Structure ab initio

In this section, the conceptual framework of molecular orbital theory is developed. Applications are presented and problems are given and solved within qualitative and semi-empirical models of electronic structure. Ab Initio approaches to these same matters, whose solutions require the use of digital computers, are treated later in Section 6. Semi-empirical methods, most of which also require access to a computer, are treated in this section and in Appendix F. 

The hrst step in theoretical predictions of pathway branching are electronic structure ab initio) calculations to define at least the lowest Born-Oppenheimer electronic potential energy surface for a system. For a system of N atoms, the PES has (iN — 6) dimensions, and is denoted V Ri,R2, - , RiN-6)- At a minimum, the energy, geometry, and vibrational frequencies of stationary points (i.e., asymptotes, wells, and saddle points where dV/dRi = 0) of the potential surface must be calculated. For the statistical methods described in Section IV.B, information on other areas of the potential are generally not needed. However, it must be stressed that failure to locate relevant stationary points may lead to omission of valid pathways. For this reason, as wide a search as practicable must be made through configuration space to ensure that the PES is sufficiently complete. Furthermore, a search only of stationary points will not treat pathways that avoid transition states. 

Structure Ab Initio energy (Hartree Units) Relative Energy (kcal/mol) Distance N5-H2 (A)... 

The activation of various reactions by Lewis acids is now an everyday practice in synthetic organic chemistry. In contrast, solvent effects on Lewis acid catalysed Diels-Alder reactions have received much less attention. A change in the solvent can affect the association step leading to the transition structure. Ab initio calculations on the Diels-Alder reaction of cyclopentadiene and methyl vinyl ketone in aqueous media showed that there is a complex of the reactants which also involves one water molecule119. In an extreme case solvents can even impede catalysis120. The use of inert solvents such as dichloromethane and chloroform for synthetic applications of Lewis acid catalysed Diels-Alder reactions is thus well justified. General solvent effects, in particular those of water, will be discussed in the following section. 

Electronic Structures. Ab initio HFS calculations for 1 (R = H) have confirmed the conclusions of an HMO analysis that the six-membered ring is an 8 ir-electron system in which the HOMO is a tt orbital ( ). These calculations provide the following additional insights into the nature of the bonding in 1 ( ). 

For a precise determination of the structures, ab initio calculations on the energies of formation and characteristic harmonic wavenumbers have been performed at the HF and MP2/6-31G(d,p) level of theory with the Gaussian 92 program for the species of interest . The ab initio calculated energies and harmonic vibrational wavenumbers are given in Table 5. 

The reduction mechanism was elucidated by calculating the electronic structures (ab initio STO 3G method) of the possible complexes and by comparing them to the a-enone structures. Thus it was demonstrated that these tropones are reduced under frontier orbital control and that carbonyl complexation by the alkali cations is essential. 

Of course, I have just emphasized the so-called direct methods, which determine molecular structures ab initio from the observed intensities, and I have not even touched upon much larger macromolecular systems, such as proteins, which consist of thousands of atoms in the molecule. These structures also can be determined by special techniques. These include such techniques as multiple isomorphous replacement and anomalous dispersion, which take advantage of our ability to modify a given crystal containing molecules consisting of thousands of atoms by diffusing into the crystal a small number of really heavy atoms without disturbing the crystal structure. One then does the diffraction experiment on these so-called derivatives as well as on the native protein that one is interested in. 

Preferred geometry of the benzene oxide-oxepin system can be predicted by molecular orbital methods. Thus benzene oxide la is predicted to be markedly non-planar (with the epoxide ring at an angle of 73° to the benzene ring), while the oxepin lb has been predicted to prefer a shallow boat structure (MINDO/3) or a planar structure ab initio) As previously mentioned, the proportion of each tautomer present at equilibrium is both temperature and solvent-dependent. Molecular orbital calculations have been used to rationalize the solvent effects, both in terms of the more polar character of the arene oxide that is favored in polar solvents and the strengthening of the oxirane C-C bond upon coordination of the oxygen atom lone pair in polar solvents. Thus values in the range 1.5-2.0 D and 0.76-1.36 D for the dipole moments of arene oxide la and oxepin lb have been calculated. 

Modern Theoretical Chemistry, Vol. II, Electronic Structure Ab-Initio Methods," Ed. H. F. Schaefer, Plenum Press, New York, 1976. 

Compounds of type 2"P, featuring two (/-phosphorus centers probably benefit from an even weaker aromatic character, but this is not the most interesting point concerning their structure. Ab initio calculations have been performed on the model compound 2"Pb [34]. The calculated geometric parameters [P-P 2.102 P-C 1.726 and 1.727 A] compare well with those found experimentally for the sterically encumbered derivative 2"Pa [34] (Fig. 4). The analysis of the electron densities of 2"Pb is of particular interest. Each di-aminophosphenium unit carries approximately +1 charge, whereas the carbon bears -1.6 charge [-1.2 in the (T-space and -0.4 in the (formal) p-orbital]... 

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