Group valence molecular orbitals

In the present work a theory for the facile construction of complex molecular orbitals from bond and group orbitals is presented and complemented by accurate drawings of the valence molecular orbitals for over one hundred molecules representing a wide range of connectivities and functional groupings. Direct applications to phenomena in organic chemistry are also discussed. 

The valence molecular orbitals of cyclopropane accessible to the helium lamp are 18 in number derived from H(ls) (13.6 eV), C(2s) (19.5 eV) and C(2p) (10.7 eV), they span the following irreducible representations of the point group. 

Fig. 9.1 The (valence) molecular orbitals of ethenedione. For the correlations with the MOs of carbon monoxide only one set of CO orbitals is shown thus for example MO 1 actually results from [0(2s)+C(2s)] + [0(2s)+C(2s)], and M02 results from [0(2s)+C(2s)] - [0(2s)+C(2s)]. These AMI MO energies are very approximate. For the construction of such MO diagrams see [55] Unlike the case of 2 CO, bringing two CH2 groups together does not lead to a triplet because CHj lacks degenerate orbitals and thus so does ethene [55]...

In particular, we have reviewed here how aromaticity can account for the electronic structure of ring-like molecules made of both main group metals and metalloids and transition metals. Of the many ways and indexes to characterize aromaticity, a loosely defined concept in itself, we have demonstrated that the very first of them, namely the analysis of the valence molecular orbitals complanented with the Aufbau principle and the Hund s rule for their occupation, and the Hiickel electron counting rules, yields a very appealing, albeit approximate, picture to assess the aromaticity of any particular ring-like molecule. 

The stability order of alkenes is due to a combination of two factors. One is a stabilizing interaction between the C=C tr bond and adjacent C-H a bonds on substituents. In valence-bond language, the interaction is called hyperconjugation. In a molecular orbital description, there is a bonding MO that extends over the four-atom C=C—< -H grouping, as shown in Figure 6.6. The more substituents that are present on the double bond, the more hyperconjugation there is and the more stable the alkene. 

In the Walsh description, these very same valence orbitals are used on each CH2 group, but one does not go to the trouble of combining them to make new orbitals pointing approximately along the bond directions.11 One uses directly the three local 2pJ/-type orbitals of the three CH2 groups to build one set of three molecular orbitals, and the three local (2s, 2pj.) out -type hybrids to build a second set of molecular orbitals. The procedure is illustrated in Fig. 26. 

To illustrate this point, the contributions of the occupied molecular orbitals to the total electron density at the nucleus are summarized in Table 5.2 for Fep4 (S - 5/2). It is evident from the table that the contributions coming from the orbitals at —6,966 eV must be assigned to the iron Is orbital, those from orbitals at —816 eV to the iron 2s orbital, and those from orbitals at —95 eV to the iron 3s orbital. In this highly symmetric complex, only two valence orbitals contribute to p(0), i.e. the —25 eV contribution from the totally symmetric ligand-group orbital that is derived from the F 2s orbitals and the —1 eV contribution from the totally symmetric... 

Equation (4-5) can be directly utilized in statistical mechanical Monte Carlo and molecular dynamics simulations by choosing an appropriate QM model, balancing computational efficiency and accuracy, and MM force fields for biomacromolecules and the solvent water. Our group has extensively explored various QM/MM methods using different quantum models, ranging from semiempirical methods to ab initio molecular orbital and valence bond theories to density functional theory, applied to a wide range of applications in chemistry and biology. Some of these studies have been discussed before and they are not emphasized in this article. We focus on developments that have not been often discussed. 

We therefore conclude that, for a combination of model, numerical and conceptual reasons the OHAO basis is well-adapted to a theory of valence. The hybrid orbital basis (for simple molecules) has a distinctive symmetry property it carries a permutation representation of the molecular symmetry group the equivalent orbitals are always sent into each other, never into linear combinations of each other. This simple fact enables the hybrid orbital basis to be studied in a way which is physically more transparent than the conventional AO basis. 

Corresponding to this valence bond view is a molecular orbital picture. The three cr-orbitals of a CH3 group are regarded as a basis from which three group orbitals may be constructed. One of the possible combinations of the tr-orbitals has the same local symmetry as the vacant p-orbital on the cationic centre, and hence may overlap with it. Therefore, a withdrawal of electrons from the methyl group can take place. The orbital from which electron density... 

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