Lowest energy structures

Figure Bl.4.8. Top the lowest-energy structures of water clusters, from n = 2 -6. Bottom a sample...

Transition structures can be dehned by nuclear symmetry. For example, a symmetric Spj2 reaction will have a transition structure that has a higher symmetry than that of the reactants or products. Furthermore, the transition structure is the lowest-energy structure that obeys the constraints of higher symmetry. Thus, the transition structure can be calculated by forcing the molecule to have a particular symmetry and using a geometry optimization technique. 

Figure 6 Steps in automated assignment. (1) Select the lowest energy structures from iteration / — 1 that are used to interpret the spectra. (2) For each peak, list all possible assignments compatible with the resonances within a frequency mnge. (3) Extract a distance for each assignment possibility from the ensemble of structures. (4) Use the distances to assign ambiguous NOEs. (5) Calibrate the peak volumes to obtain distance restraints. (6) Calculate structures based on the new restraints.

Calculate the average CCCC torsion angle for the lowest-energy structure of each molecule (use absolute values). Order these structures from most eclipsed to most staggered . Which ring adopts the most eclipsed structure Which ring adopts the most staggered structure ... 

The crown conformation is not necessarily the most stable structure for free (uncomplexed) crown ethers. Examine the lowest energy structure of 18-crown-6, and compare it to the crown structure. Explain why the crown structure is less stable. Use equation (1) to calculate the equilibrium ratio of lowest-energy and crown conformers of 18-crown-6 at room temperature. What causes a shift in conformation in the presence of metal cations ... 

The mirror plane is defined by the dummy atoms. The migrating hydrogen H le is not allowed to move out of the plane of symmetry, and must consequently have the same distance to C4 and C5. A minimization will locate the lowest energy structure within the given Cs symmetry, and a subsequent frequency calculation will reveal that the optimized structure is a TS, with the imaginary frequency belonging to the a" representation (breaking the symmetry). 

Each equivalent atom (the same element, the same number of bonds and lone pairs) has the same formal charge. A check on the calculated formal charges is that their sum is equal to the overall charge of the molecule or ion. For an electrically neutral molecule, the sum of the formal charges is zero. Compare the formal charges of each possible structure. The structure with the lowest formal charges represents the least disturbance of the electronic structures of the atoms and is the most plausible (lowest energy) structure. 

J. M. (1998) Lowest Energy Structures of Gold Nanoclusters. Physical Review Letters, 81, 1600-1603. 

Wang, J., Wang, G. and Zhao, J. (2002) Density-functional study of Au (2-20) clusters Lowest-energy structures and electronic properties. Physical Review B -Condensed Matter, 66,035418-1-035418-6. 

The lowest energy structures were found to be the above carbon and above bond geometries (Fig. 6d and e, respectively). This is a function of the anisotropy of the electron density around the iodine and the geometry dependent polarization of the dihalogen. 

Table 3-3. Differences in individual residue contribution to TS stabilization. All values are relative to the TS from path B (lowest energy structure). Negative values mean that that particular residue helps stabilize die TS while a positive value means that the residue destabilizes the TS. Dashes mean that the absolute difference in contribution of that residue was less than 0.5 kcal/mol. Total value includes all residues in the enzyme...

Fig. 12. DFT-predicted lowest energy structure of oxidized species 7. From Ref. (48).

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