Computational Chemistry

(Steven Felgate) #1

Chapter 1, Harder Questions, Answers


Q4


Is it surprising that the geometry and energy (compared to that of other isomers) of a
molecule can often be accurately calculated by a ball-and springs model (MM)?
Since in some ways molecules really do behave like ball-and-springs toys, it is
not surprising that such a model enables one to calculate geometries and energies,
but what is surprising is the accuracy possible with such calculations. Let’s explore
these two assertions.
In some ways molecules really do behave like ball-and-springs toys.
There are two assumptions here: that molecules have definite bonds, and that
these bonds behave like springs.



  1. Do molecules have definite bonds? A molecule is a collection of relatively
    immobile atomic nuclei and rapidly moving electrons, with the “relatively
    immobile” nuclei vibrating about equilibrium positions. At first sight this
    picture offers no hint of the existenceofbonds.ItmightseemthatIRspectra
    show that molecules have definite bonds, since these spectra are interpreted in
    terms of bond vibrations (stretching, bending, and torsional motions). Do the
    fundamental vibrations, the normal-modevibrations (which in principle can be
    calculated by any of the standard computational chemistry methods used to
    optimize molecular geometry, and fromwhich the experimentally observed
    vibrations can be “synthesized”) really show the presence of the conventional,
    standard bonds of simple valence theory? Actually, the vibrational spectra
    show only that nuclei are vibrating along certain directions, relative to the axes
    of a coordinate system in which the molecule is placed. An IR spectrum
    computed by assigning to the conventional bonds stretching and bending
    force constants is said to correspond to avalence forcefield.Suchaforcefield
    often serves to create a good Hessian (Chapter 2) to initiate optimization of an
    input structure to a minimum (but not a transition state), but does not always
    account for the observed IR bands, due to coupling of normal-mode vibra-
    tions [1].
    That molecules do have definite bonds, and that these tend to correspond in
    direction and number to the conventional bonds of simple valence theory, is
    indicated by the quantum theory of atoms-in-molecules (AIM, or QTAIM) [2].
    This is based on an analysis of the variation of electron density in molecules.

  2. Do bonds behave like springs? It is well-established that for the small vibrational
    amplitudes of the bonds of most molecules at or below room temperature, the
    spring approximation, i.e. the simple harmonic vibration approximation, is fairly
    good, although for high accuracy one must recognize that molecules are actually
    anharmonic oscillators [3].
    Is the accuracy of geometries and relative energies obtainable from MM
    surprising?


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