Energy mapping

The different chain conformations observed in different polymorphic forms of a polymer are generally associated to nearly equivalent minima in the conformational energy maps, calculated for isolated chain models [2, 3],... 

As an example we report in this paper the conformational energy maps of two already cited stereoregular polymers, which have been obtained very recently, syndiotactic polystyrene s-PS and syndiotactic polybutene s-PB (Fig. 4 and 5, respectively). In fact, the energy map calculated for s-PS shows... 

Figure 2. Potential energy maps of a) GalA(l->2)Rha as a function of the glycosidic dihedrals, b) the same disaccharide with the galacturonic acid acetylated at 02 and 03. The conformation used to build integer helices is indicated.

Figure 1.2 Free energy map forthe associative mechanism of ORR at Pt metal and the steps considered in this mechanism [Nprskov et al., 2004].

Sayano, K. Kono, H. Gromiha, M. M. Sarai, A., Multicanonical Monte Carlo calculation of the free-energy map of the base-amino acid interaction, J. Comput. Chem. 2000, 21, 954-962... 

Recently, a similar analysis of the conformational energy has been performed also for various new syndiotactic polymers.27,47 The conformational energy maps of syndiotactic polypropylene (sPP),48 polystyrene (sPS),49 poly butene (sPB),25 and poly(4-methyl-l-pentene) (sP4MP)26 are reported in Figure 2.12. A line repetition group s(M/N)2 for the polymer chain, and, hence, a succession of the torsion angles. .. 0i, 0i, 02, 02,..., has been... 

Figure 2.16 reports the conformational energy maps as a function of the torsion angles 0i and 02 of the two single bonds adjacent to the double bonds for 03 = T = 180° for cis-1,4-poly (1,3-butadicnc) (cisPBD),69 tranx-l,4-poly(l,3-butadiene) (transPBD),70 ds-l,4-poly (isoprene) (cisPI),68 trans-1,4-poly(isoprene) (transPI),71 ds-l,4-poly(2,3-dimethyl-l,3-butadiene) (cisPMBD),68 and lrans-, 4-poly(2,3-dimethy 1-1,3-butadicnc) (transPMBD).68 These polymers are representative examples of polydienes with A = A = H... 

Figure 2. The contour energy map for the reaction ofprotonated acetone oxime (1) calculated by HF/6-31G. Numbers on contour lines are relative energies with respect to TS in kcal mot1.

The classical CoMFA procedure relies on sterical and electrostatic fields or on spatial interaction energy maps of the potential ligands with standardized hydrophobic or polar probe molecules [56]. In this work, the modified ComPharm approach described in detail elsewhere [25] will be used. Its key differences with respect to classical CoMFA are the following ... 

Such energy maps depict the heights of the barriers and the widths of the minima, as well as showing the positions of the minima. 

Figure 4. Conformational map for dihydropyran. Because of the double bond, 4 atoms are always almost coplanar and a limited number of conformations is probable. The energy contours are at 2 kcal/mol intervals, starting 1 kcal/mol above the minima. The favored conformations are half-chairs, and the easiest paths of transition between the two are through the boat forms. The symmetry of this energy map applies only to dihydropyran, and not to derivatives which cause increases and decreases in the sizes of the allowed (low-energy) areas. This map was calculated with MMP2(85) at increments of 0.1 A shift of the two non-planar atoms. Three of the carbon atoms were held in a plane while C6 and 01 were held at specific distances above and below the plane. Otherwise, the structure was fully relaxed at each increment. The reader may enjoy plotting the indicated path of conformational interchange (pseudorotation) on a copy of Figure 3.

Figure 7. A "snapshot" of a typical cellulosic chain trajectory taken from a Monte Carlo sample of cellulosic chains, all based on die conformational energy map of Fig. 6. Filled circles representing glycosidic oxygens, linked by virtud bonds spanning the sugar residues (not shown), allow one to trace the instantaneous chain trajectory in a coordinate system that is rigidly fixed to the residue at one end of the chain. Projections of the chain into three mutually orthogonal planes assist in visualization of the trajectory in three dimensions.

Figure 10. Relaxed (adiabatic) conformational energy map for p-maltose as computed by Brady and coworkers.i3 Contours are drawn at 2,4,6, 8, and 10 kcal/mol above the minimum near < ), y = -60°, -40°. The p-maltose structure may be derived from that of p-cellobiose in Fig. 1 by inversion of the stereochemical configuration at Cl.

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