Chemistry Reference
In-Depth Information
SUMMARY OF QM METHODS
We address two main categories of QM methods, i.e computationally inexpensive semi-empirical for systems with
experimental information and first principles methods without the usage of experimental data. Semi empirical,
ab
initio
and DFT are among the most used QM methods whereas the fastest but least accurate are the semi empirical
methods. The accurate
ab initio
methods are more computationally expensive [463-521].
The semi-empirical methods can treat valence electrons explicitly and use simplified versions of equations from
ab
initio
methods, including parameters fitted to experimental data. They can handle however larger systems. Despite
the fact that it is sometimes difficult to determine the quality of the results, since the calculations may require large
parameter sets and input from experiments or
ab initio
calculations, semiempirical AM1 binding enthalpies
sometimes show a good correlation with those computed at the MP2 level of theory. Nonetheless, although
computationally demanding, first-principles methods, due to their enormous structural diversity, are in general better
suited for dealing with drugs.
The level of sophistication used determines the number of atoms or electrons which can be included in the
simulation. At the lower level we have the empirical potentials (10
1
to 10
6
atoms), Tight-binding calculations,
Slater-Koster approximations on the order of 10
4
atoms. Higher level methods include density functional theory
(DFT), i.e DFT based calculations with basis sets (GTO, plane waves) and correlations (LDA+corrections), Self
consistent field (SCF) Hartree-Fock calculations using basis sets (STO, GTO, planes waves) and correlations (MP
perturbation theory, CI, CC, CCSD, etc) are used. The SCF and DFT covers the range up to 10
2
atoms [519].
Empirical or ab initio derived force fields and semi-classical statistical mechanics are used for the atomistic methods
to determine thermodynamic and transport properties. The quality of the force fields may have a strong influence on
the results. Molecular mechanics energy functions which relates the total potential energy of the system to its atomic
coordinates can be used for large systems. The potential energy contribution to the internal energy is expressed as a
sum of terms including typically electrostatics, bonds, angles, torsion and van der Waals effects. The real differences
in the various models are not apparent from their functional form, but contained in their embedded parameters.
The total potential energy is differentiable with respect to atomic coordinates allowing calculation of the force
exerted on every atom, yielding the 'force field' which can be used to propagate simulations using molecular
dynamics (MD). The various force-fields are known by their acronyms to the practioners, eg OPLS (Optimized
Potentials for Liqid Simulations) [464], AMBER (Assisted model building with energy refinement) [465],
CHARMM (Chemistry at Harvard Molecular Mechanics) [466].
Using
ab initio
methods the QM Schrodinger (or Dirac) equation can be numerically solved to calculate drugs as
well as ligand-protein properties from first principles. However, in addition to being numerically expensive they can
only study fast processes and relatively small systems. Nonetheless, they can yield essentially exact properties using
only the atomic coordinates and species as input offering ways to systematically improve the results, assess the
quality and handle processes that involve bond breaking/formation as well as chemical reactions.
The calculations can for example be upscaled by calculating diffusivities, elastic tensors, viscosities from atomistic
simulations for later use in continuum models. Force-fields can be determined for later use in MD simulations. The
calculations can be downscaled by fitting two-electron integrals in semi-empirical electronic structure methods to
electron affinities and ionization energies and empirical force fields can be fitted to reproduce experimental
thermodynamics properties.
The high computational demands on first-principles-based calculations placed a strong limitation on scientific
research projects. Density functional theory radically changed this scenario opening the way for accurate
descriptions of the electronic structure in various fields at yet a more computationally affordable cost. DFT-based
applications in drug design have since appeared in the literature at an increasing pace. Electron correlation effects,
neglected in the Hartree-Fock theory, are included in gradient-corrected DFT at a similar computational cost.
Difficulties may be encountered in describing London dispersion forces which may be important for interactions
involving drug-target complexes [469].
