Performing Ab Initio Calculations

The role of coordinated ethylene is evidenced by the recent ab initio calculation performed by Espelid and Borve [121-123], who have shown that ethylene may coordinate in two different ways to the reduced Cr(II) species, either as a molecular complex or covalently bound to chromium. At longer Cr-C distances (2.36-2.38 A) an ethylene-chromium zr-complex forms, in which the four d electrons of chromium remain high-spin coupled and the coordination interaction is characterized by donation from ethylene to chromium. Cr(II) species in a pseudo-tetrahedral geometry may adsorb up to two equivalents of ethylene. In the case of a pseudo-octahedral Cr(II) site a third ethylene molecule can also be present. The monoethylene complex on the pseudo-tetrahedral Cr(II) site was also found to undergo a transformation to covalently bound complex, characterized by shorter Cr-C distances (about... 

The ab initio calculations performed here at the HF/SV4PP/6-31G level of theory. 

Various approaches have been used to model the interaction between the metal electrode and the water molecules. They range from simple Lennard-Jones or Morse potentials, which have been adjusted to give good values for experimental porperties like the energy of adsorption of a water molecule, to potentials derived from ab initio calculations performed for a cluster of metal atoms and one water molecule. 

This important aspect has been investigated by Kulkarni [31] on the basis of high-level ab initio calculations performed for complexes YH -XHm with Y = Li, B, and A1 and X = F, Cl, O, N, and P. The equilibrium structures of the complexes have been optimized at the MP2/6-31-H-G(d,p) and MP2/6-311-H-G(2d,2p) levels. Then, beginning with the equilibrium structures, transition states in the dehydrogenation reaction... 

Electron spin resonance (ESR) methods have been used to observe the formation of the radical cations and dications of benzoll,2- 4,5- ]bis[l,2,3]trithiole 13 and benzo[l,2-4 4,5- ]bis[l,2,3]dithiazole 17, and the experimental results confirm the ab initio calculations performed <2003EJ04902, 1997JA12136>. ESR has also been used to confirm the formation of superoxides upon photolysis of aryl benzobisthiazoles and aryl benzobisoxazoles in the presence of molecular oxygen <2003MM4699>. 

In spite of ab initio calculations performed on these molecules [47], more detail can be found in the semi-empirical quantum mechanics approach developed in [48]. The most relevant results will be described. 

Solid-phase 13C NMR chemical shift differences of ca. 8.5 ppm were observed between the two aryl-O-C carbons of benzo-9-crown-3 derivatives 29a-c. This was explained using results of ab initio calculations performed on anisole,... 

For the thiophene, the shift in energy between the contribution by the a- and /3-carbon atoms (i.e., bonded to sulfur and not) was reported as being 0.34 eV <1971MI237>. This splitting was found somewhat smaller than the 0.59 eV separation obtained from ab initio calculations performed by Gelius et al. <1970CPL(4)471> but larger than... 

The MNDO and ab initio calculations performed on unsubstituted derivatives reveal for this reaction a conrotatory process involving an exo-exo singlet rc-biradical <94IC596>. 

This was shown especially well with 1,1-dilithioethane II, which we were able to synthesize although — according to ab initio calculations performed in cooperation with Schleyer — it is even 17.6 kcal/mol (73.6 kJ/mol) (3-21G) less stable than 1,2-dilithioethane 7... 

Ab initio calculations performed by Bigot and Roux have led to an alternative mechanism involving two photochemical steps and the intermediacy of an azirine, as shown in Scheme 40 . Hydrogen atom transfer from the enamine nitrogen to the nitrile carbon of 173 would generate diradical intermediate 177, which would then collapse to the postulated azirine 178. In a second photochemical step, the azirine would then undergo carbon-carbon bond homolysis to 179 followed by reclosure to the imidazole 176. In support of this proposed second photochemical step, structurally similar azirines have been shown to undergo facile carbon-carbon bond photolysis . This mechanism does not, however, explain the initial formation of a thermally unstable intermediate with the observed IR stretch, since azirines of this type are thermally stable at room temperature . ... 

All calcnlations reported in the literature have been concerned with only the simplest vinyl azide and vinyinitrene, CH2=CH-Ng and CHg-CH-N, respectively. " Until recently, all the theoretical stndies on the vinyl azide to azirine transformation nsed semiempirical calcnlations or ab initio calculations performed at relatively low levels of theory, at least by current standards. Significantly, early calculations on the vinylnitrene-azirine interconversion have focused only on the closed-shell singlet excited state ( A ) of vinyinitrene (VN). 

By virtue of the results obtained for BaF, these error margins appear to be somewhat too narrow. With empirical data extracted from molecular beam experiments, Kozlov [149] obtained in 1985 a value for the parity violating effective constant Wpy of 212 Hz and a value of 180 Hz with data derived from electron paramagnetic resonance (EPR) spectra of the matrix-isolated molecule. With a different method for the treatment of the spin-orbit interaction, Kozlov and Labzowsky [32] obtained in 1995 Wpy = 240 Hz and 210 Hz, respectively. The ab initio calculations performed by Kozlov, Titov, Mosyagin and Souchko [171] with RECPs, however, resulted in Wpv = 111 Hz on the self-consistent field (SCF) level and Wpy = 181 Hz on the SCF level with an effective operator technique designed to take... 

Ceo fullerides exhibit several interesting phenomena related with the presence of strong correlations such as high temperature superconductivity or antiferromagnetism. The existence of non-conventional behaviors can be anticipated from the fact that both the electron-phonon and electron-electron interactions are, respectively, comparable and much larger than the narrow bandwidth predicted by standard electronic structure calculations (a few hundreds of meV). These systems are therefore close to a metal-insula-tor transition of the Mott-Hubbard type and the validity of the adiabatic approximation, assumed in most electronic structure calculations, can be questioned. From the experimental point of view the band derived from the molecular LUMO is usually seen as a quite broad feature, much wider that the theoretical estimates, in photoemission experiments. However, the observation of the band dispersion has proven elusive in ARPES studies until very recently. In a recent joint experimental and theoretical paper, Yang et al. [158] have reported the first photoemission measurement of the band dispersion for a K-doped Qo monolayer deposited on a Ag(lll) substrate. The results have been compared with ab initio calculations performed with SIESTA. In those calculations the Ag substrate was modeled by a slab con-... 

The VEH band structure calculations have been carried out using the geometries depicted in Fig. 2 as unit cells, and assuming a fully coplanar conformation,with all the vinyl groups in trans position with respect to adjacent rings (see Fig. 3a). This assumption has been taken on the basis of the accurate ab initio calculations performed to study the rotation potential of the vinyl group in 2-VT, 2-VF, and 2-VPy. For all of these monomers, the trans rotamer is predicted as the most stable conformation. The VEH band structures calculated for the all-cis conformations displayed in Fig 3b show no significant difference with respect to those obtained for trans conformations and they will not be discussed here. 

In early theoretical studies the photodissociation of CH3I was treated as an effective two-mode system with CH3 considered as one particle. As with ICN, a new era began with ab initio calculations performed by Morokuma and coworkers on a reasonably high level of electronic structure theory. These authors determined six- and nine-dimensional adiabatic and diabatic PESs, which were used in classical surface hopping trajectory calculations. Hammerich et al. performed large-scale five-dimensional wave packet calculations using these PESs. As concluded by Eppink and Parker One caveat of the ab initio surfaces is that they do not successfully reproduce the experimental absorption spectrum, which peaks to the red side of and is broader than the spectrum predicted by the theoretical treatments.. .. Furthermore, the predicted I quantum yields of the most... 

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