Energy differences between conformers

Figure 8 Calculated conformational energy differences between axial and equatorial methyl-cyclohexane in kcal/mol. The dashed line shows the experimental value.

Atactic poly(methyl methacrylate)-Q FTIR spectroscopic analysis of the conformational energy differences between rotational isomeric states is presented. [32]... 

Conformational free energy simulations are being widely used in modeling of complex molecular systems [1]. Recent examples of applications include study of torsions in n-butane [2] and peptide sidechains [3, 4], as well as aggregation of methane [5] and a helix bundle protein in water [6]. Calculating free energy differences between molecular states is valuable because they are observable thermodynamic quantities, related to equilibrium constants and... 

The second application of the CFTI approach described here involves calculations of the free energy differences between conformers of the linear form of the opioid pentapeptide DPDPE in aqueous solution [9, 10]. DPDPE (Tyr-D-Pen-Gly-Phe-D-Pen, where D-Pen is the D isomer of /3,/3-dimethylcysteine) and other opioids are an interesting class of biologically active peptides which exhibit a strong correlation between conformation and affinity and selectivity for different receptors. The cyclic form of DPDPE contains a disulfide bond constraint, and is a highly specific S opioid [llj. Our simulations provide information on the cost of pre-organizing the linear peptide from its stable solution structure to a cyclic-like precursor for disulfide bond formation. Such... 

The free energy differences obtained from our constrained simulations refer to strictly specified states, defined by single points in the 14-dimensional dihedral space. Standard concepts of a molecular conformation include some region, or volume in that space, explored by thermal fluctuations around a transient equilibrium structure. To obtain the free energy differences between conformers of the unconstrained peptide, a correction for the thermodynamic state is needed. The volume of explored conformational space may be estimated from the covariance matrix of the coordinates of interest, = ((Ci [13, lOj. For each of the four selected conform-... 

The second application of the CFTI protocol is the evaluation of the free energy differences between four states of the linear form of the opioid peptide DPDPE in solution. Our primary result is the determination of the free energy differences between the representative stable structures j3c and Pe and the cyclic-like conformer Cyc of linear DPDPE in aqueous solution. These free energy differences, 4.0 kcal/mol between pc and Cyc, and 6.3 kcal/mol between pE and Cyc, reflect the cost of pre-organizing the linear peptide into a conformation conducive for disulfide bond formation. Such a conformational change is a pre-requisite for the chemical reaction of S-S bond formation to proceed. The predicted low population of the cyclic-like structure, which is presumably the biologically active conformer, agrees qualitatively with observed lower potency and different receptor specificity of the linear form relative to the cyclic peptide. 

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... 

Although the same theoretical studies indicate very small energy differences between the syn and anti conformers of the 3-carbaldehydes of furan, thiophene and pyrrole with a slight preference for the syn conformer, in chloroform solution the furan- and thiophene-3-carbaldehydes adopt the anti conformers to the extent of 100 and 80% respectively (82X3245). However, A-substituted 3-(trifluoroacetyl)pyrroles exist in solution as mixtures of rotational isomers (80JCR(S)42). 

For 1,3-dithiolanes the ring is flexible and only small energy differences are observed between the diastereoisomeric 2,4-dialkyl derivatives. The 1,3-oxathiolane ring is less mobile and pseudoaxial 2- or 5-alkyl groups possess conformational energy differences (cf. 113 114) see also the discussion of conformational behavior in Section 4.01.4.3. 

The free energy difference between two stable conformations can be obtained by a thermodynamic integration approach [38,39]. Let q and represent the centers of the two corresponding energy wells. The free energy derivative is seen to be... 

A prototype of such phenomena can be seen in even the simplest carboxylic acid, acetic acid (CH3CHOOH). Acidity is determined by the energy or free energy difference between the dissociated and nondissociated forms, whose energetics usually depend significantly on their conformation, e.g., the syn/anti conformational change of the carboxyl-ate group in the compound substantially affects the acid-base equilibrium. The coupled conformation and solvent effects on acidity is treated in Ref. 20. 

Energy differences between conformations of substituted cyclohexanes can be measured by several physical methods, as can the kinetics of the ring inversion processes. NMR spectroscopy has been especially valuable for both thermodynamic and kinetic studies. In NMR terminology, the transformation of an equatorial substituent to axial and vice versa is called a site exchange process. Depending on the rate of the process, the difference between the chemical shifts of the nucleus at the two sites, and the field strength... 

The free-energy difference between conformers is referred to as the conformational free energy. For substituted cyclohexanes, it is conventional to specify the value of — AC ° for the equilibrium... 

Cyclopentane is nonplanar, and the two minimum-energy geometries are the envelope and half-chair. In the envelope conformation, one carbon atom is displaced from the plane of the other four. In the half-chair conformation, three carbons are coplanar, vdth one of the remaining two being above the plane and the other below. The energy differences between the conformers are very small, and interconversion is rapid. All of the carbon atoms r idly move through planar and nonplanar positions. The process is called pseudorotation. 

Estimate the energy difference between the stable and unstable chair conformations of each of the following trimethylcyclohexanes ... 

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