MOLECULAR MECHANICS

     

    Alternative name: (empirical) force field calculations  

    * Definition: "a calculational method to give accurate a priori structures and energies for molecules" [Allinger]

     

    * Based on classical-mechanical model of molecular structures (it is assumed that a set of equations exist which are of the form of the classical equations of motions)

     

    * Energy of a molecule is represented as the sum of contributions due to bond stretching, bond bending, van der Waals attractions and repulsions between nonbonded atoms, electrostatic interactions due to polar bonds, and energy changes accompanying internal rotation about single bonds

    * Molecular mechanics calculations produce:

              (1) equilibrium structures (and transition states)

              (2) energies: strain energies and heats of formation

              (3) vibrational frequencies  

    HISTORY  

    Andrews 1930  basic ideas from vibrational spectroscopy  
    Hill    1946

     include van der Waals interactions in 
         force field  
    Westheimer and Mayer 1946  application: racemization
    Dostrovsky, Hughes, Ingold 1946  application: SN2 reaction  
    Hendrickson 1960  utilize computer  
    Wiberg  1965  first general computer program  
    Allinger 1973  MM1 (first MM package)
    Allinger 1977  MM2 & MMP2
    Allinger 1989  MM3  
    commercial companies 1990

     molecular modelling software with
     sophisticated graphical input and output  
    academics and companies 1990s  universal force fields  

                               

    BASIC CONCEPT  

    * Mechanical model: a molecule is considered to be a series of masses (atoms) attached by springs (bonds)

    * A molecule can be described by a collection of atomic nuclei distribution on a potential energy surface

    * Born-Oppenheimer approximation: one can consider separately the motions of electrons and the motion of nuclei, because of their large difference in mass

              (1) quantum mechanics: consider the electron explicitly and the potential energy function is a sum of the nuclear energy and the electronic energy obtained by an approximation solution of the electronic Schrödinger equation

              (2) molecular mechanics: electrons are not considered explicitly and the potential energy of a molecule is a function of geometrical variables and the parameters of the model are chosen to fit experimental data  

    * Potential energy surface of a molecule with n atoms (3n coordinates) can be approximated by a Taylor series expansion about the point of minimum energy (V0) in terms of displacement coordinates and derivatives of the potential energy (valid for small displacement)

              di, dj and dk = displacement coordinates

              fi, fij and fijk = first, second and third derivatives with respect to displacement coordinates  

    * From the analysis of vibrational spectrum, it is possible to derive force constants

     

    * Harmonic force field: motion in each of the coordinates is independent of motion in the others, i.e. the force constant matrix is diagonal

     

     

    * Total energy of a molecule is the sum of bond stretch, angle bend, torsional and nonbonded contributions, etc.

     

    FORCE FIELDS

    * Definition: a force field is an empirical fit to a Born-Oppenheimer potential energy surface  

    * One must select the coordinate to be used, the functional form(s) of the energy in terms of the coordinates, and the function parameters

     

    * Force fields are determined by parameterizing potential energy functions so that it can reproduce a range of properties for stable molecules (both experiments and high-level ab initio results)