Or
whereVrrepresents bond length energies,Vθrepresents bond angle energies,Vωrepresents
dihedral angle energies, and Vnbrepresents non-bonded interaction energies (van der
Waals and electrostatic), and Vhbrepresents hydrogen bonding interactions. Typically,
the bond stretching and bending functions are derived from Hooke’s law harmonic
potentials; a truncated Fourier series approach to the torsional energy permits accurate
reproduction of conformational preferences.
The molecular mechanics method is extremely parameter dependent. A force field
equation that has been empirically parameterized for calculating peptides must be used
for peptides; it cannot be applied to nucleic acids without being re-parameterized for
that particular class of molecules. Thankfully, most small organic molecules, with mol-
ecular weights less than 800, share similar properties. Therefore, a force field that has
been parameterized for one class of drug molecules can usually be transferred to
another class of drug molecules. In medicinal chemistry and quantum pharmacology, a
number of force fields currently enjoy widespread use. The MM2/MM3/MMX force
fields are currently widely used for small molecules, while AMBER and CHARMM are
used for macromolecules such as peptides and nucleic acids.
1.6.1.3 QM/MM Calculations
Both quantum mechanics and molecular mechanics permit optimization of the geome-
try of a molecule. However, each method has its strengths and weaknesses. Molecular
mechanics calculations are extremely fast and efficient in providing information about
the geometry of a molecule (especially a macromolecule); unfortunately, molecular
mechanics provides no useful information about the electronic properties of a drug mol-
ecule. Quantum mechanics, on the other hand, provides detailed electronic information,
but is extremely slow and inefficient in dealing with larger molecules. For detailed cal-
culations on small molecules, high level ab initio molecular orbital quantum mechanics
calculations are preferred. For calculations on larger molecules, including peptidic
48 MEDICINAL CHEMISTRY
Vω=∑Vn
2( 1 +cos(nφ−γ)) (1.11)Vnb=∑
i<j(
Aij
r^12 ij−
Bij
rij^6+
qiqj
εrij)
(1.12)
Vhb=∑
(
Cij
rij^12−
Dij
r^10 ij)
(1.13)
V=
∑
kr(r−r 0 )^2 +∑
kθ(θ−θ 0 )^2 +∑Vn
2( 1 +cos(nφ−γ))+
∑
i<j(
Aij
rij^12−
Bij
rij^6+
qiqj
εrij)
+
∑
(
Cij
rij^12−
Dij
rij^10)
+Vcross