Butane dihedral angle

The top part of Fig. 1 shows the time evolution of the central dihedral angle of butane, r (defined by the four carbon atoms), for trajectories... 

Fig. 1. The time evolution (top) and average cumulative difference (bottom) associated with the central dihedral angle of butane r (defined by the four carbon atoms), for trajectories differing initially in 10 , 10 , and 10 Angstoms of the Cartesian coordinates from a reference trajectory. The leap-frog/Verlet scheme at the timestep At = 1 fs is used in all cases, with an all-atom model comprised of bond-stretch, bond-angle, dihedral-angle, van der Waals, and electrostatic components, a.s specified by the AMBER force field within the INSIGHT/Discover program.

Fig. 4. The average end-to-end-distance of butane as a function of timestep (note logarithmic scale) for both single-timestep and triple-timestep Verlet schemes. The timestep used to define the data point for the latter is the outermost timestep At (the interval of updating the nonbonded forces), with the two smaller values used as Atj2 and At/A (for updating the dihedral-angle terms and the bond-length and angle terms, respectively).

Ethanediol, like n-butane, exists as an equilibrium mixture of two distinct conformers anti (OCCO dihedral angle = 180°) and gauche (OCCO dihedral angle 60°). 

The structure of a second polymorph of 4,5-diphenyl- lH-imidazole has been discussed, with the new form exhibiting significantly different phenyl/imidazole dihedral angles and mode of crystal packing relative to the known form [53], A new triclinic polymorph of 1,4-dibenzoyl-butane was found, differing from the monoclinic form in the torsional angles of the central chain [54], Two polymorphs of diphenyl-(4-pyridyl)methyl methacrylate have been found, where the molecules in the two forms contain weak C—H— n and C—H O/N contacts that lead to the existence of different conformations [55]. 

June et al. (85) presented united-atom calculations for butane and for hexane in silicalite, whereby the bond and dihedral angles of the alkanes were allowed to vary. In addition, the calculation of hexane took account of an additional intramolecular Lennard-Jones potential for nonbonded atoms more than three bonds apart (which prevents the alkane crossing over itself). The interaction parameters for the alkane molecules were taken from Ryckaert and Bellmans (3), and those governing the interaction of the alkanes with the zeolite from a previous study of the low-occupancy sorption of alkanes in silicalite (87). Variable loadings of alkanes were considered from 1 to 8 molecules per unit cell were considered, and calculations were allowed to run for 500 ps for diffusion at 300 K. 

Fig. 3.5 Variation of the energy of butane with dihedral angle. The curve can be represented by a sum of cosine functions...

Two groups, the methyl groups in this case, are said to be anti if the dihedral angle between them is I80c. The and conformation is the most stable conformation of butane because it is staggered and has the two large methyl groups as far apart as possible. 

Plot of energy versus dihedral angle for conformations of butane. Test yourself on the concepts in this figure at OrganicChemistryNow. 

Conformations of Butane (page 190) 6.7 Plot of Energy versus Dihedral Angle for Conformations of Butane (page 191)... 

Newman projections, looking along the central C2—C3 bond, for four conformations of butane. Construct butane with your molecular models, and sight down the C2—C3 bond. Notice that we have defined the dihedral angle d as the angle between the two end methyl groups. 

Figure 6 Potential energy of n-butane as a function of the dihedral angle about the central C—C bond.

Graph Energy versus dihedral angle for butane... 

Problem 3.3 Both calculations and experimental evidence indicate that the dihedral angle between the methyl groups in the gauche conformation of ii-butane is actually somewhat larger than dO"". How would you account for this ... 

Conformation analysis is particularly important in aliphatic systems. Taking butane as an example, there is obviously an infinite number of possible dihedral angles that the two methyl groups can adopt with respect to each other. However, two of the conformers are of particular interest in that they represent the states of lowest and highest interaction between the hydrogens on the adjacent methyl groups these are the staggered and eclipsed conformers respectively. 

Butane has two gauche conformations in which the dihedral angle between the CH3 groups is 60°, and an anti conformation, which is the most stable, with a corresponding dihedral angle of 180°. 

The more involved rotation around the central C-C bond in butane contains a conformation called gauche in which the dihedral angle between the methyl groups is 60°. When this angle is 180° the conformation is tram. 

Some calculated vicinal l3C—l3C coupling constants in Hz for butane, 2-butanol, and butanoic acid at 30° intervals of the dihedral angle (80)... 

Doddrell et al. (80, 66) have examined the angular dependence of V(C-C) in a number of aliphatic and alicyclic alcohols. In contrast to the carboxylic acids, 37(C-C) is observed to be a maximum, 5-4 Hz, for a dihedral angle near 0°. For the trans arrangement, — 180°, 3/(C-C) is 3-2 Hz. At dihedral angles of 90 and 270°, 3/(C-C) is less than 0-4 Hz. Observed 3/(C-C) values for the alcohols and carboxylic acids (66, 80, 52) have been compared with values calculated (INDO-FPT) for the model compounds butane, 2-butanol, and butanoic acid. The calculated coupling constants are given in Table V. (80) Also, experimental and calculated 3J(C-C) values for the carboxylic acids are shown in Fig. 2. The calculations, which assumed only the Fermi contact... 

With acyclic dienes, the quantum yield for cyclobutene formation (cb) rarely exceeds ca 0.1, the expected result of the fact that the planar s-trans conformer normally comprises the bulk (96-99%) of the conformer distribution at room temperature. However, cb is often significantly larger than the mole fraction of s-cis form estimated to be present in solution. For example, 1,3-butadiene, whose near-planar (dihedral angle 10-15° 05,i06 s-cw con fonner comprises ca 1% of the mixture at 25 °C, yields cyclobutene with <1>CB = 0.04 " , along with very small amounts of bicyclo[1.1.0]butane. A second well-known example is that of 2,3-dimethyl-l,3-butadiene (23 ca 4% gauche s-cis at 25 °C ), which yields 1,2-dimethylcyclobutene (25) with cB = 0.12 (equation 16) ". Most likely, these apparent anomalies can be explained as due to selective excitation of the s-cis conformers under the experimental conditions employed, since it is well established that s-trans... 

In (7.165), we have written the mole fraction of the A and B conformers. These are also the probabilities of finding the solute s in A or B, respectively. When the conformation changes continuously, say in butane, as a function of the dihedral angle 4>, (7.165) generalizes to... 

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