Library

Notes: An algorithm for the analytical computation of solvent-excluded volume is presented as part of our efforts to develop an improved computational model for a solvent effect term, in which the work required to create a cavity in the solvent is expressed as a function of the solvent-excluded volume. In this article we describe mathematical developments in the analytical integration of solvent-accessible surface (SAS) area, the singularities in SAS area and volume functions, and the procedures required to detect and treat singularities. Techniques to increase algorithm performance are presented, which improve computational speed by about five times, on the average. The accuracy of the analytical method for volume computation is compared with the accuracy of two numerical methods: the numerical integration of SAS area and the point-by-point scanning method. This algorithm calculates the volume of the spheres confined among their intersection planes and resembles a numerical integration of surface area by summing up volume layers. These characteristics make the algorithm useful in analytically calculating the work required to create a convex cavity in a solvent and the work (pΔV) associated with a change in the solvent-excluded volume of the solute due to solvent pressure. © 1995 by John Wiley & Sons, Inc.

Notes: The conformational properties of the recently synthesized highly strained permethylcyclohexane molecule 2 have been studied by empirical force field calculations using three different potentials (CFF, MM2, MM2′) and second-derivative optimization methods. A comparison of the results with the conformational behavior of parent cyclohexane 1 leads to the following conclusions: The best conformation of 2 is a chair minimum whose six-membered ring is flatter than that of 1, due to the strong H…H repulsions introduced by the methyl groups. The twist minimum of 2 is energetically less favorable than the chair by an amount similar to 1. A potential energy barrier Δ V# for the chair inversion of 2 of 15.32 kcal/mol results with the CFF, only about three kcal/mol higher than for 1. The free energy of activation ΔG# for this process obtained with the CFF is 16.96 kcal/mol (at 333 K) and agrees well with the experimental value of 16.7(2) kcal/mol.1 MM2 and MM2′ give substantially lower and higher potential energy inversion barriers Δ V# of 9.03 and 20.29 kcal/mol, respectively, which is attributed to inappropriate torsional energy terms in these force fields. The characteristic difference in the conformational behavior of 2 and 1 concerns the boat forms which are substantially less favorable in the per-methyl compound than in 1. Expectedly, strong H…H repulsions between the 1,4 diaxial flagpole-bowsprit methyl groups in 2 are responsible for this difference. The particularly high strain of the boat forms of 2 leads to flexibility differences as compared to 1 which in turn affect the relative entropies of the various statiomers (stationary point conformations); e.g., the chair ring inversion activation entropies of 2 and 1 are predicted by the CFF calculations to have opposite signs (-4.82 and 3.41 cal/mol K, respectively, at 298 K). The twist and half-twist statiomers of 2 are much more rigid than those of 1, which is a consequence of the substantially larger boat barriers along their pseudorotational interconversion paths. The boat transition state separating two enantiomeric twist minima represents a barrier calculated to be more than tenfold higher for 2 than for 1 (CFF Δ V# values 11.14 and 0.92 kcal/mol, respectively); likewise the half-boat chair inversion barrier of 2 is calculated 5.07 kcal/mol less favorable than the respective half-twist barrier. These statiomers are practically equienergetic in the case of 1. Except for the axial flagpole-bowsprit CH3 substituents of the boat forms, the methyl groups of all the relevant calculated statiomers of 2 are more or less staggered. The rotational barrier of the equatorial methyl groups of the chair minimum of 2 is computationally predicted to be 5.78 kcal/mol (ΔG#), i.e., unusually high. Interesting vibrational effects are brought about by the strong H…H repulsions in 2; thus the chair minimum has a largest C—H stretching frequency estimated to be 3050 cm-1 and involves several particularly low frequencies which have a substantial influence on its entropy. CFF calculations for the lower homologue permethylcyclopentane 5 indicate that its pseudorotational properties are similar to those of cyclopentane 4, in contradistinction to the pair 2/1.

Notes: With the purpose of deciphering conformational inversion processes of typical mobile bicyclic molecules, torsional energy surfaces near the enantiomers of bicyclo[4.2.1]nonan-9-one (1) and bicyclo-[4.2.2]decane (2) were prepared using molecular mechanics with an improved two-bond drive technique. Inversion of 1 takes place most favorably via a Cs transition state with the tetramethylene chain over the ethano bridge [1B, ΔH± 6.1 (calculated) vs. 6.8 (observed) kcal/mol]. An alternative pathway involving a Cs local energy minimum (1C), in which the tetramethylene chain is bent over the carbonyl, has a barrier 2.4 kcal higher than 1B. The global energy minimum conformation of 2 has boat-chair cyclooctane and twist-boat cyclohexane rings (BCTB), and enantiomerizes into its mirror image (BCTB') via three intermediates: TCTB, CB, and TCTB'. The highest point in the proposed pathway, a saddlepoint CB, is calculated to lie 8.0 kcal/mol above BCTB (observed ΔH± 7.8 kcal/mol). The advantage of the two-parametric over the one-parametric torsional energy surface is discussed.

Notes: A modified version (MM2′) of the Allinger's 1977 force field is checked against cycloheptane and cyclooctane. Cycloheptane is characterized by two pseudorotating itineraries, chair/twist-chair and boat/twist-boat, separated by a barrier of 8.5 kcal mol-1. The activation energy in the C/TC pseudorotation is estimated to be 0.96 kcal mol-1, while B and TB transform into each other freely at an energy level 3.8 kcal mol-1 above the global energy minimum (TC). With cyclooctane the lowest energy is calculated for the boat-chair form which participates in a pseudorotational process with TBC through a saddle point lying 3.5 kcal mol-1 above BC. The chair/chair and boat/boat families contain only one local minimum, crown and BB, respectively, on the MM2′ surface. The results are presented as an illustration for quick coverage of torsional energy surface by two-bond driver calculation with the block-diagonal Newton-Raphson minimization, followed by the force search of stationary points by full-matrix Newton-Raphson optimization.