Relationships molecular point symmetry

Figure 13.17 Molecular structure of some sulfides of arsenic, stressing the relationship to the AS4 tetrahedron (point group symmetry in parentheses).

As was discussed earlier in Section 1.2.8 a complication arises in that two of these properties (solubility and vapor pressure) are dependent on whether the solute is in the liquid or solid state. Solid solutes have lower solubilities and vapor pressures than they would have if they had been liquids. The ratio of the (actual) solid to the (hypothetical supercooled) liquid solubility or vapor pressure is termed the fugacity ratio F and can be estimated from the melting point and the entropy of fusion. This correction eliminates the effect of melting point, which depends on the stability of the solid crystalline phase, which in turn is a function of molecular symmetry and other factors. For solid solutes, the correct property to plot is the calculated or extrapolated supercooled liquid solubility. This is calculated in this handbook using where possible a measured entropy of fusion, or in the absence of such data the Walden s Rule relationship suggested by Yalkowsky (1979) which implies an entropy of fusion of 56 J/mol-K or 13.5 cal/mol-K (e.u.)... 

Individual molecular orbitals, which in symmetric systems may be expressed as symmetry-adapted combinations of atomic orbital basis functions, may be assigned to individual irreps. The many-electron wave function is an antisymmetrized product of these orbitals, and thus the assignment of the wave function to an irrep requires us to have defined mathematics for taking the product between two irreps, e.g., a 0 a" in the Q point group. These product relationships may be determined from so-called character tables found in standard textbooks on group theory. Tables B.l through B.5 list the product rules for the simple point groups G, C, C2, C2/, and C2 , respectively. 

Hence, now we are left with the problem of estimating the entropy of fusion at the melting point. Unfortunately, A A, (Pm) (Table 4.5) is much more variable than AvapS( (Tb) (Table 4.2). This might be expected since AfusSt (Tm ) is equal to SiL (Tm) - SiS (Tm) and both of these entropies can vary differently with compound structure. One reason is that molecular symmetry is an important determinant of the properties of a solid substance in contrast to a liquid, where the orientation of a molecule is not that important (Dannenfelser et al., 1993). Nevertheless, as demonstrated by Myrdal and Yalkowski (1997), a reasonable estimate of A S) (Tm) can be obtained by the empirical relationship (Table 4.5) ... 

From the conceptual point of view, there are two general approaches to the molecular structure problem the molecular orbital (MO) and the valence bond (VB) theories. Technical difficulties in the computational implementation of the VB approach have favoured the development and the popularization of MO theory in opposition to VB. In a recent review [3], some related issues are raised and clarified. However, there still persist some conceptual pitfalls and misinterpretations in specialized literature of MO and VB theories. In this paper, we attempt to contribute to a more profound understanding of the VB and MO methods and concepts. We briefly present the physico-chemical basis of MO and VB approaches and their intimate relationship. The VB concept of resonance is reformulated in a physically meaningful way and its point group symmetry foundations are laid. Finally it is shown that the Generalized Multistructural (GMS) wave function encompasses all variational wave functions, VB or MO based, in the same framework, providing an unified view for the theoretical quantum molecular structure problem. Throughout this paper, unless otherwise stated, we utilize the non-relativistic (spin independent) hamiltonian under the Bom-Oppenheimer adiabatic approximation. We will see that even when some of these restrictions are removed, the GMS wave function is still applicable. 

Figure 6. Relationship between coordinates and molecular conformation. Italicized symbols label the loci of the possible symmetry point groups, assuming the nuclei to be identical. Where unassigned, the symmetry point group will be Cs.

The symmetry operations that belong to a particular point group constitute a mathematical group, which means that as a collection they exhibit certain interrelationships consistent with a set of formal criteria. An important consequence of these mathematical relationships is that each point group can be decomposed into symmetry patterns known as irreducible representations which aid in analyzing many molecular and electronic properties. An appreciation for the origin and significance of these symmetry patterns can be obtained from a qualitative development. ... 

---