Biomedical Engineering Reference
In-Depth Information
The individual monomers X-H and Y retain their chemical identity to a large extent on
hydrogen bond formation; in other words no new covalent bond gets made. A great deal
of evidence suggests that simple electrostatic models of the hydrogen bond give perfectly
acceptable quantitative descriptions of the structure, vibrations and electric dipole moments
of such hydrogen bonded species.
The hydrogen-bonded species
FHF
−
is well known and has been well studied, but it cannot be written
F
−
H ...F
−
because the proton is equally shared between the two fluorine atoms. Such a species is best
thought of as covalently bound, and has to be treated by the methods of molecular quantum
theory.
Having warned about bond breaking and bond making, I should tell you that a great deal
of molecular modelling is concerned with the prediction and rationalization of molecular
bond lengths and bond angles. Here we usually deal with isolatedmolecules in the gas phase
and the theoretical treatments often refer to 0 K. A surprising amount of progress can be
made by treatingmolecules as structureless balls (atoms) held together with springs (bonds).
The array of balls and springs is then treated according to the laws of classical mechanics.
Such calculations are remarkably accurate, and are taken very seriously.
3.1 Vibrational Motion
To get started, consider a particle of mass
m
lying on a frictionless horizontal table, and
attached to the wall by a spring as shown in Figure 3.1.
m
Table
Figure 3.1
Ball attached to wall by spring
The particle is initially at rest, when the length of the spring is
R
e
(where the subscript 'e'
stands for equilibrium). If we stretch the spring, it exerts a restoring force on the particle
whilst if we compress the spring there is also a force that acts to restore the particle to its
equilibrium position. If
R
denotes the length of the spring, then the extension is
R
-
R
e
and
