Parametrization of the Becke3-LYP hybrid functional for a series of small molecules using quantum molecular similarity techniques

The a0, ax, and ac semiempirical parameters of the original Becke three-parameter method have been optimized by minimizing the difference between the density given by this method and the singles and doubles quadratic configuration interaction (QCISD) generalized density using quantum molecular similarity measures. The optimization is performed including the hybrid energy functional in a self-consistent fashion and employing the relaxed geometry at each set of a0, ax, and ac parameters. This method has been applied to a series of 16 small molecules with different bonding patterns. Results show that, at least in diatomic molecules, it is possible to obtain a set of parameters that reproduces almost exactly the QCISD electron density. The optimized parameters for the studied molecules follow two main general trends: (a) the parameters governing the amount of gradient corrections for exchange and correlation have similar values (ac ≈ ax); and (b) the larger the exact exchange included, the smaller the gradient correction for exchange needed (a0 ≈ 1 − ax). Especially interesting are the values obtained for the a0 parameter, which reflect how much exact exchange should be included in the description of a particular system. Finally, for H2 and LiH, we have carried out a search for other possible local minima on the quadratic error integral surface concluding that for these molecules there is not a unique set of parameters that produces a B3LYP density of QCISD quality. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1666–1678, 2001