Classifying molecular orbitals and electronic states

According to the above simplistic considerations, it is expected that the energy of the electron in (Tg is less than in cr. In fact, a negative charge 

Expressions for the energies associated with the cti and m.o.s can be obtained through the following integrals (expectation value of the hamiltonian H)  

Problem 4.4 Find that, with a = —14 eV andP = — Q eV, the anti-bonding m.o. is stabilized to a lesser extent than the bonding m.o, is destabilized (i.e. the bonding m.o. is less bonding than the anti-bonding m.o. is anti-bonding). 

We now turn to the excited m.o.s 2str and 2p7r of Fig. 4.2 which become a.o.s of H ( = 2) when the internuclear distance goes to infinity. The 2p7r m.o. is doubly degenerate and can be approximated as follows 

17) there is constructive interference of the two a.o.s involved in each m.o. which means that these m.o.s are bonding, although of higher energy than a and cr(. For ity (and for each 2p y orbital) the xz plane is a nodal plane, and for (and for 2p ) the nodal plane is xy. On account of this, they are called tt molecular orbitals, when viewed from the direction of the X axis, they resemble p atomic orbitals. It is noted that they change sign upon inversion in the centre of the molecule the parity is u (tt ). 

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It is apparent that the molecular orbital theory is a very useful method of classifying the ground and excited states of small molecules. The transition metal complexes occupy a special place here, and the last chapter is devoted entirely to this subject. We believe that modem inorganic chemists should be acquainted with the methods of the theory, and that they will find approximate one-electron calculations as helpful as the organic chemists have found simple Hiickel calculations. For this reason, we have included a calculation of the permanganate ion in Chapter 8. On the other hand, we have not considered conjugated pi systems because they are excellently discussed in a number of books. 

A representative molecular orbital diagram for an octahedral d-block metal complex ML6 is shown in Figure 1.8. The MOs are classified as bonding (oL and ttL), nonbonding (jtM) and antibonding (o, nl and ). The ground-state electronic configuration of an octahedral complex... 

Electronic states of an atom or a molecule are obtained by considering the properties of all the electrons in all the orbitals. The properties of the electrons in the unfilled shells are the main contributors. It is useful to classify electronic states in terms of their symmetry properties as defined by the group operations pertinent to that particular molecular species. Mulliken s terminology is based on the following rules (small letters are used for one electron orbitals and capital letters for molecular states) ... 

The (R,S) stereoisomer of a model complex of 8 possesses C symmetry and allows us to classify the molecular orbitals in terms of the irreducible representations ag and a. It turned out that HOMO and LUMO belong to different irreducible representations. Exchange of occupation of these orbitals thus leads to different electronic configurations. While only one of the two electronic configurations corresponds to the ground state and then has a valid description in the framework of DFT, both electronic configurations can be subjected to a geometry optimization in C, symmetry and yield two different structures the results of the optimizations are depicted in Fig. 15. We took the... 

For the sake of simplicity, electronic transitions in metal complexes are usually classified on the basis of the predominant localization, on the metal or on the ligand(s), of the molecular orbitals involved in the transition (4). This assumption leads to the well-known classification of the electronic excited states of metal complexes into three types, namely, metal-centered (MC), ligand-centered (LC), and charge-transfer (CT). The CT excited states can be further classified as ligand-to-metal charge-transfer (LMCT) and metal-to-ligand charge-transfer (MLCT). 

Two properties that are characteristic of second-row atoms in the Periodic Table, compared to the corresponding valence isoelectronic first-row atoms, are hypervalency (increased coordination) and the relative importance of d-type orbitals to their molecular electronic structure description. Hypervalency in sulphur compounds is represented by trivalent, tetravalent and hexavalent sulphur where a central sulphur atom is bonded to more than two ligand atoms or groups, compared to the oxygen atom which is almost exclusively divalent. Sulphur-containing compounds are typically classified in this manner9. Here, we have not differentiated between coordination number, valency and oxidation state. This point will be addressed later. 

Now we would like to use a transition state ring bond order uniformity (n-molecular orbital delocalization) as a measure of its stability, and therefore the selectivity between two or more isometric transition state structures. A view that transition state structures can be classified as aromatic and antiaromatic is widely accepted in organic chemistry [54], A stabilized aromatic transition state will lead to a lower activation barrier. Also, it can be said that a more uniform bond order transition state will have lower activation barriers and will be allowed. An ideal uniform bond order transition state structure for a six-membered transition state structure is presented in Scheme 4. According to this definition, a six-electron transition state can be defined through a bond order distribution with an average bond order X. Less deviation from these ideally distributed bond orders is present in a transition state which is more stable. Therefore, it is energetically preferred over the other transition state structures. 

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