Cyclohexane calculated energy differences

The calculated energy difference is 7.5 kcal/mol in favor of cyclohexyl radical according to the 6-31G calculations. Including the entropy contribution lowers this number to around 5 kcal/mol. Were the reaction under thermodynamic control, only cyclohexane would be observed, and interpretations (b) and (c) cannot be correct. 

Figure 7 Calculated energy differences in kcal/mol between the twist-boat and chair conformers of cyclohexane. The dashed line indicates the experimental value.

These heat of formation parameters may be considered as shifting the zero point of Fpp to a common origin. Since corrections from larger moieties are small, it follows that energy differences between systems having the same groups (for example methyl-cyclohexane and ethyl-cyclopentane) can be calculated directly from differences in steric energy. 

Fig. 16. Three dimensional conformational map of cyclohexane. The representation is analogous to that of Fig. 15 the third (vertical) coordinate is the potential energy. The given calculated potential energy differences (kcal mole-1) of the minima and transition states are drawn to scale. The interconnecting curves are drawn qualitatively they are merely meant to indicate the absence of intermediate further minima and maxima. See ref. 106 for details of analytical representations of conformational maps of cyclohexane...

The conformational energies derived from gas phase NMR of 1,2-dimethoxyethane can be most reliably compared with the results of theoretical calculations where a single molecule is treated. Adoption of the Jt and Jg values obtained leads to the energy difference Eio) = - 1.26 kJ mol-1 between the gauche and the trans state. This result is consistent with E(c) < 2.1 kJ mol-1 obtained from measurements in cyclohexane. 

As in example 2.3, we picture the liquid as being composed of cubic molecules. The size of each cube was calculated from the density of cyclohexane to be a = 0.565 nm. In the bulk each molecule is supposed to directly interact with 6 neighbors. The energy per bond is thus AvapU/6Na- At the rim two bonds less can be formed and the energy loss per molecule is 2AvapU / Na- Thus the energy difference per unit length is... 

For relief and reassurance, Table 5.13 shows the relative energies of some isomers calculated at modest levels, namely HF/3-21G1 1, HF/6-31G, and MP2/6-31G. For a reality check, we also see values from G3(MP2) and experiment (experiment fulvene/benzene, [229/230] cyclopropane/propene, [231/231] dimethyl ether/ethanol, [232/233] methylcyclopentane/cyclohexane, [230/234]). The energy differences chosen for this illustration are enthalpy differences, because differences in heats of formation yield these, and heats of formation represent the most extensive compilations of experimental energy quantities relevant to our... 

These equations can be used for any process with two states in equilibrium. As an example, monosubstituted cyclohexanes exist as two different chair conformations that rapidly interconvert at room temperature, with the conformation having the substituent in the roomier equatorial position favored (Section 4.13). Knowing the energy difference between the two conformations allows us to calculate the amount of each at equilibrium. 

We saw in Problem 4.21 that c(.< decalin is less stable than trans-decalin. Assume that the 1,3-diaxial interactions in rctR.s-decalin are similar to thase in axial methyl-cyclohexane [that is, one CH2-H interaction costs 3.8 kJ/mol (0.9 kcal/raoDI, and calculate the magnitude of the energy difference between cis- and trccns-decalin. 

As Table 1.1 shows, fluorine is the second smallest element, with size approximately 20% larger than the smallest element, hydrogen. Table 1.2 summarizes four steric parameters for various elements and groups (i) Taft steric parameters Es [44], (ii) revised Taft steric parameters E [45], (iii) Charton steric parameters o [46], and (iv) A values [47], The steric parameters, Es, E, and u are determined on the basis of relative acid-catalyzed esterification rates, while the A values are derived from the Gibbs free energy difference calculated from the ratios of axial and equatorial conformers of monosubstituted cyclohexanes by NMR. 

The energy difference provided by MO calculations, with or without the inclusion of solvent, serves as a direct measure of the anomeric energy, AE(AE3), when its absolute definition by Eq. 4 is used. However, the more-frequent use of a relative definition by Gibbs energy difference in Eq. 1 warrant an attempt to recalculate the AE(AE3) data to the values AG(AE 1). Such a procedure is, of necessity, an approximation, because the assumption that AG° = AE(AE3) neglects the entropy and volume changes of conformers owing to absence of suitable information, and the cyclohexane-based and solvent-independent A values must be used. 

Proton NMR studies of N-methyl formamide (NMF) and NMA at high dilution in deuterated solvents have shown that the level of cis isomer of NMF is 8% in water, 10.3% in chloroform, 8.8% in benzene, and 9.2% in cyclohexane, while the level of cis-NMA (a model for the secondary peptide bond) is 1.5% in water and does not change very much in nonpolar solvents [18]. Ab initio molecular calculations suggest that the small difference in dipole moments in cis and trans forms explain the relative insensitivity of amides to solvent change, unlike esters [22,41], This may be explained by nearly identical free energies of solvation for the two isomers [18]. The energy difference between cis and trans isomers in aqueous solution (AG° = 2.5 kcal mol-1) accounts for the preferential trans conformation adopted by most peptide bonds. Similar results were obtained with nonproline tertiary amides [22]. 

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

Nuclear magnetic resonance data on cyclohexane are reproduced together with heat capacity information in Fig. 3.2. The transition parameters are listed in Table 3.1. Below 150 K the experimental proton NMR second moment of 26.0 + 0.5 G corresponds to that calculated for a crystal of rigid molecules of Djj dymmetry in the chair conformation. The decrease in secoixi moment from 155 to 180 K is caused by jump-reorientation about the triad axis with a 46 kJ/mol activation energy. The experimental second moment somewhat below T of 6.4 G corresponds to the calculated value of 6.1 l.OG for such motion. At the transition the ond moment drops to 1.4 G which is in line with additional reorientation about aU other axes (1.3 to 1.1 G calculated for different assumptions). Above 240 K,... 

Angular strain in the cyclohexane molecule can be relieved by its adopting either the chair (6) or the boat (c) conformation (Pig. 1), and various attempts have been made to calculate the energy difference between these two conformations. In one empirical method. Turnercompares the boat and chaii conformations with the n butane molecule. 

The minimum energy conformation of cyclohexane calculated with a molecular mechanics program is shown in Figures 3.31 and 3.32, and the summary of the different contributions to the steric energy are listed in Table 3.7. Note that the Cl—C2—C3—C4 dihedral angle is 56.33°, producing a torsional energy. Ex, of 0.343 kcal/mol. This value is quite close to the experimental value of 56.1°. ... 

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