B88 functional

The particular form of Eq. (110) was chosen to satisfy a large number of exact constraints. Although PW91 is modeled after the B88 functional, it does not yield the correct asymptotic behavior of the exchange energy density, a property abandoned in favor of more desirable constraints. The function sinh (ci 5) in Eq.(llO) is only a B88 relic. 

The PWx86 functional (which has no empirical parameters) and the B88 functional work about equally well in predicting molecular properties. 

PW91), respectively. While the PW91 correlation had only a small effect, the inclusion of B88 exchange caused a dramatic improvement. The mean absolute deviation for the calculated dissociation energies of 55 molecules in the G1 test set decreased from 36.2 kcal/mol (LDA) to 3.7 kcal/mol (B88). For comparison, the state-of-the-art G2 method had a deviation of 1.2 kcal/mol [17]. Becke presented these results at the 7th International Congress in Quantum Chemistry at Menton, France, in July 1991. The performance of the B88 functional was even more remarkable for a method that is no more expensive computationally than HF theory. The implications for larger molecules and for the future of quantum chemistry were obvious. 

Perdew and Wang have proposed an exchange functional similar to B88 to be used in connection with the PW91 correlation functional given below (eq. (6.30)). 

For the function F two main classes of realizations have been put forward (see in particular Adamo, di Matteo, and Barone, 1999). The first one is based on a GGA exchange functional developed by Becke, 1988b. As outlined above, this functional is abbreviated simply as B (sometimes one also finds B88)... 

Rashin et al.45 obtained the dipole moment of 32 molecules of biological relevance by means of the DFT(SVWN) and DFT(B88/P86) calculations. The results showed a rather weak dependence of calculated dipole moments on the functional form of the exchange-correlation functional but a strong dependence on the basis set. 

The dependence of the DFT results on the basis set used to expand the Kohn-Sham orbitals is illustrated in Table 4.3, which collects equilibrium geometry properties of water dimer obtained with the same exchange-correlation functional (B88/P86) but with different basis sets. 

Table 4.3. Water dimer properties the interaction energy (Ei t) in kcal/mol, the intermolecular distance (R00) in A, and the dipole moment p. in Debye, calculated using the B88/P86 exchange-correlation functional and different basis sets.

Kieninger and Suhai122 applied the DFT(SVWN), DFT(B88/P86), and DFT(PW86/P86) methods to study the NH3. . NH+ complex. The BSSE corrected interaction enthalpies obtained using nonlocal functionals were in a fair agreement with the results deduced from experiment and with the ones derived from the MP4 calculations. The corresponding values amounted to -32.0, -26.0, —27.6, —25.9, and —24.8 kcal/mol for DFT(SVWN), DFT(B88/P86), DFT(PW86/P86), MP4, and experiment, respectively. 

To calculate free energies of solvation for several organic molecules, Fortunelli and Tomasi applied the boundary element method for the reaction field in DFT/SCRF framework173. The authors demonstrated that the DFT/SCRF results obtained with the B88 exchange functional and with either the P86 or the LYP correlation functional are significantly closer to the experimental ones than the ones steming from the HF/SCRF calculations. The authors used the same cavity parameters for the HF/SCRF and DFT/SCRF calculations, which makes it possible to attribute the apparent superiority of the DFT/SCRF results to the density functional component of the model. The boundary element method appeared to be very efficient computationally. The DFT/SCRF calculations required only a few percent more CPU time than the corresponding gas-phase SCF calculations. 

In 1988, Becke proposed a gradient-corrected scheme for the exchange functional ( B88 ), ensuring that this should have the correct asymptotic limit (1/r) as oo [16] ... 

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