Hybrid function

Density functional theory calculations have shown promise in recent studies. Gradient-corrected or hybrid functionals must be used. Usually, it is necessary to employ a moderately large basis set with polarization and diffuse functions along with these functionals. 

Both HF and DFT calculations can be performed. Supported DFT functionals include LDA, gradient-corrected, and hybrid functionals. Spin-restricted, unrestricted, and restricted open-shell calculations can be performed. The basis functions used by Crystal are Bloch functions formed from GTO atomic basis functions. Both all-electron and core potential basis sets can be used. 

All of the predicted structures are at least reasonably good. The two hybrid functionals produce the best structures, in excellent agreement with the experimental geometry. The SVWN and SVWNS functionals both produce good structures, while the BLYP geometry is the least accurate. 

Only the values computed by the hybrid functionals and MP2 are at all reasonable, and the B3PW91 value is in excellent agreement with experimental observations. Thi MP2 and B3LYP values are only modestly outside of the desired accuracy of 2 kcal-mol In Chapter 7, we will consider methods which were developed to consistently produce such very accurate thermochemical results. 

Seluflon Clearly, a hybrid functional is the best choice for this problem. We ran B3LYP calculations using the 6-31G(d), 6-31-i-G(d) and 6-311G(2d) basis sets. Here are the results ... 

Gaussian98 gives a choice of six exchange functionals and seven correlation functionals, together with a number of so-called hybrid functionals. These latter... 

Quantum-chemical calculations which utilize the density functional theory (DFT) are now perhaps amongst the most frequently performed because of their relatively low cost and high accuracy. Structural results obtained from DFT based methods are often as good as those derived from MP2 calculations. It is well documented that DFT methods, especially those involving hybrid functionals such as B3LYP, B3P86 and B3PW91, yield reliable... 

SCHEME 2.16 Additional reaction pathway for the generation of the quinone methide in the gas phase oxidation of 2-methylphenyl radical, investigated by the hybrid functional MPW1K (reproduced from Ref. [23] with permission from American Chemical Society). 

In addition, another computational study in the frame of DFT, using the hybrid functional MPW1K,53 had suggested that o-QM may be an intermediate in the reaction of the peroxy radical (HO2") with the benzyl radical at the ortho-position (Scheme 2.16),54 which should be significant in atmospheric processes and low-temperature combustion systems (T < 1500 K). 

Remarkably, the BLYP functional approaches or sometimes surpasses the accuracy of hybrid functionals if small basis sets are used (see Table 9-5). 

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