Torsional potential energy curves

Figure 12-1 Fundamental characteristics of the phenylacetylene monomer unit. In this chapter the three basic phenylacetylene valence angles will be represented with a dot ( ) and line (—) convention, as shown in the structure key. The phenylacetylene linkage is characterized by a flexible bending force constant, F(S) [5], and an sp -sp bond order of 1.18. The indicated bond distances are taken from the crystal structure of tolane [6]. The bottom plot shows the torsional potential energy curve in tolane as determine by supersonic jet spectroscopy (adapted from [8]). The outer edges of van der Waals spheres for the two ortho hydrogens on one side of tolane are separated by nearly 2 A in the planar conformation. The result is a virtually barrierless rotation.

The internal symmetry number (Tint equals the number of minima (or maxima) in the torsional potential energy curve, which can be calculated with quantum chemical programs by scans along the internal rotor coordinate. 

Although the phase space of the nonadiabatic photoisomerization system is largely irregular, Fig. 36A demonstrates that the time evolution of a long trajectory can be characterized by a sequence of a few types of quasi-periodic orbits. The term quasi-periodic refers here to orbits that are close to an unstable periodic orbit and are, over a certain timescale, exactly periodic in the slow torsional mode and approximately periodic in the high-frequency vibrational and electronic degrees of freedom. In Fig. 36B, these orbits are schematically drawn as lines in the adiabatic potential-energy curves Wo and Wi. The first class of quasi-periodic orbits we wish to consider are orbits that predominantly... 

For butane (Fig. 3.5), using Eq. 3.4 and experimenting with a curve-fitting program shows that a reasonably accurate torsional potential energy function can be created with five parameters, k0 and ki k4 ... 

Fig. 19. Potential energy curves and energy relationships in rhodopsin. Curve I Excited state of rhodopsin and bathorhodopsin. Curve II Ground state of rhodopsin and bathorhodopsin. Curve 111 Ground stale of isolated chromophore. Symbols , and 2 are quantum yields for reaching the single potential minimum along the 11,12 torsional coordinate. From Rosenfeld et al. [201].

The potential energy V( ) is periodic during torsional rotation, giving n peaks and troughs during 360 rotation (re is an integer and is known from the molecular symmetry). This potential energy curve can be approximated by a cosine function of the form ... 

Figure 2.2. Potential energy curves of the ground state and some excited states of ethylene as a function of the torsional angle (by permission from Michl and Bona(ii( -Kouteck, 1990).

Figure 1. Theoretical potential-energy curves for rotation about the anomeric bond from ah initio Hartree-Fock 431-G calculations on dimethoxymethane. is the glycosidic O-5-C-l-O-l-CH i torsion angle. is the C-5-0-5-C-1-0-1 torsion angle and is 60° for a-D-pyranosides, 180° for fl-v-pyranosides (see...

Fig. 9.7. Top Potential energy curve for the rotation about the 0-ethyl bond in ethyl formate according to a microwave study by Wilson [25]. Bottom Histograms of C(0)-0-C-C torsion angles of 395 esters of primary alcohols with <7(C-C)s 0.005 A (left) and 397 ethyl esters with CTSO.Ol A (right) found in the CSD release of July 199t...

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