Determination of Molecular Structure

In this section we present illustrative applications of structure determination of molecular materials directly from powder XRD data, illustrating the current scope of methodologies in this field and highlighting some of the specific issues (and challenges) discussed above. 

A complete NMR crystallography protocol for the structure determination of molecular crystals has also been presented by Salager and co-workers [71, 72], The protocol combines proton spin-diffusion (PSD) restraints with molecular modeling to determine the crystalline structure of thymol. The best structures then undergo structure refinement using DFT geometry optimization and are selected based on their agreement with experimental H and C CS. 

Chemists rely on diffraction methods for the structural determination of molecular solids (i.e. solids composed of discrete molecules), non-molecular solids (e.g. ionic materials) and, to a lesser extent, gaseous molecules. As the technique has been developed, its range of applications has expanded to include polymers, proteins and other macromolecules. The most commonly applied techniques are single crystal and powder X-ray diffraction. Electron diffraction is important for the structural elucidation of molecules in the gas phase and for the study of solid surfaces. Neutron diffraction is used for the accurate location of light atoms (e.g. H, D or Li), or if one needs to distinguish between atoms of similar atomic numbers, e.g. C and N, or Ni and Cu. 

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

It is not the purpose of this book to discuss in detail the contributions of NMR spectroscopy to the determination of molecular structure. This is a specialized field in itself and a great deal has been written on the subject. In this section we shall consider only the application of NMR to the elucidation of stereoregularity in polymers. Numerous other applications of this powerful technique have also been made in polymer chemistry, including the study of positional and geometrical isomerism (Sec. 1.6), copolymers (Sec. 7.7), and helix-coil transitions (Sec. 1.11). We shall also make no attempt to compare the NMR spectra of various different polymers instead, we shall examine only the NMR spectra of different poly (methyl methacrylate) preparations to illustrate the capabilities of the method, using the first system that was investigated by this technique as the example. 

In the chapter on vibrational spectroscopy (Chapter 6) 1 have expanded the discussions of inversion, ring-puckering and torsional vibrations, including some model potential functions. These types of vibration are very important in the determination of molecular structure. 

The determination of molecular structure by microwave spectroscopy (Section VII,A), the measurement of acid-base equilibria by ICR (Section VII,F), and theoretical calculations, especially accurate for the gas phase, are the main novelties of this section. 

The highly detailed results obtained for the neat ionic liquid [BMIM][PFg] clearly demonstrate the potential of this method for determination of molecular reorienta-tional dynamics in ionic liquids. Further studies should combine the results for the reorientational dynamics with viscosity data in order to compare experimental correlation times with correlation times calculated from hydrodynamic models (cf [14]). It should thus be possible to draw conclusions about the intermolecular structure and interactions in ionic liquids and about the molecular basis of specific properties of ionic liquids. 

Regularities observed in the behavior of gases have contributed much to our understanding of the structure of matter. One of the most important regularities is Avogadro s Hypothesis Equal volumes of gases contain equal numbers of particles (at the same pressure and temperature). This relationship is valuable in the determination of molecular formulas—these formulas must be known before we can understand chemical bonding. 

Fig. 8. Illustration of the use of periodic boundary conditions in the determination of molecular electronic structure. The unit cell is shown by the dashed line. As the unit cell size is increased the calculated properties converge toward those of the isolated molecule...

The determination of molecular structure is the simplest application of molecular modelling. Most liquid crystal molecules are found to have a number of conformations which are thermally accessible at room temperature. 

Ciguatoxin. The toxin was isolated from moray eels and purified to crystals by Scheuer s group (1). Structural determination of the toxin by x-ray or NMR analyses was unsuccessful due to the unsuitability of the crystals and due to the extremely small amount of the sample. The toxin was presumed to have a molecular formula of C Hg NO from HRFAB-MS data (MH+, 1111.5570) and to have six hydroxyls, five methyls, and five double bonds in the molecule (2). The number of unsaturations (18 including the five double bonds) and the abundance of oxygen atoms in the molecule point to a polyether nature of the toxin. The toxin, or a closely related toxin if not identical, is believed to be the principal toxin in ciguatera. Ciguatoxin was separable on an alumina column into two interconvertible entities presumably differing only in polarity (J). 

Single crystal x-ray diffraction is, without doubt, one of the most important techniques for the determination of molecular structures in the solid state. The technique is also pivotal to the determination of accurate bond lengths in molecules. However, the analysis of x-ray... 

Versluis, F., Ziegler, T., 1988, The Determination of Molecular Structures by Density Functional Theory. The Evaluation of Analytical Energy Gradients by Numerical Integration , J. Chem. Phys., 88, 322. 

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