Estimating Conformational Populations

Why are these physical chemistry concepts being discussed in a reactions-synthesis book It will be apparent throughout this book that the conformation of a molecule has a critical effect on the reactivity and stereochemistry of many reactions (see chapter 6 for examples). In many cases, the various strain energies that influence the conformation of a molecule can be quantified and the percentage of each conformation can be calculated. With such information, more reasonable predictions of reactivity and stereochemistry can be made. The following protocols are therefore presented in an attempt to reinforce the idea that conformational 

We will focus on cyclohexane derivatives to illustrate the fundamental idea When a reagent approaches a cyclohexane ring, the conformation of the ring will influence how the reagent interacts with any functional group on that ring. The populations of the two chair conformations that dominate the conformational population of cyclohexanes can influence the relative rate and the stereochemical outcome of a given reaction. The relative populations of the two chair conformations in cyclohexane derivatives can be predicted with some 

For a given temperature, the entropy term will be small relative to AF° (taken to be AH° hereafter) and a 

The entropy term in not zero, of course, but since tbe AS° term is usually measured in calories and the AH° term in kilocalories, ignoring AS° will introduce only a small error into the calculation. This difference is demonstrated in Lowry and Richardson s list of AH° and S°298 values for a variety of specific bonds. In the C—Me bond, for example, AH° is -10.08 kcal moTl (42.2 kJ mol l), whereas S°298 is 30.4 cal moTl (127.2 J mol l, 0.03 kcal mol i). Similarly, AH° for cyclopropane is listed as 27.6 kcal moT (115.5 kJ mol l), whereas S°298 is 32.1 cal moT (134.3 J mol i, 0.03 kcal mol l).  

The AH° term is related to AG°, the free energy, which is related to the equilibrium constant by the expression  

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As mentioned above, the percentage of a given conformation is an essential factor in determining the rate and viability of a given reaction and these calculations allow the synthetic chemist to estimate conformational populations. Just as the minor chair conformation influences the rate, so other conformations (boat, twist-boat, etc.) can also exert an influence, depending on their relative populations. 

We noted in Section 13.13 that an NMR spectrum is an average spectrum of the conformations populated by a molecule. From the following data, estimate the percentages of axial and equatorial bromine present in bromocyclohexane. 

Conformational populations of cyanomethylphosphine oxides (136) have been estimated from dipole moments and indicate a preference for the tra/15-conformation. The moments of the o-, m- and p-chloro- and tolyl-derivatives of triaryl phosphites (137, Y = ) and triaryl phosphates (137 Y = O) indicate that the oxygen atom in the latter series causes the aryl rings to rotate further away from a position in which their planes all meet along the molecular symmetry axis. Conformational studies have also been carried out on the dioxaphosphorinanes. The moments of the isomeric series (138a) and (138b) were in the ranges 3.7—4.2 and 5.4—5.5 D respectively. ... 

Stereochemical equilibration of DCP in DMSO at 343 K in the presence of LiCI yields a mixture containing 36.4 I + 0.3) % of the meso isomer. The statistical weight parameters evaluated from this result are used for theoretical calculation of the proportions of various conformers in meso and racemic DCP, and also in the three diastereoisomers of TCH. Calculations for TCH are compared with estimates of others for NMR coupling constants. It is shown that the less-favoured conformations, often ignored, contribute appreciably to the conformer populations of... 

Inductive effects on dipole moments and the effects of intervening atoms on electrostatic interaction energies are represented by polarizability centers In conjunction with bond centered dipoles. Solvation energies are estimated by means of a continuum dlpole-quadrupole electrostatic model. Calculated energies of a number of conformations of meso and racemic 2,4-dichloropentane and the iso, syndio, and hetero forms of 2,4,6-triehloroheptane give satisfactory representations of isomer and conformer populations. Electrostatic effects are found to be quite important. 

The first such approach to the interpretation of optical rotation in terms of the conformational properties of carbohydrates was made by Whifien in 1956. He proposed that the observed rotation of an optically active molecule can be regarded as an algebraic summation of partial rotatory contributions of various conformational elements of asymmetry. For these contributions, empirical values were determined that allowed estimation of the net rotations of various cyclic sugars and cyclitols with fair accuracy. A more extensive treatment was presented by Brewster,and it was applied to a wide range of optically active, acyclic and cyclic compounds. The best correlations between the calculated and the experimental values were obtained with compounds that do not absorb in the near-ultraviolet and have predictable, fixed conformations, or for which the conformational populations can be reliably estimated. In the carbohydrate field, the calculations are quite simple for the poly-hydroxycyclohexanes, - and differences between the calculated and observed values for the rotation have been interpreted in terms of conformational equilibria. Similar comparisons have been made for the methyl D-aldopyranosides, although the lack of precision in the correlation does not allow a detailed treatment in terms of conformational populations. 

If we know how much gauche character (Bg = fractional population of 0 = 120° conformations (See J. D. Honeycutt in this volume who describes the methodology used to calculate the bond conformational populations), then we can estimate the y-gauche shielding (yc-c) produced at the methyl carbons in butane, for example. When the observed shielding ASCHs = SCHslbutane) —5CH3 (propane) =... 

On the haaLs of the esooerimental observations and the assumptions described in the following, amide proton titration shifts can be used to estimate the population of specific hydrogen bonded structures in the ensemble of species constituting the solution conformation of polypeptide chains. 

For the discussion of conformation of poly(i -oxypropylene) molecules, we have to consider stereochemistry with respect to C-C and C-0 bonds along a polymer chain, 40-CH(CH3)-CH2)n In order to get Information on the rotational Isomers around the C-C bond, a deuterated poly(/ -oxypropylene) was prepared starting from 2Ms-deuterated methyloxirane monomer (7),W. The vicinal coupling constants, Jac, between the methj ne and the methine protons were found to be 5.3, 4.9 and 5.2 (Hz) In cyclohexane, chloroform and benzene, respectively. By assuming the standard values J o =2.6 (Hz) and Ji8f=9.3 (Hz) reported In a variety of 1,2-d1oxygen-subst1tuted propane derivatives. It was possible to estimate the population of the three rotational Isomers In cyclohexane, chloroform and benzene, respectively. 

The analysis of solution experiments is complicated by the fact that the gauche conformer population is enhanced by interactions with strongly polar solvents such as water. Andersson and Karlstromg [40] estimate that water stabilizes the TGT versus the TTT conformer by 1.0-1.5kcal/mol. Inomata and Abelo [41] used recently gas-phase NMR measurements as a source of structural information on D(CH3). They reproduced the gas-phase NMR data using a RIS (Rotational Isomeric State) model where the TGT conformation is preferred over the TTT conformation by 0.4 kcal/mol. This minor energy difference requires a very careful... 

Tvaroska made a simulation of maltose in various solvents" Based on coordinates gotten from us, he estimated the influence of changing solvent properties on relative conformer populations. One interesting result is that in many solvents a more balanced population is expected than what is calculated for the naked molecule. Our l68... 

Unsymmetrically substituted pentadienyl anions populate six planar conformations, which are in equilibration13 a 18. The energy barrier for a torsion in the potassium compound (R = primary alkyl) was estimated to be approximately 35 keal/mol for the 1,2-bond and 15 keal/mol for the 2,3- and 3,4-bonds. The barriers are much lower in the lithium compound. Not only the rate, but also the position of the equilibrium is greatly influenced by the cation from trapping experiments18 it was concluded that the exo-VJ anion is most stable for lithium and the exo-U form for potassium. 

The ability to detect discrete rovibronic spectral features attributed to transitions of two distinct conformers of the ground-state Rg XY complexes and to monitor changing populations as the expansion conditions are manipulated offered an opportunity to evaluate the concept of a thermodynamic equilibrium between the conformers within a supersonic expansion. Since continued changes in the relative intensities of the T-shaped and linear features was observed up to at least Z = 41 [41], the populations of the conformers of the He - lCl and He Br2 complexes are not kinetically trapped within a narrow region close to the nozzle orifice. We implemented a simple thermodynamic model that uses the ratios of the peak intensities of the conformer bands with changing temperature in the expansion to obtain experimental estimates of the relative binding energies of these complexes [39, 41]. 

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