March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)

Chapter 4. Stereochemistry and Conformation

4.O. Molecular Mechanics⁴¹²

Molecular Mechanics⁴¹³ describes a molecule in terms of a collection of bonded atoms that have been distorted from some idealized geometry due to nonbonded van der Waals (steric) and Coulombic (charge–charge) interactions. This approach is fundamentally different from MO theory that is based on quantum mechanics and that make no reference whatsoever to chemical bonding. The success of molecular mechanics depends on the ability to represent molecules in terms of unique valence structures, on the notion that bond lengths and angles may be transferred from one molecule to another and on a predictable dependence of geometrical parameters on the local atomic environment.

The molecular mechanics energy of a molecule is given as a sum of contributions arising from distortions from ideal bond distances (stretch contributions), bond angles (bend contributions) and torsion angles (torsion contributions), together with contributions from non-bonded interactions. This energy is commonly referred to as a strain energy, meaning that it reflects the inherent strain in a real molecule relative to a hypothetical idealized (strain-free) form.

(4.1)

Stretch and bend terms are most simply given in terms of quadratic (Hooke's law) forms:

(4.2)

(4.3)

r and α are the bond distance and angle, respectively, and r^eq and α^eq are the ideal bond length and angle, respectively.

Torsion terms need to properly reflect the inherent periodicity of the particular bond involved in a rotation. For example, the threefold periodicity of the carbon–carbon bond in ethane may be represented by a simple cosine form.

(4.4)

Ω is the torsion angle, ω^eq is the ideal torsion angle and k^torsion is a parameter. Torsion contributions to the strain energy usually will also need to include contributions that are onefold and twofold periodic. These can be represented in the same manner as the threefold term.

(4.5)

Nonbonded interactions involve a sum of van der Waals (VDW) interactions and Coulombic interactions. The Coulombic term accounts for charge–charge interactions.

(4.6)

The VDW is made up of two parts, the first to account for strong repulsion on nonbonded atoms as they closely approach, and the second to account for weak long-range attraction, r is the nonbonded distance.

Molecular mechanics methods differ both in the form of the terms that make up the strain energy and in their detailed parameterization. Older methods (e.g., SYBYL⁴¹⁴) use very simple forms and relatively few parameters, while newer methods (e.g., MM3,⁴¹⁵ MM4,⁴¹⁶ and MMFF⁴¹⁷) use more complex forms and many more parameters. In general, the more complex the form of the strain energy terms and the more extensive the parameterization, the better the results. Of course, more parameters mean that more (experimental) data will be needed in their construction. Because molecular mechanics is not based on “physical fundamentals,” but rather is essentially an interpolation scheme, its success depends on the availability of either experimental or high-quality theoretical data for parameterization. A corollary is that molecular mechanics would not be expected to lead to good results for “new” molecules, that is, molecules outside the range of their parameterization.

The two most important applications of molecular mechanics are geometry calculations on very large molecules (e.g., on proteins) and conformational analysis on molecules for which there may be hundreds, thousands, or even tens of thousands of distinct structures. It is here that methods based on quantum mechanics are simply not (yet) practical. It should be no surprise that equilibrium geometries obtained from molecular mechanics are generally in good accord with experimental values. There are ample data with which to parameterize and evaluate the methods. However, because there are very few experimental data relating to the equilibrium conformations of molecules and energy differences among different conformations, molecular mechanics calculations for these quantities need to be viewed with a very critical eye. In time, high-quality data from quantum mechanics will provide the needed data and allow more careful parameterization (and assessment) than now possible.

The most important limitation of molecular mechanics is its inability to provide thermochemical data. The reason for this is that the mechanics strain energy is specific to a given molecule (it provides a measure of how much this molecule deviates from an ideal arrangement), and different molecules have different ideal arrangements. For example, acetone and methyl vinyl ether have different bonds and would be referenced to different standards. The only exception occurs for conformational energy differences or, more generally, for energy comparisons among molecules with exactly the same bonding (e.g., cis- and trans-2-butene).

Because a molecular mechanics calculation reveals nothing about the distribution of electrons or distribution of charge in molecules, and because mechanics methods have not (yet) been parameterized to reproduce transition state geometries, they are of limited value in describing either chemical reactivity or product selectivity. There are, however, situations where steric considerations associated with either the product or reactants are responsible for trends in reactivity and selectivity, and here molecular mechanics would be expected to be of some value.

Because of the different strengths and limitations of molecular mechanics and quantum chemical calculations, it is now common practice to combine the two, for example, to use molecular mechanics to establish conformation (or at least a set of reasonable conformations) and then to quantum calculations to evaluate energy differences.

In practical terms, molecular mechanics calculations may easily be performed on molecules comprising several thousand atoms. Additionally, molecular mechanics calculations are sufficiently rapid to permit extensive conformational searching on molecules containing upward of a hundred atoms. Modern graphical based programs for desktop computers make the methods available to all chemists.