Density Functional Theory computational details

Abstract Recent density functional theory computations of cobalt-catalyzed hydroformylation of propene, A -vinyl acetamide, 1,3-butadiene, acetylene, propyne, and allene and the urea formation from methyl amine as well as Pauson-Khand reaction have been reviewed. The detailed catalytic mechanism and regioselectivity have been discussed and compared with the available experimental data. It shows that modem computational chemistry provides not only qualitative but also quantitative aspects of catalytic reactions. 

A detailed structural analysis of a series of N-acetylated 4-DMAP salts using X-ray crystallography, variable-temperature IR and NMR spectroscopy as well as DFT (density functional theory) computation has been reported by Schreiner et al. 

Chapter 6, Selecting an Appropriate Theoretical Method, discusses the model chemistry concept introduced in Chapter 1 in detail. It covers the strengths, computational cost and limitations of a variety of popular methods, beginning with semi-empirical models and continuing through Hartree-Fock, Density Functional Theory, and electron correlation methods. 

However, even the best experimental technique typically does not provide a detailed mechanistic picture of a chemical reaction. Computational quantum chemical methods such as the ab initio molecular orbital and density functional theory (DFT) " methods allow chemists to obtain a detailed picture of reaction potential energy surfaces and to elucidate important reaction-driving forces. Moreover, these methods can provide valuable kinetic and thermodynamic information (i.e., heats of formation, enthalpies, and free energies) for reactions and species for which reactivity and conditions make experiments difficult, thereby providing a powerful means to complement experimental data. 

Detection of the dA N1 and dC N3 adducts may not in one sense be particularly important for DNA based on their central position within the helical conformation and hydrogen bonding network.37,38 Still, the deoxynucleoside studies helped to focus attention on the reversibility of alkylation by QM and provided insight into the reactions of duplex DNA described below in Section 9.3. Reaction at the deoxynucleoside level also provided an essential system for developing a theoretical treatment of QM reaction.50-52 Computations based on density functional theory well rationalized the published results on d A and correctly anticipated the results on dG and dC reviewed above and described in more detail in Chapter 2 (Freccero). 

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). 

It is important to realize that each of the electronic-structure methods discussed above displays certain shortcomings in reproducing the correct band structure of the host crystal and consequently the positions of defect levels. Hartree-Fock methods severely overestimate the semiconductor band gap, sometimes by several electron volts (Estreicher, 1988). In semi-empirical methods, the situation is usually even worse, and the band structure may not be reliably represented (Deak and Snyder, 1987 Besson et al., 1988). Density-functional theory, on the other hand, provides a quite accurate description of the band structure, except for an underestimation of the band gap (by up to 50%). Indeed, density-functional theory predicts conduction bands and hence conduction-band-derived energy levels to be too low. This problem has been studied in great detail, and its origins are well understood (see, e.g., Hybertsen and Louie, 1986). To solve it, however, requires techniques of many-body theory and carrying out a quasi-particle calculation. Such calculational schemes are presently prohibitively complex and too computationally demanding to apply to defect calculations. 

The identification of unknown chemical compounds isolated in inert gas matrices is nowadays facilitated by comparison of the measured IR spectra with those computed at reliable levels of ab initio or density functional theory (DFT). Furthermore, the observed reactivity of matrix isolated species can in some instances be explained with the help of computed reaction energies and barriers for intramolecular rearrangements. Hence, electronic structure methods developed into a useful tool for the matrix isolation community. In this chapter, we will give an overview of the various theoretical methods and their limitations when employed in carbene chemistry. For a more detailed qualitative description of the merits and drawbacks of commonly used electronic structure methods, especially for open-shell systems, the reader is referred to the introductory guide of Bally and Borden.29... 

The use of computational chemistry to address issues relative to process design was discussed in an article. The need for efficient software for massively parallel architectures was described. Methods to predict the electronic structure of molecules are described for the molecular orbital and density functional theory approaches. Two examples of electronic stracture calculations are given. The first shows that one can now make extremely accurate predictions of the thermochemistry of small molecules if one carefully considers all of the details such as zero-point energies, core-valence corrections, and relativistic corrections. The second example shows how more approximate computational methods, still based on high level electronic structure calculations, can be used to address a complex waste processing problem at a nuclear production facility (Dixon and Feller, 1999). 

A review of the Journal of Physical Chemistry A, volume 110, issues 6 and 7, reveals that computational chemistry plays a major or supporting role in the majority of papers. Computational tools include use of large Gaussian basis sets and density functional theory, molecular mechanics, and molecular dynamics. There were quantum chemistry studies of complex reaction schemes to create detailed reaction potential energy surfaces/maps, molecular mechanics and molecular dynamics studies of larger chemical systems, and conformational analysis studies. Spectroscopic methods included photoelectron spectroscopy, microwave spectroscopy circular dichroism, IR, UV-vis, EPR, ENDOR, and ENDOR induced EPR. The kinetics papers focused on elucidation of complex mechanisms and potential energy reaction coordinate surfaces. 

In order to get more detailed information about, e.g., bond strengths and equilibrium geometries in transition metal systems it is necessary to include electron correlation. This can be done either by traditional ab initio quantum chemistry models, e.g., Cl-methods and coupled cluster methods, or by density functional theory (DFT) based methods. Correlated ab initio methods are often computationally very demanding, especially in cases where multi-reference based treatments are needed. Also, the computational cost of these methods increases dramatically with the size of the system. This implies that they can only be applied to rather small systems. 

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