Stable conformers

The classical microscopic description of molecular processes leads to a mathematical model in terms of Hamiltonian differential equations. In principle, the discretization of such systems permits a simulation of the dynamics. However, as will be worked out below in Section 2, both forward and backward numerical analysis restrict such simulations to only short time spans and to comparatively small discretization steps. Fortunately, most questions of chemical relevance just require the computation of averages of physical observables, of stable conformations or of conformational changes. The computation of averages is usually performed on a statistical physics basis. In the subsequent Section 3 we advocate a new computational approach on the basis of the mathematical theory of dynamical systems we directly solve a... 

Conformational Adjustments The conformations of protein and ligand in the free state may differ from those in the complex. The conformation in the complex may be different from the most stable conformation in solution, and/or a broader range of conformations may be sampled in solution than in the complex. In the former case, the required adjustment raises the energy, in the latter it lowers the entropy in either case this effect favors the dissociated state (although exceptional instances in which the flexibility increases as a result of complex formation seem possible). With current models based on two-body potentials (but not with force fields based on polarizable atoms, currently under development), separate intra-molecular energies of protein and ligand in the complex are, in fact, definable. However, it is impossible to assign separate entropies to the two parts of the complex. 

Reduce stress on molecules caused hy a simulation at elevated tern peratiires. The cooling process, called sim n lated annealing, takes new, high energy conformational slates toward stable conformations. 

Tiiinpiiraiiii (3 is handled the sanii way in Langavin dynamics as it iisin molecular dynamics. High tern peraLurc runs m ay he n sed to overcome poten lial cnergy barriers. Cooling a system to a low tern -peratnre in steps may result in a different stable conformation than would be round by direct geometry optimization. 

We have it on good authority (Ege, 1998) that the gauche minimum on the potential energy coordinate is about 0.9 kcal moI higher in energy than the anti conformation. This establishes a two-state energy system for the stable conformers, gauche and anti (Fig. 4-19). 

False minima may entrap the unwary a structure may be mistaken for the ground state that does not represent the most stable conformer. If so, the calculated... 

Polymers can be crystalline, but may not be easy to crystallize. Computational studies can be used to predict whether a polymer is likely to crystallize readily. One reason polymers fail to crystallize is that there may be many conformers with similar energies and thus little thermodynamic driving force toward an ordered conformation. Calculations of possible conformations of a short oligomer can be used to determine the difference in energy between the most stable conformer and other low-energy conformers. 

Structures A B and C represent different conformations of hydrogen peroxide Conformations are different spatial arrangements of a molecule that are generated by rotation about single bonds Although we can t tell from simply looking at these struc tures we now know from experimental studies that C is the most stable conformation... 

Of the two conformations of ethane the staggered is 12 kJImol (2 9 heal mol) more stable than the eclipsed The staggered conformation is the most stable conformation the eclipsed is the least stable conformation Two main explanations have been offered for the difference in stability between the two conformations One explanation holds that repulsions between bonds on adjacent atoms destabilize the eclipsed conformation The other suggests that better electron delocalization stabilizes the staggered conformation The latter of these two explanations is now believed to be the correct one... 

Higher alkanes having unbranched carbon chains are like butane most stable m then-all anti conformations The energy difference between gauche and anti conformations is similar to that of butane and appreciable quantities of the gauche conformation are pres ent m liquid alkanes at 25°C In depicting the conformations of higher alkanes it is often more helpful to look at them from the side rather than end on as m a Newman projec tion Viewed from this perspective the most stable conformations of pentane and hexane... 

Their heats of combustion (Table 3 2) reveal that trans 1 4 dimethylcyclohexane is 7 kJ/mol (17 kcal/mol) more stable than the cis stereoisomer It is unrealistic to believe that van der Waals strain between cis substituents is responsible because the methyl groups are too far away from each other To understand why trans 1 4 dimethylcyclo hexane is more stable than cis 1 4 dimethylcyclohexane we need to examine each stereoisomer m its most stable conformation... 

The most stable conformation of trans 1 4 dimethylcyclohexane has both methyl groups in equatorial orientations The two chair conformations of trans 1 4 dimethyl cyclohexane are not equivalent to each other One has two equatorial methyl groups the other two axial methyl groups... 

Orientation of methyl groups m most stable conformation Heat of combustion heat of combustion More stable stereoisomer... 

Both methyl groups are equatorial m the most stable conformation of trans 1 2 dimethyl cyclohexane... 

The most stable conformation of cis 1 3 dimethylcyclohexane has both methyl groups equatorial... 

If a disubstituted cyclohexane has two different substituents then the most stable conformation is the chair that has the larger substituent m an equatorial orientation This IS most apparent when one of the substituents is a bulky group such as tert butyl Thus the most stable conformation of cis 1 tert butyl 2 methylcyclohexane has an equatorial tert butyl group and an axial methyl group... 

Less stable conformation (More stable conformation... 

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

Section 3 1 The most stable conformation of ethane is the staggered conformation It IS approximately 12 kJ/mol (3 kcal/mol) more stable than the eclipsed, which IS the least stable conformation... 

Most stable conformation of as 1 3 dimethylcyclohexane (no axial methyl groups)... 

The two most stable conformations of conjugated dienes are the s cis and s trans The s trans conformation is normally more stable than the s cis Both conformations are planar which allows the p orbitals to overlap to give an extended tt system... 

Typical carbon-oxygen bond distances m ethers are similar to those of alcohols (—142 pm) and are shorter than carbon-carbon bond distances m alkanes (—153 pm) An ether oxygen affects the conformation of a molecule m much the same way that a CH2 unit does The most stable conformation of diethyl ether is the all staggered anti conformation Tetrahydropyran is most stable m the chair conformation—a fact that has an important bearing on the structures of many carbohydrates... 

The most stable conformation of 1 3 dioxan 5 ol is the chair form that has its hydroxyl group in an axial orientation Suggest a reasonable explanation for this fact Building a molecular model IS helpful... 

Construct a molecular model of trans 2 bromocyclohexanol in its most stable conformation This conformation is ill suited to undergo epoxide formation on treatment with base Why2 What must happen in order to produce 1 2 epoxycyclohexane from trans 2 bromocyclohexanoP... 

The most stable conformation of acetone has one of the hydrogens of each methyl group eclipsed with the carbonyl oxygen Construct a model of this conformation... 

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