Dihedral angle 3/cccc

Step through the sequence of structures depicting rotation about the C i - C+ bond in 2-methyl-2-butyl cation. Plot energy (vertical axis) vs. CCCC dihedral angle (horizontal axis). What is the preferred conformation, with the ethyl group in plane or perpendicular to the plane ... 

Fig. 5.13. Result of principal component analysis on the metallacyclopentene fragment of (s-c(s-/7 -butadiene) metallocene complexes (Figure 5.12). The coordinate PRINl measures the dihedral angle between the CCCC and the CMC planes, PRIN2 measures the bite distance CH2. .. CHj. The point at PRINl = 0 corresponds to a planar fragment. The distribution of data points is roughly semicircular and symmetrical with respect to a vertical mirror line. The length of the arc from this line to any point is defined as the distance Xq between ground-state and transition state...

Figure 8. MNDOC-CI results for tetramethylene a) state energies and b) SOC values as a function of the CCCC dihedral angle y and the CCC valence angle 0 (rotational angles a and p of the terminal methylene groups optimized for T ).

Figure 9. Triplet PE and SOC surfaces of tetramethylene for rotations a and p of the radical centers a) syn conformation (CCCC dihedral angle y = 0°), b) gauche conformation (y = 60°) and c) anti conformation (y = 180°) (MNDOC-CI results for a CCC valence angle y = 105°).

CH2CN C—H 1.09 CCC 110.4 dihedral angle of CCCC for gauche conformer 75 ... 

FIGURE 15.13 Electronic energy (including nuclear repulsion) for CH3CH2CH2CH3 versus the CCCC dihedral angle. 

Sometimes one wants to hold one or more geometrical parameters constant during an optimization. For example, to find the electronic energy [/ as a function of the torsional angle in butane (Fig. 15.13), we would do several calculations, in each of which the dihedral angle D(CCCC) is held constant at a different value, while all other internal coordinates are optimized. The procedure for doing this in Gaussian is described in Problem 15.41. 

The s-trans conformation is the dominant one observed for 1,3-butadiene. However, the UV, IR, and Raman spectra of 1,3-butadiene show the presence of small amounts of a second conformation. High-level ab initio calculations and analysis of sf>ectra of gas-phase butadiene indicate that this second conformation is probably the nonplanar gauche form with a CCCC dihedral angle of 38° 10° [M. A. Murcko et al., J. Phys. Chem., 100,16162 (1996) G. R. De Mare et al., J. Phys. Chem. A, 101,3998 (1997)]. 

Internal Coordinates for the Out-of-plane Modes. Two sets of out-ofplane coordinates will be introduced. The first consists of the six equivalent bendings (y) of a carbon-hydrogen bond out of the plane of the three nearest carbons. For the second, six torsions of the type CCCC will be employed 8). Thus 6i is the dihedral angle between the planes of CrCi-C2 and C1-C2-C3 and is therefore a measure of how much the partial double bond C1-C2 has been twisted. 

Repeat Prob. 15.7 for the gauche and the anti eonformers of butane (see Fig. 15.13). Be sure and give the CCCC dihedral angle for each. Comment on the dipole moment values. 

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