Dominant effects in chemical reactions:

1. Steric (dominate in organic/inorganic reactions)
2. Electrostatic
3. Resonance
   
   Plus, interactions among these.
   • This division is unnecessary in QM, but, in the cases where QM is not applicable due to size of molecular system, these divisions are made, and strategies used to attain estimates of each. Calculations required for steric effects are relatively simple (in principle) and can be carried out completely where sterics dominate. then, the qualitative principles controlling steric effects become clear and the quantitative methods can be applied where other influences are of comparable importance with steric ones.
   • Whenever there is severe steric interference between atoms or groups of atoms, the strain can be partially relieved by deformation of valence angles, to allow atoms to move apart. Of course, such bending introduces some strain, however the bond deformation always proves to be less than that energy 'saved' by allowing the atoms to move apart.
   • Assume a principle that stretching of valence bonds contributes little to the relief of steric strain; the major effects are those of bond bending.
   • Both force constants and Van der Waals potentials are required for steric effects.
     
     
   A. Force constants
   Hooke's Law: When the ith particle in a molecule is displaced from equilibrium by a distance qi, it is acted on by restoring force such that
   
   F=-kiqi
   
   The potential of the particle(classical) is
   
   V=1/2 kiqi2 v=(1/2r)(ki/mi)**1/2
   
   (for more than one particle, m1 is the reduced mass)
   
   If the atoms strictly obey Hooke's Law, it would be possible to separate the vibrations into 3n-5(3n-6) completely independent harmonic oscillators (the "normal" vibrations) such that:
   
   V=1/2Ekiqi2
   
   Since it is not strictly obeyed, however, this is only an approximation. For simple molecules, those independent 'normal' displacements can be found. Example: CO2
   
   A complete description of the potential fields in any molecule will suffice for calculation of all vibrational frequencies. Unfortunately, it is difficult to go the other way and calculating the potential energy function from the vibrational frequencies is difficult,
   
   However, a useful potential function can be found by the 'valence bond' approximation, where it is assumed that forces between atoms operate only along valence bonds and that a force constant may be assigned to the stretching/compression of each valence bond and to the bending of each valence angle.
   
   Example: CO2
   2 force constants needed
   ki: Stretching C=O
   k2 bending O=C=O
   
   Since 3 frequencies are known:
   v1 1337cm-1
   v2: 667cm-1
   v3 2349cm-1
   
   from which only 2 force constants can be obtained, the calculations automatically provide a test of internal consistency. Agreement actually obtained from this model for CO2 is fair:
   
   k8: 0.77x10-11 erg/radian2
   k2: 15.5+/-1.3x105 dynes/cm
   (+/- due to the fact that the harmonic approximation is not quite right)(Problem) The approximation is satisfactory for estimate of steric strain.
   
   With more complicated molecules, the calculation of force constants for stretching a C-H bond, bending a C-C-H angle, etc. The fact that force constants for particular bonds are roughly independent of the details of the molecule in which they occur is of course related to the approximate constancy of group frequencies on IR spectra (Andrews paper).
   
   B. Van der Waals Potential Functions
   
   Defn: Potential functions for the interaction between two atoms (or molecules) where these atoms (molecules) are not connected by valence forces.
   • In principle the Van der Waals potential for any particular pair of atoms can be calculated from a consideration of the deviation of the corresponding gas from ideal behavior.
   • A series of Van der Waals potential curves for the interactions of various pairs of 'non-bonded' atoms show considerable similarity as to shape. apparently non-bonded atoms interact very much less specifically than bonded atoms: the attraction and repulsion of closed electronic shells is more or less independent of the electronic kernels and nuclei they enclose.
   • A crude but moderately satisfactory Van der Waals potential function, is the Lennard-Jones potential.
     
     
   The parameters must be selected for each individual pair of atoms that interact. When these parameters for rare-gas atoms are correctly chosen, calculations based on the Lennard-Jones potential (and on more refined potential functions) approximate the deviations of the gas from ideal behavior.
   • 
     The Van der Waals radii of atoms are well known, usually from X-ray data in crystals. A crude approximation of the Van der Waals potential functions can, therefore, be made by assuming that the shape of the curve for any two atoms will approximate that for the rare gas with about the same interatomic separation at the energy minimum (i.e., where the Van der Waals radius of the rare gas is nearest to the average of the Van der Waals radii of the interacting atoms).