Rotational Lists

Description by rotational lists was introduced by Cook and Rohde [110] in the specification of the Standard Molecular Data (SMD) format [111]. In this stereochemical approach, the basic geometrical arrangements around a stcrcoccntcr arc defined in a list (c.g., square, tetrahedron, etc.). The atoms in those stcrcoclcmcnts are also labeled with numbers in a pre-defined way (Figure 2-72),... 

Thus, each stereochemical stnicttirc can be described and recognised with this rotational list if the structure is designated, c.g., in the STEREO block of the SMD format. The compact and extensible representation of the rotational list can include additional information, such as the name specification of the geometiy or whether the configuration is absohtte, relative, or racemic (Eigitre 2-73). 

Figure 2-72. A selection of stereochemical arrangements in a rotational list.

Specific rotations listed are for solutions of low concentration, at equilibrium in water at room temperature, generally about 20°. 

Solutions of such isomers rotate the plane of plane-polarized light. The direction of rotation is indicated by -f (dextrorotatory) and — (levorotatory). The degree of rotation listed in tables is based on a light path of 10 cm through a solution of the substance with a concentration of 1 g per 1 ml. Some comprehensive tables of specific rotation also specify wave length and temperature. Experimental determinations on far less concentrated solutions may be converted to specific rotation, since the rotation is proportional to concentration. 

Finally, we consider the complete molecular Hamiltonian which contains not only temis depending on the electron spin, but also temis depending on the nuclear spin / (see chapter 7 of [1]). This Hamiltonian conmiutes with the components of Pgiven in (equation Al.4,1). The diagonalization of the matrix representation of the complete molecular Hamiltonian proceeds as described in section Al.4,1.1. The theory of rotational synnnetry is an extensive subject and we have only scratched the surface here. A relatively new book, which is concemed with molecules, is by Zare [6] (see [7] for the solutions to all the problems in [6] and a list of the errors). This book describes, for example, the method for obtaining the fimctioiis ... 

Lonally, the templates were chosen by trial and error or exhaustive enumeration. A itafional method named ZEBEDDE (ZEolites By Evolutionary De novo DEsign) en developed to try to introduce some rationale into the selection of templates et al. 1996 Willock et al. 1997]. The templates are grown within the zeolite by an iterative inside-out approach, starting from a seed molecule. At each jn an action is randomly selected from a list that includes the addition of new (from a library of fragments), random translation or rotation, random bond rota-ing formation or energy minimisation of the template. A cost function based on erlap of van der Waals spheres is used to control the growth of the template ale ... 

If the rotational motion of the molecules is assumed to be entirely unhindered (e.g., by any environment or by collisions with other molecules), it is appropriate to express the time dependence of each of the dipole time correlation functions listed above in terms of a "free rotation" model. For example, when dealing with diatomic molecules, the electronic-vibrational-rotational C(t) appropriate to a specific electronic-vibrational transition becomes ... 

Consider a quantity of some liquid, say, a drop of water, that is composed of N individual molecules. To describe the geometry of this system if we assume the molecules are rigid, each molecule must be described by six numbers three to give its position and three to describe its rotational orientation. This 6N-dimensional space is called phase space. Dynamical calculations must additionally maintain a list of velocities. 

The three levels of structure listed above are also useful categories for describing nonprotein polymers. Thus details of the microstructure of a chain is a description of the primary structure. The overall shape assumed by an individual molecule as a result of the rotation around individual bonds is the secondary structure. Structures that are locked in by chemical cross-links are tertiary structures. 

Table 5.2 lists some of the molecules which have been detected. It is interesting to note that some of them, such as the linear triatomics C2H, HCO and N2H, were found in the interstellar medium before they were searched for and found in the laboratory. In all molecules, except OH and NH3, the transitions observed are rotational in nature. 

The following is a list of the known alkaloids, with their specific rotations, as recorded by Smith and Timmis, or by Stoll, Burckhardt and Hofmann. ... 

This table gives the displacements for the normal mode corresponding to the imaginary frequency in terms of redundant internal coordinates (several zero-valued coordinates have been eliminated). The most significant values in this list are for the dihedral angles D1 through D6. When we examine the standard orientation, we realize that such motion corresponds to a rotation of the methyl group. 

The mouse, together with one or more keys, is used both to select and manipulate (translate, rotate and scale) molecules. Available functions are listed at the right and also in Manipulating Molecules (Help menu). 

Some physical properties of the three stereoisomers are listed in Table 9.3. The (+)- and (-j-tartaric acids have identical melting points, solubilities, and densities but differ in the sign of their rotation of plane-polarized light. The meso isomer, by contrast, is diastereomeric with the (+) and (-) forms. As such, it has no mirror-image relationship to (+)- and (-)-tartaric acids, is a different compound altogether, and has different physical properties. 

The entropic hypothesis seems at first sight to gain strong support from experiments with model compounds of the type listed in Table 9.1. These compounds show a huge rate acceleration when the number of degrees of freedom (i.e., rotation around different bonds) is restricted. Such model compounds have been used repeatedly in attempts to estimate entropic effects in enzyme catalysis. Unfortunately, the information from the available model compounds is not directly transferable to the relevant enzymatic reaction since the observed changes in rate constant reflect interrelated factors (e.g., strain and entropy), which cannot be separated in a unique way by simple experiments. Apparently, model compounds do provide very useful means for verification and calibration of reaction-potential surfaces... 

Diheterolevulosans, 209-211, 240 Dihexulose dianhydrides, 207 -266, see also Caramels Di-D-fructose dianhydrides 13C NMR spectra, 245-246 conformation, electronic control, 224-228 conformational rigidity, energetic outcomes, 228 hexulopyranose rings, 226 historical overview, 210-213 H NMR spectra, 248 -249 intramolecular hydrogen-bonds, 227 isomerization, 231 -232 1,2-linked, ero-anomeric effect, 224-225 listing, 240-241 nomenclature, 208-210 optical rotations and melting points, 242-243 protonic activation... 

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