Molecular Structure and Bonding

Molecular Mechanics


Background When it is of interest to study structure and bonding in very large molecular systems comprising hundreds or even thousands of atoms, many of the more sophisticated molecular modeling techniques are too demanding of computer time resources to be of general use. Molecular mechanics calculations, also known as force field calculations, can be of considerable use in the qualitative descriptions in these cases. In these cases, we concentrate on the structural aspect and not on the electronic and/or spectroscopic properties. In essence, we describe the potential energy surface without invoking any quantum mechanical calculations or descriptions. The Born-Oppenheimer approximation, fundamental to our molecular description, states that the Schrodinger Equation for a molecule can be separated into a part describing the motions of the electrons and a part describing the motions of the nuclei and that these two motions can be studied independently. This can be interpreted in one of two manners, one of which allows the study of the electronic structure, one of which allows the study of the molecular mechanics structure.

Electronic Structure: It is common practice to establish the positions of the nuclei of the system by some method and then to study the electronic structure using fixed nuclear positions.

Molecular Mechanics (Vibrational Spectroscopy): The motions of the nuclei are studied and the electrons are not explicitly examined at all, but are assumed to find an optimal distribution about the nuclei.

The Born-Oppenheimer surface is then a multidimensional surface describing the energy of the molecule in terms of nuclear positions.

Energy = f(nuclear positions)

Based on our history of physical and chemical experiences, we can think of molecules as mechanical assemblies made up of simple elements like balls (atoms), rods or sticks (bonds), and flexible joints (bond angles and torsion angles). Present: Molecular mechanics tends to be one of the standard methods of structural chemistry.

Potential Function:

  • There are many variations in the functional forms of force fields.
  • This function is presumed to have a minimum corresponding to stable equilibrium geometries.
  • Treatment relies heavily on availability of exptal data for parameterization; thus, EFF methods are interpolations and sometimes extrapolations of existing data.
    Assumptions:

    Force Field (the set of potential functions): Example: Bond Potential Internal Energy: Vibrational Spectroscopic Force Fields:
    1. General Harmonic Force Fields (GHFF)
      • All elements of the F matrix are considered in the analysis
      • Good for very small molecules with high symmetry
    2. Constrained Force Fields (CFF)
      • More appropriate for larger molecules
      • Systematic simplifications are made of the complete force field
      • Basic assumption: off-diagonal elements of the F matrix are much smaller than diagonal elements and can be set to zero. (i.e., higher freq. stretch will not interact much with a low freq. bend.)
        1. Direct constraints Force Field
        • Fixes values of all interaction force constants from vibrations separated by at least two noncommon atoms.
    Force Field:

    Potential Functions: Classification of Force Fields:

    Vibrational Spectroscopic Force Fields:
    1. General Harmonic Force Fields (GHFF)
      • All elements of the F matrix are considered in the analysis
      • Good for very small molecules with high symmetry
    2. Constrained Force Fields(CFF)
      • More appropriate for larger molecules
      • Systematic simplifications are made of the complete force field
      • Basic assumption: off-diagonal elements and can be set to zero.(i.e., higher freq. stretch will not interact much with a low freq.. bend.)


      Direct constraints Force Field
      • Fixes values of all interaction force constants from vibrations separated by at least two noncommon atoms.
      1. Valence Force Field
        • All interaction force constants between stretching and bending of different bonds set equal to zero.
        • No cross terms included.

        Too simplistic for quantitative application. A slight relaxation is to allow some stretch-stretch and stretch-bend terms.
      2. Central Force Fields
        • Steric effects considered in a very limited way
        • Describes angle bending in terms of nonbonded interaction distances. Rarely used. Like VFF, this is too simplistic to explain molecular frequencies. Relaxation of some constraints improves the situation by allowing interactions between interbond parameters.
      3. Urey-Bradley Force Field: Adds 1,3 interactions longer ranged nb terms
        • In addition to conventional stretching and bending force constants, all interactions that are stretching/stretch-bend coordinated are defined in terms of interactions between nonbonded atoms.
          Well established shortcomings. Inadequacies are limited by allowing stretch-stretch and stretch-bend interactions missing in the simple model (Modifies Urey-Bradley Force Field)
        • Nonbonded terms can eliminate need for cross terms (eliminates force constants; therefore replaced w/ others ~ same # of parameters on Valence Force Field and Urey-Bradley Force Field.

        Orbital Valence Force Field
        • Like the UBFF in its treatment of interactions in terms of repulsions between nonbonded atoms.
        • Unlike UBFF, treats angle distortions in terms of maximizing orbital overlap.
      Molecular Mechanics Force Fields/Empirical Force Fields (EFF)
      1. Modified Urey-Bradley Force Fields
      2. Central Force Fields
      3. Valence Force Fields (most popular)

      Note:
      • The MM representation is a gross oversimplification, justified only by history of research.
      • Authors of various EFF's partition the component terms in vastly different ways:
        • Some have every conceivable kind of interaction treated.
        • Others have only 5 - 10 terms,>li>Missing terms accounted by judicious parameterization
      • The numerical value of V has no inherent physical meaning.
      • Directly dependent on potential functions and parameters.
      • Difference between energies of isomers is usually predicted well implying that MM is usually well suited for confrontational analysis.