BLYP density functional theory

In addition to conventional ab initio methods, techniques based on the density functional theory (DFT) have also been used to study the Diels-Alder reaction between butadiene and ethylene97-99. With these kinds of methods, a concerted mechanism through a symmetric transition state is also predicted. Several kinds of density functionals have been used. The simplest one is based on the Local Density Approach (LDA), in which all the potentials depend only on the density. More sophisticated functionals include a dependence on the gradient of the density, such as that of Becke, Lee, Yang and Parr (BLYP). 

Notes CCSD(T) coupled cluster method. BLYP, B3LYP, mPWPW91, and TPSS Various density functional theory-based methods. 

Three density functional theories (DFT), namely LDA, BLYP, and B3LYP, are included in this section. The simplest is the local spin density functional LDA (in the SVWN implementation), which uses the Slater exchange functional [59] and the Vosko, Wilk and Nusair [60] correlation functional. The BLYP functional uses the Becke 1988 exchange... 

Density functional theory (DFT) [9] is becoming increasingly important in determining chemical properties. Typical methods involve the BLYP functional and the hybrid B3LYP procedure. DFT methods are attractive in that they are often highly cost effective and therefore offer the possibility of application to quite large systems, provided that they are suitably reliable. 

The first way has been followed in what has become known as Car-Parrinello molecular dynamics (CPMD) (9). A solute and 60-90 solvent molecules are considered to represent the system, and the QM calculations are performed with density functionals, usually of generalised gradient approximation type (GGA), such as the Becke-Lee-Young-Parr (BLYP) (10) or the Perdew-Burke-Enzerhofer (PBE) (11,12) functionals. It is clear that the semiempirical character of concurrent density functional theory (DFT) methods and the use of these simple functionals imply a number of error sources and do not really provide a method-inherent control procedure to test the reliability of results. Recently it has been shown that these functionals even do not enable a correct description of the solvent water itself, as at ambient temperature they will describe water not as liquid but as supercooled system... 

Fig. 3 Calculated verrsus experimental 1H-2H (H-D) spin-spin coupling constants in the complexes [( /2-H2)Osn(NH3)4L], from density functional theory (DFT) calculations (BLYP). The ligand L is indicated in the graphic. The dashed line does not represent a fit but indicates where JHDCalc. = JHDObs. (Reprinted with permission from Ref. [100], copyright 1994 American Chemical Society)...

The interaction of the acetylene molecule with the (100) surface of copper was studied using the cluster model approach. All the calculations have been performed using the Density Functional Theory. The BLYP method included in the Gaussian 98 [30] package was used. This method combines the gradient corrected exchange functional of Becke [31] with the gradient corrected correlation functional of Lee et al [32]. 

Density functional theory has also been applied to the Cope rearrangement. Nonlocal methods, such as BLYP and B3LYP, find a single transition state with approximately 2 A. The barrier height is in excellent agreement with experiment. These first DFT results were extremely encouraging because DFT computations are considerably less resonrce-intensive than MRPT. Moreover, analytical first and second derivatives are available for DFT, allowing for efficient optimization of stmc-tures (particularly transition states) and the computation of vibrational frequencies needed to characterize the nature of the stationary points. Analytical derivatives are not available for MRPT calculations, which means that there is a more difficult optimization procedure and the inability to fully characterize structures. 

The most recent study, using UHF, MP2, BLYP and B3LYP methodologies, reached somewhat different conclusions. Density functional theory calculations showed one imaginary frequency for the rhombic structure (four equivalent bonds, 157.3 pm), suggesting that it is a (very low-lying) transition structure between two parallelograms (two pairs of equivalent bonds, 149.5 and 169.5 pm, respectively)... 

Over the decade 1995-2005, ab initio quantum chemistry has become an important tool in studying imidazole derivatives. Two highly productive approaches are often utilized for the calculations the wave function-based methods (e.g., Hartree-Fock theory and second-order Moller-Plesset perturbation theory (MP2)) and the density functional theory (DFT) based methods (e.g., gradient-corrected (BLYP) and hybrid (B3LYP) methods). 

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