DFT-based methods

Quantum-chemical calculations which utilize the density functional theory (DFT) are now perhaps amongst the most frequently performed because of their relatively low cost and high accuracy. Structural results obtained from DFT based methods are often as good as those derived from MP2 calculations. It is well documented that DFT methods, especially those involving hybrid functionals such as B3LYP, B3P86 and B3PW91, yield reliable... 

The above results demonstrate that computational screening is promising technique for use in electrocatalyst searches. The screening procedure can be viewed as a general, systematic, DFT-based method of incorporating both activity and stability criteria into the search for new metal alloy electrocatalysts. By suggesting plausible candidates for further experimental study, the method can, ultimately, result in faster and less expensive discovery of new catalysts for electrochemical processes. 

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. 

For example, despite the high symmetry of C60, no calculation of its NMR properties at the MP2 level has been reported so far. DFT-based methods, on the other hand, can readily be applied to this and to larger fullerenes, see Buhl et al., 1999. 

In this section, we present some applications of DFT-based methods to the characterization of the structural, electronic, and dynamic properties of metal complexes of pharmaceutical inter-... 

This indicates that the deviations are due to systematic errors, for example deficiencies of the applied methods and basis sets. DFT-based methods, such as GIAO/DFT calculations are known to overestimate paramagnetic contributions to the chemical shielding. This results, for critical cases with small HOMO/LUMO separations, in overly deshielded competed chemical shifts. Notorious examples for these deficiencies are 29Si or 13C NMR chemical shift computations of silylenes, silylium ions or dienyl cation .(5/-54) Taking into account the deficiencies of the applied method, and bearing in mind very reasonable correlations shown in Figures 4 and 5, the computational results do support the structural characterization of the synthesized vinyl cations. 

For characteristics of TM oxides such as Li Mn02 or Li o02 that can be experimentally determined, it is found that the calculated results presented in this paper are in good agreement with experiment. Additionally, previous studies have found that various properties of 3d TM oxides can be determined with good accuracy using DFT-based methods. 

Methods of density functional theory (DFT) originate from the Xa method originally proposed by Slater [78] on the base of statistical description of atomic electron structure within the Thomas-Fermi theory [79]. From the point of view of Eq. (3), fundamental idea of the DFT based methods consist first of all in approximate treatment of the electron-electron interaction energy which is represented as ... 

During last decades the DFT based methods have received a wide circulation in calculations on TMCs electronic structure [34,85-88]. It is, first of all, due to widespread use of extended basis sets, allowing to improve the quality of the calculated electronic density, and, second, due to development of successful (so called - hybrid) parameterizations for the exchange-correlation functionals vide infra for discussion). It is generally believed, that the DFT-based methods give in case of TMCs more reliable results, than the HER non-empirical methods and that their accuracy is comparable to that which can be achieved after taking into account perturbation theory corrections to the HER at the MP2 or some limited Cl level [88-90]. 

This all explains the nature of failures of the DFT based methods in those cases, when correlations substantially come into play as in e.g. d -iron (II) ferrocene molecule. Here the errors even of advanced DFT methods become catastrophic. For example, in Ref. [86] the calculated enthalpies of dissociation of ferrocene to the free Fe + ion and two Cp anions (Cp = C5H5 - cyclopentadienyl) depending on the functional used appear to be by 3-4 eV smaller than the experimental value. The reason is transparent... 

Another group of approaches can be qualified as an attempt of using DFT based methods in order to evaluate the parameters of the CFT/LFT theory. In this respect the papers [87,115] must be mentioned. The latter, in a sense, follows the same line as the old semiempirical implementation [77] where the MOs for the TMC molecule are first obtained by an approximate... 

Some authors claim that DFT based methods to calculate coupling constants are not adequate to deal with NMR couplings involving a lone-pair... 

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. 

As should be evident from various chapters in this volume, the theoretical description of NMR shieldings and chemical shifts has seen a tremendous development during the past few years, and a number of methods are now at a point to be truly useful to experimental researchers as well as to answer fundamental questions. DFT based methods are a major aspect of these developments. The particular strength of DFT is perhaps its computational expedience, paired with accuracy and reliability. Hence, DFT applications are particularly useful for large and/or heavy systems including metal complexes or biological molecules. 

Relativistic effects cannot be neglected if heavier systems are studied we have discussed the major relativistic effects on calculated NMR shieldings and chemical shifts in this chapter. Besides relativistic effects, electron correlation has to be included for even a qualitatively correct treatment of transition metal or actinide complexes. So far, DFT based methods are about the only approaches that can handle both relativity and correlation, and DFT is, for the time being, the method of choice for these heavy element compounds. In this chapter, we have presented results from two relativistic DFT methods, the Pauli- (QR-) and ZORA approaches. 

With the advent of appropriate DFT-based methods, NMR properties of transition-metal compounds have now become amenable to theoretical computations (8). Suitable density functionals have been identified (9) which permit calculations of transition-metal chemical shifts with reasonable accuracy, typically within a few percent of the respective shift ranges. Thus, it is now possible to investigate possible NMR/reactivity correlations for transition-metal complexes from first principles several such studies have already been undertaken (10,11,12). 

Figure J Absorption spectra of the S15H12 cluster calculated using different DFT based methods LDA-RPA black (black), GW-RPA red (dark gray), BSE violet (light gray), TDLDA blue (light black).

---