A broad diverse test set of alkanes and cycloalkanes previously studied with MM4 calculations has had the heats of formation calculated by several different quantum mechanical methods: HartreeFock, MP2, and MP4, and also by B3LYP and B3LYP + dispersion energy. Overall, three computational methods (MM4, MP4, and B3LYP + dispersion) yield results that are generally of experimental accuracy. These results are analyzed and compared in some detail.

The carbon-carbon single bond is of central importance in organic chemistry. When the molecular mechanics MM4 force field was developed beginning in the early 1990s, C-C bond lengths were not known very reliably for many important molecules, and bond lengths greater than 1.6 Å were quite poorly known experimentally. Quantum-mechanically computed values could not yet be obtained with useful accuracy in a general way. This paper examines structures now available from experiment and quantum-mechanical computations and extends the fit of the MM4 methodology to include new bond distances as long as 1.71 Å.

Molecular mechanics (MM4) studies have been carried out on the catenane (C13H26)2, specifically 13‐13D2. The structure obtained is in general agreement with second‐order perturbation theory. More importantly, the MM4 structure allows a breakdown of the energy of the molecule into its component classical parts. This allows an understanding of why the structure is so distorted, in terms of CC bonding and nonbonding interactions, van der Waals repulsion, CCC and CCH angle bending, torsional energies, stretch‐bend, torsion‐stretch, and bend–torsion–bend interactions. Clearly, the hole in 113‐membered ring is too small for the other ring to fit through comfortably. There are too many atoms trying to fit into the limited space at the same time, leading to large van der Waals repulsions. The rings distort in such a way as to enlarge this available space, and lower the total energy of the molecule. While the distortions are spread around the rings, one of the nominally tetrahedral CCC bond angles in each ring is opened to 147.9° by MM4 (146.8° by MP2). The stability of the compound is discussed in terms of the strain energy. © 2015 Wiley Periodicals, Inc.

Catenanes are playing an increasingly important role in supramolecular chemistry. In attempting to identify the minimum number of carbon atoms in a viable catenane, the B3LYP, BP86, M06-2X, MM3, and MM4 methods were applied to study representative [2]catenane models, which consist of two mechanically interlocked saturated n-cycloalkanes ([CnH2n]2). The structures, energy variations, and electron density differences vary nearly monotonically from n = 18 to 11. For example, the B3LYP/DZP++ dissociation energies [CnH2n]2 → 2CnH2n are 101, 121, 159, 191, 222, 252, 290, and 323 kcal/mol from n = 18 to 11, respectively. However, there is much variation among the energetic predictions with the B3LYP, BP86, M06-2X, MM3, and MM4 methods. The distances of the longest C-C single bond in each catenane are 1.593 (n = 18), 1.604 (n = 17), 1.631 (n = 16), 1.640 (n = 15), 1.667 (n = 14), 1.669 (n = 13), 1.680 (n = 12), and 1.689 Å (n = 11). These results display something of a shoulder in the vicinity of n = 14. This may suggest that [C15H30]2 is the smallest catenane that will resist fragmentation under specified laboratory conditions.

Molecular mechanics gives us a well known model of molecular structure. It is less widely recognized that valence bond theory gives us structures which offer a direct interpretation of molecular mechanics formulations and parameters. The electronic effects well-known in physical organic chemistry can be directly interpreted in terms of valence bond structures, and hence quantitatively calculated and understood. The basic theory is outlined in this paper, and examples of the effects, and their interpretation in illustrative examples is presented.

Foreword. Preface. Acknowledgments. 1 INTRODUCTION. What, Exactly, is a Molecular Structure? References. 2 EXPERIMENTAL MOLECULAR STRUCTURES. Electron Diffraction. Microwave Spectroscopy. X-Ray Crystallography. The Phase Problem. Rigid-Body Motion. Molecular Mechanics in Crystallography. Neutron Diffraction. Nuclear Magnetic Resonance Spectra 19. Bond Lengths Depend on Method Used to Determine Them. References. 3 MOLECULAR STRUCTURES BY COMPUTATIONAL METHODS. A Brief History of Computers. Computational Methods. Semiempirical Quantum Mechanical Methods. Self-Consistent Field Method. Ab Initio Methods. Density Functional Theory. Molecular Mechanics. References. 4 MOLECULAR MECHANICS OF ALKANES. Potential Energy Surface. Force Constant Matrix. Diagonal Part. Vibrational Spectra. Off-Diagonal Part. Stretch Bend Effect. Urey Bradley Force Field. van der Waals Forces. Dr. Miller s Nuclear Explosion. van der Waals Interactions between Nonidentical Atoms. Congested Molecules. Tetracyclododecane. Vibrational Motions of Compressed Hydrogens. Other Very Short H***H Distances. Alkanes Summary. Extension of The Alkane Force Field. Alkenes. Functional Groups in Molecular Mechanics. References. 5 CONJUGATED SYSTEMS. Introduction. Structures of Conjugated Hydrocarbons. in-[34,10][7]Metacyclophane. Aromatic Compounds. Simple Benzenoid Compounds. Corannulene. C60-Fullerene. Aromaticity. Cyclooctatetraene. [10] [16]Annulenes. [18]Annulene. Triquinacene (Homoaromaticity). Electronic Spectra. Structures of Conjugated Heterocycles. Porphyrins. References. 6 "EFFECTS" IN ORGANIC CHEMISTRY. Electronegativity Effect. Electronegativity Effect on Bond Lengths. Electronegativity Effect on Bond Angles. C H Bond Length versus Vibrational Frequency. Hyperconjugation. Baker Nathan Effect. References. 7 MORE "EFFECTS" NEGATIVE HYPERCONJUGATION. Bohlmann Effect. Anomeric Effect. Dimethoxymethane. Energetic Effects. Structural Effects. Angle Effects. 2-Methoxytetrahydropyran. -Halo Ketone Effect. Molecular Mechanics Model. Energetics. Summary. References. 8 ADDITIONAL STEREOCHEMICAL EFFECTS IN CARBOHYDRATES. Glucose. Gauche Effect. Polyoxyethylene (POE). Delta-Two Effect. Glucose Diastereomers. Cellobiose Analog. External Anomeric Torsional Effect. References. 9 LEWIS BONDS. Hydrogen Bonds. Quantum Mechanical Description of a Hydrogen Bond. Hydrogen Bonding Models in Molecular Mechanics. Hydrogen Fluoride Dimer. Water Dimer. Methanol Dimer. Ethylene Glycol. Other Lewis Bonds. Amine Carbonyl Interactions. References. 10 CRYSTAL STRUCTURE CALCULATIONS. Crystalline Phase. Anticipation of Unit Cell. A Priori Calculations of Crystal Structures. Molecular Mechanics Applications to Crystals. Comparison of X-Ray Crystal Structure with Calculated Structures. Benzene Crystal. Biphenyl. Ditrityl Ether. More of the [18]Annulene Story. References. 11 HEATS OF FORMATION. Benson s Method. Statistical Mechanics. Heats of Formation of Alkanes from Molecular Mechanics. Tim Clark Story. Thermodynamic Properties of Alkanes. Heats of Formation from Quantum Mechanics: Alkanes. Strain Energy. Ring Strain Energy. Dodecahedrane. Heats of Formation of Unsaturated Hydrocarbons. [18]Annulene, Aromaticity. Fullerene. Heats of Formation of Functionalized Molecules. References. Concluding Remarks. Appendix. Introduction. Jargon. Basis Set Superposition Error. Carbohydrate Conformational Nomenclature. Conformational Search Routine. Driver Routine. Molecular Mechanics Programs. Nuclear Explosion Preventer. Quantum Chemistry Progam Exchange. Ring Counting. Stereographic Projections. References. Index.

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This chapter contains sections titled: Potential Energy Surface Force Constant Matrix Stretch–Bend Effect Urey–Bradley Force Field van der Waals Forces Congested Molecules Alkanes Summary Extension of The Alkane Force Field Alkenes Functional Groups in Molecular Mechanics References

Enantioselective preference in the asymmetric synthesis where cyclohexene oxide is transformed enantioselectively to chiral (S)- or (R)-2-cyclohexen-1-ol by the reaction with the appropriate chiral lithium amide reagent has been evaluated theoretically using the MM3 force field. The plausible possible structures for each precursor (reaction intermediate complex) leading to a (S)- or (R)-2-cyclohexen-1-ol have been optimized with the extended MM3 force field applicable to the lithium amide functional group, and the populations of their (S)- or (R)-reaction intermediate complexes at an ambient temperature (298K) were calculated. The initial structure for evaluating the reaction intermediates of this asymmetric synthesis was constructed on the basis of the optimized ab initio transition state structure (MP2/6-31+G∗) comprising lithium amide LiNH2 and propene oxide. To the thus obtained transition state structure composed of LiNH2 and propene oxide, the other remaining Cartesian coordinates for the actual reaction intermediates composed of the chiral lithium amides and cyclohexene oxide were added to make the reaction intermediate structure. The conformational search for the reaction intermediate has been carried out by using the Stochastic search Algorithm, and the optimized geometries and their conformational energies (steric energies) have been calculated by the MM3 force field. The populations calculated from the conformational energies of the reaction intermediate leading to the (S)- or (R)-2-cyclohexen-1-ol were shown to be linearly well correlated with the experimentally reported enantiomer excess (% ee) values. The critical factors to control the enantioselectivity were investigated on the basis of the optimized structures of the reaction intermediate complexes. The MM3 force field approach was shown to be applicable to the theoretical evaluation of the enantioselectivity and be useful for designing a new functional chiral lithium amide reagent for the asymmetric synthesis.

The MM4 force field has been extended to include aliphatic amines. About 20 amines have been examined to obtain a set of useful molecular mechanics parameters for this class. The vibrational spectra of seven amines (172 frequencies) calculated by MM4 have an overall rms error of 27 cm(-1), compared with corresponding MM4 value of 24 cm(-1) for alkanes. The rms and signed average errors of the moments of inertia of nine simple amines compared with the experimental data were 0.18% and -0.004%, respectively. The heats of formation of 30 amines were also studied. The MM4 weighted standard deviation is 0.41 kcal/mol, compared with experiment. Electronegativity effects occur in the hydrocarbon portion of an amine from the nitrogen, and are accounted for by including electronegativity induced changes in bond lengths and angles, and induced dipole-dipole interactions in the molecule. Negative hyperconjugation results from the presence of the lone pair of electrons on nitrogen, and leads to the Bohlmann bands in the infrared, and also to strong and unusual geometric changes in the molecules (Bohlmann effect), all of which are fairly well accounted for. The conformational energies in amines appear to be less straightforward than those for most other classes of molecules, apparently because of the Bohlmann effect, and these are probably not yet completely understood. In general, the agreement between the MM4 calculated results and the available data is reasonably good.

Cycloundecane (1) was shown to exist at -183.1 degrees C as a mixture of the [12323] (approximately 59%) and [335] (approximately 41%) conformations. Populations were determined from the (13)C NMR spectrum, and assignments were based on the (13)C spectra, calculated free energies and chemical shifts, and information from the literature, including X-ray studies of solid derivatives and calculated barriers.