Ab initio and DFT Calculations

2 Ab initio and DFT Calculations. - For small molecules consisting of light atoms, the ab initio correlated methods implemented by Gauss in coupled cluster theory are the most accurate. In this review period the chemical shifts in the (E) and (Z)- isomers of the penta-l,3-dienyl-2-cation were calculated at MP2/tzp 

Existing basis sets perform poorly for transition metals, the major problem being the D shell. An improved 6-3IG basis set (called m6-31G) for first-row transition metals has been proposed, with new orbital exponents and contraction coefficients for the D shell, which performs uniformly well across the entire first-row transition metal series from Sc to Cu. The quality of the new basis set is demonstrated for accurate prediction of ionization energies and bond dissociation energies, as well as structural parameters and harmonic vibrational frequencies of diatomic and polyatomic molecules. Because of its uniformly good performance for all first row transition metals, this m6-31G basis set, and its derivatives, e.g., m6-31G, is recommended over the original 6-3IG set or its derivatives. We await applications to shielding calculations. 

Systematic studies have been carried out on S isotropic shielding, in Ches-nut s scaled DFT method mentioned in the above Section and in his estimated infinite order Moller-Plesset (EMPI) approaches, for a wide variety of sulfur containing compounds spanning the entire S chemical shift range. Agreement 

---

Table 1.18. Comparison of Ab Initio and DFT Calculations of Atomization Energies in keal/mol.

Both Fe(ll)(TPP) and Fe(II)(OEP) have positive electric quadrupole splitting without significant temperature dependence which, however, cannot be satisfactorily explained within the crystal field model [117]. Spin-restricted and spin-unrestricted Xoi multiple scattering calculations revealed large asymmetry in the population of the valence orbitals and appreciable 4p contributions to the EFG [153] which then was further specified by ab initio and DFT calculations [154,155]. 

Table 1 Scaling factors used to improve the frequency predictions of ab initio and DFT calculations...

The accuracy of the semiempirical results may be different for different classes of compounds, and there are elements that are more difficult than others. Such variations in the accuracy are again less pronounced in high-level ab initio and DFT calculations. 

Ab initio and DFT calculations of the Diels-Alder reactions of vinylallene and diallene with dipolarophiles show that these reactions are concerted processes and that cumulated dienes are less reactive than non-cumulated dienes.153 Electron-rich... 

In closing this section, a discussion of basis sets is in order. Almost all ab initio and DFT calculations require the use of a basis set, a set of functions in terms of which the molecular orbitals are constructed. In almost all cases, the functions chosen are atom-centered functions designed to mimic the shape of atomic orbitals. It is known that orbitals for many-electron atoms resemble the hydrogenic orbitals, and it is also observed that molecular orbitals can be expanded very efficiently in terms of atomic orbitals. One might think that a relatively small set of functions, essentially the optimized occupied atomic orbitals of the atoms making up the system, could be used... 

Thermal rearrangement of 6-methylenebicyclo[3.2.0]hept-2-ene to 5-methylenenor-bomene has been investigated by modelling the product distribution from monodeuter-ated substrates using ab initio and DFT calculations. An excellent fit was obtained using a mixture of biradical and concerted mechanisms. Thus it was shown that [1,3]... 

This section is devoted to the results of ab initio and DFT calculations of PL properties of a variety of point defects in silica nanomaterials, including NBO atoms and their combinations with OVs (Subsection 3.1), silanone and dioxasilyrane defects (Subsection 3.2), and A1 impurity (Subsection 3.3). We demonstrate that the aforementioned defects can give rise to various IR and visible red and green PL bands. 

We have performed ab initio and DFT calculations of model clusters simulating various point defects, impurities, and their combinations in... 

Ab initio and DFT calculations are now routinely applied to study molecules of increasing complexity. Sometimes the results of these calculations are valuable in their own right. But more often than not these results serve as a guide or as a complement to experimental work. Clearly computational chemistry is revolutionizing how chemistry is done. In the remaining part of this chapter, the discussion will be devoted to ab initio and DFT methods. 

Relativistic effects in heavy atoms are most important for inner-shell electrons. In ab initio and DFT calculations these electrons are often treated through relativistic effective core potentials (RECP), also known as pseudopotentials. This approach is sometimes called quasirelativistic, because it accounts for relativity effects in a rather simplified scalar way. The use of pseudopotentials not only takes into account a significant part of the relativistic corrections, but also diminishes the computational cost. 

The conformational equilibria of 2-substituted 1,3-dithianes 63 were determined by application of variable temperature 13C NMR spectroscopy (cf. Scheme 20) (99T359). The thermodynamic data, given in Table IX, provide strong evidence that the predominance of the axial conformer in 63 is enthalpic in origin more polar solvents stabilize the more polar equatorial conformation. Both ab initio and DFT calculations reproduce the experimental results (99T359). 

Figure 4. The four highest energy occupied MOs of the ethene-l,2-dithiolate (edt2-) ligand as determined by ab initio and DFT calculations. Note that both in-plane and out-of-plane orbitals are present.

These observations led to the question whether the work on silylium cations in solution is still justified and whether one should continue to publish research results on silylium cations in the top ranking journals of chemistry. Despite of the many failures, it was in particular Lambert who continued to work on the problem ignoring all criticism and trying to get a solution with better and better chemical tools. Independent of Lambert, Cremer and co-workers carried on with both ab initio and DFT calculations to solve the question of blocking the Si+ center of a silylium cation in a more efficient way against solvent attacks. The break through in the computational work was supported by two developments which on first sight had little to do with the silylium cation problem. 

The equilibrium molecular geometry of thiophene has been determined from a combination of gas-phase electron diffraction (ED) vibrational and microwave data and ab initio and DFT calculations (Table 19) <2001JST(567)29>. 

---