Molecular orbitals definition

The term species may mean a discrete molecule, a simple or complex ion or even a solid exhibiting non-molecularity in one or more dimensions (graphite as an example). Free atoms seldom act as Lewis acids and bases. They usually have one or more unpaired electrons and flieir reactions are more accurately classified as free radical. The donor orbital is usually die highest occupied molecular orbital HOMO, and the acceptor orbital is usually the lowest unoccupied molecular orbital or LUMO. The molecular orbital definitions have a number of important consequences ... 

Depending on the application, models of molecular surfaces arc used to express molecular orbitals, clcaronic densities, van dor Waals radii, or other forms of display. An important definition of a molecular surface was laid down by Richards [182] with the solvent-accessible envelope. Normally the representation is a cloud of points, reticules (meshes or chicken-wire), or solid envelopes. The transparency of solid surfaces may also be indicated (Figure 2-116). 

Information on nucleophilic addition chemistry of quinones and various mechanistic rationali2ations have been discussed, and molecular orbital calculations have been proposed as more definitive approaches for explanation and prediction (63). 

Figure 6.14c shows the electron backdonation interaction (electrons are transferred from the Fermi level of the metal to the hybridized 27t molecular orbital which was originally empty, thus this is, by definition, a backdonation interaction). 

Cyclopropane, C.H, is a hydrocarbon composed of a three-membered ring of carbon atoms, (a) Determine the hybridization of the carbon atoms, (b) Predict the CCC and HCH bond angles at each carbon atom on the basis of your answer to part (a), (c) What must the real CCC bond angles in cyclopropane be (d) What is the defining characteristic of a cr-bond compared with a ir-bond, for example (e) How do the C—C cr-bonds in cyclopropane extend the definition of conventional o-bonds (f) Draw a picture depicting the molecular orbitals to illustrate your answer. 

As is apparent from the above definitions, each of these effective matrices depend on basis sets and molecular orbitals of both fragments. It is also important to observe that these matrices possess a correct asymptotic behavior as at large interfragment distances they become the usual overlap and Fock matrices of the separate fragments, while the paired secular systems uncouple and converge to the separate Roothaan equations for the single monomers. Finally, as it is usual in a supermolecular approach, the interaction energy is expressed as... 

This expression indicates that there is a decreased probability (indicated by the term —2(/>A(/>B) of finding the electrons in the region between the two nuclei. In fact, there is a nodal plane between the positive and negative (with respect to algebraic sign) of the two regions of the molecular orbital. As a simple definition, we can describe a covalent bond as the increased probability of finding electrons between two nuclei or an increase in electron density between the two nuclei when compared to the probability or density that would exist simply because of the presence of two atoms. 

This quantity can be viewed as a generalization of Fukui s frontier molecular orbital (MO) concept [25] and plays a key role in linking Frontier MO theory and the HSAB principle. It can be interpreted either as the sensitivity of a system s chemical potential to an external perturbation at a particular point r, or as the change of the electron density p(r) at each point r when the total number of electrons is changed. The former definition has recently been implemented to evaluate this function [26,27] but the derivative of the density with respect to the number of electrons remains by far the most widely used definition. 

By virtue of the definition of Eq. (16) it is recognized that this expression represents the sum of the self-energies of all occupied molecular orbitals. The higher the self-energy of a particular orbital, the smaller the space to which this orbital is confined. The localization sum of Eq. (28) represents, therefore, an average measure for the degree of concentration of all orbitals in the set. 

Practitioners of quantum chemistry employed both the visual imagery of nineteenth-century theoretical chemists like Kekule and Crum Brown and the abstract symbolism of twentieth-century mathematical physicists like Dirac and Schrodinger. Pauling s Nature of the Chemical Bond abounded in pictures of hexagons, tetrahedrons, spheres, and dumbbells. Mulliken s 1948 memoir on the theory of molecular orbitals included a list of 120 entries for symbols and words having exact definitions and usages in the new mathematical language of quantum chemistry. 

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