Density functional theory computational considerations

Vibrational Spectra Many of the papers quoted below deal with the determination of vibrational spectra. The method of choice is B3-LYP density functional theory. In most cases, MP2 vibrational spectra are less accurate. In order to allow for a comparison between computed frequencies within the harmonic approximation and anharmonic experimental fundamentals, calculated frequencies should be scaled by an empirical factor. This procedure accounts for systematic errors and improves the results considerably. The easiest procedure is to scale all frequencies by the same factor, e.g., 0.963 for B3-LYP/6-31G computed frequencies [95JPC3093]. A more sophisticated but still pragmatic approach is the SQM method [83JA7073], in which the underlying force constants (in internal coordinates) are scaled by different scaling factors. 

One of the simplest chemical reactions involving a barrier, H2 + H —> [H—H—H] —> II + H2, has been investigated in some detail in a number of publications. The theoretical description of this hydrogen abstraction sequence turns out to be quite involved for post-Hartree-Fock methods and is anything but a trivial task for density functional theory approaches. Table 13-7 shows results reported by Johnson et al., 1994, and Csonka and Johnson, 1998, for computed classical barrier heights (without consideration of zero-point vibrational corrections or tunneling effects) obtained with various methods. The CCSD(T) result of 9.9 kcal/mol is probably very accurate and serves as a reference (the experimental barrier, which of course includes zero-point energy contributions, amounts to 9.7 kcal/mol). 

Whereas density functional theory guaranties that for the ground electronic state of molecules the electron density determines the energy, the actual construction of such energy functions from first principles is a problem of considerable complexity. The electron densities computed by the MEDLA method suggest various approximations to the molecular energy of large systems. 

As indicated in Chapter 1, there is now considerable interest in the application of computer simulation (e.g. GCMC) and density functional theory (DFT) to physisorp-tion in model pore structures. It is already possible to predict the behaviour of some simple fluids in model micropores of well-defined size and shape and further progress is to be expected within the next few years. 

We do not report here the methods that were used to deduce the computational results, nor do we present a critical evaluation of the reliability of the results. For such considerations, we refer to the literature (25,28). Most of the results that we consider here were obtained by using state-of-the art density functional theory (DFT) computational techniques applied to models of surfaces, which were generated by assembling metal slabs of particular thicknesses and directions. 

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. 

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