Chemistry Reference
In-Depth Information
classical form of molecular modelling remains both very accessible and of value, since
the great computational speed achievable with the simple equations employed allows the
procedure to be used for conformational energy searching, molecule-protein docking and
molecular dynamics that all demand a large number of energy calculations.
More elaborate modelling based on a pure theoretical model for the atom, an
ab initio
(from the beginning) approach, is limited by computer power, and as yet finds limited
application in coordination and biological chemistry. However, a middle ground approach,
using density functional theory (DFT) which has a more limited theoretical base, has
grown in popularity and applicability. These so-called '
in silico
' (or silicon chip-based)
approaches may present the future for an important aspect of chemistry - prediction of
function. A screen-based model to probe a large family of related compounds certainly is
more attractive than many hours of tedious repetitive laboratory work involving synthesis
and testing to discover the most efficient compound for a particular task.
Let's explore the simplest type of 'in silico' technology, the so-called
molecular me-
chanics
, which treats atoms and their electron sets as hard spheres and bonds as springs.
Because molecules have preferred bond distances and angles, all deformations away from
ideal cost energy, and it is the sum of all deformations and other unfavourable nonbonded
interactions that add up to an overall energy associated with stability. Comparison of
calculated energies for different isomers of the same molecule, for example, allows pre-
diction of the most stable isomer. This is a valid application, as is the calculation of en-
ergy for different conformations of a molecule. However, comparisons of energy between
different molecules is inappropriate, since they will contain different numbers of atoms
and bonds and thus will differ inherently, so that their relative energies offer little real
meaning.
The total strain energy of a system can be considered to arise from bond length distortion
(stretching or compressing a bond away from its ideal, represented here as
E
str
), bond angle
distortion (bending bonds to open out or close up an ideal angle;
E
bend
), torsional effects
(twisting of groups around a particular bond relative to each other;
E
tor
) and nonbonded
contributions (van der Waals attraction, steric repulsion and electrostatic attraction or
repulsion;
E
nb
). This can be expressed by (8.5).
E
total
=
E
str
+
E
bend
+
E
tor
+
E
nb
(8.5)
The origins of these effects are represented simplistically in Figure 8.17. Each of the
contributions may be represented by simple classical equations (e.g.
E
bend
=
{
k
(
−
0
)
2
0
the ideal angle, summed for all angles
in the system under examination). The full sets of equations are not pursued here, but can
be found in specialist texts and web sites.
Software packages work by varying atom locations by small amounts, performing a
calculation, and comparing it with the previous calculation. A stepwise process leads to a
minimum. This may be the global minimum for the system (that is, the best solution), or
a local minimum (a low-energy situation, but not the lowest-energy minimum available).
The latter can be tested for by starting from a quite different shape and allowing the process
to repeat. An array of sophisticated approaches is employed in software packages, but
in the end this is still really a classical ball-and-stick modelling method, with inherent
limitations. Despite this, the approach is efficient and the outcomes, with 'training' of the
system through the use of appropriate force field parameters, are surprisingly good if using
packages developed with suitable parameters for metal ions as well as nonmetallic elements.
'Docking' (directed noncovalent bonding) between even large biomolecules and complexes
, where
k
is the force field parameter and
}
