Chemistry Reference
In-Depth Information
Hartree Fock, Slater, B88 exchange functional of Becke as well as the Lee-Yang-Parr (LYP) and Vosko-Wilk-
Nusair (VWN) correlation potentials.
Although B3LYP has often replaced MP2 in theoretical energy evaluations it has been unable, for example, to
predict the correct isomerization energy for simple alkanes yielding an increasing error with the size of the alkane
systems [497].
Effectively, although widely used in the computational chemistry community, the most popular functional B3LYP
reportedly has some shortcoming, i.e it systematically underestimates reaction barrier heights, it is better for main-
group chemistry than for transiton metals and it is inaccurate for interactions dominated by medium-range
correlation energy, such as van der Waals attraction, alkane isomerization energies and aromatic-aromatic stacking.
Many new DFT functionals have been proposed in order to determine which functional should be used when
B3LYP fails. In addition, in drug discovery the geometrical optimization is important and to do this appropriately
efficient energy gradient techniques are required for the DFT methods.
There is controversy regarding the dispersion problem. Some workers prefer to avoid hybrid functionals entirely.
Others attribute DFT problems to the improper treatment of medium range correlation. It has also been concluded
that the inclusion of dispersion correction in B3LYP will significantly reduce the maximum absolute errors although
2.0 kcal/mol seems to be an accuracy limit in predicting isomerization energies and heats of formation [497].
Some well-known challenges of the DFT methods are the electron density and the self interaction error,
conventionally defined as inexactness for one-electron densities. Since the HF has a long range property and does
not suffer from self-interaction it has been included in the hybrid functionals to compensate for the DFT short-
comings. The HF and DFT exchange contributions are mixed in the half-and-half functional (BHandHLYP) in a 1:1
ratio [472,494].
Various popular functional have been proposed to improve the DFT functional exchange potential. The OPTX
functional includes left-right correlation in addition to exchange. Another approach designed to treat biological
systems, i.e H-bonding, adopts Gaussian-like behavior at long-range for an exact exchange energy density at long-
range [485-486]. We thus have the B3lyp variants, O3LYP and X3LYP [519].
Considerable effort have been placed in recent years to obtain optimum generalized gradient approximation (GGA)
functionals to solve the local limitation of DFT methods. Among these new functionals we have the PBEPBE and
THCTH. PBE exchange is a simplified GGA functional whereas all of the parameters are fundamental constants
with no empirical parameters. HCTH on the other hand contains 15 adjustable parameters [484, 519].
Early studies have shown that although other properties are seriously degraded, the accuracy of reaction barrier
heights can be dramatically improved by increasing the percentage of 'exact' exchange in the 40 - 50% region.
Other workers have indicated that in order to correct excess exchange mixing for the ground state it is necessary to
include the kinetic energy density yielding BMK with 42% exact exchange [489].
Another method, the CAM-B3LYP (Coulomb-attenuating method-B3LYP) combines the features of hybrid
functional with the long-range corrected functional. The exchange functional is a mixture of exact, i.e. Hartree-Fock
and DFT exchange whereas the ratio of exact to DFT exchange varies in different regions of the molecule. This
method appears to handle well charge transfer. Other approaches use empirical fits to calibrate new designed
functionals. Some functionals such as MO52X, use for refinement of their parameters databases sets which include
thermochemistry, diverse barrier heights, transition-metal reaction energies and noncovalent interaction energies.
This method has been successful for investigating the isomerization energies of alkanes [520].
The M06 family of functionals seems promising for application to larger systems having been constructed to
account for effects of noncovalent interaction and including variable amounts of HF exchange. Each individual
functional has been designed for a particular application and together shows a good across the board performance.
The M06-class functionals depend on spin densities, spin density gradients, spin kinetic energy densities and for
