LYP functional

Geometries, hyperfme structure, and relative stabilities of the different positional isomers of monodeuterated benzene cations have been studied theoretically by density functional theory, using the B3-LYP functional, and experimentally by ESR and ENDOR spectroscopy. A comparison between theoretical and experimental results at 30 K gives acceptable agreement, but further experiments on multiply deuterated species should improve the analysis by making the effects of deuteration larger. 

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,... 

Table 2. Correlation energy of the uniform electron gas, comparing the highly-accurate parametrization of Perdew and Wang [4] with the LYP functional [10]...

A second observation about the LYP functional is that it predicts no correlation energy for a fully spin-polarized system of electrons. Yet, in the uniform-density limit, the correlation energy at full spin-polarization is about half that of the unpolarized system [3, 4, 57]. Even in the Ne atom, the parallel-spin contribution accounts for about 24% of the total correlation energy (Sect. 3.4). 

The simulation of growth, structural stability and electronic structure was performed with the following quantum chemical methods Hartree-Fock (approximation NDDO (PM5)) and DFT (B88-LYP functional). The broken bonds of silicon atoms were saturated with hydrogen atoms. 

The geometries of the ground state as well as of the singly and doubly ionized Uracil molecules have been optimized by means of DFT calculations using the B3-LYP functional. The vertical and adiabatic first and second ionization potentials presented in Table 2 compare favourably to previous calculations [25, 26] and to experimental data [27,28],... 

Ecovr is the gradient corrected correlation, namely the Lee-Yang-Parr (LYP) functional [31]... 

A more recent correlation functional is that of Lee, Yang, and Parr[54], which is often used in conjunction with Becke exchange to form BLYP. The enhancement factor for BLYP is plotted in Figure 12. The LYP functional starts from the Colle-... 

The final point on analytic KS second derivatives which we will discuss concerns the effect of the grid derivative terms. Though the implementation of the matrix Q in the CPKS equations and the explicit second derivatives of the XC energy was not covered here, the former involves first derivatives of the points and weights while the latter involves second derivatives of these. Table 4 lists analytic frequencies for selected small molecules, using the B-LYP functional [16, 18] with the 6-31G(d) basis set, excerpted from a previous study [55] on the effect of grid derivatives. 

The LYP functional as given by Eq. (157) is a meta-GGA, because it depends on the Laplacian of the density. Miehlich et al. [193] pointed out that V p(r) can be eliminated from the LYP formula by partial integration. Their transformed version of LYP,... 

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