Qualitative theories density functional theory

It is a truism that in the past decade density functional theory has made its way from a peripheral position in quantum chemistry to center stage. Of course the often excellent accuracy of the DFT based methods has provided the primary driving force of this development. When one adds to this the computational economy of the calculations, the choice for DFT appears natural and practical. So DFT has conquered the rational minds of the quantum chemists and computational chemists, but has it also won their hearts To many, the success of DFT appeared somewhat miraculous, and maybe even unjust and unjustified. Unjust in view of the easy achievement of accuracy that was so hard to come by in the wave function based methods. And unjustified it appeared to those who doubted the soundness of the theoretical foundations. There has been misunderstanding concerning the status of the one-determinantal approach of Kohn and Sham, which superficially appeared to preclude the incorporation of correlation effects. There has been uneasiness about the molecular orbitals of the Kohn-Sham model, which chemists used qualitatively as they always have used orbitals but which in the physics literature were sometimes denoted as mathematical constructs devoid of physical (let alone chemical) meaning. 

Generally, all band theoretical calculations of momentum densities are based on the local-density approximation (LDA) [1] of density functional theory (DFT) [2], The LDA-based band theory can explain qualitatively the characteristics of overall shape and fine structures of the observed Compton profiles (CPs). However, the LDA calculation yields CPs which are higher than the experimental CPs at small momenta and lower at large momenta. Furthermore, the LDA computation always produces more pronounced fine structures which originate in the Fermi surface geometry and higher momentum components than those found in the experiments [3-5]. 

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... 

This survey of theoretical methods for a qualitative description of homogeneous catalysis would not be complete without a mention to the Hartree-Fock-Slater, or Xot, method [36]. This approach, which can be formulated as a variation of the LDA DFT, was well known before the formal development of density functional theory, and was used as the more accurate alternative to extended Hiickel in the early days of computational transition metal chemistry. 

Density functional theory (DFT) is an entrancing subject. It is entrancing to chemists and physicists alike, and it is entrancing for those who like to woik on mathem cal physical aspects of problems, for those who relish computing observable properties from theory and for those who most enjoy developing correct qualitative descriptions of phenomena in the service of the broader scientifrc community. 

Density functional theory purists are apt to argue that the Hohenberg-Kohn theorem [1] ensures that the ground-state electron density p(r) determines all the properties of the ground state. In particular, the electron momenmm density n( ) is determined by the electron density. Although this is true in principle, there is no known direct route from p to IT. Thus, in practice, the electron density and momentum density offer complementary approaches to a qualitative understanding of electronic structure. 

Various theoretical methods and approaches have been used to model properties and reactivities of metalloporphyrins. They range from the early use of qualitative molecular orbital diagrams (24,25), linear combination of atomic orbitals to yield molecular orbitals (LCAO-MO) calculations (26-30), molecular mechanics (31,32) and semi-empirical methods (33-35), and self-consistent field method (SCF) calculations (36-43) to the methods commonly used nowadays (molecular dynamic simulations (31,44,45), density functional theory (DFT) (35,46-49), Moller-Plesset perturbation theory ( ) (50-53), configuration interaction (Cl) (35,42,54-56), coupled cluster (CC) (57,58), and CASSCF/CASPT2 (59-63)). 

Nucleophilic vinylic substitutions of 4//-pyran-4-onc and 2,6-dimethyl-4//-pyran-4-one with a hydroxide ion in aqueous solution were calculated by the density functional theory (B3LYP) and ab initio (MP2) methods using the 6-31+G(d) and 6-31G (d) basis sets. The aqueous solution was modelled by a supermolecular approach, where 11 water molecules were involved in the reaction system. The calculations confirmed a different addition-elimination mechanism of the reaction compared with that in the gas phase or non-polar solution. Addition of OH- at the C(2) vinylic carbon of the pyranone ring with an activation barrier of 10-11 kcalmol-1 (B3LYP) has been identified as the rate-determining step, in good quantitative and qualitative agreement with experimental kinetics. Solvent effects increase the activation barrier of the addition step and, conversely, decrease the barrier of the elimination step.138... 

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