student of thermodynamics is to distinguish those equations that are based on the ideal gas approximation (and thus are practically never true) from those of rigorous thermodynamic quality. We shall often flag equations of the former type with IG (ideal gas), for example... 

The first assignment step was to detect planar rings that obey the Hiickel rule of 4n+2 p-electrons and flag them as aromatic, i.e. force all the atoms into an sp2 hybridization state. For planarity recognition, three arbitrarily chosen adjacent ring atoms form a base plane. Subsequently, for each atom of the ring, the distance to this base plane is computed, d being zero for the ideal case. In vector notation, the plane equation can be described as follows ... 

The model is restricted to compounds that display acid-base bonding and therefore it cannot be used to describe metallic or organic bonding. Within these limits, the Valence Sum Rule is found to be widely obeyed and has proved remarkably useful in the analysis of inorganic structures. The Equal Valence Rule is less universal and fails when the environment of an atom is distorted as a result of its internal electronic structure or as the result of the application of the Distortion Theorem in constrained structures. In some highly constrained structures the Valence Sum Rule may also be violated, indicating the presence of internal strain and flagging the possible existence of a complex crystal chemistry. 

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