Structural problems stable conformations

Problem 9.16 (a) Draw the possible chair conformational structures for the following pairs of dimethylcy-dohexanes (i) cis- and trans-1,2-, (ii) cis- and frans-1,3- (iii) cis- and trans-lA-. (b) Compare the stabilities of he more stable conformers for each pair of geometric isomers, (c) Determine which of the isomers of limethylcyclohexane are chiral. <... 

A puzzling problem was posed by Levinthal many years ago.329 We usually assume that the peptide chain folds into one of the most stable conformations possible. However, proteins fold very rapidly. Even today, no computer would be able, in our lifetime, to find by systematic examination the thermodynamically most stable conformation.328 It would likewise be impossible for a folding protein to "try out" more than a tiny fraction of all possible conformations. Yet folded and unfolded proteins often appear to be in a thermodynamic equilibrium Experimental results indicate that denatured proteins are frequently in equilibrium with a compact denatured state or "molten globule" in which hydrophobic groups have become clustered and some secondary structures exists.330-336 From this state the polypeptide may rearrange more slowly through other folding intermediates to the final "native conformation."3363 3361 ... 

In essence, there are only two really important themes in chemistry structure and reactivity. In structural problems, we usually compare the relative stabilities of two isomers (1 and 2) or conformers (3 and 4). Their energy differences are of the order of a few percent. Thus, benzene (1) is more stable than Dewar benzene (2) by 60 kcal mol-1, about 5% of its molecular energy (-1230 kcal mol-1) 3 Similarly, frans-butadiene (3) is more stable than ds-butadiene (4) by 2.7 kcal mol-1, or 3% of its energy of formation. 

Since polymorphs yield the same molecules upon transition to a less dense phase (liquid or vapour) and upon dissolution, the possibility of polymorph interconversion brings about the problem of structural nonrigidity in solution and in the solid state [24], Isomerization processes in the solid state are well known and there is the intriguing possibility that less stable conformations are stabilized in the solid state by the packing. 

Strategy The three substituents have the orientations shown in the first structure. To decide if the conformation shown is the more stable conformation or the less stable conformation, perform a ring-flip on the illustrated conformation and do a calculation like those in the previous problem. Notice that each conformation has a CI-CH3 gauche interaction, but we don t need to know its energy cost because it is present in both conformations. 

PROBLEM 3.10 Write structural formulas or make molecular models for the most stable conformation of each of the following compounds ... 

Use models to solve this problem.) (a) Write a conformational structure for the most stable conformation of 1,2-diethyl-cyclohexane and write its mirror image, (b) Are these two molecules superposable (c) Are they interconvertible through a ring flip (d) Repeat the process in part (a) with OT-l,2-diethylcyclohexane. (e) Are these structures superposable (f) Are they interconvertible ... 

As shown in Chapter 6, the solution of the Schrodinger equation in the adiabatic approximation can be divided into two tasks the problem of electronic motion in the field of the clamped nuclei (this will be the subject of the next chapters) and the problem of nuclear motion in the potential energy determined by the electronic energy. The ground-state electronic energy E (R) of eq. (6.8) (where k = 0 means the ground state) will be denoted in short as V(R), where R represents the vector of the nuclear positions. The function V R) has quite a complex structure and exhibits many basins of stable conformations (as well as many maxima and saddle points). 

Once the physico-chemical basis of secondary structure packing is determined, and once the local interactive forces that give rise to secondary structure are known, it vrill be possible to predict both the folding pathway and the final stable conformation of a protein from its amino-add sequence. There are three approaches to these problems, (a) One can correlate sequence and structure using data from as many proteins as possible and derive empirical probabilities for any particular sequence-forming secondary structure, (b) One can derive semi-empirical energy functions for amino-add sequences based on allowed conformation around the... 

PROBLEM 5.42 Draw the planar structure for each of the following compounds. Next, draw the most stable conformation for each in three dimensions. 

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