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Both the MPWB1K and BB1K methods benefited from the one-parameter hybrid Fock-Kohn-Sham operator in which different percentages of Hartree-Fock exchange operator are used. This is written as follows: F, FH, XF HFE, 1, X)FSE, FGCE, FCor where FH is the Hartree operator, FHFE is the Hartree-Fock exchange operator, FSE is the Dirac-Slater local density functional for exchange, FGCE is the gradient correction for the exchange functional, and FCor is the total correlation functional including both local and gradient-corrected parts; also a kinetics energy density term is included. In the BB1K method, the Becke88 exchange functional for F GCE and Becke95 correlation functional for FCor are used. In a similar way, in the MPWB1K method the same correlation functional has been used, and the difference is utilizing the modified Perdew-Wang functional as an
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Cor are used. In a similar way, in the MPWB1K method the same correlation functional has been used, and the difference is utilizing the modified Perdew-Wang functional as an exchange functional. X is the fraction of Hartree-Fock exchange operator and is 0.44 and 0.42 for MPWB1K and BB1K, respectively. BB1K and MPWB1K can be implemented in GAUSSIAN 03 by using the b1b95 IOp(3/76=0580004200) and mpwb95/6-31+G(d,p) IOp(3/76=0560004400) keywords, respectively. Additional information on the implementation of these methods can be found on the Internet at http://comp.chem.umn.edu/info/DFT.htm.
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