LYP correlation functional

A closer look at the original data published by Johnson, Gill, and Pople, 1993, reveals that use of the gradient-corrected LYP correlation functional instead of VWN increases atomization energies for non-hydride species quite significantly, while those containing hydrogen atoms are reduced. This rather systematic trend is portrayed in Table 9-2 for a few example cases. 

Use of the LYP correlation functional apparently reduces the overbinding proportional to the number of hydrogen atoms by about 1 kcal/mol per H from CH to CH4. On the contrary, for the nonhydride diatomics listed, the atomization energies increase by 4-5 kcal/ mol per atom upon substitution of VWN by the LYP functional. For species like C2H2,... 

The idea of modifying existing functionals by fitting particular terms to accurate experimental data has been tempting to others, too. Stewart and Gill, 1995, have reparameterized a simplified LYP correlation functional formalism, and tested its performance for atomiza-... 

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. 

The keyword for a given density-functional method is formed by concatenating the symbols for its exchange and correlation functionals. For example, combining the Becke three-term (B3) exchange functional with the Lee-Yang-Parr (LYP) correlation functional leads to the popular B3LYP density functional method. 

Table 8.5 also indicates that the most popular functionals fail to be as accurate for molecules containing third-row main-group elements as they are for molecules made up of elements from the first two rows. The LYP correlation functional seems to perform particularly badly, while the PW91 functional is more robust. 

Becke exchange and LYP correlation functional Complete Active Space Self-Consistent Field Configuration Interaction Complete Neglect Differential Overlap Density Functional Theory... 

Table 2-7. Acronyms and abbreviations used for approximate exchange, correlation, and exchange-correlation functionals discussed in this work and corresponding to their common use in the literature. In some cases, the same label is applied for exchange, correlation, or exchange-correlation functionals (PW91 for instance). In some cases, the labels used in the text are obtained as combinations of the ones included here B3LYP denotes the combination of the B3 exchange- and LYP correlation functionals, for instance...

Following these works, we have introduced a parameter-free version of the B3LYP approach, in which only the HF and the DF exchange contributions are mixed together in the ratio 1/4, while the correlation part is entirely included at the DF level [54], Starting fron eqn (48), we have defined the BILYP protocol, which uses the Becke exchange and LYP correlation functionals as ... 

These geometrical trends are reflected in the computed energetical parameters (see table XI). In particular, an increasing of the Cl-C distance induces a significant stabilization of the SP structure with respect to the minimum. The effect may be so relevant to induce a negative value for AE . This is true for all the conventional DF methods considered in the present paper, as well as all the ACMs which embody the LYP correlation functional. In particular, the BILYP method predicts an overall barrier of -0.8 kcal/mol. In contrast, the mPWlPW approach predicts a positive, albeit small, value for AE thus restoring the right trend. 

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