Map, energy contour

FIGURE 2. An energy contour map for diethylmethylamine recomputed using the MM2-91 force field. The separation between contour lines is 1.0 kcal mol-1... 

MAECIS also contains a molecular conformation analysis system (4). This system allows the user to generate all possible conformations of the current molecule over a series of single bond rotations. Energy contour maps can be obtained for the various conformations and this allows for the selection of low energy conformations for further manipulation or calculations. 

Murrell and co-workers290 have reported MBS and DZ calculations on the nitro-methyl anion CH2N02 in its planar and pyramidal forms. The most stable form is planar, and is expected to protonate on the oxygen, whereas the pyramidal form would protonate on C. This conclusion was not obvious from charges alone, but was evident on examination of potential energy contour maps. 

Fig. 60 Potential energy contour map of torsion angles 0i, 02 for DPP. Some pathways observed in simulations are drawn (from [51])...

Fig. 63 Potential energy contour map of torsion angles 04,05 for PDC. The intramolecular energy minima are represented by the symbol x. Some pathways observed in simulations are drawn. The end of the path indicated by the empty symbol is the starting position, and the position marked with a. filled symbol is the last simulated point (from [51])...

Polypropylene and polyacetaldehyde are the simplest of the above polymers, having only two internal rotation angles, x and Tg, in the main chain. Figure 1 shows the potencial energy contour map for polyacetaldehyde. The crosses indicate the potential minima, and the closed circles the x-ray structure determined by Natta et al. (28). The two minima correspond to the right- and left-hand helices. 

Figure 2 shows the energy contour map for isotactic poly( methyl methacrylate). The lowest energy minimum was found at the position corresponding to a (12/1) helix contrary to the expectation of the (5/1) helix. The minimum corresponding to the (5/1) helix is higher than the (12/1) helix by 3 kcal/mole of monomer unit. This result led to the postulation of the double stranded helix for this polymer. 

Fig. 2. Conformational energy contour map of JV-acetyl-Giy-W -methylamide (A), N-acetyl-Ala-AT-methylamide (B) (taken from Zimmerman et al., 1977), and N-acetyl-a-Aib-...

Fig. 40.—Energy contour-map of system for the addition of a bromine molecule to the carbon-carbon double bond. The north and south axis refers to the distance between Br-Br and C-C. The east-west axis refers to the distance between bromine atoms. Contour lines are projections of energy plotted at right angles to the plane.

Figure 9 Conformational energy contour map of N-acetyl-N -methylalanine amide, for x1 = 60°. Locations of minima are indicated by the filled circles. The contour lines are labeled with energy in kcal/mol above the minimum-energy point at (4>,

As in Figure 15, the hard-sphere map is superposed on the energy contour map in Figure 16 and again illustrates the dominance of the repulsive part of the Lennard-Jones potential. The gap in both the hard-sphere and energy contour maps near (< >,i ) = (90°, 120°) arises because these helices have very low axial translation that is, the chain does not advance rapidly enough along the helix axis to allow sufficient spatial separation between atoms on adjacent turns of the helix. 

Similar energy contour maps and the relative stabilities of right- and left-handed a helices have been computed for other homopolymers, and Table 1 compares the computed and observed preferred twists of a number of a-helical... 

The quantity U , i , x is computed by summing over the ECEPP energies of all pairs of nonbonded atoms of the whole molecule. Equations [11] and [12] are used to compute conditional free energy (4>,i]i) contour maps, similar to standard conformational energy (< >, ) contour maps, for each residue of the polypeptide. The probable conformation of the /th residue is taken as the one of lowest conditional free energy, and the probable conformation of the whole polypeptide chain is assumed to be the combination of the probable conformations of the individual residues. 

Figure 7.31. Energy contour maps for the face-to-face [2 -I- 2] cycloaddition of two acrylonitrile molecules in the syn head-to-tail arrangement, showing (a) the lowest excited state S, and (b) the ground state S . Possible reaction paths via the low-energy conical intersection are indicated by arrows.

The 2-D energy contour map illustrating the potential energy barriers to rotation around two dihedral angles, O and of cellobiose. (Adopted from Kajiwara and Miyamoto [34)... 

With cellulose, the region of angular orientation that produces the lowest point on the energy contour map is narrow and well defined. Any distortion out of the most relaxed position involves significant energy input. Several positions of relaxed state are identified on the ener-... 

In either event once an analysis is complete the scientist can ask for the low energy conformations, look at energy contour maps, place the molecule in various conformations for visual inspection, etc. 

The energetically easiest route from reactants to products on the potential-energy contour map defines the potential-energy profile. 

Figure 58. Energy contour map (Ramachandran plot) for versus of the alanine dipeptide. Solid lines mark the five lowest-energy contours at 1 kcal/mol and the bottom contour is marked with a heavy line dashed lines mark the higher contours at 1-kcal/mol intervals (a) vacuum potential surface (b) solvent-modified potential surface.

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