Free bond rotation

Equivalent hydrogens within a molecule are in identical chemical environments. - In a molecule, hydrogens are equivalent if they are bonded to the same sp carbon atom and there is free bond rotation involving that carbon atom in the molecule. 

A lack of free bond rotation, such as what occurs in small rings or with al-kenes, can make hydrogens bonded to the same carbon atom nonequivalent. - There might be overall symmetry in the molecule making sets of hydrogens equivalent. 

Cyclodextrins are macrocyclic compounds comprised of D-glucose bonded through 1,4-a-linkages and produced enzymatically from starch. The greek letter which proceeds the name indicates the number of glucose units incorporated in the CD (eg, a = 6, /5 = 7, 7 = 8, etc). Cyclodextrins are toroidal shaped molecules with a relatively hydrophobic internal cavity (Fig. 6). The exterior is relatively hydrophilic because of the presence of the primary and secondary hydroxyls. The primary C-6 hydroxyls are free to rotate and can partially block the CD cavity from one end. The mouth of the opposite end of the CD cavity is encircled by the C-2 and C-3 secondary hydroxyls. The restricted conformational freedom and orientation of these secondary hydroxyls is thought to be responsible for the chiral recognition inherent in these molecules (77). 

The chemistry of propylene is characterized both by the double bond and by the aHyUc hydrogen atoms. Propylene is the smallest stable unsaturated hydrocarbon molecule that exhibits low order symmetry, ie, only reflection along the main plane. This loss of symmetry, which implies the possibiUty of different types of chemical reactions, is also responsible for the existence of the propylene dipole moment of 0.35 D. Carbon atoms 1 and 2 have trigonal planar geometry identical to that of ethylene. Generally, these carbons are not free to rotate, because of the double bond. Carbon atom 3 is tetrahedral, like methane, and is free to rotate. The hydrogen atoms attached to this carbon are aUyflc. 

A cycloalkane is a saturated cyclic hydrocarbon with the general formula C H2 . In contrast to open-chain alkanes, where nearly free rotation occurs around C, -C bonds, rotation is greatly reduced in cycloalkanes. Disubstituted cycloalkanes can therefore exist as cis-trans isomers. The cis isomer has both substituents on the same face of the ring the trans isomer has substituents on opposite faces. Cis-trans isomers are just one kind of stereoisomers—isomers... 

Although essentially free rotation is possible around single bonds (Section 3.6), the same is not true of double bonds. For rotation to occur around a double bond, the -rrbond must break and re-form (Figure 6.2). Thus, the barrier to double-bond rotation must be at least as great as the strength of the 7r bond itself, an estimated 350 kj/mol (84 kcal/mol). Recall that the barrier to bond rotation in ethane is only 12 kj/mol. 

Two other theories as to the mechanism of the benzidine rearrangement have been advocated at various times. The first is the rc-complex mechanism first put forward and subsequently argued by Dewar (see ref. 1 pp 333-343). The theory is based on the heterolysis of the mono-protonated hydrazo compound to form a n-complex, i.e. the formation of a delocalised covalent it bond between the two rings which are held parallel to each other. The rings are free to rotate and product formation is thought of as occurring by formation of a localised a-bond between appropriate centres. Originally the mechanism was proposed for the one-proton catalysis but was later modified as in (18) to include two-protons, viz. 

Double bonds and their influence on molecular shape are vitally important for living organisms. For instance, they enable you to read these words. Vision depends on the shape of the molecule retinal in the retina of the eye. cis-Retinal is held rigid by its double bonds (41). When light enters the eye, it excites an electron out of the iT-bond marked by the arrow. The double bond is now weaker, and the molecule is free to rotate about the remaining o-bond. When the excited electron falls back, the molecule has rotated about the double... 

In this case the excited molecules produced on interaction with radiation undergo spin reversal to yield a triplet state with a much longer lifetime than that of the singlet excited state. One or more jt-bonds are broken in the triplet state since one of the n-electrons affected is in an antibonding n molecular orbital. This means that the o-bond is free to rotate and cis and trans isomers can be formed next to each other on recombination of the double bond. 

In longer chained hydrocarbons, the carbon atoms have a zig-zag structure. Also, it is important to note that the atoms are free to rotate about any single bond. 

Figure 2.3 Fragment of polypeptide chain backbone illustrating rigid peptide bonds and the intervening N—Ca and Ca—C backbone linkages, which are free to rotate...

The proton motion from Asp27 to 04 comprises a trajectory of approximately 0.6 A (Figure 6). There is a decrease in the free energy due to the surroundings, which corresponds to nearly 4.5 kcal/mol of stabilization by the protein. Further stabilization occurs as the 04-H04 bond rotates toward the N5 atom, which corresponds to a proton movement of about 1.4 A (Figure 6b)... 

We simulated [38] the orientation TCF for sub-ensembles of molecules that have different OH stretch frequencies at t 0. We found that within 100 fs there was an initial drop that was frequency-dependent, with a larger amplitude of this drop for molecules on the blue side of the line. For times longer than about 1 ps the decay times for all frequencies were the same. We argued that since molecules on the red side of the line have stronger H bonds, they are less free to rotate than molecules on the blue side, leading to a smaller initial decay. For times... 

Free-Energy Barriers to Bond Rotation (kcal/mol) in nr j... 

Consider the dissociation of an ion AM" that may either dissociate to form the fragments and M or the INC [A", M] allowing free mutual rotation and thus reorientation of the particles. Within the INC, A" and M can recombine only if they attain a well-defined mutual orientation, i.e., the system has to freeze rotational degrees of freedom. Such a configuration allowing covalent bonds to be formed is termed locked-rotor critical configuration [169-171,177] and any reac-... 

If the fi C—X bond is free to rotate away from periplanarity, then fi C—H bonds will adopt the geometry reqnired for hyperconjugation [as shown for carbocation (6)] and Markovnikov regiochemistry will be favoured. The results are consistent with ab initio theoretical calculations and can be rationalized using a simple electrostatic model."... 

Table 8 Free energy of activation for bond rotation and the conformational distribution of ...

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